Full thread (65 messages)
From: cityoftheasleep (2011-01-16)
Subject: Feed Me More "Worst" Scales
Okay, folks. I've been so pleased with the songs that have come out of these "worst" scales that it's becoming a for-real album, so I'm not going to demo any more single tracks here on MMM.
Currently, I have four tracks finished, 3 of which most of you have heard: 3 in scales by Michael, 1 in a scale by John. I have one in progress in 14-EDO (which is sounding AWESOME right now, this tuning is really not putting up much of a fight at all), and then I have to write one in 11-EDO (since Carl alluded to it somewhere--I don't know how to write SATB properly, but I'll aim for four-part harmony if I can pull it off) and one in my own "worst" scale of the 24-EDO improper octatonic/diminished scale. That makes a total of 7 songs.
I want to do more, to make a full-length album, so that means more scales. Gene, John, and Michael--I promise I will get to some 11-limit Hobbits, Blue Temperament, and Dimension EC after this, and that I will try to make them sound as good as I can (rather than bad), but I'm really in the groove with these bad scales right now and I want to keep going. Rather than "fighting" me, I feel like these scales all lead me off in a very alien direction, pursuing compelling musical realities which feel natural despite being as "at odds as possible" with human ideas about harmony. It's also not something that is typically done by people in the microtonal world--plenty of people are exploring the "good" scales, so I feel like SOMEBODY should explore the "bad" ones.
If I have to, I'll come up with bad scales on my own; I've got a few ideas of how to do it, including high-error regular temperaments, high-prime subgroup tonality diamonds/CPS's/temperaments (maybe 2.17.23?), a high-prime-harmonics-only rational intonation scale (plus the 2nd harmonic because I'm still stuck with Logic, so maybe 37:41:43:47:53:59:61:67:71:74?) and just searching through my database of MOS scales in various EDOs for particularly nasty-looking ones (though it seems to be difficult to get anything consistently worse than 11-EDO). I'm tempted to do 10-EDO just because Bill Sethares mentioned it as being particularly difficult to use without adaptive timbres, even though I know from experience it sounds pretty good, what with its excellent approximation to the 13th harmonic, above-average approximation to the 7th harmonic, and passable approximations to the 3rd and 15th harmonics. I'm tempted to throw in 13-EDO as well, just because it has such a bad rap and there is such a dearth of decent-sounding music written for it, but I don't expect it to challenge me. Do any of these seem like a worthwhile challenge to take on?
Really, though, what I want are scales that make experienced tuning theorists shudder, or scales that result from turning optimization procedures on their heads. Scales that make you think "now this...this is truly terrible, and only a maniac would consider using it." At this point, it's not even about trying to prove anything, I know I'm not going to change any minds and that's just fine. It is like I said above: these bad scales inspire me, because they lead me in directions I would never think to go. You may think I'm nuts, that my behavior is morally degenerate, and that my madness should not be encouraged, but please: if you can think of a scale that you find utterly repugnant and useless, I'd love to know what it is.
-Igs
From: Michael (2011-01-16)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Igs>"I have one in progress in 14-EDO (which is sounding AWESOME right now, this
tuning is really not putting up much of a fight at all"
Awesome.....can't wait to hear it. I want to see if you can pull a
"Knowsur" on us with your insane use of "terrible" 7TET-multiple scales.
>"and one in my own "worst" scale of the 24-EDO improper octatonic/diminished
>scale. That makes a total of 7 songs. "
Agreed...your scale with its clustering under 24EDO is pretty lousy. :-D
Hmm....
One idea is (since clustering is now deemed legal here :-D) to split up
28TET into another "cluster scale". It hits the critical band almost dead on
for its semitone as has several almost-as-bad-sounding quarter tones. Here is
the scale (assuming 1 as the root in 28TET...) I think there's a 9/7-ish large
interval somewhere in there using octave equivalence and the 11/8 isn't too
harsh...but that's about it!
The scale is (by note number in 28TET).......
Mike "Critically Bland" Scale (under 28TET)
1
2 (1.02506)
3 (1.05076)
---------------
15 (1.379)
16 (1.41421)
18 (1.48599)
19 (1.56142)
---------------
>"I want to do more, to make a full-length album, so that means more scales.
>Gene, John, and Michael--I promise I will get to some 11-limit Hobbits, Blue
>Temperament, and Dimension EC after this"
Far as Dimension EC...I know I posted two versions but, just to be clear,
this is the most updated one.
! E:\DIMENSION EC.scl
!
Dimension EC Scale
12
!
119.558
196.1985
315.6413
352.7508
505.7750
620.4284
701.9550
822.85912
891.9594
1011.52634
1047.1581
2/1
Also I have high hopes for some of Gene's "Hobbit" scales...particularly
Mineva and somewhat Ares.
Far as "good" scales I would also throw Wilson's "Hexanies" 6-tone scale onto
that list (which is used frequently by Marcus Satellite).
[Non-text portions of this message have been removed]
From: cityoftheasleep (2011-01-16)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], Michael <djtrancendance@...> wrote:
> Mike "Critically Bland" Scale (under 28TET)
>
> 1
> 2 (1.02506)
> 3 (1.05076)
> ---------------
> 15 (1.379)
> 16 (1.41421)
> 18 (1.48599)
> 19 (1.56142)
> ---------------
Sadly, I can't tune that in Logic, since I can only go +/- 100 cents from each step of 12-equal. So for any three consecutive notes, the distance between the first note and the third has to be 100 cents or greater. I can tell you though--if I could tune that scale, I'd use it to make some meditative drone music, using the strong beating as a trance inducer. This is one area that cluster scales like this one really excel, much more so than any scale optimized for consonant harmony. It's the whole "binaural beating/"digital drugs" thing. When I get around to purchasing LMSO, I'll try to tune up some cluster scales and explore the possibilities there.
In the meantime, let me say that I *almost* picked the 28-EDO "extra-proper" diminished scale over the 24-EDO improper one. I may still; I haven't tuned up either of them, but they both *look* horrendous. 28-EDO is definitely capable of some nasty sounds.
-Igs
-Igs
From: gdsecor (2011-01-17)
Subject: Re: Feed Me More "Worst" Scales
--- In [email protected], "cityoftheasleep" <igliashon@...> wrote:
>
> Okay, folks. I've been so pleased with the songs that have come out of these "worst" scales that it's becoming a for-real album, so I'm not going to demo any more single tracks here on MMM.
>
> ...
> I want to do more, to make a full-length album, so that means more scales. Gene, John, and Michael--I promise I will get to some 11-limit Hobbits, Blue Temperament, and Dimension EC after this, and that I will try to make them sound as good as I can (rather than bad), but I'm really in the groove with these bad scales right now and I want to keep going. Rather than "fighting" me, I feel like these scales all lead me off in a very alien direction, pursuing compelling musical realities which feel natural despite being as "at odds as possible" with human ideas about harmony. It's also not something that is typically done by people in the microtonal world--plenty of people are exploring the "good" scales, so I feel like SOMEBODY should explore the "bad" ones.
>
> If I have to, I'll come up with bad scales on my own; I've got a few ideas of how to do it, including high-error regular temperaments, high-prime subgroup tonality diamonds/CPS's/temperaments (maybe 2.17.23?), a high-prime-harmonics-only rational intonation scale (plus the 2nd harmonic because I'm still stuck with Logic, so maybe 37:41:43:47:53:59:61:67:71:74?) and just searching through my database of MOS scales in various EDOs for particularly nasty-looking ones (though it seems to be difficult to get anything consistently worse than 11-EDO). ...
>
> Really, though, what I want are scales that make experienced tuning theorists shudder, or scales that result from turning optimization procedures on their heads. Scales that make you think "now this...this is truly terrible, and only a maniac would consider using it." At this point, it's not even about trying to prove anything, I know I'm not going to change any minds and that's just fine. It is like I said above: these bad scales inspire me, because they lead me in directions I would never think to go. You may think I'm nuts, that my behavior is morally degenerate, and that my madness should not be encouraged, but please: if you can think of a scale that you find utterly repugnant and useless, I'd love to know what it is.
Hi Igs,
As possibly the first person ever to produce a composition in 11-EDO (on a retuned electronic organ back in 1970, and yet another on a Scalatron in 1975 -- I still have recordings of both), I couldn't resist a challenge like this. I spent about 1/2 hour last night constructing a one-dimensional tuning that has nothing reasonably approximating a fourth (3:4), fifth (2:3), octave (1:2, eleventh (3:8), twelfth (1:3), or fifteenth (1:4), and hopefully nothing close to any other consonant interval (at least within an octave). Here's what I came up with.
I started with the four intervals smaller and larger than a fourth and fifth having maximum harmonic entropy, using the curve Paul Erlich produced for me on the HE list: 459, 542, 654, and 758 cents. I tried constructing scales using various fractions of these intervals as generators and found that 1/3 of 542 cents produces a heptatonic scale with severely stretched octaves. If you want to pin the generator down to an exact value, I would suggest 1/3 of 541.4188 cents (the noble mediant between 4/3 and 11/8), which gives 180.4729 cents, a tad smaller than 10/9.
To try this out with Scala, enter the following on the command line:
equal 7 1263.31
set notation e7
While you have fun with this one, I'll see if I can come up with anything better -- oops, I mean worse! 8>}
--George
From: Ozan Yarman (2011-01-17)
Subject: Re: [MMM] Re: Feed Me More "Worst" Scales
Dear George, long time no chat! This new scale by you seems to have
interesting potentials. I am almost tempted to try out something myself
with it. But what name do you plan to give the scale?
Oz.
--
✩ ✩ ✩
www.ozanyarman.com
gdsecor wrote:
> --- In [email protected], "cityoftheasleep"<igliashon@...> wrote:
>> Okay, folks. I've been so pleased with the songs that have come out of these "worst" scales that it's becoming a for-real album, so I'm not going to demo any more single tracks here on MMM.
>>
>> ...
>> I want to do more, to make a full-length album, so that means more scales. Gene, John, and Michael--I promise I will get to some 11-limit Hobbits, Blue Temperament, and Dimension EC after this, and that I will try to make them sound as good as I can (rather than bad), but I'm really in the groove with these bad scales right now and I want to keep going. Rather than "fighting" me, I feel like these scales all lead me off in a very alien direction, pursuing compelling musical realities which feel natural despite being as "at odds as possible" with human ideas about harmony. It's also not something that is typically done by people in the microtonal world--plenty of people are exploring the "good" scales, so I feel like SOMEBODY should explore the "bad" ones.
>>
>> If I have to, I'll come up with bad scales on my own; I've got a few ideas of how to do it, including high-error regular temperaments, high-prime subgroup tonality diamonds/CPS's/temperaments (maybe 2.17.23?), a high-prime-harmonics-only rational intonation scale (plus the 2nd harmonic because I'm still stuck with Logic, so maybe 37:41:43:47:53:59:61:67:71:74?) and just searching through my database of MOS scales in various EDOs for particularly nasty-looking ones (though it seems to be difficult to get anything consistently worse than 11-EDO). ...
>>
>> Really, though, what I want are scales that make experienced tuning theorists shudder, or scales that result from turning optimization procedures on their heads. Scales that make you think "now this...this is truly terrible, and only a maniac would consider using it." At this point, it's not even about trying to prove anything, I know I'm not going to change any minds and that's just fine. It is like I said above: these bad scales inspire me, because they lead me in directions I would never think to go. You may think I'm nuts, that my behavior is morally degenerate, and that my madness should not be encouraged, but please: if you can think of a scale that you find utterly repugnant and useless, I'd love to know what it is.
>
> Hi Igs,
>
> As possibly the first person ever to produce a composition in 11-EDO (on a retuned electronic organ back in 1970, and yet another on a Scalatron in 1975 -- I still have recordings of both), I couldn't resist a challenge like this. I spent about 1/2 hour last night constructing a one-dimensional tuning that has nothing reasonably approximating a fourth (3:4), fifth (2:3), octave (1:2, eleventh (3:8), twelfth (1:3), or fifteenth (1:4), and hopefully nothing close to any other consonant interval (at least within an octave). Here's what I came up with.
>
> I started with the four intervals smaller and larger than a fourth and fifth having maximum harmonic entropy, using the curve Paul Erlich produced for me on the HE list: 459, 542, 654, and 758 cents. I tried constructing scales using various fractions of these intervals as generators and found that 1/3 of 542 cents produces a heptatonic scale with severely stretched octaves. If you want to pin the generator down to an exact value, I would suggest 1/3 of 541.4188 cents (the noble mediant between 4/3 and 11/8), which gives 180.4729 cents, a tad smaller than 10/9.
>
> To try this out with Scala, enter the following on the command line:
> equal 7 1263.31
> set notation e7
>
> While you have fun with this one, I'll see if I can come up with anything better -- oops, I mean worse! 8>}
>
> --George
>
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>
[Non-text portions of this message have been removed]
From: cityoftheasleep (2011-01-17)
Subject: Re: Feed Me More "Worst" Scales
Hi George! Thanks for taking up the challenge!
> I started with the four intervals smaller and larger than a fourth and fifth having maximum > harmonic entropy, using the curve Paul Erlich produced for me on the HE list: 459, 542,
> 654, and 758 cents. I tried constructing scales using various fractions of these intervals as > generators and found that 1/3 of 542 cents produces a heptatonic scale with severely
> stretched octaves. If you want to pin the generator down to an exact value, I would suggest > 1/3 of 541.4188 cents (the noble mediant between 4/3 and 11/8), which gives 180.4729
> cents, a tad smaller than 10/9.
Brian Wong suggested almost this exact same scale to me back on the Xenharmonic NING, the first time I posed this "worst scale" challenge. I didn't try it out back then because I can't technically do non-octave scales in Logic...but it just occurred to me that I might have a work-around.
This scale is virtually identical to 20-ED8 (20 equal division of 8/1), eventually missing the 8/1 by only 9.458 cents. Thus, most of the intervals that will turn up in it are virtually identical to octave-transpositions of those in 20-ED2, a tuning I know and love. I even have a refretted guitar in it! I will be happy to compose in it if you really think it will be difficult, especially because it will allow me to use a guitar, but I don't anticipate much of a challenge. I leave it to you to decide if this is the tuning you want me try.
-Igs
From: cityoftheasleep (2011-01-17)
Subject: Re: Feed Me More "Worst" Scales
--- In [email protected], "gdsecor" <gdsecor@...> wrote:
> As possibly the first person ever to produce a composition in 11-EDO (on a retuned
> electronic organ back in 1970, and yet another on a Scalatron in 1975 -- I still have
> recordings of both
Oh, and I would LOVE to hear these if you have them in a digital format.
-Igs
From: gdsecor (2011-01-17)
Subject: [MMM] Re: Feed Me More "Worst" Scales
--- In [email protected], Ozan Yarman <ozanyarman@...> wrote:
>
> Dear George, long time no chat! This new scale by you seems to have
> interesting potentials. I am almost tempted to try out something myself
> with it. But what name do you plan to give the scale?
>
> Oz.
Hi Oz,
Good to hear from you again.
I was thinking about a name but couldn't come up with anything good (or bad) enough. However, since Igs indicated that I'm not the first one to suggest this scale, I don't think I should be the one to name it.
Best,
--George
From: cityoftheasleep (2011-01-17)
Subject: [MMM] Re: Feed Me More "Worst" Scales
In honor of its purpose of creating maximum discord, why not call it "Kallisti" after the inscription on the golden apple of Eris from Greek Mythology?
