Topic: Compact 5-limit MOS

5 scales

Thread (36 messages)

From: Gene Ward Smith (2007-02-14)
Subject: Compact 5-limit MOS

Speaking of the 5-limit, there are all these reasonably sized 5-limit 
MOS scales which don't seem to be getting any attention, despite 
their formal similarity with the diatonic scale. I think an 
interesting challenge would be to take a break from doing goofy equal 
divisions and give one a try. Diatonic, of course, is famous, and 
porcupine and dischismci have I think gotten some attention, but what 
about these:

Magic in 7 or 10 notes.

I've given magic a shot--anyone else? The 10 note scale ought to give 
considerable scope for 5-limit fun and games. Recommended tuning: 
13deg41.

Hanson in 7 or 11 notes.

I guess Hanson must have used it. Who else? 11 notes of it look like 
a great way to do 5-limit stuff, with the option of smuggling in some 
cheesy 7-limit stuff also. Recommended tuning: 14deg53

Sensi, 11 notes.

As a bonus, some 7-limit stuff. Recommended tuning: 31deg84, though 
46deg17 would be just fine if you want to work with a smaller 
division.

Schismatic, 12 notes

It worked for the late middle ages. Recommended tuning: 31deg53. Or 
hell, Pythagorean if you like.

Surely someone out there could take a break from 13edo and do a Magic
[10]?

From: Aaron Krister Johnson (2007-02-14)
Subject: Re: Compact 5-limit MOS

See my questions/comments below...

--- In [email protected], "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> Speaking of the 5-limit, there are all these reasonably sized 5-limit 
> MOS scales which don't seem to be getting any attention, despite 
> their formal similarity with the diatonic scale. I think an 
> interesting challenge would be to take a break from doing goofy equal 
> divisions and give one a try. Diatonic, of course, is famous, and 
> porcupine and dischismci have I think gotten some attention, but what 
> about these:
> 
> Magic in 7 or 10 notes.
> 
> I've given magic a shot--anyone else? The 10 note scale ought to give 
> considerable scope for 5-limit fun and games. Recommended tuning: 
> 13deg41.

So this means the 13th degree of 41-edo as a generator, right?

> Hanson in 7 or 11 notes.
> 
> I guess Hanson must have used it. Who else? 11 notes of it look like 
> a great way to do 5-limit stuff, with the option of smuggling in some 
> cheesy 7-limit stuff also. Recommended tuning: 14deg53
> 
> Sensi, 11 notes.
> 
> As a bonus, some 7-limit stuff. Recommended tuning: 31deg84, though 
> 46deg17 would be just fine if you want to work with a smaller 
> division.

You lost me here---is that the 46th degree of 17-edo, or the 17th
degree of 46-edo? HUH?

> Schismatic, 12 notes
> 
> It worked for the late middle ages. Recommended tuning: 31deg53. Or 
> hell, Pythagorean if you like.
> 
> Surely someone out there could take a break from 13edo and do a Magic
> [10]?

Sounds interesting....right now I'm looking at the properties of 171
and 441 as JI approximations in my 'micro_composer' (old alias:
'et_compose' (as you know those divisions are great for 7-limit, but
they are good in general one would think)...care to paste .scl files
of the above suggestions?

-A.

From: Gene Ward Smith (2007-02-14)
Subject: Re: Compact 5-limit MOS

--- In [email protected], "Aaron Krister Johnson" 
<aaron@...> wrote:

> You lost me here---is that the 46th degree of 17-edo, or the 17th
> degree of 46-edo? HUH?

It's 17deg46. I picked this up from Ozan, but maybe I shoulf go back to 
saying 17/46.

From: Aaron Krister Johnson (2007-02-14)
Subject: Re: Compact 5-limit MOS

--- In [email protected], "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> --- In [email protected], "Aaron Krister Johnson" 
> <aaron@> wrote:
> 
> > You lost me here---is that the 46th degree of 17-edo, or the 17th
> > degree of 46-edo? HUH?
> 
> It's 17deg46. I picked this up from Ozan, but maybe I shoulf go back to 
> saying 17/46.

I prefer the compactness of x/y notation, but perhaps XdegY is less
ambiguous because the x/y notation might be mistaken out of context as
linear ratios instead of exponents of two.

So, I think Ozan is onto something. What confused me is that you meant
17th degree of 46-edo, whic would be 17deg46, but you wrote 46deg17.

-A.

From: c.m.bryan (2007-02-14)
Subject: Re: [MMM] Compact 5-limit MOS

Hello Gene, thanks for pointing these out.  I'm currently playing with
different MOS.  I'm looking at the tuning encyclopedia for magic, but
having trouble deciphering some of the lingo.  Poptimal generator?
TOP period/generator?  One-sentence definitions of these would be
helpful.

Hanson and sensi I can't find in the encyclopedia, so i'll search the
tuning archives.

-Chris Bryan



On 14/02/07, Gene Ward Smith <genewardsmith@...> wrote:
>
>
>
>
>
>
> Speaking of the 5-limit, there are all these reasonably sized 5-limit
>  MOS scales which don't seem to be getting any attention, despite
>  their formal similarity with the diatonic scale. I think an
>  interesting challenge would be to take a break from doing goofy equal
>  divisions and give one a try. Diatonic, of course, is famous, and
>  porcupine and dischismci have I think gotten some attention, but what
>  about these:
>
>  Magic in 7 or 10 notes.
>
>  I've given magic a shot--anyone else? The 10 note scale ought to give
>  considerable scope for 5-limit fun and games. Recommended tuning:
>  13deg41.
>
>  Hanson in 7 or 11 notes.
>
>  I guess Hanson must have used it. Who else? 11 notes of it look like
>  a great way to do 5-limit stuff, with the option of smuggling in some
>  cheesy 7-limit stuff also. Recommended tuning: 14deg53
>
>  Sensi, 11 notes.
>
>  As a bonus, some 7-limit stuff. Recommended tuning: 31deg84, though
>  46deg17 would be just fine if you want to work with a smaller
>  division.
>
>  Schismatic, 12 notes
>
>  It worked for the late middle ages. Recommended tuning: 31deg53. Or
>  hell, Pythagorean if you like.
>
>  Surely someone out there could take a break from 13edo and do a Magic
>  [10]?
>
>                    



-- 
Rop tú mo baile,
a Choimdiu cride:
ní ní nech aile
acht Rí secht nime.

