Topic: Struggling to find a practical tuning for my goals

9 scales

Thread (45 messages)

From: Aaron Wolf (2006-05-06)
Subject: Struggling to find a practical tuning for my goals

Greetings everyone,

While I continue to plan for ways to realize an acoustically based 
instrument that will meet my goals, I'm starting to experiment with 
synth tuning stuff.  I recently got Max Magic Microtuner and I'm 
trying to find a balanced, compromised tuning that will be a useful 
compositional field to explore and reach the goals I have.

Here's where I'm at:

I want to generally be near-just, and I also want a scale that is 
even *enough* to play chromatically in a way that sounds relatively 
smooth in direct ascent or descent.  In order to be manageable and 
have a decent range, I want to limit myself to a smaller number of 
notes.

I figured that a good balance would be to have a modally focused, 
very closely related set of notes, and then use pitch bend to shift 
the whole series for major harmonic changes.  I don't want to use 
pitch bend for acheiving a harmonic relation, but using it to change 
the overall key seems reasonable.  So I figured that, for example, if 
I were using strict JI, I'd use 7/5 instead of 45/32, because that'd 
blend better with the tonic 1/1 and then I'd pitch bend 1/1 up to 
9/8 and 5/4 would become 45/32.  This made sense because it 
would be in context of 9/8 that I would use 45/32.  I'm a little 
worried about this approach using a lot of pitch bending and being 
confusing, but I'm thinking I could get used to it.

Additionally, simply to keep everything straight and work with 
standard sequencers layouts, I figured that using exactly 24 notes 
would be a good balance because I'd have much more to work with 
than using only 12, but I can still easily realte things in terms of the 
names and positions they will be in a standard sequencer piano roll.

I'm looking for constructive criticism.  I want to end up with a balance 
where I know what I've compromised, but I have a decent little universe
 of music to explore, especially using the idea of pitch bending to 
any new key.

If I were to temper, I really don't want it to be too dramatic.  About 
the only thing I'd like to temper out is the 14/9 - 25/16 kleisma.  
And I'm leaning toward using simple fixed JI.

I'd absolutely minimally have 7-prime-limit and have decent focus on 
9 and 15.  Overall, I'm wanting to go essentially otonal.  I'd like to 
explore 11 and 13, though I'm less confident with them.  I'd even like 
to have 17 or 19, but I'm leaning towards making those the exception 
that I'd have to do extra junk to get to, and not have them in my 
normal system.  But I'm not sure.

What I want ideally is not practical.  And as far as tempering, I'd have
to try things to see how acceptible tempering could be to me.  I really
would like to be able to have about 60+ JI notes per octave available 
and be able to easily call forth the exact ones I want at any instant, and 
also have 6 or 7 octaves to play with.  What I'm trying to do here is to 
accept the reality of the tools and possibilities I really have and make 
myself a dynamic little box that I can explore and enjoy and accept that 
it just doesn't have everything, but I'll figure out how to make good 
music with what is there in the box.

While I'd like to have 7/4, 16/9, and 9/5, they are too close together to 
sound evenly sequential without filling in 50+ total notes per octave.  
I'd like to see every step in the scale be around 30-75 cents, ideally closer 
to 50 to make the scale even.  My thinking was to use 7/4 and 9/5, and 
leave 16/9 as a note I would get to by pitch bending the whole system to 
4/3 or 16/9 or something else where 16/9 would then exist relative to 
the original 1/1.  I have a real hard time making these tough decisions 
though.  But the overall point is: I can get anything when I really need it, 
I'm trying to have something worth exploring that will lead me in ways I 
like to new music.

So in addition to help on the specifics, I'm hoping to get feedback on 
whether people think my approach and attitude is reasonable.
Thanks so much!

In Harmony,
Aaron

From: Carl Lumma (2006-05-06)
Subject: Re: Struggling to find a practical tuning for my goals

Hi Aaron,

If Gene can get his e-mail trouble sorted out, I'm sure he'll
give you some great solutions.  In the meantime...