-Igs
--- In [email protected], "gdsecor" <gdsecor@...> wrote:
>
>
> --- In [email protected], Ozan Yarman <ozanyarman@> wrote:
> >
> > Dear George, long time no chat! This new scale by you seems to have
> > interesting potentials. I am almost tempted to try out something myself
> > with it. But what name do you plan to give the scale?
> >
> > Oz.
>
> Hi Oz,
>
> Good to hear from you again.
>
> I was thinking about a name but couldn't come up with anything good (or bad) enough. However, since Igs indicated that I'm not the first one to suggest this scale, I don't think I should be the one to name it.
>
> Best,
>
> --George
>
From: gdsecor (2011-01-17)
Subject: Re: Feed Me More "Worst" Scales
--- In [email protected], "cityoftheasleep" <igliashon@...> wrote:
>
> Hi George! Thanks for taking up the challenge!
>
> > I started with the four intervals smaller and larger than a fourth and fifth having maximum harmonic entropy, using the curve Paul Erlich produced for me on the HE list: 459, 542, 654, and 758 cents. I tried constructing scales using various fractions of these intervals as generators and found that 1/3 of 542 cents produces a heptatonic scale with severely stretched octaves. If you want to pin the generator down to an exact value, I would suggest 1/3 of 541.4188 cents (the noble mediant between 4/3 and 11/8), which gives 180.4729 cents, a tad smaller than 10/9.
>
> Brian Wong suggested almost this exact same scale to me back on the Xenharmonic NING, the first time I posed this "worst scale" challenge. I didn't try it out back then because I can't technically do non-octave scales in Logic...but it just occurred to me that I might have a work-around.
>
> This scale is virtually identical to 20-ED8 (20 equal division of 8/1), eventually missing the 8/1 by only 9.458 cents. Thus, most of the intervals that will turn up in it are virtually identical to octave-transpositions of those in 20-ED2, a tuning I know and love. I even have a refretted guitar in it! I will be happy to compose in it if you really think it will be difficult, especially because it will allow me to use a guitar, but I don't anticipate much of a challenge. I leave it to you to decide if this is the tuning you want me try.
Hey, since it's your album, it's your call, so go ahead and use every 3rd tone of 20-EDO. It will certainly present more possibilities.
For one thing, since 20-EDO has 3 separate stretched heptatonic scales, you would have the ability to make a sort of "modulation" to another key by changing to another 20-EDO subset. You could also treat any tone outside your current heptatonic subset as a kind of chromatic alteration or as a pivot tone leading into a different key. However, a modulation of this sort could be a bit tricky, something like changing from one whole-tone scale to the other in 12-ET.
--George
From: gdsecor (2011-01-17)
Subject: Re: Feed Me More "Worst" Scales
--- In [email protected], "cityoftheasleep" <igliashon@...> wrote:
>
> --- In [email protected], "gdsecor" <gdsecor@> wrote:
> > As possibly the first person ever to produce a composition in 11-EDO (on a retuned
> > electronic organ back in 1970, and yet another on a Scalatron in 1975 -- I still have
> > recordings of both
>
> Oh, and I would LOVE to hear these if you have them in a digital format.
>
> -Igs
The originals are on open reel tape. I'll have to transfer them to digital files when I get some free time (pretty busy these days).
--George
From: Carl Lumma (2011-01-18)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Try 257 EDO. Use the whole scale. Good luck! -C.
At 11:40 AM 1/16/2011, you wrote:
>Okay, folks. I've been so pleased with the songs that have come out
>of these "worst" scales that it's becoming a for-real album, so I'm
>not going to demo any more single tracks here on MMM.
From: cityoftheasleep (2011-01-18)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], Carl Lumma <carl@...> wrote:
>
> Try 257 EDO. Use the whole scale. Good luck! -C.
Oh, Carl, you silly goose...you KNOW I'm limited to 12-note subsets. I'd have to run 22 different synth tracks to make that work! My computer would probably explode. Compositionally, though, it really wouldn't be difficult at all. If I took advantage of some commatic-drifting progressions, I could hit all 257 notes in 10 minutes or so, and sound just fine doing it, too. Something tells me your heart just wasn't in this.
-Igs
From: genewardsmith (2011-01-18)
Subject: Re: Feed Me More "Worst" Scales
--- In [email protected], "cityoftheasleep" <igliashon@...> wrote:
>
> --- In [email protected], Carl Lumma <carl@> wrote:
> >
> > Try 257 EDO. Use the whole scale. Good luck! -C.
>
> Oh, Carl, you silly goose...you KNOW I'm limited to 12-note subsets.
That's too bad, because I was going to suggest you use it for a 17-limit version of miracle, using <<257 407 596 721 889 951 1050|| with a generator of 25\257. A 72 note MOS would be good, but you might prefer the 113 MOS.
From: Graham Breed (2011-01-18)
Subject: Re: [MMM] Feed Me More "Worst" Scales
On 17 January 2011 01:41, cityoftheasleep <igliashon@...> wrote:
> Sadly, I can't tune that in Logic, since I can only go +/-
> 100 cents from each step of 12-equal. . . .
You can try random scales. I don't think they're actively bad, but we
know there are no bad scales (at least, none worth bothering with) and
randomness should avoid any built-in goodness. When I looked at them
before, I found randomizing the deviations relative to 12-equal
produced more stable results than finding random pitches within an
octave, because of natural clustering. But if the tuning's +/- 1200,
here are some examples. If you want pure octaves, you can make the
octaves pure.
Cents list that you can easily make into a Scala file:
170.0
239.6
391.0
347.6
413.8
570.3
757.7
885.5
997.6
933.1
1096.8
1225.1
Deviations:
70.0
39.6
91.0
-52.4
-86.2
-29.7
57.7
85.5
97.6
-66.9
-3.2
25.1
87.0
293.8
382.0
408.4
538.1
581.9
768.0
850.7
988.9
1079.2
1198.6
1146.4
-13.0
93.8
82.0
8.4
38.1
-18.1
68.0
50.7
88.9
79.2
98.6
-53.6
107.4
110.9
302.3
480.7
441.9
648.7
683.3
836.4
973.5
994.0
1038.5
1104.3
7.4
-89.1
2.3
80.7
-58.1
48.7
-16.7
36.4
73.5
-6.0
-61.5
-95.7
They're easy to generate, of course, so I'm sure you can come up with some more.
Graham
From: Carl Lumma (2011-01-18)
Subject: Re: [MMM] Feed Me More "Worst" Scales
At 09:24 PM 1/17/2011, you wrote:
>--- In [email protected], Carl Lumma <carl@...> wrote:
>>
>> Try 257 EDO. Use the whole scale. Good luck! -C.
>
>Oh, Carl, you silly goose...you KNOW I'm limited to 12-note subsets.
>I'd have to run 22 different synth tracks to make that work! My
>computer would probably explode.
Oh, I think I see what you're saying. Real musicians like have
limitations, both with electronic and with physical instruments.
Thus, it is a bad scale. QED.
>Something tells me
>your heart just wasn't in this.
On the contrary, I've already won.
-Carl
From: cityoftheasleep (2011-01-18)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], Carl Lumma <carl@...> wrote:
> Oh, I think I see what you're saying. Real musicians like have
> limitations, both with electronic and with physical instruments.
> Thus, it is a bad scale. QED.
Well, that's a different definition of "bad" than I've been using. There are multitudes of excellent-sounding chords possible in 257, so there is nothing necessarily psychoacoustically "bad" about how it sounds. As for limitations--I can think of nothing more limiting than being forced to use all the notes in a tuning, especially one so large.
> >Something tells me
> >your heart just wasn't in this.
>
> On the contrary, I've already won.
It's easy to win a battle if you don't have an opponent. Your choice of 257-EDO as "bad" has nothing to do with either its harmonic or melodic qualities and everything to do with its size and impracticality, which is tangential to the original point that I was once attempting to make--that scales designed to minimize (rather than maximize) consonance will not be musically useless, because it is next to impossible to escape consonance all together (and that a little bit of consonance is all you need to make music). My actual making of music in these scales is also a bit tangential, since it's enough to analyze the various possible intervals in the various "anti-optimal" scales I've been given to see that approximately-consonant intervals do arise in various places.
The real point, of course, is that the relevance of consonance depends entirely on the goals of the musician making the music (and the listener hearing it). As I particularly seem to enjoy working with scales designed to be dissonant, I have solicited the community here to provide me with more scales. Perhaps I erred in adopting the somewhat-ambiguous terms "bad" and "worst" as short-hand for "permitting a minimum of consonant harmony". But regardless, I don't think 257-EDO has much to do with what I was asking for.
-Igs
From: Carl Lumma (2011-01-18)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Igs wrote:
>Well, that's a different definition of "bad" than I've been using.
Size is an important part of the equation. If we're just talking
about concordance, my challenge to you is coming. I'm waiting for
Manuel to fix some bugs in a new Scala feature he's implementing.
At the rate Manuel works, that will only be a few days.
Also it's worth pointing out that writing beautiful music in a
"bad" scale says nothing absent a comparison to the other side of
the coin, as Gene suggested.
Also it's worth pointing out that when you're given a "bad" scale,
you clearly try to analyze it in regular mapping esque ways. You
use concepts like MOS, harmonic series chords, etc etc. You are
considerably better versed in microtonal theory than most. I don't
think you sought out these materials for your health.
-Carl
From: cityoftheasleep (2011-01-18)
Subject: Re: Feed Me More "Worst" Scales
--- In [email protected], Carl Lumma <carl@...> wrote:
>
> Igs wrote:
> >Well, that's a different definition of "bad" than I've been using.
>
> Size is an important part of the equation. If we're just talking
> about concordance, my challenge to you is coming. I'm waiting for
> Manuel to fix some bugs in a new Scala feature he's implementing.
> At the rate Manuel works, that will only be a few days.
I eagerly await it.
> Also it's worth pointing out that writing beautiful music in a
> "bad" scale says nothing absent a comparison to the other side of
> the coin, as Gene suggested.
Au contraire, it says that you can write beautiful music in a bad scale! Even if the music might be in some way better in a "good" tuning, if it's good in a bad tuning, that is enough. Some temperaments also simply cannot be tuned well, so comparison with a "good" tuning is not even possible for some pieces.
> Also it's worth pointing out that when you're given a "bad" scale,
> you clearly try to analyze it in regular mapping esque ways. You
> use concepts like MOS, harmonic series chords, etc etc. You are
> considerably better versed in microtonal theory than most. I don't
> think you sought out these materials for your health.
Actually, that's not entirely true. Looking for harmonic series chords is a new development for me, I wrote the entirety of "Map of an Internal Landscape" on the strength of the MOS paradigm and my ears alone. Approaching Michael's and John's scales, I pretty much tossed theory out the window and let my ears guide me, though I did map out the different modes to get a better sense of all the intervals I was dealing with. Only after the pieces were written did I do any sort of harmonic series analysis. Even my well-documented infatuation with tunings that yield good 16:18:21 chords arose not from a search for that chord but from the discovery that a major 2nd plus a subminor 3rd yielded a pleasing chord in 18-EDO, which analysis then revealed to be 16:18:21. I've only recently taken up this approach because it seems helpful in finding note combinations I wouldn't ordinarily explore.
-Igs
From: Michael (2011-01-18)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Igs>"Well, that's a different definition of "bad" than I've been using."
Assuming an instrument (even digital) with 257 values per octave....keeping
good track of everything as a composer without using subsets of that tuning
would be nightmarish....I think that's a large part of the point Carl was
making. Far as easy to compose with...257TET is probably pretty awkward....even
if a lot of mathematical possibilities are there I'd be surprised to find a
composer who can keep track of all of them in real-time!
Imagine a fretless piano (which wouldn't act unlike having 257 notes) IE
that worked like a huge touch-screen with one side being the lowest and the
other the highest. Now imagine playing a major chord on different parts of such
an instrument....most every other time you hit it you will slide a bit
off...until, say, you've slowly slid the middle note and top down so much each
time you are now playing something that sounds more like a
neutral/diminished-ish chord than a major chord.
>"Perhaps I erred in adopting the somewhat-ambiguous terms "bad" and "worst" as
>short-hand for "permitting a minimum of consonant harmony"."
So you are aiming to work in scales that have few "opportunities" for
consonance rather than simply "are generally tricky to compose with" in other
words...correct? And your goal, so to speak, is to prove that the musician can
choose to make consonance matter less in a song...not just to himself but also
to the listener?
[Non-text portions of this message have been removed]
From: Michael (2011-01-18)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Carl>"Also it's worth pointing out that when you're given a "bad" scale, you
clearly try to analyze it in regular mapping esque ways. You
use concepts like MOS, harmonic series chords, etc etc."
If I'm hearing this correctly, this has been my point for ages. If a scale
had 100 bad chords and 4 fairly good ones (so far as the harmonic series
goes)...I swear Igs would likely make most of the chords in the song...minus a
few chords played for very short durations...those four chords. My
counter-challenge would be "hey dude...can you do anything polyphonic (yes,
multiple instruments and multiple notes at once!) under that scale which doesn't
hang on those 4 chords, sounds very distinct in mood from the first song despite
using the same instrumental arrangement, and still sounds stable?" So Igs may
say "even your ridiculously beating scale would be great for a really spacey
ambient jazz song"...I'd argue "sure...but that scale has so few 'good' choices
you're probably stuck with that mood and tonal color...unlike the vast choices
of tonal color and mood in many 'good' scales.
What would be a real hoot...IMVHO...is to compare not one but 3 or so songs
Igs wrote in each tuning...each aiming for a much different mood than any of the
other songs. In such a situation...I think the mood-shallowness of many of the
"bad" tunings would begin to show.
I am also curious as to what Carl will come up with as a "bad" consonance
scale. Perhaps something involving a slew of dyads around noble mediants? :-D
[Non-text portions of this message have been removed]
From: Carl Lumma (2011-01-18)
Subject: Re: [MMM] Re: Feed Me More "Worst" Scales
>Au contraire, it says that you can write beautiful music in a bad
>scale!
Who said you couldn't?
-Carl
From: Michael (2011-01-18)
Subject: Re: [MMM] Re: Feed Me More "Worst" Scales
Igs>"I wrote the entirety of "Map of an Internal Landscape" on the strength of
the MOS paradigm and my ears alone. Even my well-documented infatuation with
tunings that yield good 16:18:21 chords arose not from a search for that chord
but from the discovery that a major 2nd plus a subminor 3rd yielded a pleasing
chord in 18-EDO, which analysis then revealed to be 16:18:21. "
Not only is that how I handle all microtonal scales, but also "even" 12TET
ones. Try a few chords in the right general area (so far as tonal center) and
try to keep track of their tensity's by ear...then move them around to make
music...without regard to their proper names or harmonic series placements.
>"I've only recently taken up this approach because it seems helpful in finding
>note combinations I wouldn't ordinarily explore. "
interesting, so you're actually lets the harmonic series "help" push you away
from chords you'd normally find by ear?
[Non-text portions of this message have been removed]
From: cityoftheasleep (2011-01-18)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], Graham Breed <gbreed@...> wrote:
> 107.4
> 110.9
> 302.3
> 480.7
> 441.9
> 648.7
> 683.3
> 836.4
> 973.5
> 994.0
> 1038.5
> 1104.3
>
> 7.4
> -89.1
> 2.3
> 80.7
> -58.1
> 48.7
> -16.7
> 36.4
> 73.5
> -6.0
> -61.5
> -95.7
>
>
> They're easy to generate, of course, so I'm sure you can come up with some more.