From: Carl Lumma (2007-02-14)
Subject: Re: [MMM] Compact 5-limit MOS

>Hanson in 7 or 11 notes.
>
>I guess Hanson must have used it. Who else? 11 notes of it look like 
>a great way to do 5-limit stuff, with the option of smuggling in some 
>cheesy 7-limit stuff also. Recommended tuning: 14deg53

I don't think Hanson did, but I could be wrong.  I wrote some
chord progressions in the 8-tone chain.  Herman may have done
some stuff with it.

-Carl

From: Carl Lumma (2007-02-14)
Subject: Re: [MMM] Compact 5-limit MOS

At 06:14 AM 2/14/2007, you wrote:
>Hello Gene, thanks for pointing these out.  I'm currently playing with
>different MOS.  I'm looking at the tuning encyclopedia for magic, but
>having trouble deciphering some of the lingo.  Poptimal generator?

Gene's been over this a hundred times, but I'm still not sure I
get it.  I think it's like, how do you decided whether you're
minimizing the error, or the squared error, or the cubed error,
etc.?  Poptimal doesn't decide, it just says there is some
exponent for which this generator minimizes the error.  Or
something.  I think there are an infinite number of poptimal
generators for any tuning.  But I could be wrong.  It's never
seemed terribly useful to me.

>TOP period/generator?  One-sentence definitions of these would be
>helpful.

TOP is Paul Erlich's scheme for tempering all the consonances
in proportion to their complexity.  Octaves the least, ratios
of 3 next, and so on.  It's generally what I'd recommend.

>Hanson and sensi I can't find in the encyclopedia, so i'll search the
>tuning archives.

Hanson used to be called kleismic.  Don't forget Google web search.

-Carl

From: Gene Ward Smith (2007-02-14)
Subject: Re: Compact 5-limit MOS

--- In [email protected], "Aaron Krister Johnson" 
<aaron@...> wrote:

> I prefer the compactness of x/y notation, but perhaps XdegY is less
> ambiguous because the x/y notation might be mistaken out of context as
> linear ratios instead of exponents of two.

It is a ratio: it's a fraction of an octave.

> So, I think Ozan is onto something. What confused me is that you meant
> 17th degree of 46-edo, whic would be 17deg46, but you wrote 46deg17.

Yeah, well, rub it in already.

From: monz (2007-02-14)
Subject: Re: Compact 5-limit MOS

Hi Gene,


--- In [email protected], "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> --- In [email protected], "Aaron Krister Johnson" 
> <aaron@> wrote:
> 
> > You lost me here---is that the 46th degree of 17-edo, or the 17th
> > degree of 46-edo? HUH?
> 
> It's 17deg46. I picked this up from Ozan, but maybe I
> shoulf go back to saying 17/46.


No, please don't do that!-- it's too easy to confuse
that with a frequency-ratio.

I personally really like the long-winded (but absolutely
accurate) way of notating it: 2^(17/46) ... but that's
just me.


-monz
http://tonalsoft.com
Tonescape microtonal music software

From: monz (2007-02-14)
Subject: temperament families (was: Compact 5-limit MOS)

Hi Chris and Gene,


--- In [email protected], c.m.bryan <chrismbryan@...> wrote:
>
> Hello Gene, thanks for pointing these out.  I'm currently
> playing with different MOS.  I'm looking at the tuning
> encyclopedia for magic, but having trouble deciphering
> some of the lingo.  Poptimal generator? TOP period/generator?
> One-sentence definitions of these would be helpful.


They're in the Encyclopedia:

http://tonalsoft.com/enc/p/poptimal.aspx

http://tonalsoft.com/enc/t/top.aspx

... but unfortunately they are pretty much one-sentence
definitions, which doesn't really explain them fully
enough. Problem is that i myself have not taken the
time to understand either of them enough to flesh out
the webpages.

For most types of temperaments, where the octave (2:1 ratio)
is the Identity Interval, "TOP" really simply means that
the octaves are tempered as well as the 3rds and 5ths.

"Poptimal" i really can't help you with -- Gene is the
one to explain that.


 
> Hanson and sensi I can't find in the encyclopedia,
> so i'll search the tuning archives.


There was a time a couple of years ago where i was in
the process of getting good basic definitions of all
the main temperament families into the Encyclopedia.
I didn't get very far, but here are the ones i got in
there:

http://tonalsoft.com/enc/k/kwazy.aspx

http://tonalsoft.com/enc/m/magic.aspx

http://tonalsoft.com/enc/m/marvel.aspx

http://tonalsoft.com/enc/m/meantone.aspx

http://tonalsoft.com/enc/m/miracle.aspx

http://tonalsoft.com/enc/m/mutt.aspx

http://tonalsoft.com/enc/m/mystery.aspx

http://tonalsoft.com/enc/o/orwell.aspx

http://tonalsoft.com/enc/s/schismic.aspx

http://tonalsoft.com/enc/s/semisixths.aspx


"Meantone" is by far the most complete of these
webpages, because that is by far the family i'm most
familiar with (and i would guess that's the case with
nearly everyone else too, except maybe Gene). 