The way I understand it, you want 24 notes/octave, as
evenly-spaced as possible (hopefully no steps smaller than
30 cents), with accurate 7-limit otonal harmony and possibly
225:224 tempered out.

That's a tall order.  I guess I don't understand the
capabilities you have with choosing pitches from a larger
set (60) during performance, or bending to desired pitches
during performance.  Dealing with a fixed set of 24 pitches,
you'll be forced to choose between accuracy and chromatic
evenness.  You could perhaps do better with another number
of notes/oct close to 24.

Anyway, assuming you do want to stick to 24 for piano-roll
purposes, the "hemifourths" and "decimal" temperaments have
MOSs of 24 notes.  Hemifourths tempers out 81:80 (like
meantone) and 49:48.  I don't think that gets you 225:224,
but maybe Gene can correct me on this.  The TOP tuning of
hemifourths has steps of 18 and 59 cents.  If the 18 cent
steps makes you balk, there's decimal.

TOP decimal's steps are 45 and 57 cents (which adds up to a
stretched octave of 1208 cents).  The result resembles
24-tET with decent 11:8s and neutral thirds, but there is
only 1 chain of (706-cent) fifths, and the 7ths are
substantially better at 758 cents (the 8 cents makes a
lot of difference in this region).

Another option would be a non-MOS "marvel" scale, I think.
Gene's the go-to man for that.

-Carl

From: Aaron Wolf (2006-05-06)
Subject: Re: Struggling to find a practical tuning for my goals

OH!  I guess I left out an extremely important detail:
I have OTHER plans in the long run for what I want to do in performance.
This is for creating computer/techno sequenced compositions that
won't ever likely get performed live!

Anyway, I'm not asking for the impossible, I'm presenting the
conflicts that I must compromise and asking for advice on how
to get a good balance.  For example, while I totally want and appreciate
both 10/9 and 9/8 and I don't want that comma tempered out, I want
to select (for the foreseeable near future) only one and access the other
via pitch bending the whole system.  So my thinking is stick with 9/8
and also have 5/3, and then when I want 10/9, I just bend the whole
system to be rooted on 4/3, and then the 5/3 becomes my 10/9.
Make sense?

I'm not looking for some weird esoteric temperament.  And as for the
near equal intervals ~50 cents, well that's a goal, a nicety, but that's
not at all the focus.  The idea is just to keep that in mind when working
out the system.

I've got some scales that could work already, but I'm not sure about some
things, and I'm looking more for feedback on whether people think this
is a good idea, and then I'll deal with getting the exact notes.

-Aaron

--- In [email protected], "Carl Lumma" <clumma@...> wrote:
>
> Hi Aaron,
> 
> If Gene can get his e-mail trouble sorted out, I'm sure he'll
> give you some great solutions.  In the meantime...
> 
> The way I understand it, you want 24 notes/octave, as
> evenly-spaced as possible (hopefully no steps smaller than
> 30 cents), with accurate 7-limit otonal harmony and possibly
> 225:224 tempered out.
> 
> That's a tall order.  I guess I don't understand the
> capabilities you have with choosing pitches from a larger
> set (60) during performance, or bending to desired pitches
> during performance.  Dealing with a fixed set of 24 pitches,
> you'll be forced to choose between accuracy and chromatic
> evenness.  You could perhaps do better with another number
> of notes/oct close to 24.
> 
> Anyway, assuming you do want to stick to 24 for piano-roll
> purposes, the "hemifourths" and "decimal" temperaments have
> MOSs of 24 notes.  Hemifourths tempers out 81:80 (like
> meantone) and 49:48.  I don't think that gets you 225:224,
> but maybe Gene can correct me on this.  The TOP tuning of
> hemifourths has steps of 18 and 59 cents.  If the 18 cent
> steps makes you balk, there's decimal.
> 
> TOP decimal's steps are 45 and 57 cents (which adds up to a
> stretched octave of 1208 cents).  The result resembles
> 24-tET with decent 11:8s and neutral thirds, but there is
> only 1 chain of (706-cent) fifths, and the 7ths are
> substantially better at 758 cents (the 8 cents makes a
> lot of difference in this region).
> 
> Another option would be a non-MOS "marvel" scale, I think.
> Gene's the go-to man for that.
> 
> -Carl
>

From: Carl Lumma (2006-05-06)
Subject: Re: Struggling to find a practical tuning for my goals

> I'm not looking for some weird esoteric temperament.