>
>
> Graham
>
This one's brilliant. I think I'll do an ambient piece with it.
-Igs
From: cityoftheasleep (2011-01-18)
Subject: [MMM] Re: Feed Me More "Worst" Scales
--- In [email protected], Carl Lumma <carl@...> wrote:
>
> >Au contraire, it says that you can write beautiful music in a bad
> >scale!
>
> Who said you couldn't?
Um, you:
> Also it's worth pointing out that writing beautiful music in a
> "bad" scale says nothing absent a comparison to the other side of
> the coin, as Gene suggested.
I'm saying the comparison is not necessary to "say something".
-Igs
From: cityoftheasleep (2011-01-18)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], Michael <djtrancendance@...> wrote:
> If I'm hearing this correctly, this has been my point for ages. If a scale
> had 100 bad chords and 4 fairly good ones (so far as the harmonic series
> goes)...I swear Igs would likely make most of the chords in the song...minus a
> few chords played for very short durations...those four chords.
That's B.S.! I have yet to write a four-chord song in any of these "bad" tunings, and I give most of the chords equal time. I certainly haven't limited myself moreso in these tunings than in any others; if the music lacks polyphonic depth, it's because my style is simple, not because I'm holding back due to the tunings. And at any rate, wait til you hear the tracks I'm writing in 14 and 11-EDO. By your standards, there should be NO "fairly-good" chords in either of these.
> My
> counter-challenge would be "hey dude...can you do anything polyphonic (yes,
> multiple instruments and multiple notes at once!) under that scale which doesn't
> hang on those 4 chords, sounds very distinct in mood from the first song despite
> using the same instrumental arrangement, and still sounds stable?"
No cohesive scale is going to have any more variety of "mood" than any other cohesive scale. The limitation in mood from the first couple of your "bad" scales is mostly because they are so distributionally-uneven. But still, I could take them in plenty of different directions.
> So Igs may
> say "even your ridiculously beating scale would be great for a really spacey
> ambient jazz song"...I'd argue "sure...but that scale has so few 'good' choices
> you're probably stuck with that mood and tonal color...unlike the vast choices
> of tonal color and mood in many 'good' scales.
You seem to think that there is more of a variety in mood between consonant chords than dissonant ones, and I have no idea why. There are plenty of moods that can be expressed better through dissonance than through consonance, but they tend not to be acknowledged because we are accustomed to using the highly-consonant 12-tET scale to express ourselves through music. Frustration, uncertainty, pensiveness, agitation, rage, desperation, exhaustion, alarm, annoyance, ambivalence, bitterness, anxiety, confusion, indignation--these are all "moods" that cry out for different shades of dissonance, for weak/tentative intervals, for rattling and jarring chords. It is best to have contrast, yes, but when so few have attempted to demonstrate the expressive powers of an expanded palette of dissonance, I can't help but find it more intriguing than exploring the vastly-overpopulated world of consonance.
> In such a situation...I think the mood-shallowness of many of the
> "bad" tunings would begin to show.
LOL, you'll be eating those words soon enough!
;->
-Igs
From: Carl Lumma (2011-01-18)
Subject: Re: [MMM] Re: Feed Me More "Worst" Scales
>> >Au contraire, it says that you can write beautiful music in a bad
>> >scale!
>>
>> Who said you couldn't?
>
>Um, you:
>
>> Also it's worth pointing out that writing beautiful music in a
>> "bad" scale says nothing absent a comparison to the other side of
>> the coin, as Gene suggested.
>
>I'm saying the comparison is not necessary to "say something".
>
>-Igs
A comparison certainly is necessary to say something about
the relative qualities of scales. My question was, who said
you that you could not make beautiful music in a bad scale?
I don't think anyone said that so it shouldn't be contrary
to anything. -Carl
From: genewardsmith (2011-01-18)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], Michael <djtrancendance@...> wrote:
s. My
> counter-challenge would be "hey dude...can you do anything polyphonic (yes,
> multiple instruments and multiple notes at once!) under that scale which doesn't
> hang on those 4 chords, sounds very distinct in mood from the first song despite
> using the same instrumental arrangement, and still sounds stable?"
I like the idea of a polyphonic challenge, but not this one. What about seeing if we can write some very polyphonic music with *lots* of chords? I'm finishing a very polyphonic three-part piece with hundreds of different types of triads in it, and I suggest after the hoopla from the UnTwelve entries dies down, we see if we can present some serious polyphony around here. Now would be a good time to start work on your polyphonic masterpiece, because I already have a head start.
From: genewardsmith (2011-01-18)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], "cityoftheasleep" <igliashon@...> wrote:
> No cohesive scale is going to have any more variety of "mood" than any other cohesive scale.
I would say 31edo clearly has more variety of moods than 4edo.
From: Michael (2011-01-19)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Me> If I'm hearing this correctly, this has been my point for ages. If a
scale
> had 100 bad chords and 4 fairly good ones (so far as the harmonic series
> goes)...I swear Igs would likely make most of the chords in the song...minus a
> few chords played for very short durations...those four chords.
Igs>I have yet to write a four-chord song in any of these "bad" tunings, and I
give most of the chords equal time.
My point wasn't that you literally use four chords but, rather, you make a
point of mostly (if not only) staying with the few "good" chords in the "bad"
scales.
>"if the music lacks polyphonic depth, it's because my style is simple, not
>because I'm holding back due to the tunings."
It may very well be a or the limiting factor that your style is relatively
"simple" IE maybe you want to keep the mood/chord... changes relatively basic as
an artistic choice... But my point is that you have not disproven my theory
that, although beautiful music can be written in bad tunings...such tunings
limit the musician's range of mood.
>No cohesive scale is going to have any more variety of "mood" than any other
>cohesive scale.
>
Really? So you are indirectly saying no microtonal tuning, for example, is
going to have/give any more mood variety than the "cohesive" 12TET tuning? Try
composing in 12TET vs. 31TET (including a fair deal of the non-12TET-like
intervals in 31TET)...I'm pretty sure you will notice a huge difference in mood
flexibility.
>"The limitation in mood from the first couple of your "bad" scales is mostly
>because they are so distributionally-uneven. But still, I could take them in
>plenty of different directions."
Guess what...I'm not convinced distributionally-uneven means "bad". My
"good" scales are that way as well (often relatively
distributionally-uneven...at least vs. TET scales)...and often as uneven as the
"bad" ones.
.
Now don't get me wrong, I'm not saying I think scales that are
distributionally-even IE TET are bad...but rather that simply because you
gravitate toward them does not automatically, if the following is what part of
your aim may be, give you the right to state distributionally-uneven scales are
automatically bad.
Plus...my scales are not very distributionally uneven at all in the first
place relative to how uneven things can get...if you want that...your clustered
24TET "anti-diatonic" scale would be a great example. :-D
It just seems indirectly (correct me if/why I'm wrong)...you are
automatically saying scales that are TET or MOS subsets of TET are always the
"most good" scales.
I recall Erv Wilson saying about MOS that his goal was something along the
lines of preserving enough TET-style even-distribution for easy playing and
chord identification with the better harmonic precision/alignment properties of
often very uneven scales. But I think the overwhelming concept is...depending
on how much someone may veer toward one of those two concepts over the other in
composing...they can easily lean toward uneven scales so much as even
ones...though getting the best of both is, to some extent, likely ideal for many
composers.
--------------------------------------------
>"You seem to think that there is more of a variety in mood between consonant
>chords than dissonant ones, and I have no idea why."
No, I believe there is more clear tension/resolve contrast in scales with as
many consonant chords as dissonant ones. And, for the record, I believe over
half the chords in 12TET are dissonant...hence the need for chord theory and the
fact so much highly dissonant music can be make of the "strong" dyads in 12TET.
I figure if I go for consonant chords...I'll be lucky to get 40% of the possible
ones sounding "consonant"...and 50% would make for an ideal contrast....and that
getting that 50% distribution is a challenge even if all dyads are consonant
What I don't believe in is that scales where a very disproportionate majority
of chords are dissonant give a "wider mood range".
>"but they tend not to be acknowledged because we are accustomed to using the
>highly-consonant 12-tET scale to express ourselves through music."
That's the thing...I don't view 12TET as "highly consonant", but rather
relatively "equally split consonant/dissonant". "highly consonant" would be
something like the pentatonic scale...where the degree of consonant chords is
far over 50% (or even over 90%!) and the mood range is greatly reduced because
the consonant/dissonant distribution does not approach even. Even more so would
be an octave equivalent scale of 1 3/2 2/1 6/2 4/1 etc. ..."perfect" consonance
and virtually no range of mood. :-D
Me> In such a situation...I think the mood-shallowness of many of the "bad"
tunings would begin to show.
Igs>"LOL, you'll be eating those words soon enough!"
So you're going to take the challenge to produce many different moods through
many different songs under a single bad tuning? That should be interesting...
:-)
[Non-text portions of this message have been removed]
From: Michael (2011-01-19)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Gene>"What about seeing if we can write some very polyphonic music with *lots*
of chords? I'm finishing a very polyphonic three-part piece with hundreds of
different types of triads in it, and I suggest after the hoopla from the
UnTwelve entries dies down, we see if we can present some serious polyphony
around here."
Awesome...yes that should be quite a challenge and good luck with your
multi-hundred chord monster. Especially this seems like a fitting challenge to
see if, say, Igs can pull it off with a "bad" scale, with my hunch that "limited
use of polyphony within a balanced resolve/tension context" (and ultimately
resulting limited range of moods) is a major compositional issue with said "bad"
scales.
>"Now would be a good time to start work on your polyphonic masterpiece, because
>I already have a head start."
Well, my first attempt at a "polyphonic masterpiece" was my Untwelve
entry...tons of 6 and 7-tone chords and there must be something over 100 triads
in there and just about the only time chords "repeat" is during solos (and, even
then, the notes in the solos often drone and combine with those chords to form
new "versions" of them).
But you're right...now's a good time to get cracking on a new song, a
"polyphonic masterpiece"follow-up. :-)
[Non-text portions of this message have been removed]
From: cityoftheasleep (2011-01-19)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], Michael <djtrancendance@...> wrote:
> My point wasn't that you literally use four chords but, rather, you > make a point of mostly (if not only) staying with the few "good"
> chords in the "bad" scales.
Well, then there are more than 4 good chords in these scales, because (as I said) I tend to give chords equal time in my pieces. Yeah, there are lots of chords I don't use, but come on--who uses every possible triadic combination within a scale in a given piece? Yeah, some chords are gonna get left out, no matter what the scale.
> It may very well be a or the limiting factor that your style is
> relatively "simple" IE maybe you want to keep the mood/chord...
> changes relatively basic as an artistic choice... But my point is > that you have not disproven my theory that, although beautiful
> music can be written in bad tunings...such tunings
> limit the musician's range of mood.
What's it gonna take, then? A whole album in a "bad" tuning? Tell you what: I'll do four tracks in 11-EDO, covering as wide a variety of moods as possible. If 11-EDO isn't a "bad" harmonic tuning, I don't know what is.
> Really? So you are indirectly saying no microtonal tuning, for
> example, is going to have/give any more mood variety than the
> "cohesive" 12TET tuning? Try composing in 12TET vs. 31TET
> (including a fair deal of the non-12TET-like
> intervals in 31TET)...I'm pretty sure you will notice a huge
> difference in mood flexibility.
Excuse me, in the process of editing and re-editing that post, I deleted an important qualifier: no cohesive scale is going to have any more mood-variety than any other cohesive scale, *provided the number of available intervals is kept constant*. Obviously if you have more intervals available, you'll have more versatility. But any D.E. scale of 7 notes is going to be as versatile as any other D.E. scale of 7 notes, although they might be very different in character. The diatonic scale is consonant as hell in meantone, but that doesn't mean it's more versatile than the 7-note MOS of Mohajira, or Amity, or Mavila.
> Guess what...I'm not convinced distributionally-uneven means
> "bad".
And who suggested that it does? I suggested that it means "limited". Because the less D.E. a scale is, the fewer instances of any one interval there will be, and thus the more restricted one will be in using a given interval. Compare playing harmonics 7-14 vs. the 31-EDO diatonic scale if you don't believe me.
> It just seems indirectly (correct me if/why I'm wrong)...you are
> automatically saying scales that are TET or MOS subsets of TET are > always the "most good" scales.
Not necessarily; there are some good well-temperaments out there that are more or less D.E., but with some very subtle variations between keys. George Secor has a particular gift with these sorts of scales. Also, not all D.E. scales are MOS or EDO-compatible. But they all have the property of maximizing uniformity, and in a uniform scale, the composer is free to play any interval from any note.
> And, for
> the record, I believe over half the chords in 12TET are
> dissonant...hence the need for chord theory and the
> fact so much highly dissonant music can be make of the "strong"
> dyads in 12TET.
Really? How are you counting? If we're looking at triads within one octave given a constant root note, I sincerely doubt this.
> What I don't believe in is that scales where a very
> disproportionate majority of chords are dissonant give a "wider
> mood range".
And I still think this is because you are failing to acknowledge the different moods that dissonant intervals are capable of producing.
> That's the thing...I don't view 12TET as "highly consonant", but
> rather relatively "equally split consonant/dissonant".
Man, I do not get your thinking. Dyadically, there are two--maybe 3--intervals in 12-tET that are dissonant: the min2, the b5/#4, and maaaaaybe the maj7. You cannot find a 12-note scale with fewer dissonances. Maybe you can find one where the dissonances are less dissonant--some well-temperaments pull this off quite artfully--but the number of dissonances will not change. If you make the scale less even so that there are fewer dissonances on one root, guess what--there will be more on another root! You can move them around as much as you want, but you can't decrease their number.
-Igs
From: Michael (2011-01-19)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Igs>"Yeah, some chords are gonna get left out, no matter what the scale."
The question then seems to become...how do (or can?) we get and idea how far
a scale can go? Agreed...no one can be expected to use every chord possible in
a scale in a single song...and if they did it would likely sound very...forced
and unnatural.
>"What's it gonna take, then? A whole album in a "bad" tuning? Tell you what:
>I'll do four tracks in 11-EDO, covering as wide a variety of moods as possible.
>If 11-EDO isn't a "bad" harmonic tuning, I don't know what is."
I don't know because I haven't tried. :-D 4 songs in 11TET should be a
pretty good test or, perhaps better yet, 4 songs in that second bad scale I gave
you IE the one you had the most challenge finding good chords in.
Well that....and asking everyone (not just us :-D) the question of what they
thought of the variety of tonal colors used in those songs vs. a shot of your
doing the same thing IE trying to find as many different moods as possible in 4
songs in a "good" scale (and comparing the results afterward).
>"no cohesive scale is going to have any more mood-variety than any other
>cohesive scale, *provided the number of available intervals is kept constant*."
Ah, good point! In this case, 7TET for the standard 7-tone diatonic under
12TET might be a good test. As would 13TET vs. 12TET (in this case, 13 TET
"should" have the advantage because it has an extra note...but I'm betting in
won't in compositional use)!