The "miracle" page is also pretty good, because i
was in on the day-to-day rediscovery of it on the
tuning list back in 2001.

For the others, i posted a template here with all
the labels filled in and all the data areas blank,
and Gene filled out several of them and sent them
to me, Herman Miller did a few others. 

But i really haven't explored these families myself
at all, except for a little bit of magic and kleisma,
because 19-edo belongs to those, and in my improvs
with Jonathan Glasier and Brink at Sonic Arts we make
it a point to avoid sounding like meantone when we
play in 19.


When the categorizing of these temperament families
first began a few years ago, there was a lot of
discussion of how we would name them, and several
of the names did change, so i'm not sure how current
my "family" webpage is:

http://tonalsoft.com/enc/f/family.aspx


If "sensi" means the same as "semisixths", then
i've already got a page on that (the last one in the
above list).

First thing we should do is clarify the list of names,
and make it as complete as we can.

Gene, can we pick up the process of putting these
definitions into the Encyclopedia? We could start
with "Hanson" ... and i'm also very unclear what
people mean by "pajara".



-monz
http://tonalsoft.com
Tonescape microtonal music software

From: Aaron Krister Johnson (2007-02-14)
Subject: Re: Compact 5-limit MOS

--- In [email protected], "monz" <monz@...> wrote:
>
> Hi Gene,

> > Gene wrote:
> > It's 17deg46. I picked this up from Ozan, but maybe I
> > shoulf go back to saying 17/46.
> 
> Monz wrote:
> No, please don't do that!-- it's too easy to confuse
> that with a frequency-ratio.
> 
> I personally really like the long-winded (but absolutely
> accurate) way of notating it: 2^(17/46) ... but that's
> just me.

Monz, you must have missed my message (#16072) that made the same point!

BTW, did you get my email correspondence regarding the ET page of your
encyclopedia?

-A.

From: monz (2007-02-14)
Subject: Re: Compact 5-limit MOS

Hi Aaron,


--- In [email protected], "Aaron Krister Johnson"
<aaron@...> wrote:
>
> --- In [email protected], "monz" <monz@> wrote:
> >
> > Hi Gene,
> 
> > > Gene wrote:
> > > It's 17deg46. I picked this up from Ozan, but maybe I
> > > shoulf go back to saying 17/46.
> > 
> > Monz wrote:
> > No, please don't do that!-- it's too easy to confuse
> > that with a frequency-ratio.
> > 
> > I personally really like the long-winded (but absolutely
> > accurate) way of notating it: 2^(17/46) ... but that's
> > just me.
> 
> Monz, you must have missed my message (#16072) that made
> the same point!


I read yours right after i sent mine. ;-)

 
> BTW, did you get my email correspondence regarding the ET
> page of your encyclopedia?


Yes, i got emails from you and several other folks,
but have been too busy to update the page yet ... my
precalculus course started a couple of weeks ago, and
i'm still struggling to remember the algebra i need.

I'll get around to it hopefully on Friday or Monday
... reminders are always good with me.

(When Paul Erlich was around, he would periodically
send me a "friendly reminder" every few months about
something i had wrong on my website that was bugging
him ... and some of those *still* haven't been fixed
after several years! ... i really do need to find some
time for the website ...)


-monz
http://tonalsoft.com
Tonescape microtonal music software

From: Gene Ward Smith (2007-02-14)
Subject: Re: Compact 5-limit MOS

--- In [email protected], "Aaron Krister Johnson" 
<aaron@...> wrote:
>
> See my questions/comments below...

Replied to on tuning:
http://launch.groups.yahoo.com/group/tuning/message/69789

From: Aaron Krister Johnson (2007-02-14)
Subject: Re: Compact 5-limit MOS

--- In [email protected], "monz" <monz@...> wrote:
>
> Hi Aaron,
> 
> 
> --- In [email protected], "Aaron Krister Johnson"
> <aaron@> wrote:
> >
> > --- In [email protected], "monz" <monz@> wrote:
> > >
> > > Hi Gene,
> > 
> > > > Gene wrote:
> > > > It's 17deg46. I picked this up from Ozan, but maybe I
> > > > shoulf go back to saying 17/46.
> > > 
> > > Monz wrote:
> > > No, please don't do that!-- it's too easy to confuse
> > > that with a frequency-ratio.
> > > 
> > > I personally really like the long-winded (but absolutely
> > > accurate) way of notating it: 2^(17/46) ... but that's
> > > just me.
> > 
> > Monz, you must have missed my message (#16072) that made
> > the same point!
> 
> 
> I read yours right after i sent mine. ;-)
> 
>  
> > BTW, did you get my email correspondence regarding the ET
> > page of your encyclopedia?
> 
> 
> Yes, i got emails from you and several other folks,
> but have been too busy to update the page yet ... my
> precalculus course started a couple of weeks ago, and
> i'm still struggling to remember the algebra i need.
> 
> I'll get around to it hopefully on Friday or Monday
> ... reminders are always good with me.
> 
> (When Paul Erlich was around, he would periodically
> send me a "friendly reminder" every few months about
> something i had wrong on my website that was bugging
> him ... and some of those *still* haven't been fixed
> after several years! ... i really do need to find some
> time for the website ...)

OR---you could wiki-fy the encyclopedia, which could make such
corrections and maintainence much easier!

Best,
Aaron

From: Gene Ward Smith (2007-02-15)
Subject: Re: Compact 5-limit MOS

--- In [email protected], "Gene Ward Smith" 
<genewardsmith@...> wrote:

> Magic in 7 or 10 notes.

Magic tempers out the magic comma of 3125/3072, which means that five 
major thirds make up a twelvth: (5/4)^5/3 = 3125/3072. The major 
thirds of 41-et are flat by about 1/5 of a magic comma, which would 
be analogous to 1/4 comma meantone. It bears the same relationship to 
magic as 31 does to meantone. The scales are constant structure MOS, 
but don't mess with them if you insist on propriety.

! magic7.scl
Magic[7] in 41-et tuning
7
!
321.951220
380.487805
702.439024
760.975610
819.512195
1141.463415
1200.000000

! magic10.scl
Magic[10] in 41-et tuning
10
!
263.414634
321.951220
380.487805
439.024390
702.439024
760.975610
819.512195
1082.926829
1141.463415
1200.000000

> Hanson in 7 or 11 notes.

Hanson tempers out the kleisma of 15625/15552, so you may also call 
it kleismic. (5/2)/(6/5)^5 = 3/(6/5)^6 = 15625/15552, which shows how 
triads are formed. 53 has minor thirds about 1/6-kleisma sharp, 
connected to its nearly pure fifths. Once again, both scales are 
improper. The cycle of minor thirds closes with a fourth for the 7-
note scale, and with a 9/7 (supermajor third) for the 11-note scale. 
The latter is a "catakleismic temperament" interval popping up in a 
mostly 5-limit (unless you want to use keemun approximations) 
context. It can be made exact by using (56/9)^(1/10) for the minor 
third. Another nice feature of the 11-note scale is its circle of six 
major thirds and five fourths, which could certainly be made use of 
structurally.

! hanson7.scl
Hanson[7] in 53-et tuning
7
!
67.924528
316.981132
384.905660
633.962264
701.886792
950.943396
1200.000000

! hanson11.scl
Hanson[11] in 53-et tuning
11
!
67.924528
135.849057
316.981132
384.905660
566.037736
633.962264
701.886792
883.018868
950.943396
1018.867925
1200.000000

> Sensi, 11 notes.

Sensi, or semisixths, tempers out the semisixths comma of 
78732/78125. While I'm just considering the 5-limit, it makes a lot 
of sense to view sensi as a basically 7-limit temperament, in which 
case the 9/7 generator is 7.77 cents sharp in the 84edo tuning I 
used. A feature Sensi[11] has in common with the diatonic scale is a 
circle of major/minor thirds--9 minor and 2 major in this case. 
Another very characteristic feature is the huge number of diminished 
seventh chords. 

! sensi11.scl
Sensi[11] (Semisixths[11]) in 84edo tunig
11
!
128.571429
257.142857
385.714286
442.857143
571.428571
700.000000
828.571429
885.714286
1014.285714
1142.857143
1200.000000

> Schismatic, 12 notes

Since Aaron is interested in 171-et, I give this in 171-et, an 
excellent schismatic tuning close to 1/10-schisma. For extra fun, 
treat it as a circulating temperament.

! schismatic12.scl
Schismatic[12] in 171-et tuning
12
!
91.228070
203.508772
294.736842
385.964912
498.245614
589.473684
701.754386
792.982456
884.210526
996.491228
1087.719298
1200.000000

Here's someone steps up to the plate and takes a swing.

From: monz (2007-02-15)
Subject: Re: Compact 5-limit MOS

--- In [email protected], "Aaron Krister Johnson"
<aaron@...> wrote:

> OR---you could wiki-fy the encyclopedia, which could make such
> corrections and maintainence much easier!


I had the idea to do something like that before Wikipedia
existed ... but at this point i plan to eventually 
incorporate the whole Encyclopedia into Tonescape's
menu system, so making it a wiki could cause problems,
from editing to copyrights.


-monz
http://tonalsoft.com
Tonescape microtonal music software

From: Gene Ward Smith (2007-02-15)
Subject: Re: Compact 5-limit MOS

--- In [email protected], "Gene Ward Smith" 
<genewardsmith@...> wrote:

I'm getting way outside of my knowledge area here, but it occurred to 
me to wonder about tuning guitars (and perhaps other stringed 
instruments) to these MOS. It seems fourths and major thirds are 
popular intervals, and I wonder if anyone can tell me if the thoughts 
below make any sense.

> > Magic in 7 or 10 notes.

Magic has a flat major fourth as a generator, and how would that work 
as an interval for tuning a guitar? It might be possible to make 
either a 19 or a 22 tone guitar on this principle, correct? Six major 
thirds and a tone give a complete cycle.

> > Hanson in 7 or 11 notes.

> Another nice feature of the 11-note scale is its circle of six 
> major thirds and five fourths, which could certainly be made use of 
> structurally.

Could this be used for tuning purposes? 19 and even 34 tone guitars 
have been made, but I don't know if in four octaves, which six major 
thirds and five fourths would give you. Of course minor thirds would 
be an alternative.

> > Sensi, 11 notes.

The sensi generator is around 443 cents, which may be a good size.

From: Carl Lumma (2007-02-15)
Subject: Re: [MMM] Re: Compact 5-limit MOS

Dave Keenan is good at this.

It's a qustion for Tuning, though, not MMM.