>"The diatonic scale is consonant as hell in meantone, but that doesn't mean
>it's more versatile than the 7-note MOS of Mohajira, or Amity, or Mavila. "
First of all, 7 tone Mohajira is awesome! :-D It makes, IMVHO, a great
argument how 11-limit can be used in a fashion nearly as
stable/predictable/balanced sounding between consonance/dissonance as the
diatonic scale under 12TET. Then again, in 7TET vs. that diatonic scale...I
think you'll notice a difference.
One notable distinction...I do think there's a major problem with moods that
become "too" bad IE a certain degree of the mood "chaos" can be anything from
happy chaos to angry chaos to panic....but if there's too much chaos it all
becomes a blur and you can't tell what "sub-mood" it is. The easiest example of
this I believe...is a song composed of noise waves...ask people, what mood is
it? :-D
>"Compare playing harmonics 7-14 vs. the 31-EDO diatonic scale if you don't
>believe me. "
Well of course...but you are taking a ridiculous extreme on the idea of
"distributionally uneven". Even the diatonic scale under 12TET has the
semi-tone half the size of the whole tone...
BTW, even try the Ptolemy Homalon scale (yep, it's a 7 tone scale under
Scala)? It has "semi-tones" of size 12/11,11/10,10/9, and 9/8...yet I swear
you'll be amazed at how many different kinds of chords are possible in it.
Methinks you have a bit of a pet bias for TET and MOS (or very close variants on
them)....and I'm prepared to do war with it. :-D
>"Not necessarily; there are some good well-temperaments out there that are more
>or less D.E., but with some very subtle variations between keys. George Secor
>has a particular gift with these sorts of scales"
Ok, so those aren't DE but instead "slight variants on D.E." Still...not
much difference...IMVHO an interval and something within 8 cents of it are
essentially the same thing...it's like a vanilla icecream with m&m's vs. one
with a cherry on top.
>"Really? How are you counting? If we're looking at triads within one octave
>given a constant root note, I sincerely doubt this. "
Not if we consider the word "triad" as meaning "any three notes". Try C C#
D#, or C C# E, or C# E F, or C D# E..... It seems you have this underlying
idea that the only thing that constitutes a triad is something under common
practice or a variant (like "super major") is a triad. My point is...suppose a
musician can pick any three notes under 12TET and play them at once...what can
go sour?...a lot! Maybe, even, I'm being a tad too easy by saying it even gets
50%.
>"Man, I do not get your thinking. Dyadically, there are two--maybe
>3--intervals in 12-tET that are dissonant: the min2, the b5/#4, and maaaaaybe
>the maj7. You cannot find a 12-note scale with fewer dissonances. "
My point is that EVEN with nearly all perfect dyads, you still will most
likely get 50%+ dissonant combinations in any decently sized (think 10+ tone)
tuning. And thus the challenge becomes to get (not "avoid passing") that 50%
for even consonance/dissonance distribution.
What I'm saying is that
A) A majority of scales are disproportionately (well over 50%) dissonant so far
as tonal combinations
B1) Thus, to achieve the goal of 50/50 dissonance/consonance...one must usually
increase consonance, not dissonance...
B2) "over consonance" is just as generally harmful for easy composition...try to
get moods out of a pentatonic scale with a large majority of consonance over
dissonance...ouch! But running into the issue of "over consonance" is VERY
unlikely...
To be fair...I do believe I have a "pet bias" for scales with more or less
equal balance between consonant and dissonant chord options. And I think 12TET
is "pretty good" for that sort of thing and much of the success of 12TET comes
from the balance between consonance and dissonance, not any so-called "abundance
of consonance". Again I swear, if 12TET had so few ways to "go
sour"...musicians very likely wouldn't be so stressed about chord theory (and
they are stressed...because there are so many overtly 'sour' options, even in
12TET)... :-D
[Non-text portions of this message have been removed]
From: cityoftheasleep (2011-01-19)
Subject: Re: Feed Me More "Worst" Scales
--- In [email protected], Michael <djtrancendance@...> wrote:
> I don't know because I haven't tried. :-D 4 songs in 11TET should be a
> pretty good test or, perhaps better yet, 4 songs in that second bad scale I gave
> you IE the one you had the most challenge finding good chords in.
11-EDO is worse. There is no place to hide in 11-EDO. Even in your 2nd "worst" scale, some approximate fifths and major 3rds popped up in a few places; in 11-EDO that cannot happen.
> Well that....and asking everyone (not just us :-D) the question of what they
> thought of the variety of tonal colors used in those songs vs. a shot of your
> doing the same thing IE trying to find as many different moods as possible in 4
> songs in a "good" scale (and comparing the results afterward).
I think a comparison between 11-EDO and 12-EDO is pretty fair; 11-EDO has about as many consonances as 12-EDO has dissonances. For rigor, both scales should be equal to control the total number of available intervals, and should be as close in size as possible (since obviously more notes = more "moods").
> Ah, good point! In this case, 7TET for the standard 7-tone diatonic under
> 12TET might be a good test. As would 13TET vs. 12TET (in this case, 13 TET
> "should" have the advantage because it has an extra note...but I'm betting in
> won't in compositional use)!
I could do 13-EDO instead, if you think that would be a better indicator, though I think 13-EDO is quite a bit more consonant than 11.
> >"The diatonic scale is consonant as hell in meantone, but that doesn't mean
> >it's more versatile than the 7-note MOS of Mohajira, or Amity, or Mavila. "
> First of all, 7 tone Mohajira is awesome! :-D It makes, IMVHO, a great
> argument how 11-limit can be used in a fashion nearly as
> stable/predictable/balanced sounding between consonance/dissonance as the
> diatonic scale under 12TET. Then again, in 7TET vs. that diatonic scale...I
> think you'll notice a difference.
7-EDO has half the intervals that the diatonic scale has, despite having the same number of notes. In the diatonic scale, every interval-class has two sizes, whereas in 7-EDO there is only one size.
I think 7-tone Mohajira is pretty great, too, but it is VERY different in mood from the diatonic. Most people I play it for find the neutral intervals rather "creepy".
> One notable distinction...I do think there's a major problem with moods that
> become "too" bad IE a certain degree of the mood "chaos" can be anything from
> happy chaos to angry chaos to panic....but if there's too much chaos it all
> becomes a blur and you can't tell what "sub-mood" it is. The easiest example of
> this I believe...is a song composed of noise waves...ask people, what mood is
> it? :-D
That's more a timbre issue than a tuning issue, or maybe a compositional one...serialist/atonal techniques are pretty much just as effective in creating chaos regardless of how consonant the tuning is.
> Methinks you have a bit of a pet bias for TET and MOS (or very close variants on
> them)....and I'm prepared to do war with it. :-D
I prefer them, yes, because they take a lot less work to understand than the alternatives, they are "neatly ordered" and there is a finite number of them below a certain note-count limit. For just sitting at a keyboard and playing, however, it makes little difference how a scale is put together, and clearly I am enjoying working with non-TET non-MOS scales in this max-dissonance project!
> Ok, so those aren't DE but instead "slight variants on D.E." Still...not
> much difference...IMVHO an interval and something within 8 cents of it are
> essentially the same thing...it's like a vanilla icecream with m&m's vs. one
> with a cherry on top.
Oh, there's a bit more than 8 cents variety in some of the tunings I'm thinking of. I forget where I found it, but I tried one well-temperament once that was designed to give major 3rds of 5/4, 9/7, and 14/11 in various keys, and minor 4rds of 6/5, 7/6, and 13/11, while still keeping the chain of fifths close enough to pure. It was pretty sweet.
> >"Really? How are you counting? If we're looking at triads within one octave
> >given a constant root note, I sincerely doubt this. "
> Not if we consider the word "triad" as meaning "any three notes". Try C C#
> D#, or C C# E, or C# E F, or C D# E..... It seems you have this underlying
> idea that the only thing that constitutes a triad is something under common
> practice or a variant (like "super major") is a triad. My point is...suppose a
> musician can pick any three notes under 12TET and play them at once...what can
> go sour?...a lot! Maybe, even, I'm being a tad too easy by saying it even gets
> 50%.
I most certainly have no such idea! Yes, I am aware that clustering notes by a semitone in 12-tET leads to dissonance, and that there are many triads in one octave where these clusters are possible. But there are many more triads that don't. I'll make a list of triads in 12-tET and post it. And anyway, how is it any different in your Dimension tuning? Or any 12-note tuning?
> My point is that EVEN with nearly all perfect dyads, you still will most
> likely get 50%+ dissonant combinations in any decently sized (think 10+ tone)
> tuning. And thus the challenge becomes to get (not "avoid passing") that 50%
> for even consonance/dissonance distribution.
> What I'm saying is that
> A) A majority of scales are disproportionately (well over 50%) dissonant so far
> as tonal combinations
I think you should attempt to verify this before making such sweeping claims. As far as I know, you haven't been including triadic analyses when working out your scales.
> B2) "over consonance" is just as generally harmful for easy composition...try to
> get moods out of a pentatonic scale with a large majority of consonance over
> dissonance...ouch! But running into the issue of "over consonance" is VERY
> unlikely...
Compare the mood of the 31-EDO diatonic to the 27-EDO diatonic. In the 31-EDO diatonic, there is essentially ONE dissonance, the 16/15 semitone; the #4 is a 7/5 (so it is now consonant), the b5 is a 10/7 (so it is now consonant), and the maj7 is nearly a perfect 15/8 (and so consonant). In the 27-EDO, the maj3 is about 444 cents, so dissonant; the maj7 is about 1166 cents, so very dissonant; the 4th and 5th are both about 10 cents off, vs. only about 5 cents in 31, so more dissonant, and the semitones at 44 cents are drastically more dissonant than the 16/15's in 31. Tell me: does the increased dissonance in 27 limit the mood-range it is capable of?
> To be fair...I do believe I have a "pet bias" for scales with more or less
> equal balance between consonant and dissonant chord options. And I think 12TET
> is "pretty good" for that sort of thing and much of the success of 12TET comes
> from the balance between consonance and dissonance, not any so-called "abundance
> of consonance". Again I swear, if 12TET had so few ways to "go
> sour"...musicians very likely wouldn't be so stressed about chord theory (and
> they are stressed...because there are so many overtly 'sour' options, even in
> 12TET)... :-D
Who are these musicians that are so stressed out by 12-tET? If you stay on the white keys of the piano (or the black keys), you're fine; if you play guitar, learning a couple chord shapes is all you need--and with the mostly-4ths open-string tuning, it's more difficult to play semitonal clusters than it is to play something consonant; as a guitarist, I feel like I have to bend over BACKWARDS to get any real dissonance in 12-tET! Most polyphonic 12-tET instruments are designed to make playing consonant chords as easy as possible.
-Igs
From: Kalle Aho (2011-01-19)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], Michael <djtrancendance@...> wrote:
>
> Igs>"Yeah, some chords are gonna get left out, no matter what the scale."
> The question then seems to become...how do (or can?) we get and idea how far
> a scale can go? Agreed...no one can be expected to use every chord possible in
> a scale in a single song...and if they did it would likely sound very...forced
> and unnatural.
>
>
> >"What's it gonna take, then? A whole album in a "bad" tuning? Tell you what:
> >I'll do four tracks in 11-EDO, covering as wide a variety of moods as possible.
> >If 11-EDO isn't a "bad" harmonic tuning, I don't know what is."
> I don't know because I haven't tried. :-D 4 songs in 11TET should be a
> pretty good test or, perhaps better yet, 4 songs in that second bad scale I gave
> you IE the one you had the most challenge finding good chords in.
>
> Well that....and asking everyone (not just us :-D) the question of what they
> thought of the variety of tonal colors used in those songs vs. a shot of your
> doing the same thing IE trying to find as many different moods as possible in 4
> songs in a "good" scale (and comparing the results afterward).
Well, if you asked me I wouldn't understand the question because I
don't know what tonal colors are. What is tonal color?
Kalle
From: Michael (2011-01-19)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Kalle>"Well, if you asked me I wouldn't understand the question because I don't
know what tonal colors are. What is tonal color?"
Tonal color is the range in sense of mood in a sound...and without
respect to rhythm or "priming" IE using one chord to prepare the listener for
another. Often the effect is that it feels like the "root/virtual pitch" of the
part being played shifts a bit.
Subtle tonal color changes would be things like changing the type of
instrument playing a melody in a song or changing from a neutral to a major
chord in the same key....while less subtle changes would include things like
changing chords to different types of chords with different root tones (IE C
major to D minor). Good tonal color, IMVHO, would come in a tuning system or
scale that allows a large range of both subtle and less subtle changes to be
explored by the composer, thus giving the composer more expressive range.
[Non-text portions of this message have been removed]
From: cityoftheasleep (2011-01-19)
Subject: Re: [MMM] Feed Me More "Worst" Scales
My analysis of three-note combinations with a constant root-tone (i.e. C) in one octave of 12-EDO:
55 total combinations
5 contain two dissonant dyads (tritone and/or minor 2nd)
25 contain one dissonant dyad (tritone or minor 2nd)
14 contain the minor 2nd only
25 contain no dissonant dyads
I did not count the major 7th as a dissonant dyad.
Note: the chords that contain one dissonant dyad are "on the fence"; I am not convinced any of them should really be called "dissonant", since they sound pretty smooth compared to the five that contain two dissonant dyads.
Consider that many chords containing the tritone approximate 7-limit consonances, like 5:6:7, 4:5:7, 6:7:10, etc., so calling them "dissonant" would be misleading. If we remove tritone-containing chords from the list, the number of single-dissonance-containing triads drops to 14, for a total of 19 dissonant triads out of 55, or an overall dissonance percentage of 34.5%. If we leave in the tritone-containing chords (i.e. assume that the 7-limit is dissonant), then we have 30 dissonances out of 55, for a percentage of 54.5% dissonant.
If you can come up with a 12-tone scale that gets a lower dissonance percentage than 54.5% without exceeding the 5-limit, or lower than 34.5% without exceeding the 7-limit, I'll be amazed. Remember, though: if it's unequal, you'll have to look at all the different roots, not just one, since there will be different triads under each root (since we are not allowing octave equivalence).
Note also that you can probably get lower than 34.5% if you are willing to accept 11-limit intervals as consonances, but I'm not in the slightest bit convinced that any 11-limit triads are any more consonant than some 5-limit triads that contain a semitone (like C-E-F or C-D-Eb). I'm barely convinced that the 11-limit otonal hexad functions as a consonance, to be honest.
-Igs
--- In [email protected], Michael <djtrancendance@...> wrote:
>
> Igs>"Yeah, some chords are gonna get left out, no matter what the scale."
> The question then seems to become...how do (or can?) we get and idea how far
> a scale can go? Agreed...no one can be expected to use every chord possible in
> a scale in a single song...and if they did it would likely sound very...forced
> and unnatural.
>
>
> >"What's it gonna take, then? A whole album in a "bad" tuning? Tell you what:
> >I'll do four tracks in 11-EDO, covering as wide a variety of moods as possible.
> >If 11-EDO isn't a "bad" harmonic tuning, I don't know what is."
> I don't know because I haven't tried. :-D 4 songs in 11TET should be a
> pretty good test or, perhaps better yet, 4 songs in that second bad scale I gave
> you IE the one you had the most challenge finding good chords in.
>
> Well that....and asking everyone (not just us :-D) the question of what they
> thought of the variety of tonal colors used in those songs vs. a shot of your
> doing the same thing IE trying to find as many different moods as possible in 4
> songs in a "good" scale (and comparing the results afterward).