-Carl

>I'm getting way outside of my knowledge area here, but it occurred to 
>me to wonder about tuning guitars (and perhaps other stringed 
>instruments) to these MOS. It seems fourths and major thirds are 
>popular intervals, and I wonder if anyone can tell me if the thoughts 
>below make any sense.
>
>> > Magic in 7 or 10 notes.
>
>Magic has a flat major fourth as a generator, and how would that work 
>as an interval for tuning a guitar? It might be possible to make 
>either a 19 or a 22 tone guitar on this principle, correct? Six major 
>thirds and a tone give a complete cycle.
>
>> > Hanson in 7 or 11 notes.
>
>> Another nice feature of the 11-note scale is its circle of six 
>> major thirds and five fourths, which could certainly be made use of 
>> structurally.
>
>Could this be used for tuning purposes? 19 and even 34 tone guitars 
>have been made, but I don't know if in four octaves, which six major 
>thirds and five fourths would give you. Of course minor thirds would 
>be an alternative.
>
>> > Sensi, 11 notes.
>
>The sensi generator is around 443 cents, which may be a good size.

From: Carl Lumma (2007-02-15)
Subject: Re: [MMM] Re: Compact 5-limit MOS

>i plan to eventually 
>incorporate the whole Encyclopedia into Tonescape's
>menu system, so making it a wiki could cause problems,
>from editing to copyrights.

Do you consider the copyright to the quoted material in
the encyclopedia Tonalsoft property?

-Carl

From: Herman Miller (2007-02-15)
Subject: Re: [MMM] Compact 5-limit MOS

Carl Lumma wrote:
>> Hanson in 7 or 11 notes.
>>
>> I guess Hanson must have used it. Who else? 11 notes of it look like 
>> a great way to do 5-limit stuff, with the option of smuggling in some 
>> cheesy 7-limit stuff also. Recommended tuning: 14deg53
> 
> I don't think Hanson did, but I could be wrong.  I wrote some
> chord progressions in the 8-tone chain.  Herman may have done
> some stuff with it.

All of my experimentation with the 11-note chain-of-minor-thirds scale 
was with the 7-limit version (keemun). I played Lecuona's _Malague\ufffda_ in 
that tuning and it mostly worked pretty well. But then I discovered 
lemba temperament and haven't gone back to doing much with keemun in a 
while.

From: Gene Ward Smith (2007-02-15)
Subject: Re: Compact 5-limit MOS

--- In [email protected], "Gene Ward Smith" 
<genewardsmith@...> wrote:

> Magic has a flat major fourth as a generator,

Major third.

From: Graham Breed (2007-02-15)
Subject: Re: [MMM] Re: Compact 5-limit MOS

On 15/02/07, Gene Ward Smith <genewardsmith@...> wrote:
>
> I'm getting way outside of my knowledge area here, but it occurred to
> me to wonder about tuning guitars (and perhaps other stringed
> instruments) to these MOS. It seems fourths and major thirds are
> popular intervals, and I wonder if anyone can tell me if the thoughts
> below make any sense.
>
> > > Magic in 7 or 10 notes.
>
> Magic has a flat major fourth as a generator, and how would that work
> as an interval for tuning a guitar? It might be possible to make
> either a 19 or a 22 tone guitar on this principle, correct? Six major
> thirds and a tone give a complete cycle.

I've thought that magic might make for a good guitar temperament, but
not worked out the details.  Meantone is good but inaccurate,
especially on the fourths and fifths which are important for a guitar
style.  Magic's the next simplest 9-limit temperament *waves hand*.
It's better tuned, and I think 9-limit harmony on a guitar would sound
cool.  There are folks who've managed JI with guitars, of course, but
I've always been frightened off by the commas.

One thing, as you corrected yourself in another message, is that the
generator's a major third.  Perfect fourths are a relatively distant
interval (five thirds down) and so a conventional tuning probably
wouldn't work at all.  (But maybe a lute tuning?)  That means you'd
have to learn a new fingering as well as getting the frets moved
around.  I don't expect anybody to be crazy enough to try that in the
near future, but perhaps I will one day ;-)

Without checking the details, I'm guessing it'd be my first choice if
I got a new re-fretted guitar.  I've done meantone, and tuned the
strings to copy the blackjack fretting we were talking about at the
time.  That sort of worked, and magic should be simpler and good
enough.  A 29-equal fretting to get mystery is also worth a thought,
but that's more of a freaky fairground tuning.  I had it on my ZTar
for a while.

Anyway, as I'm not planning to mutilate another guitar it's not
something I've thought through.


                          Graham

From: Aaron Krister Johnson (2007-02-15)
Subject: Tonalsoft, the encyclopedia, etc.

--- In [email protected], "monz" <monz@...> wrote:
>
> --- In [email protected], "Aaron Krister Johnson"
> <aaron@> wrote:
> 
> > OR---you could wiki-fy the encyclopedia, which could make such
> > corrections and maintainence much easier!
> 
> 
> I had the idea to do something like that before Wikipedia
> existed ... but at this point i plan to eventually 
> incorporate the whole Encyclopedia into Tonescape's
> menu system, so making it a wiki could cause problems,
> from editing to copyrights.

hmm....legally, ethically, community-wise, putting it into Tonescape's
menu seems like a bad idea, just on the surface of it. It just seems
too much going against the grain of an open community of contributors,
which is de facto how the encyclopedia stands. Granted, Tonescape is a
corporation I suppose, and you *are* after all, the maintainer and
host of the encyclopedia, but the tuning community has contributed
enormous amounts of material to it---I don't understand how your
company could 'own' it to the point of actually coding it into non
open-source software; in fact, I would think, although I'm not a
lawyer, that it would have to be defined as an open-source project of
sorts, unless you got permission from each and every contributer to
profit from it's existence. 

Maybe I'm not privy to certain information, and all the authors and
quoted sources have already conceded that the encyclopedia is owned by
Tonalsoft, since you host it....

Anyway, why not just have a helper app open a local file version with
a local browser? This way, as the online excyclopedia gets updated,
you can zip it into an archive, and have your users download it.

My wish and hope would be that the encyclopedia *not* disappear from
the web once you do that, if you do that!

Best,
Aaron.

From: monz (2007-02-15)
Subject: Re: Tonalsoft, the encyclopedia, etc.

Hi Aaron,


I don't want to get too far into this yet, because Tonescape
is far from ready for the Encyclopedia to be included
into it. But basically we intended to ask contributors
to sign license agreements with us which allow us to
include their contributions into the version of the
Encyclopedia that lives inside Tonescape. 

The main reason i want to include the Encyclopedia
into the software is because, instead of having 
static graphics which just give one "bird's eye view"
of a tuning, you would get the complete 3-D rotatable
Lattice-with-sound which is a part of Tonescape. 
The idea is to link the Encyclopedia pages directly
into the way Tonescape operates. You'd be able to
read the Encyclopedia page about a tuning topic, see
and play with the Lattice of it, as well as any
musical illustrations that are there, and then
actually compose your own examples, without needing
any extraneous browsers, text editors, etc. etc.

Anyway, as i said, Tonalsoft needs some serious investor
interest to proceed any farther than what we are offering
right now, and what we have right now still needs a little
fixing up. So i'll bring this up again later when the
time is appropriate.


-monz
http://tonalsoft.com
Tonescape microtonal music software



--- In [email protected], "Aaron Krister Johnson"
<aaron@...> wrote:
>
> --- In [email protected], "monz" <monz@> wrote:
> >
> > --- In [email protected], "Aaron Krister Johnson"
> > <aaron@> wrote:
> > 
> > > OR---you could wiki-fy the encyclopedia, which could make such
> > > corrections and maintainence much easier!
> > 
> > 
> > I had the idea to do something like that before Wikipedia
> > existed ... but at this point i plan to eventually 
> > incorporate the whole Encyclopedia into Tonescape's
> > menu system, so making it a wiki could cause problems,
> > from editing to copyrights.
> 
> hmm....legally, ethically, community-wise, putting it into Tonescape's
> menu seems like a bad idea, just on the surface of it. It just seems
> too much going against the grain of an open community of contributors,
> which is de facto how the encyclopedia stands. Granted, Tonescape is a
> corporation I suppose, and you *are* after all, the maintainer and
> host of the encyclopedia, but the tuning community has contributed
> enormous amounts of material to it---I don't understand how your
> company could 'own' it to the point of actually coding it into non
> open-source software; in fact, I would think, although I'm not a
> lawyer, that it would have to be defined as an open-source project of
> sorts, unless you got permission from each and every contributer to
> profit from it's existence. 
> 
> Maybe I'm not privy to certain information, and all the authors and
> quoted sources have already conceded that the encyclopedia is owned by
> Tonalsoft, since you host it....
> 
> Anyway, why not just have a helper app open a local file version with
> a local browser? This way, as the online excyclopedia gets updated,
> you can zip it into an archive, and have your users download it.
> 
> My wish and hope would be that the encyclopedia *not* disappear from
> the web once you do that, if you do that!
> 
> Best,
> Aaron.
>

From: Aaron Krister Johnson (2007-02-15)
Subject: Re: Tonalsoft, the encyclopedia, etc.

Hey Monz!

What ou say makes sense. And the software sounds awfully cool!

-A.


--- In [email protected], "monz" <monz@...> wrote:
>
> Hi Aaron,
> 
> 
> I don't want to get too far into this yet, because Tonescape
> is far from ready for the Encyclopedia to be included
> into it. But basically we intended to ask contributors
> to sign license agreements with us which allow us to
> include their contributions into the version of the
> Encyclopedia that lives inside Tonescape. 
> 
> The main reason i want to include the Encyclopedia
> into the software is because, instead of having 
> static graphics which just give one "bird's eye view"
> of a tuning, you would get the complete 3-D rotatable
> Lattice-with-sound which is a part of Tonescape. 
> The idea is to link the Encyclopedia pages directly
> into the way Tonescape operates. You'd be able to
> read the Encyclopedia page about a tuning topic, see
> and play with the Lattice of it, as well as any
> musical illustrations that are there, and then
> actually compose your own examples, without needing
> any extraneous browsers, text editors, etc. etc.
> 
> Anyway, as i said, Tonalsoft needs some serious investor
> interest to proceed any farther than what we are offering
> right now, and what we have right now still needs a little
> fixing up. So i'll bring this up again later when the
> time is appropriate.
> 
> 
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
> 
> 
> 
> --- In [email protected], "Aaron Krister Johnson"
> <aaron@> wrote:
> >
> > --- In [email protected], "monz" <monz@> wrote:
> > >
> > > --- In [email protected], "Aaron Krister Johnson"
> > > <aaron@> wrote:
> > > 
> > > > OR---you could wiki-fy the encyclopedia, which could make such
> > > > corrections and maintainence much easier!
> > > 
> > > 
> > > I had the idea to do something like that before Wikipedia
> > > existed ... but at this point i plan to eventually 
> > > incorporate the whole Encyclopedia into Tonescape's
> > > menu system, so making it a wiki could cause problems,
> > > from editing to copyrights.
> > 
> > hmm....legally, ethically, community-wise, putting it into Tonescape's
> > menu seems like a bad idea, just on the surface of it. It just seems
> > too much going against the grain of an open community of contributors,
> > which is de facto how the encyclopedia stands. Granted, Tonescape is a
> > corporation I suppose, and you *are* after all, the maintainer and
> > host of the encyclopedia, but the tuning community has contributed
> > enormous amounts of material to it---I don't understand how your
> > company could 'own' it to the point of actually coding it into non
> > open-source software; in fact, I would think, although I'm not a
> > lawyer, that it would have to be defined as an open-source project of
> > sorts, unless you got permission from each and every contributer to
> > profit from it's existence. 
> > 
> > Maybe I'm not privy to certain information, and all the authors and
> > quoted sources have already conceded that the encyclopedia is owned by
> > Tonalsoft, since you host it....
> > 
> > Anyway, why not just have a helper app open a local file version with
> > a local browser? This way, as the online excyclopedia gets updated,
> > you can zip it into an archive, and have your users download it.
> > 
> > My wish and hope would be that the encyclopedia *not* disappear from
> > the web once you do that, if you do that!
> > 
> > Best,
> > Aaron.
> >
>