>
> >"no cohesive scale is going to have any more mood-variety than any other
> >cohesive scale, *provided the number of available intervals is kept constant*."
> Ah, good point! In this case, 7TET for the standard 7-tone diatonic under
> 12TET might be a good test. As would 13TET vs. 12TET (in this case, 13 TET
> "should" have the advantage because it has an extra note...but I'm betting in
> won't in compositional use)!
>
>
> >"The diatonic scale is consonant as hell in meantone, but that doesn't mean
> >it's more versatile than the 7-note MOS of Mohajira, or Amity, or Mavila. "
> First of all, 7 tone Mohajira is awesome! :-D It makes, IMVHO, a great
> argument how 11-limit can be used in a fashion nearly as
> stable/predictable/balanced sounding between consonance/dissonance as the
> diatonic scale under 12TET. Then again, in 7TET vs. that diatonic scale...I
> think you'll notice a difference.
>
>
> One notable distinction...I do think there's a major problem with moods that
> become "too" bad IE a certain degree of the mood "chaos" can be anything from
> happy chaos to angry chaos to panic....but if there's too much chaos it all
> becomes a blur and you can't tell what "sub-mood" it is. The easiest example of
> this I believe...is a song composed of noise waves...ask people, what mood is
> it? :-D
>
> >"Compare playing harmonics 7-14 vs. the 31-EDO diatonic scale if you don't
> >believe me. "
> Well of course...but you are taking a ridiculous extreme on the idea of
> "distributionally uneven". Even the diatonic scale under 12TET has the
> semi-tone half the size of the whole tone...
> BTW, even try the Ptolemy Homalon scale (yep, it's a 7 tone scale under
> Scala)? It has "semi-tones" of size 12/11,11/10,10/9, and 9/8...yet I swear
> you'll be amazed at how many different kinds of chords are possible in it.
> Methinks you have a bit of a pet bias for TET and MOS (or very close variants on
> them)....and I'm prepared to do war with it. :-D
>
> >"Not necessarily; there are some good well-temperaments out there that are more
> >or less D.E., but with some very subtle variations between keys. George Secor
> >has a particular gift with these sorts of scales"
> Ok, so those aren't DE but instead "slight variants on D.E." Still...not
> much difference...IMVHO an interval and something within 8 cents of it are
> essentially the same thing...it's like a vanilla icecream with m&m's vs. one
> with a cherry on top.
>
> >"Really? How are you counting? If we're looking at triads within one octave
> >given a constant root note, I sincerely doubt this. "
> Not if we consider the word "triad" as meaning "any three notes". Try C C#
> D#, or C C# E, or C# E F, or C D# E..... It seems you have this underlying
> idea that the only thing that constitutes a triad is something under common
> practice or a variant (like "super major") is a triad. My point is...suppose a
> musician can pick any three notes under 12TET and play them at once...what can
> go sour?...a lot! Maybe, even, I'm being a tad too easy by saying it even gets
> 50%.
>
> >"Man, I do not get your thinking. Dyadically, there are two--maybe
> >3--intervals in 12-tET that are dissonant: the min2, the b5/#4, and maaaaaybe
> >the maj7. You cannot find a 12-note scale with fewer dissonances. "
> My point is that EVEN with nearly all perfect dyads, you still will most
> likely get 50%+ dissonant combinations in any decently sized (think 10+ tone)
> tuning. And thus the challenge becomes to get (not "avoid passing") that 50%
> for even consonance/dissonance distribution.
> What I'm saying is that
> A) A majority of scales are disproportionately (well over 50%) dissonant so far
> as tonal combinations
> B1) Thus, to achieve the goal of 50/50 dissonance/consonance...one must usually
> increase consonance, not dissonance...
> B2) "over consonance" is just as generally harmful for easy composition...try to
> get moods out of a pentatonic scale with a large majority of consonance over
> dissonance...ouch! But running into the issue of "over consonance" is VERY
> unlikely...
>
> To be fair...I do believe I have a "pet bias" for scales with more or less
> equal balance between consonant and dissonant chord options. And I think 12TET
> is "pretty good" for that sort of thing and much of the success of 12TET comes
> from the balance between consonance and dissonance, not any so-called "abundance
> of consonance". Again I swear, if 12TET had so few ways to "go
> sour"...musicians very likely wouldn't be so stressed about chord theory (and
> they are stressed...because there are so many overtly 'sour' options, even in
> 12TET)... :-D
>
>
> [Non-text portions of this message have been removed]
>
From: Michael (2011-01-19)
Subject: Re: [MMM] Re: Feed Me More "Worst" Scales
>"11-EDO is worse. There is no place to hide in 11-EDO. Even in your 2nd
>"worst" scale, some approximate fifths and major 3rds popped up in a few
>places; in 11-EDO that cannot happen."
Funny because in 11TET, the 7th, minor 3rd, and diminished 5th actually
aren't too bad. So you can get some fairly solid minor 7th tetrads from any
root note. Not to mention that the 5/3, even though about 13 cents off...is
"cancelled-out" by the other strong dyads making a decent minor 6th tetrad.
As we both know, no scale is going to be able to have absolutely no good
combinations and maybe you still think, even with the said-above strong chords,
that 11TET is worse than my bad scale...I still have my doubts. The only hard
part about 11TET...is you can't get the usual 4:5:6 major chord anywhere
whatsoever...but it look like, if you accept the minor as a resting point, it
should still be relatively "ok" far as bad scales go. :-D
>"I could do 13-EDO instead, if you think that would be a better indicator,
>though I think 13-EDO is quite a bit more consonant than 11."
Either one would be fine...both have about the same number of notes as 12
but, IMVHO, much less possibilities so far as tonal color. 12TET seems to be
able to go from very dark to very light and many shades of light and dark in
between....11 and 13 seem to have almost completely dark and relatively few, if
rather unique, shades of dark.
>"That (composing a song with a noise wave) is more a timbre issue than a tuning
>issue, or maybe a compositional one...serialist/atonal techniques are pretty
>much just as effective in creating chaos regardless of how consonant the tuning
>is."
Put it this way...I agree that just about any tuning can be made to sound
like chaos...but it becomes problematic when it's very hard to bring up any
emotion in a tuning beside choas...IE at the very least a tuning should be able
to manage "distinct shades of chaos".
>"Oh, there's a bit more than 8 cents variety in some of the tunings I'm
>thinking of. I forget where I found it, but I tried one well-temperament once
>that was designed to give major 3rds of 5/4, 9/7, and 14/11 in various keys,
>and minor 4rds of 6/5, 7/6, and 13/11, while still keeping the chain of fifths
>close enough to pure. It was pretty sweet."
I stand corrected...the "gap" between 13/11 and 6/5 (though not so much
between 7/6 and 6/5) I admit would likely have a significant impact as being
"non DE".
>"But there are many more triads that don't. I'll make a list of triads in
>12-tET and post it. And anyway, how is it any different in your Dimension
>tuning? Or any 12-note tuning?"
Well you hit the spot right...tonal clusters show off a lot of the bad triads
in 12TET (a bit more than half of them, in fact). That and even the diminished
triad in 12TET hits a fair (though not startling) degree of dissonance.
So within a 5th interval the following chords from the same root, IMVHO, sound
dissonant in 12TET:
C C# D#,
C C# E,
C D# E.
C D# F# (diminished...relatively non-clustered)
C E F#, ("reverse diminished"...not sure of the formal name...relatively
non-clustered)
C F F#
C F# G
...now how many consonant one can you find using notes between C and G?
Also, to note, Dimension is significantly different than 12TET in a few aspects,
including that
A) It includes a purer version of the diatonic scale IE almost exactly the same
as that in 31TET
B) It "pads" a good few of the 18/17-ish semi-tones responsible for so many of
the bad triads with 12/11 or 11/10 semi-tones.
....so it tries to make the most consonant versions of said above chords and
pushes some of them toward sounding "occasionally usable as resolve
points...though still tense enough to also be used as tension points".
>"I think you should attempt to verify this before making such sweeping claims.
>As far as I know, you haven't been including triadic analyses when working out
>your scales."
I have not...but considering the most sour dyads are abundant in the most
sour triads (IE even the 12TET tritone at C F#, which is not clustered like C
C#) and far more rarely take place in other chords...I don't think it's a leap
at all to say correcting them should help other chords. BTW, I have tested
triads (specifically some of the most odd/bad versions of ones in my Dimension
scale) about a month ago...it's the "Dimension Scale Triads" file in my folder.
>"Compare the mood of the 31-EDO diatonic to the 27-EDO diatonic. In the 31-EDO
>diatonic, there is essentially ONE dissonance, the 16/15 semitone; the #4 is a
>7/5 (so it is now consonant), the b5 is a 10/7 (so it is now consonant), and
>the maj7 is nearly a perfect 15/8 (and so consonant). In the 27-EDO, the maj3
>is about 444 cents, so dissonant; the maj7 is about 1166 cents, so very
>dissonant; the 4th and 5th are both about 10 cents off, vs. only about 5 cents
>in 31, so more dissonant, and the semitones at 44 cents are drastically more
>dissonant than the 16/15's in 31. Tell me: does the increased dissonance in 27
>limit the mood-range it is capable of?"
I would say yes....though do to the sheer number of notes in both scales (and
none of the notes being anywhere near close enough to the others to be heard as
unisons) that 27TET will have a decent mood range...just not nearly so good as
31TET. 31TET does one thing incredibly admirable to me vs. 12TET...it kills the
12TET tritone and replaces it with a much more balanced 10/7...at least with a
diatonic scale in 31TET, you can make a fairly safe bet that the only way to get
dissonance is to cluster.
>"Who are these musicians that are so stressed out by 12-tET? If you stay on
>the white keys of the piano (or the black keys), you're fine;"
You still get the tri-tone, you still get two 16/15's, actually, I'm pretty
sure you still get at least one transposed version of all the bad triads I
mentioned above!
Now with a pentatonic scale IE C D E G A...you'd be "fine"...no tritone no
clusters no nothing...but (as said before) that falls under my radar as "too
much consonance" and, as such, it's hard to get dissonant moods and good
tension/release contrast that way (not to mention having only 5 notes for
melodic variety hurts a ton).
>"as a guitarist, I feel like I have to bend over BACKWARDS to get any real
>dissonance in 12-tET!"
I'll just have to leave that as a matter of personal opinion... What I've
found often happens is it's quite easy to simply end up playing a chord that's
out-of-key by mistake on a guitar, and not terribly hard to hit semi-tones by
mistake (and, on the flip side, how many good chords do you really have if you
can't be taught where the "good vs. bad" uses of semi-tones are?) :-D
[Non-text portions of this message have been removed]
From: Mike Battaglia (2011-01-19)
Subject: Re: [MMM] Feed Me More "Worst" Scales
On Wed, Jan 19, 2011 at 2:55 PM, cityoftheasleep
<igliashon@...> wrote:
>
> If you can come up with a 12-tone scale that gets a lower dissonance percentage than 54.5% without exceeding the 5-limit, or lower than 34.5% without exceeding the 7-limit, I'll be amazed. Remember, though: if it's unequal, you'll have to look at all the different roots, not just one, since there will be different triads under each root (since we are not allowing octave equivalence).
We need to run this test with triadic entropy, now that we can thanks
to Steve. And then we need to run it with tetradic entropy, so we can
double the bottom note.
-Mike
From: gdsecor (2011-01-19)
Subject: Re: Feed Me More "Worst" Scales
--- In [email protected], "cityoftheasleep" <igliashon@...> wrote:
>
> --- In [email protected], "gdsecor" <gdsecor@> wrote:
> >
> > --- In [email protected], Ozan Yarman <ozanyarman@> wrote:
> > >
> > > Dear George, long time no chat! This new scale by you seems to have
> > > interesting potentials. I am almost tempted to try out something myself
> > > with it. But what name do you plan to give the scale?
> > >
> > > Oz.
> >
> > Hi Oz,
> >
> > Good to hear from you again.
> >
> > I was thinking about a name but couldn't come up with anything good (or
> > bad) enough. However, since Igs indicated that I'm not the first one to
> > suggest this scale, I don't think I should be the one to name it.
> >
> > Best,
> >
> > --George
>
> In honor of its purpose of creating maximum discord, why not call it "Kallisti" after the inscription on the golden apple of Eris from Greek Mythology?
>
> -Igs
My first reaction is that the meaning of "Kallisti" ("to the fairest [one]") would seem a bit enigmatic, and that "Eris" (goddess of discord) might be more straightforward. But after further thought, I've come to the conclusion that it's rather fitting in that it is indeed puzzing why such a fair lad as yourself would want to feast on a tuning as bitterly discordant as this.
--George (alias "Hermes")
From: Kalle Aho (2011-01-19)
Subject: Tonal Color
--- In [email protected], Michael <djtrancendance@...> wrote:
>
> Kalle>"Well, if you asked me I wouldn't understand the question because I don't
> know what tonal colors are. What is tonal color?"
>
> Tonal color is the range in sense of mood in a sound...and without
> respect to rhythm or "priming" IE using one chord to prepare the listener for
> another. Often the effect is that it feels like the "root/virtual pitch" of the
> part being played shifts a bit.
That's pretty cryptic. A bit? What if it changes a lot?
> Subtle tonal color changes would be things like changing the type of
> instrument playing a melody in a song or changing from a neutral to a major
> chord in the same key....while less subtle changes would include things like
> changing chords to different types of chords with different root tones (IE C
> major to D minor). Good tonal color, IMVHO, would come in a tuning system or
> scale that allows a large range of both subtle and less subtle changes to be
> explored by the composer, thus giving the composer more expressive range.
I still can't say what you mean by "tonal color" but I try: if I
remember correctly you would say that a harmonic series segment like
7:8:9:10:11:12:13:14 has less tonal color than the diatonic scale. Am
I correct? If I am, then it seems to me that it boils down to the
number of identities the notes of scale can take. I mean the notes
of the diatonic scale have different roles in different chords while
the notes in a harmonic series segment strongly suggest a single
fundamental, thus no sense of shifting, harmonic movement or chord
changes.
Kalle
From: Michael (2011-01-19)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Igs>"Consider that many chords containing the tritone approximate 7-limit
consonances, like 5:6:7, 4:5:7, 6:7:10, etc., so calling them "dissonant" would
be misleading"
Not in 12TET! In my mind...there is a good "tritone " at 10/7 and another
at 7/5. Guess what...the 12TET tri-tone is dead in between them and lousy at
imitating either one, well over 15 cents off either way!
Like I said before...I highly regard 31TET in that it effectively kills the
lousy 12TET tri-tone and provides good approximations of the good 7-limit
alternatives instead. I never said "tritones are bad"...just the 12TET one. :-D
Igs>"55 total combinations
5 contain two dissonant dyads (tritone and/or minor 2nd)
25 contain one dissonant dyad (tritone or minor 2nd)
14 contain the minor 2nd only
25 contain no dissonant dyads"
Looks relatively like my predicted 50/50 to me (plus or minus about 5%
error). Triadic entropy, agreed with Mike B, would be another good test to
run.... BTW, to make things more interesting...remember the 6th in 12TET also
is pretty far off...and the 3rds and 7th are "just passable" in 12TET...it would
be interesting the see what the best 12-tone subset in 31TET could do in
comparison....
>"If you can come up with a 12-tone scale that gets a lower dissonance
>percentage than 54.5% without exceeding the 5-limit, or lower than 34.5%
>without exceeding the 7-limit, I'll be amazed. Remember, though: if it's
>unequal, you'll have to look at all the different roots, not just one, since
>there will be different triads under each root (since we are not allowing
>octave equivalence)."
I think the latest/2nd version of Dimension EC I posted does the trick far as
approaching around (rough guess) 40-50% dissonance...although it does use the
11th and 15th limit (mainly taking advantage of 11/9, 11/6, and 22/15 as
"neutral" seconds, fifths, and sevenths of sorts)! Far as something in by and
large only the 7th limit that gets close...the 12-tone Minerva scale Gene posted
is just about the best thing I've seen so far for the... And yes, that's
considering all root tones in both cases: neither scales are equally spaced...
[Non-text portions of this message have been removed]
From: Mike Battaglia (2011-01-19)
Subject: Re: [MMM] Tonal Color
On Wed, Jan 19, 2011 at 5:01 PM, Kalle Aho <kalleaho@...> wrote:
>
> > Subtle tonal color changes would be things like changing the type of
> > instrument playing a melody in a song or changing from a neutral to a major
> > chord in the same key....while less subtle changes would include things like
> > changing chords to different types of chords with different root tones (IE C
> > major to D minor). Good tonal color, IMVHO, would come in a tuning system or
> > scale that allows a large range of both subtle and less subtle changes to be
> > explored by the composer, thus giving the composer more expressive range.
>
> I still can't say what you mean by "tonal color" but I try: if I
> remember correctly you would say that a harmonic series segment like
> 7:8:9:10:11:12:13:14 has less tonal color than the diatonic scale. Am
> I correct?
I personally agree with this. Perhaps tonal variety is more what's
being talked about. Paul Erlich elucidated a bit on this concept in
his paper "The Forms of Tonality," where he differentiated between
tonal scales that are static vs dynamic. A 8:16 harmonic scale, for
example, would be very "static," and something like Ionian would be
very dynamic. Mixolydian, on the other hand, is static.
Paul had a precise, rigorous definition of this which had something to
do with leading tones; I don't remember exactly what it is. I have a
more intuitive definition that I'd quantify with how many different
VF's are present in a scale, but I haven't worked it all out yet.
> If I am, then it seems to me that it boils down to the
> number of identities the notes of scale can take. I mean the notes
> of the diatonic scale have different roles in different chords while
> the notes in a harmonic series segment strongly suggest a single
> fundamental, thus no sense of shifting, harmonic movement or chord
> changes.
Right, that's the intuitive definition I've arrived at as well. No
need to explain then I guess :)
-Mike
From: Daniel Forró (2011-01-20)
Subject: Re: [MMM] Re: Feed Me More "Worst" Scales
On 20 Jan 2011, at 5:27 AM, Michael wrote:
>
> Now with a pentatonic scale IE C D E G A...you'd be "fine"...no
> tritone no
> clusters no nothing..
We can use clusters. Or how would you call a chord using all 5 notes?
They are modal clusters.
C6/2add in jazz/pop of course, but we are not limited to jazz/pop in
the composition. In different context we don't need to use such
chord signs.
> .but (as said before) that falls under my radar as "too
> much consonance" and, as such, it's hard to get dissonant moods and
> good
> tension/release contrast that way (not to mention having only 5
> notes for
> melodic variety hurts a ton).
There's still left a lot of space for compositional work and
creativity. We have only 5 notes, but lot of possible intervals, each
with two directions.
Also chords can be built from different intervals, so we can make
chords based mainly on seconds, or thirds, and typical for
pentatonics are chord of quartal structure. Then we have inversions -
chords made from fifth, sixths and seventh, or even wider intervals.
Depending on their exact location in musical space, they can sound
more dissonant.
And then there are different kinds of pentatonics, like Japanese
hirajoshi with halftones and major thirds...
Daniel Forro
[Non-text portions of this message have been removed]
From: Chris Vaisvil (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
I think the major loop hole is sticking with octaves.
Igs may be limited (hey - you should get a copy of GPO - fairly in
expensive) but what if we start thinking of things like divisions of
irrational numbers?
Ah... here we go.
Igs - I did a scale - the phi to the twelfth root.
http://micro.soonlabel.com/12th-root-phi/
there is a scala file, midi file I used in pianoteq and the example mp3 file.
When I posted it I received *no* feedback - sort of like what happened
when I posted my piece of John O'Sullivan's "bad" tuning - there I
actually asked and was told it was atrocious.
Perhaps you can have better luck with 12th root of phi
! C:\Cakewalk\scales\12throotofphi.scl
!
12th root pf phi
11
!
69.42116
138.84232
208.26348
277.68464
347.10580
416.52696
485.94813
555.36929
624.79045
694.21161
763.63277
Or is it 12th root in 11 - I dunno - I'm a dunce with scala.
Nonetheless - no one liked it - but me - apparently.
From: Chris Vaisvil (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
lets try this
! E:\Cakewalk\scales\12root618phi.scl
!
12 root of 0.61803 phi
12
!
51.50250
103.00500
154.50750
206.01000
257.51250
309.01500
360.51750
412.02000
463.52250
515.02500
566.52750
618.03000
On Wed, Jan 19, 2011 at 7:47 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
> I think the major loop hole is sticking with octaves.
>
> Igs may be limited (hey - you should get a copy of GPO - fairly in
> expensive) but what if we start thinking of things like divisions of
> irrational numbers?
>
> Ah... here we go.
>
> Igs - I did a scale - the phi to the twelfth root.
>
> http://micro.soonlabel.com/12th-root-phi/
>
> there is a scala file, midi file I used in pianoteq and the example mp3 file.
> When I posted it I received *no* feedback - sort of like what happened
> when I posted my piece of John O'Sullivan's "bad" tuning - there I
> actually asked and was told it was atrocious.
>
> Perhaps you can have better luck with 12th root of phi
>
>
> ! C:\Cakewalk\scales\12throotofphi.scl
> !
> 12th root pf phi
> 11
> !
> 69.42116
> 138.84232
> 208.26348
> 277.68464
> 347.10580
> 416.52696
> 485.94813
> 555.36929
> 624.79045
> 694.21161
> 763.63277
>
> Or is it 12th root in 11 - I dunno - I'm a dunce with scala.
>
> Nonetheless - no one liked it - but me - apparently.
>
From: cityoftheasleep (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], Michael <djtrancendance@...> wrote:
> Not in 12TET! In my mind...there is a good "tritone " at 10/7 and another
> at 7/5. Guess what...the 12TET tri-tone is dead in between them and lousy at
> imitating either one, well over 15 cents off either way!
Yeah, about as far off as 400 cents is from 5/4, 300 cents from 6/5, etc. etc. If you can buy 22/15 as a consonant stand-in for a 3/2, I don't see how it is any harder to swallow 600 cents as an acceptable stand-in for 7/5 and 10/7. And FWIW, the 600-cent tritone is used to approximate 7/5 and 10/7 in a lot of 7-limit temperaments, any that vanish the 50/49 comma, as in 22-EDO's 4:5:6:7 tetrads, and 18- and 26-EDO's very passable 5:6:7 triads, even in 16-EDO's very persuasive 4:5:7 triads. As a dyad, sure, 600 cents is a pretty weak approximation to the septimal tritones, but in chords it fares much better. If you don't believe me, I suggest you ask around on the Tuning List.
> Like I said before...I highly regard 31TET in that it effectively kills the
> lousy 12TET tri-tone and provides good approximations of the good 7-limit
> alternatives instead. I never said "tritones are bad"...just the 12TET one. :-D
And yet, in Meantone[12], the percentage of dissonant triads goes up from 12-Equal. Don't believe it? Calculate it yourself!
> Igs>"55 total combinations
> 5 contain two dissonant dyads (tritone and/or minor 2nd)
> 25 contain one dissonant dyad (tritone or minor 2nd)
> 14 contain the minor 2nd only
> 25 contain no dissonant dyads"
>
> Looks relatively like my predicted 50/50 to me (plus or minus about 5%
> error). Triadic entropy, agreed with Mike B, would be another good test to
> run.... BTW, to make things more interesting...remember the 6th in 12TET also
> is pretty far off...and the 3rds and 7th are "just passable" in 12TET...it would
> be interesting the see what the best 12-tone subset in 31TET could do in
> comparison....
"Just passable"? Again such harsh critiques from the man who readily accepts such intervals as 11/9, 22/15, and 50/33 as consonances supposedly on par with 3/2 and 5/4. And either way, it's only 50/50 if you deny that 12-tET's approximations to 7-limit triads are consonances...which is hypocritical to do if you allow its approximations to 5-limit consonances to stand as consonances, since the error is not much greater. They may not be near Just, but they're close enough to function consonantly in music (in ways that triads in, say, 8- or 11-EDO typically don't). As I see it, it's closer to 30/70 dissonance/consonance (or maybe 40/60 if you're being strict). Also, you should know that I calculated the average dyadic harmonic entropy for every EDO from 5 to 37, and the only EDOs lower than 12 were 5 and 7.
> >"If you can come up with a 12-tone scale that gets a lower dissonance
> >percentage than 54.5% without exceeding the 5-limit, or lower than 34.5%
> >without exceeding the 7-limit, I'll be amazed. Remember, though: if it's
> >unequal, you'll have to look at all the different roots, not just one, since
> >there will be different triads under each root (since we are not allowing
> >octave equivalence)."
>
> I think the latest/2nd version of Dimension EC I posted does the trick far as
> approaching around (rough guess) 40-50% dissonance...although it does use the
> 11th and 15th limit (mainly taking advantage of 11/9, 11/6, and 22/15 as
> "neutral" seconds, fifths, and sevenths of sorts)!
I'd do a triadic analysis before making any claims if I were you. Even supposing you are right in your guess, the fact that your Dimension EC scale is judging consonance against the 11-limit and 12-tET is being judged against the 5-limit (to get the 54.5% figure I posted), well...the fact that you only improve on 12-tET by 5% to 15% despite adding two additional primes doesn't say much. And I'm still not convinced it's fair to call 11/9, 11/6, and 22/15 "consonances".
> Far as something in by and
> large only the 7th limit that gets close...the 12-tone Minerva scale Gene posted
> is just about the best thing I've seen so far for the... And yes, that's
> considering all root tones in both cases: neither scales are equally spaced...
I still don't believe you've done a triadic analysis for all the root tones in the scale. Unless you can talk specific numbers, you're just blowing hot air.
-Igs
From: Michael (2011-01-20)
Subject: Re: [MMM] Tonal Color
Me> Tonal color is the range in sense of mood in a sound...and without
> respect to rhythm or "priming" IE using one chord to prepare the listener for
> another. Often the effect is that it feels like the "root/virtual pitch" of
>the
>
> part being played shifts a bit.
Kalle>"That's pretty cryptic. A bit? What if it changes a lot?"
Well, the term is fairly artistic, so of course it's somewhat left to
subjective interpretation.
>"I still can't say what you mean by "tonal color" but I try: if I remember
>correctly you would say that a harmonic series segment like 7:8:9:10:11:12:13:14
>has less tonal color than the diatonic scale. Am
>
I correct?
Exactly....
>"it boils down to the number of identities the notes of scale can take. I mean
>the notes of the diatonic scale have different roles in different chords while
>the notes in a harmonic series segment strongly suggest a single
fundamental"
Right, tonal color implies this sort of "shifting"... And, to note, some
chords seem to cause more shifting than others....
[Non-text portions of this message have been removed]
From: cityoftheasleep (2011-01-20)
Subject: [MMM] Re: Feed Me More "Worst" Scales
--- In [email protected], Daniel Forró <dan.for@...> wrote:
>
> There's still left a lot of space for compositional work and
> creativity. We have only 5 notes, but lot of possible intervals, each
> with two directions.
Indeed, and a listen to classical Chinese guqin music will reveal the great depth and subtlety contained within the basic Pythagorean pentatonic scale.
-Igs
From: Mike Battaglia (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
On Wed, Jan 19, 2011 at 8:17 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In [email protected], Michael <djtrancendance@...> wrote:
> > Not in 12TET! In my mind...there is a good "tritone " at 10/7 and another
> > at 7/5. Guess what...the 12TET tri-tone is dead in between them and lousy at
> > imitating either one, well over 15 cents off either way!
>
> Yeah, about as far off as 400 cents is from 5/4, 300 cents from 6/5, etc. etc. If you can buy 22/15 as a consonant stand-in for a 3/2, I don't see how it is any harder to swallow 600 cents as an acceptable stand-in for 7/5 and 10/7. And FWIW, the 600-cent tritone is used to approximate 7/5 and 10/7 in a lot of 7-limit temperaments, any that vanish the 50/49 comma, as in 22-EDO's 4:5:6:7 tetrads, and 18- and 26-EDO's very passable 5:6:7 triads, even in 16-EDO's very persuasive 4:5:7 triads. As a dyad, sure, 600 cents is a pretty weak approximation to the septimal tritones, but in chords it fares much better. If you don't believe me, I suggest you ask around on the Tuning List.
I think that this can be formalized into a concrete psychoacoustic
statement: the perception of a mistuned interval is influenced by the
sounds of other mistuned intervals. By itself, 600 cents might not
really sound like 7/5, but in a 22-tet 4:5:6:7 tetrad, it points to
the correct VF just fine. And the fifths of 15-equal can sound pretty
irritatingly sharp, but if you throw in a sharpened 5/4 as well, the
whole thing sounds like a uniformly stretched major triad, which is a
sound I personally like a lot.
I was listening to this Sevish tune:
http://ia700400.us.archive.org/24/items/Sevish_-_Golden_Hour/Sevish_-_03_-_Dirty_Drummer_vbr.mp3
I heard the first interval as a really flat 3/2, and when the minor
third above the root plays in the second voice, it ends up sounding
"neutral" (or even slightly major to me) in comparison because the 3/2
is so flat. This is an almost perfect 6/5 we're talking about here,
but if your brain is really wrapped around that 650 cents as some kind
of flat pelog fifth, then it alters the sound of the 6/5.
-Mike
From: john777music (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Hi Chris,
I don't remember you posting a piece using my "bad" tuning. Can you give me a link to the piece or a message number?
The 12th-root-phi mp3 sounds pretty atrocious, definitely a contender for the "worst" tuning.
John.
--- In [email protected], Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I think the major loop hole is sticking with octaves.
>
> Igs may be limited (hey - you should get a copy of GPO - fairly in
> expensive) but what if we start thinking of things like divisions of
> irrational numbers?
>
> Ah... here we go.
>
> Igs - I did a scale - the phi to the twelfth root.
>
> http://micro.soonlabel.com/12th-root-phi/
>
> there is a scala file, midi file I used in pianoteq and the example mp3 file.
> When I posted it I received *no* feedback - sort of like what happened
> when I posted my piece of John O'Sullivan's "bad" tuning - there I
> actually asked and was told it was atrocious.
>
> Perhaps you can have better luck with 12th root of phi
>
>
> ! C:\Cakewalk\scales\12throotofphi.scl
> !
> 12th root pf phi
> 11
> !
> 69.42116
> 138.84232
> 208.26348
> 277.68464
> 347.10580
> 416.52696
> 485.94813
> 555.36929
> 624.79045
> 694.21161
> 763.63277
>
> Or is it 12th root in 11 - I dunno - I'm a dunce with scala.
>
> Nonetheless - no one liked it - but me - apparently.