From: Jon Szanto (2007-02-16)
Subject: Re: [MMM] Compact 5-limit MOS

Dan,

{you wrote...}
>for anyone out of the loop that's interested in playing along at home, is there a neat and orderly place where all these names--"lemba" et al--are compiled along with their definitions?

Son, you must be joking.

Cheers,
Jon

From: Carl Lumma (2007-02-16)
Subject: Re: [MMM] Compact 5-limit MOS

At 04:52 PM 2/15/2007, you wrote:
>for anyone out of the loop that's interested in playing along at home,
>is there a neat and orderly place where all these names--"lemba" et
>al--are compiled along with their definitions?
>
>http://www.myspace.com/danstearns 

The short answer is, sadly, no.  Google web search is your best
bet.  Herman Miller does have a great page on lemba in particular.
It remains for someone with the passion, time, and knowledge to
put this all together in a way that mortals can understand.

-Carl

From: Jacob (2007-02-16)
Subject: Re: Compact 5-limit MOS

--- In [email protected], Carl Lumma <ekin@...> wrote:
>
> At 04:52 PM 2/15/2007, you wrote:
> >for anyone out of the loop that's interested in playing along at home,
> >is there a neat and orderly place where all these names--"lemba" et
> >al--are compiled along with their definitions?
> >
> >http://www.myspace.com/danstearns 
> 
> The short answer is, sadly, no.  Google web search is your best
> bet.  Herman Miller does have a great page on lemba in particular.
> It remains for someone with the passion, time, and knowledge to
> put this all together in a way that mortals can understand.
> 
> -Carl
>

Ok, I'll start, at least, over at xenharmonic.wikispaces.com .  I
can't promise I'll get very far, or that I actually understand
anything properly, but by golly this is something that should have
happened by now if the linear-temperament contingent ever expects its
neologisms to make a dent in the language.

roger,
jacob

From: monz (2007-02-16)
Subject: Re: Compact 5-limit MOS

Hey guys, did you miss this?

http://launch.groups.yahoo.com/group/MakeMicroMusic/message/16081


I just renewed my call for those who know to help me
put more about temperament families into the Encyclopedia.
But at least you can get a start from the links i put
into that message.


-monz
http://tonalsoft.com
Tonescape microtonal music software



--- In [email protected], "Jacob" <jbarton@...> wrote:
>
> --- In [email protected], Carl Lumma <ekin@> wrote:
> >
> > At 04:52 PM 2/15/2007, you wrote:
> > >
> > > for anyone out of the loop that's interested in
> > > playing along at home, is there a neat and orderly
> > > place where all these names--"lemba" et al--are
> > > compiled along with their definitions?
> > >
> > > http://www.myspace.com/danstearns 
> > 
> > The short answer is, sadly, no.  Google web search
> > is your best bet.  Herman Miller does have a great page
> > on lemba in particular.
> > It remains for someone with the passion, time, and
> > knowledge to put this all together in a way that mortals
> > can understand.
> > 
> > -Carl
> >
> 
> Ok, I'll start, at least, over at xenharmonic.wikispaces.com .
> I can't promise I'll get very far, or that I actually
> understand anything properly, but by golly this is
> something that should have happened by now if the
> linear-temperament contingent ever expects its
> neologisms to make a dent in the language.
> 
> roger,
> jacob
>

From: Herman Miller (2007-02-16)
Subject: Re: [MMM] Compact 5-limit MOS

daniel_anthony_stearns wrote:
> for anyone out of the loop that's interested in playing along at home,
> is there a neat and orderly place where all these names--"lemba" et
> al--are compiled along with their definitions?

Paul Erlich's "Middle Path" paper is probably the best reference at the 
moment. As far as the web, there's a list of 7-limit temperaments on 
Gene's page, but the definitions (in the form of wedgies) are of limited 
use.

http://66.98.148.43/~xenharmo/sevnames.htm

I thought there were better references than that, but I can't find them. 
In the meantime, I threw together a quick list of regular temperaments 
based on an old document (some of the names may be out of date, and this 
is by no means a complete list).

http://www.io.com/~hmiller/music/temp-list.html

Not all of these names are in current use (some of them may have been 
suggested once and subsequently forgotten).

The period and generator shown represents the TOP tuning of each 
temperament -- some temperaments have a large tolerance for tuning, but 
others need to be tuned more precisely. I made some charts which give a 
rough idea of how various 5-limit temperaments hold up when the tuning 
of the generator and the period is changed: they're in the files section 
of the tuning-math Yahoo group.

http://tech.groups.yahoo.com/group/tuning-math/files/Rank%202%20Consistency/

(Generally speaking the darker areas are better, and the more accurate 
temperaments require more precise tuning.)