>
From: Chris Vaisvil (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
http://micro.soonlabel.com/bad/
bad-bad-john.mp3
You are the only one to respond.
On Wed, Jan 19, 2011 at 8:33 PM, john777music <jfos777@...> wrote:
>
>
> Hi Chris,
>
> I don't remember you posting a piece using my "bad" tuning. Can you give me
> a link to the piece or a message number?
>
> The 12th-root-phi mp3 sounds pretty atrocious, definitely a contender for
> the "worst" tuning.
>
> John.
>
>
> --- In [email protected] <MakeMicroMusic%40yahoogroups.com>,
> Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > I think the major loop hole is sticking with octaves.
> >
> > Igs may be limited (hey - you should get a copy of GPO - fairly in
> > expensive) but what if we start thinking of things like divisions of
> > irrational numbers?
> >
> > Ah... here we go.
> >
> > Igs - I did a scale - the phi to the twelfth root.
> >
> > http://micro.soonlabel.com/12th-root-phi/
> >
> > there is a scala file, midi file I used in pianoteq and the example mp3
> file.
> > When I posted it I received *no* feedback - sort of like what happened
> > when I posted my piece of John O'Sullivan's "bad" tuning - there I
> > actually asked and was told it was atrocious.
> >
> > Perhaps you can have better luck with 12th root of phi
> >
> >
> > ! C:\Cakewalk\scales\12throotofphi.scl
> > !
> > 12th root pf phi
> > 11
> > !
> > 69.42116
> > 138.84232
> > 208.26348
> > 277.68464
> > 347.10580
> > 416.52696
> > 485.94813
> > 555.36929
> > 624.79045
> > 694.21161
> > 763.63277
> >
> > Or is it 12th root in 11 - I dunno - I'm a dunce with scala.
> >
> > Nonetheless - no one liked it - but me - apparently.
> >
>
>
>
[Non-text portions of this message have been removed]
From: john777music (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
I remember it now, thanks.
--- In [email protected], Chris Vaisvil <chrisvaisvil@...> wrote:
>
> http://micro.soonlabel.com/bad/
>
> bad-bad-john.mp3
>
> You are the only one to respond.
>
> On Wed, Jan 19, 2011 at 8:33 PM, john777music <jfos777@...> wrote:
>
> >
> >
> > Hi Chris,
> >
> > I don't remember you posting a piece using my "bad" tuning. Can you give me
> > a link to the piece or a message number?
> >
> > The 12th-root-phi mp3 sounds pretty atrocious, definitely a contender for
> > the "worst" tuning.
> >
> > John.
> >
> >
> > --- In [email protected] <MakeMicroMusic%40yahoogroups.com>,
> > Chris Vaisvil <chrisvaisvil@> wrote:
> > >
> > > I think the major loop hole is sticking with octaves.
> > >
> > > Igs may be limited (hey - you should get a copy of GPO - fairly in
> > > expensive) but what if we start thinking of things like divisions of
> > > irrational numbers?
> > >
> > > Ah... here we go.
> > >
> > > Igs - I did a scale - the phi to the twelfth root.
> > >
> > > http://micro.soonlabel.com/12th-root-phi/
> > >
> > > there is a scala file, midi file I used in pianoteq and the example mp3
> > file.
> > > When I posted it I received *no* feedback - sort of like what happened
> > > when I posted my piece of John O'Sullivan's "bad" tuning - there I
> > > actually asked and was told it was atrocious.
> > >
> > > Perhaps you can have better luck with 12th root of phi
> > >
> > >
> > > ! C:\Cakewalk\scales\12throotofphi.scl
> > > !
> > > 12th root pf phi
> > > 11
> > > !
> > > 69.42116
> > > 138.84232
> > > 208.26348
> > > 277.68464
> > > 347.10580
> > > 416.52696
> > > 485.94813
> > > 555.36929
> > > 624.79045
> > > 694.21161
> > > 763.63277
> > >
> > > Or is it 12th root in 11 - I dunno - I'm a dunce with scala.
> > >
> > > Nonetheless - no one liked it - but me - apparently.
> > >
> >
> >
> >
>
>
> [Non-text portions of this message have been removed]
>
From: Michael (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Igs>"Yeah, about as far off as 400 cents is from 5/4, 300 cents from 6/5, etc.
etc. If you can buy 22/15 as a consonant stand-in for a 3/2, I don't see how it
is any harder to swallow 600 cents as an acceptable stand-in for 7/5 and 10/7."
Simple...because I don't consider 22/15 as a "badly rounded version of 5th",
but rather it's own dignified entity. Same goes for 11/9...it's not a badly
rounded 6/5 or 5/4 but it's own entity...the neutral third.
>"as in 22-EDO's 4:5:6:7 tetrads, and 18- and 26-EDO's very passable 5:6:7
>triads, even in 16-EDO's very persuasive 4:5:7 triads."
But most of the other dyads in those chords are rather close to pure (and
certainly, in many cases above, much more pure than those in 12TET!)...I'd argue
they simply balance out that highly impure version of the tri-tone.
>"And yet, in Meantone[12], the percentage of dissonant triads goes up from
>12-Equal. Don't believe it? Calculate it yourself! "
I never said anything about 12-tone meantone under 31TET...I was talking
about the 7-tone diatonic scale under 31TET.
Me>"remember the 6th in 12TET also is pretty far off...and the 3rds and 7th are
"just passable" in 12TET...it
> would be interesting the see what the best 12-tone subset in 31TET could do in
>comparison....
Igs>""Just passable"? Again such harsh critiques from the man who readily
accepts such intervals as 11/9, 22/15, and 50/33 as consonances supposedly on
par with 3/2 and 5/4."
You're missing my point. I never said a near-pure 11/9, 22/15 were more
consonant than a fairly impure 3/2, 5/4, etc.
What I rather mean is that say you have a chord with a 5/4 and a
tri-tone...if the 5/4 is fairly off pure...it leaves less "slack" for the
tri-tone to be off to make the chord with both end up sounding stable.
>"Also, you should know that I calculated the average dyadic harmonic entropy for
>every EDO from 5 to 37, and the only EDOs lower than 12 were 5 and 7."
Seriously? If so...that really makes me start to doubt dyadic harmonic
entropy as a theory... But I have a good clue why what you just said could
occur... Personally I already have gripes about how it champions the 5th as
some ridiculous number of times more consonant than a major fourth...and the
fourth much more consonant than the major third and then the minor third, that
and so on. My guess is 12TET got nailed for having a bad IE 13+ cent off major
and minor third...and the fact those "good" dyads were so far off killed their
chances to help "balance out" the bad ones on the average.
>"Even supposing you are right in your guess, the fact that your Dimension EC
>scale is judging consonance against the 11-limit and 12-tET is being judged
>against the 5-limit (to get the 54.5% figure I posted), well...the fact that you
>only improve on 12-tET by 5% to 15% despite adding two additional primes doesn't
>say much. And I'm still not convinced it's fair to call 11/9, 11/6, and 22/15
>"consonances"."
Have you tried 11/6 vs. even diatonic JI's 15/8? I'm sure 11/6 is right up
there in consonance... Far as 11/6 and 11/9...I would put them in the boat of
"more 7-limit consonance-like than 11-limit like"...while I'd say the bad ones
sound "more 13-limit-like and almost flat out noisy".
Now if you want dissonance, try the 11-limits 16/11, 20/11, and 14/11 vs.
the ones above. You seem to be saying "all 11-limit dyads must be more-or-less
judged as equal so far as consonance"...and I swear nothing could be further
from the truth! Furthermore take the higher limit 22/15 vs. the lower limit
16/11...or 15/8 vs. 20/11. I swear that's about as obvious as you can get far
as examples that prove higher odd-limit dyads are not necessarily less consonant
than lower limit ones...
To me, once you go over 7-limit or so...limits are not a reliable predictor of
consonance anymore...
Me>"the 12-tone Minerva scale Gene posted is just about the best thing I've seen
so far for that... And yes, >that's considering all root tones in both cases:
neither scales are equally spaced...
Igs>"I still don't believe you've done a triadic analysis for all the root tones
in the scale. Unless you can talk specific numbers, you're just blowing hot
air."
I did dyadic analysis and, I swear, an (even) better alternative to triadic
analysis AKA composing and actually using triads from the scale. Not like you
believe me but...to be sure...I'll make some triads in a sound example with
Gene's posted 12-tone Minerva scale as proof. :-)
[Non-text portions of this message have been removed]
From: genewardsmith (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], "cityoftheasleep" <igliashon@...> wrote:
> "Just passable"? Again such harsh critiques from the man who readily accepts such intervals as 11/9, 22/15, and 50/33 as consonances supposedly on par with 3/2 and 5/4. And either way, it's only 50/50 if you deny that 12-tET's approximations to 7-limit triads are consonances...which is hypocritical to do if you allow its approximations to 5-limit consonances to stand as consonances, since the error is not much greater.
Spare us! 400 cents is 14 cents sharper than 5/4. In comparison, 7/4 is ***31 cents flatter***. Minor difference? I don't think so. But the agony doesn't stop there--300 cents is 33 cents sharper than 7/6. 7/5 is about the best 12 can do for the 7-limit, and as pointed out, it's lousy.
From: genewardsmith (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], "genewardsmith" <genewardsmith@...> wrote:
> Spare us! 400 cents is 14 cents sharper than 5/4. In comparison, 7/4 is ***31 cents flatter***.
Um, than 1000 cents. Bot 7 and 5 are sharp, but 7 is seriously sharp to the point that you should probably call 1000 cents 16/9 and admit 12 doesn't really do the 7-limit.
From: Mike Battaglia (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
On Wed, Jan 19, 2011 at 10:25 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In [email protected], "genewardsmith" <genewardsmith@...> wrote:
>
> > Spare us! 400 cents is 14 cents sharper than 5/4. In comparison, 7/4 is ***31 cents flatter***.
>
> Um, than 1000 cents. Bot 7 and 5 are sharp, but 7 is seriously sharp to the point that you should probably call 1000 cents 16/9 and admit 12 doesn't really do the 7-limit.
I think that the fact that 1000 cents and 969 cents sound at least a
little bit alike is testament to the fact that 7/4 probably colors the
sound of 1000 cents though.
I also think it's possible to make 1000 cents sound like 7/4, if you
fill in the gaps to make a 4:5:6:7 in which all of the dyads are
1000/969 as wide as they should be.
-Mike
From: genewardsmith (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], Mike Battaglia <battaglia01@...> wrote:
> I think that the fact that 1000 cents and 969 cents sound at least a
> little bit alike is testament to the fact that 7/4 probably colors the
> sound of 1000 cents though.
Oh, I agree. When I had this conversation with Paul, IIRC he agreed also. But you can hear the damned thing not fusing with your "tetrad", so I think generally it's better to just admit it's a dominant 7th chord.
> I also think it's possible to make 1000 cents sound like 7/4, if you
> fill in the gaps to make a 4:5:6:7 in which all of the dyads are
> 1000/969 as wide as they should be.
Did you try this? It seems to me it would pretty much sound like crap.
From: Carl Lumma (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Gene wrote:
>Spare us! 400 cents is 14 cents sharper than 5/4. In comparison, 7/4
>is ***31 cents flatter***.
>
>Um, than 1000 cents. Bot 7 and 5 are sharp, but 7 is seriously sharp
>to the point that you should probably call 1000 cents 16/9 and admit
>12 doesn't really do the 7-limit.
Igs and I discussed this offlist recently. I won't speak for
him but we worked over examples in 12, JI, 19, and 22. For me the
12-ET chord clearly implies 4:5:6:7, even though it sounds like a
cardboard factory. 22 sounds better than 19 but only marginally.
1/1-5/4-3/2-16/9 also approximates 4:5:6:7 but 1/1-5/4-3/2-9/5 has
its own identity. I would like comments on this but please, really
play around in this region of tetrad space before passing judgement.
Speaking of which, having a continuous tetrad space would be handy.
(I still think http://mathworld.wolfram.com/QuadriplanarCoordinates.html
are the way to go.)
-Carl
From: genewardsmith (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], Carl Lumma <carl@...> wrote:
> Igs and I discussed this offlist recently. I won't speak for
> him but we worked over examples in 12, JI, 19, and 22. For me the
> 12-ET chord clearly implies 4:5:6:7, even though it sounds like a
> cardboard factory.
As I said, I had the same conversation with Paul years ago; at first I thought we were not agreeing but it turned out we did. But a JI 1-5/4-3/2-16/9 implies the JI tetrad in that sense also, but still it sounds different and in terms of functional harmony is different.
From: Carl Lumma (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
At 08:58 PM 1/19/2011, you wrote:
>
>
>--- In [email protected], Carl Lumma <carl@...> wrote:
>
>> Igs and I discussed this offlist recently. I won't speak for
>> him but we worked over examples in 12, JI, 19, and 22. For me the
>> 12-ET chord clearly implies 4:5:6:7, even though it sounds like a
>> cardboard factory.
>
>As I said, I had the same conversation with Paul years ago; at first I
>thought we were not agreeing but it turned out we did. But a JI
>1-5/4-3/2-16/9 implies the JI tetrad in that sense also,
Yes I think I said that. -C.
From: cityoftheasleep (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Before I get started, I'm going to ask that we move any further discussion on this topic to Tuning. Please copy, paste, and reply in a new thread there.
--- In [email protected], Michael <djtrancendance@...> wrote:
>
> Simple...because I don't consider 22/15 as a "badly rounded version of 5th",
> but rather it's own dignified entity. Same goes for 11/9...it's not a badly
> rounded 6/5 or 5/4 but it's own entity...the neutral third.
Really now? 22/15 is its "own" entity? Can you distinguish it from 25/17? Can you tune it by ear? Can you "sing it" over a drone and NOT hit 25/17 instead?
And either way, you say it functions like a fifth, you refer to it as a type of fifth all the time.
> >"as in 22-EDO's 4:5:6:7 tetrads, and 18- and 26-EDO's very passable 5:6:7
> >triads, even in 16-EDO's very persuasive 4:5:7 triads."
>
> But most of the other dyads in those chords are rather close to pure (and
> certainly, in many cases above, much more pure than those in 12TET!)...I'd argue
> they simply balance out that highly impure version of the tri-tone.
Regardless--if the 12-tone chords I mentioned AREN'T approximating the 7-limit, then what are they?
> >"And yet, in Meantone[12], the percentage of dissonant triads goes up from
> >12-Equal. Don't believe it? Calculate it yourself! "
> I never said anything about 12-tone meantone under 31TET...I was talking
> about the 7-tone diatonic scale under 31TET.
...which extends to Meantone[12]. We're talking about 12-note scales, remember? The point I'm trying to make is that if you improve the consonance of one subset beyond 12-equal, the consonance of other subsets will drop, resulting in a net decrease in consonant chords within the overall scale, unless you change the definition of what you are counting as "consonant".
> You're missing my point. I never said a near-pure 11/9, 22/15 were more
> consonant than a fairly impure 3/2, 5/4, etc.
Well, you sure seem to be implying that you think that, since you optimize your scales to nail those 11-limit intervals equally as well as lower-limit ones, giving them the same priority in tuning. And you've often expressed a preference for a "good" 11-limit interval over a "bad" (i.e. 15 cents off) 5-limit one. Correct me if I'm wrong, but isn't your method in crafting scales based on attempting to get more "good" intervals by changing the definition of "good" to include intervals like 11/9, 22/15, 50/33, etc., basically to make an exaggerated high-limit well-temperament whereby different keys have different subsets of target dyads, but ONLY target dyads are included (i.e. there's no harmonic "waste" like the 40/27 wolf-fifth in 5-limit JI)? So by your standards it would be better to have a scale with a few good 5/4s, a few good 11/9's, a few good 3/2's, a few good 22/15's, as opposed to a scale with all "mediocre" 5/4's and "mediocre" 3/2's?