From: Graham Breed (2007-02-16)
Subject: Re: [MMM] Compact 5-limit MOS

On 16/02/07, daniel_anthony_stearns <daniel_anthony_stearns@...> wrote:
>
> for anyone out of the loop that's interested in playing along at home,
> is there a neat and orderly place where all these names--"lemba" et
> al--are compiled along with their definitions?

My catalog's here:

http://x31eq.com/catalog.htm

but I gave up a long time ago because there were so many new names
being minted.  So it doesn't have lemba.  I thought about setting up a
database with definition, name, theoretical and musical references and
the like, but it's too big a job for this holiday.


                                   Graham

From: Herman Miller (2007-02-17)
Subject: Re: [MMM] Compact 5-limit MOS

Carl Lumma wrote:
> At 04:52 PM 2/15/2007, you wrote:
>> for anyone out of the loop that's interested in playing along at home,
>> is there a neat and orderly place where all these names--"lemba" et
>> al--are compiled along with their definitions?
>>
>> http://www.myspace.com/danstearns 
> 
> The short answer is, sadly, no.  Google web search is your best
> bet.  Herman Miller does have a great page on lemba in particular.
> It remains for someone with the passion, time, and knowledge to
> put this all together in a way that mortals can understand.

Are you thinking of the porcupine temperament page?

http://www.io.com/~hmiller/music/temp-porcupine.html

I have the start of a lemba page, but haven't got around to making it 
usable yet. Still, the chart showing the mixed Sagittal lemba notation, 
and the comparison of TOP lemba with just intervals, may be useful.

http://www.io.com/~hmiller/music/lemba.html

From: Carl Lumma (2007-02-17)
Subject: Re: [MMM] Compact 5-limit MOS

>>> for anyone out of the loop that's interested in playing along at home,
>>> is there a neat and orderly place where all these names--"lemba" et
>>> al--are compiled along with their definitions?
>>>
>>> http://www.myspace.com/danstearns 
>> 
>> The short answer is, sadly, no.  Google web search is your best
>> bet.  Herman Miller does have a great page on lemba in particular.
>> It remains for someone with the passion, time, and knowledge to
>> put this all together in a way that mortals can understand.
>
>Are you thinking of the porcupine temperament page?
>
>http://www.io.com/~hmiller/music/temp-porcupine.html

I was thinking of:

http://www.io.com/~hmiller/music/zireen-music.html

>I have the start of a lemba page, but haven't got around to making it 
>usable yet. Still, the chart showing the mixed Sagittal lemba notation, 
>and the comparison of TOP lemba with just intervals, may be useful.
>
>http://www.io.com/~hmiller/music/lemba.html

This is all overlapping in IE6 'n shit.

-Carl

From: Herman Miller (2007-02-17)
Subject: Re: [MMM] Compact 5-limit MOS

Carl Lumma wrote:

>> I have the start of a lemba page, but haven't got around to making it 
>> usable yet. Still, the chart showing the mixed Sagittal lemba notation, 
>> and the comparison of TOP lemba with just intervals, may be useful.
>>
>> http://www.io.com/~hmiller/music/lemba.html
> 
> This is all overlapping in IE6 'n shit.
> 
> -Carl

I have no idea what your problem might be, unless you're viewing it 
through some kind of proxy that alters the formatting of the page or 
something. It's nothing more than plain text and images. The main chart 
was missing "width" and "height", but that shouldn't cause any trouble, 
once the image is loaded...

The only other thing I can think of is the "meta" header that sets the 
character set to UTF-8, but IE6 shouldn't have any problem at all with 
that. Still, I don't need it for that page, so I took it out.

From: Carl Lumma (2007-02-17)
Subject: Re: [MMM] Compact 5-limit MOS

At 01:26 PM 2/17/2007, you wrote:
>Carl Lumma wrote:
>
>>> I have the start of a lemba page, but haven't got around to making it 
>>> usable yet. Still, the chart showing the mixed Sagittal lemba notation, 
>>> and the comparison of TOP lemba with just intervals, may be useful.
>>>
>>> http://www.io.com/~hmiller/music/lemba.html
>> 
>> This is all overlapping in IE6 'n shit.
>> 
>> -Carl
>
>I have no idea what your problem might be,

Hm, it's working fine now.

-Carl

From: George D. Secor (2007-02-22)
Subject: Re: Compact 5-limit MOS

--- In [email protected], "Aaron Krister Johnson" 
<aaron@...> wrote:
>
> --- In [email protected], "Gene Ward Smith"
> <genewardsmith@> wrote:
> >
> > --- In [email protected], "Aaron Krister Johnson" 
> > <aaron@> wrote:
> > 
> > > You lost me here---is that the 46th degree of 17-edo, or the 
17th
> > > degree of 46-edo? HUH?
> > 
> > It's 17deg46. I picked this up from Ozan, but maybe I shoulf go 
back to 
> > saying 17/46.
> 
> I prefer the compactness of x/y notation, but perhaps XdegY is less
> ambiguous because the x/y notation might be mistaken out of context 
as
> linear ratios instead of exponents of two.
> 
> So, I think Ozan is onto something. What confused me is that you 
meant
> 17th degree of 46-edo, whic would be 17deg46, but you wrote 46deg17.

I believe that Oz got it from me (look thru the old Sagittal "A 
Common Notation for ..." messages on tuning-math beginning in 2002 
and you'll see that Dave Keenan and I used it extensively).  I 
proposed the idea of using a degree-sign instead of a slash over 30 
years ago, and you'll find it in the documentation on the Sagittal 
website, and also in my 17-tone XH18 paper (written late in 2001).

Unfortunately, since the degree sign isn't a member of the usual 
ASCII set, we've had to substitute the more cumbersome "deg" in text 
messages.

--George