> >"Also, you should know that I calculated the average dyadic harmonic entropy for
> >every EDO from 5 to 37, and the only EDOs lower than 12 were 5 and 7."
>
> Seriously? If so...that really makes me start to doubt dyadic harmonic
> entropy as a theory... But I have a good clue why what you just said could
> occur... Personally I already have gripes about how it champions the 5th as
> some ridiculous number of times more consonant than a major fourth...and the
> fourth much more consonant than the major third and then the minor third, that
> and so on. My guess is 12TET got nailed for having a bad IE 13+ cent off major
> and minor third...and the fact those "good" dyads were so far off killed their
> chances to help "balance out" the bad ones on the average.
You misunderstand: low entropy = high concordance, so 12-tET has the 3rd highest average concordance; only 5-EDO and 7-EDO are more concordant on average. As you go higher in the EDO's, you do get tunings where some interval classes go down in entropy--like in 19, the maj and min 3rd and 6th are all lower in entropy than in 12-tET--but always at the expense of adding intervals which are higher in entropy (like how 19-EDO has two minor 2nds, two major 7ths, two tritones, and not-so-hot subminor and supermajor 3rds and 6ths which are all near maxima of entropy, for a total of 10 high-entropy intervals vs. 12-tET's 3). 5-EDO has the lowest overall entropy, because two out of five intervals are near the two lowest-entropy intervals in the first octave (4/3 and 3/2).
> Have you tried 11/6 vs. even diatonic JI's 15/8? I'm sure 11/6 is right up
> there in consonance...
As a dyad, sure. But a neutral 7th chord is waaaay down there, unless you omit the 3rd and make a 6:9:11 triad (which is pretty smooth). If you try to put a neutral 7th on top of a major or minor 3rd, the result is pretty gnarly.
> Far as 11/6 and 11/9...I would put them in the boat of
> "more 7-limit consonance-like than 11-limit like"...while I'd say the bad ones
> sound "more 13-limit-like and almost flat out noisy".
Yeah, I'll admit that 11/9 isn't much nastier than 9/7, but still...even a pure 11/9 I would rate as less consonant than any of the thirds in 12-tET.
> Now if you want dissonance, try the 11-limits 16/11, 20/11, and 14/11 vs.
> the ones above. You seem to be saying "all 11-limit dyads must be more-or-less
> judged as equal so far as consonance"...and I swear nothing could be further
> from the truth!
No, I'm not saying that...but I do think they are all drastically LESS consonant than anything in the 5-limit, and they are generally rather difficult to integrate with 5-limit intervals.
> To me, once you go over 7-limit or so...limits are not a reliable predictor of
> consonance anymore...
On this, we agree. And Carl has warned me that Tenney Height stops being a reliable predictor of consonance once the product exceeds about 70. And the reason for this is that above the 7-limit, the periodicity of the dyads in question because too complex to be identified...it's like polyrhythms, playing 2 against 3 is elementary, 4 against 5 a little harder but do-able, 7 against 3 a little advanced, but 11 or 13 against 4 is almost impossible for all but the most skilled. An interval like 22/15 lacks all the perceptual qualities associated with something like 5/4 or 7/6 or whatever, it's not beatless and it doesn't do the "periodicity buzz" thing and it can't readily be differentiated from the nearby and only slightly more complex 25/17. With intervals like these, H.E. seems to take over and proximity to lower-limit ratios seems to be a bigger factor. Though intervals like 11/6, 11/7, 11/8, 11/9 might be on the threshold of Just.
> I did dyadic analysis and, I swear, an (even) better alternative to triadic
> analysis AKA composing and actually using triads from the scale. Not like you
> believe me but...to be sure...I'll make some triads in a sound example with
> Gene's posted 12-tone Minerva scale as proof. :-)
No, sorry, that is NOT a "better alternative". You have no idea how many dissonant and consonant triads there are in a scale just by playing in it. I've been playing and composing in 12-tET for years and I could not have guessed that the triad analysis I did would have come out the way it did. Unless you are willing to count and quantify the triads, any claims you make about a scale having more consonant chords than another scale are hogwash.
-Igs
From: cityoftheasleep (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
--- In [email protected], "genewardsmith" <genewardsmith@...> wrote:
> Spare us! 400 cents is 14 cents sharper than 5/4. In comparison, 7/4 is ***31 cents
> flatter***. Minor difference? I don't think so. But the agony doesn't stop there--300 cents is > 33 cents sharper than 7/6. 7/5 is about the best 12 can do for the 7-limit, and as pointed > out, it's lousy.
I didn't say 12 was *good* in the 7-limit. But if we're going to allow an error as much as 15 cents to be called an approximation--even though all hint of beatlessness and fusion is lost--what's another 15? The way I think about approximation is thus: it's sensible to say one chord approximates another if the latter chord is the nearest beatless chord to the former. Is there anything beatless closer to the 12-tET dom7 chord than a 4:5:6:7?
-Igs
From: Michael (2011-01-20)
Subject: Re: [MMM] Feed Me More "Worst" Scales
Igs>"Really now? 22/15 is its "own" entity? Can you distinguish it from 25/17?
Can you tune it by ear? Can you "sing it" over a drone and NOT hit 25/17
instead?"
25/17 is well within 7 cents of 22/15...actually I'm pretty sure within
about 3-4 cents of it (even near Gene's ideal limits). So of course you can
confuse the two. Guess what...there have been listening tests that have said
people actually like hearing/singing the pure fifth about 4 cents or so sharp.
You're penny-picking here....
>"And either way, you say it functions like a fifth, you refer to it as a type of
>fifth all the time."
Well...that doesn't mean I said it's a type of pure fifth (it certainly
isn't)! The closest thing I can think of, like I said before, is the neutral
third which, yes, to an extent can flip between feeling major and minor...but,
to an extent, has its own sound. IMVHO, one would be foolish to think of a
neutral third as "just a horribly detuned major or minor 3rd".
Load up a 22/15 in Scala and it says "diminished 5th". And that's much like
what it sounds like...comparing the tonal flavor of a major triad to a 5:6:7
chord...the latter sounds "diminished" in mood, but still relatively stable and
certainly not a "sour version of the major arrived at by mistake".
>"Regardless--if the 12-tone chords I mentioned AREN'T approximating the 7-limit,
>then what are they?"
What are they? Lousy chords (so far as establishing a tonal color/mood in
many cases, at least)! :-D No but seriously...there are a lot of conflicting
relations between notes in 12TET. Many of them summarize the x/16 or 16/x
o-tonal/u-tonal harmonic or sub-harmonic series (think 16/9, 27/16, etc.) than
anything 5-limit-ish or even 7-limit ish...
The 12TET tri-tone gets caught dead center between the 10/7 and 7/5, which
both "cast their shadows" over it and pull it both ways strongly and the mind
can't decide which one as the other interval always has such a strong grip it
won't let it "move"... 17/12 (the lowest limit fraction anywhere very near it)
doesn't have a fighting chance standing between two 7-limit fractions.
So the 12TET tri-tone ends up landing it in the middle of nowhere, far as
having it's own identity. This differs from, say 11/9...which is far enough
from the major and minor 3rd, IMVHO, to escape exclusive pull to either of them
(more than 20 cents away from each) and carry its own identity.
>"The point I'm trying to make is that if you improve the consonance of one
>subset beyond 12-equal, the consonance of other subsets will drop, resulting in
>a net decrease in consonant chords within the overall scale"
I get what you are saying, but I don't believe it. What I think kills the
whole 12TET (and meantone) scale-making ethic is the idea of killing otherwise
good combination left right and center to try and maintain perfect 5ths and the
chords based around them. Start allowing the occasional diminished 5th, neutral
second, stretched 5th, and such...and I don't see any reason the subsets will
have to drop. The Minerva scale Gene posted, IMVHO, is a great example of this.
>"Well, you sure seem to be implying that you think that, since you optimize your
>scales to nail those 11-limit intervals equally as well as lower-limit ones,
>giving them the same priority in tuning."
Depends what you mean by "priority"...
A) There are some odd 20% 11-limit or more dyads in my Dimension tuning. The
rest (AKA the large majority) include some 7-limit but mostly 5 or less limit.
The idea, again, is to balance the higher limit intervals in chords with lower
limit ones. So in a way they get "lower" priority IE there are far less of them
than any other type of interval...on purpose.
B) I'm actually more concerned about the accuracy/pureness of 11+ limit
intervals in my scale than the lower limit ones. 11-limit+ intervals change
mood GREATLY with even slight error. Try 11/6 vs. 20/11...despite being about
13 cents away from each other to mood difference is huge. Same goes for 22/15
vs. 16/11..similar cent error between the tones...huge difference in mood!
Now for 5/4...6/5...you can add 13 cents error and barely feel
it...there's no interval strong enough to fight anything fairly near them and
whatever you put near them easily serves the same musical purpose. You don't
have that "slack" in 11+ limit....
>"So by your standards it would be better to have a scale with a few good 5/4s, a
>few good 11/9's, a few good 3/2's, a few good 22/15's, as opposed to a scale
>with all "mediocre" 5/4's and "mediocre" 3/2's?"
Not even close! I'm saying it's better to have a scale with lots of good
5-limit intervals, some good 7-limit ones, and a small (say 20% or less of
dyads) to "allow" a few better higher limit intervals...
.....then it is to try to brute-force everything into 5-limit and end up making
many of the dyads highly mediocre...to the point you get crap like the 12TET
tritone that can't even "find an identity" and the 6th that's a whole lot more
like a 16/9 than a 9/5.
>"You misunderstand: low entropy = high concordance, so 12-tET has the 3rd
>highest average concordance; only 5-EDO and 7-EDO are more concordant on
>average."
My bad...now I get it. Now the fact 7TET and 5TET are rated so well is
bugging me instead (lol).
>"5-EDO has the lowest overall entropy, because two out of five intervals are
>near the two lowest-entropy intervals in the first octave (4/3 and 3/2)."
Right, harmonic entropy champions lowest entropy intervals as having far more
influence than anything else...and completely ignores things like the effect of
higher-limit intervals or peaks of dissonance near certain 11-limit intervals
like 20/11, but not others. So I think it almost completely ignores a
significant piece of the puzzle (yes, I consider the "20%" mentioned before as a
significant piece).
>"If you try to put a neutral 7th on top of a major or minor 3rd, the result is
>pretty gnarly."
But you see...here you go insisting only on the most common "common practice"
chords as benchmarks. Why not try a 4th with your 11/6...or a neutral
second? That's the sort of thinking I use in the Dimension
tuning....sometimes the thing that feels the most resolved in context....is NOT
a common practice type chord...but something completely different. And
sometimes...two good 11-limit dyads can make a right (note the third dyad formed
between a 11/9 neutral second and the 11/6 neutral 7th is (gasp!) a perfect
fifth that balances them out! :-D
Me> To me, once you go over 7-limit or so...limits are not a reliable
predictor of consonance anymore...
Igs>On this, we agree. And Carl has warned me that Tenney Height stops being a
reliable predictor of consonance once the product exceeds about 70.
Exactly! All these things we've been doing so far as harmonic entropy and
such as well (based on Tenney Height) tend to fall apart over 7-limit as well.
I think the real question becomes...how can we, with composition and theory,
"trick" many parts of the 11-limit into working with lower-limits and not
sounding out of place.
>"Though intervals like 11/6, 11/7, 11/8, 11/9 might be on the threshold of
>Just."
Because they are ratios using the lowest numbers for the limit they are in?!
Again, if you guess that, I'd use 15/8 and 22/15 as 15-limit counter examples.
Another counter-example...14/11 I'd actually say is worse than something like
15/11 as 14/11 is so near 9/7 the two rather fight over identity.
>"No, I'm not saying that...but I do think they are all drastically LESS
>consonant than anything in the 5-limit, and they are generally rather difficult
>to integrate with 5-limit intervals."
See the above chord examples I made with the 11/6 neutral 7th. Or my
"Dimension chord examples" in my folder...all of which use 22/15's.
>"No, sorry, that is NOT a "better alternative". You have no idea how many
>dissonant and consonant triads there are in a scale just by playing in it."
We agree to disagree? But to be fair...I made another post topic where I
managed to get about 47% dissonant triads in 12TET...and quantify it...including
doing an nCr calculation to get the total number of triads possible starting
from C. Look for the post titled "Dissonant triads in 12TET". Next, if you
want, I can do the same sort of thing with "Consonant triads in Minerva".... :-)
[Non-text portions of this message have been removed]
From: Kalle Aho (2011-01-20)
Subject: Re: [MMM] Tonal Color
--- In [email protected], Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Jan 19, 2011 at 5:01 PM, Kalle Aho <kalleaho@...> wrote:
> >
> > > Subtle tonal color changes would be things like changing the type of
> > > instrument playing a melody in a song or changing from a neutral to a major
> > > chord in the same key....while less subtle changes would include things like
> > > changing chords to different types of chords with different root tones (IE C
> > > major to D minor). Good tonal color, IMVHO, would come in a tuning system or
> > > scale that allows a large range of both subtle and less subtle changes to be
> > > explored by the composer, thus giving the composer more expressive range.
> >
> > I still can't say what you mean by "tonal color" but I try: if I
> > remember correctly you would say that a harmonic series segment like
> > 7:8:9:10:11:12:13:14 has less tonal color than the diatonic scale. Am
> > I correct?
>
> I personally agree with this. Perhaps tonal variety is more what's
> being talked about. Paul Erlich elucidated a bit on this concept in
> his paper "The Forms of Tonality," where he differentiated between
> tonal scales that are static vs dynamic. A 8:16 harmonic scale, for
> example, would be very "static," and something like Ionian would be
> very dynamic. Mixolydian, on the other hand, is static.
>
> Paul had a precise, rigorous definition of this which had something to
> do with leading tones; I don't remember exactly what it is. I have a
> more intuitive definition that I'd quantify with how many different
> VF's are present in a scale, but I haven't worked it all out yet.
Paul's static vs. dynamic concept differentiates between different
modes (rotations) of the same scale so your definition can't be about
the same thing. In dynamic tonality the characteristic dissonance
resolves to a consonance of the tonic chord in contrary motion and
in rarer steps. In static tonality the characteristic dissonance is
included in a chord of the next limit. The characteristic dissonance
is a dissonant interval that spans the same number of steps as some
consonance of the scale, like the diminished fifth for example.
In mixolydian it forms an approximate 7-limit major tetrad with the
tonic triad. BTW, I often wonder about the aeolian dynamic tonality,
how common is this in music? I mean, what we call "aeolian cadence" is
*not* something like D B F A -> A C E A.
> > If I am, then it seems to me that it boils down to the
> > number of identities the notes of scale can take. I mean the notes
> > of the diatonic scale have different roles in different chords while
> > the notes in a harmonic series segment strongly suggest a single
> > fundamental, thus no sense of shifting, harmonic movement or chord
> > changes.
>
> Right, that's the intuitive definition I've arrived at as well. No
> need to explain then I guess :)
>
> -Mike
>