What I wrote may sound esoteric, but it isn't.

> I've got some scales that could work already,

Why don't you post them?  It would give us the best
idea what you're after.

-C.

From: Aaron Wolf (2006-05-06)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Carl Lumma" <clumma@...> wrote:
>
> > I'm not looking for some weird esoteric temperament.
> 
> What I wrote may sound esoteric, but it isn't.
> 
> > I've got some scales that could work already,
> 
> Why don't you post them?  It would give us the best
> idea what you're after.
> 
> -C.
>

Here's one point in a process.  Every time I go through it I feel like changing
something.  I'm just not sure.  What I've saved at the moment:

1/1
33/32
16/15 (was 17/16 yesterday)
35/32
9/8
7/6
11/9
5/4
9/7 (I'm not sure I'm into utonal 7s though)
4/3
11/8
7/5
23/16
3/2
14/9
8/5
5/3
12/7
7/4
9/5
15/8
31/16
[2/1]

Again, don't go with "Aaron requires a 24-note scale" or anything else
like that.  I'm thinking that will be more practical when trying to learn
to actually use this to make music within normal sequencer software.
I'm wanting to know if people who've gotten into this stuff think that
makes sense, or might there be other ways to learn to be comfortable
composing and making sense of things with a different number of
notes?  Really, I just wish I could have labels in the sequencer that
could be ratios instead of letter names or MIDI note numbers.  Then
I'd have no problem getting comfortable with any number of notes,
because I'd follow everything by the ratio name.

-Aaron

From: Keenan Pepper (2006-05-06)
Subject: Re: [tuning] Struggling to find a practical tuning for my goals

On 5/5/06, Aaron Wolf <[email protected]> wrote:
[...]
> I want to generally be near-just, and I also want a scale that is
> even *enough* to play chromatically in a way that sounds relatively
> smooth in direct ascent or descent.  In order to be manageable and
> have a decent range, I want to limit myself to a smaller number of
> notes.

Well, that about sums up the goals of "mainstream" tuning theory. You
can't have all three at the same time, but you can have any two:

near-just intervals + even scale -> complex temperaments, large-number edos
near-just intervals + small number of notes -> pure JI: hexanies etc.
even scale + small number of notes -> simple temperaments, small-number edos

And of course there are compromises that give you a decent blend of
all three, but the Fundamental Theorem of Arithmetic is at work here.

Of course, some people like Dan Stearns have no concern for any of the three. =P

[...]
> If I were to temper, I really don't want it to be too dramatic.  About
> the only thing I'd like to temper out is the 14/9 - 25/16 kleisma.
> And I'm leaning toward using simple fixed JI.

You can always use the 225/224 planar temperament, or something like
Schismatic or Miracle, which also temper out other intervals but they
are even smaller than 225/224.

[...]
> While I'd like to have 7/4, 16/9, and 9/5, they are too close together to
> sound evenly sequential without filling in 50+ total notes per octave.

Actually 41-edo does this very well. It's a pity, 41 is a really nice
temperament, but I can't remember a single piece written in it.

You don't even have to use 41 equal steps. You can use just intervals
that correspond to steps of 41-edo and large ranges of them come out
nice and even, for example:

10/9 9/8 8/7 7/6 32/27 6/5 11/9 5/4 81/64 9/7 21/16 4/3

There's always a Pythagorean interval in the middle, an interval of 5
on one side, and an interval of 7 on the other side, because 64/63 and
81/80 are tempered to the same thing. Even if you don't actually
temper anything it's a convenient way to organize pitches of just
intonation.

[...]

Keenan

From: Keenan Pepper (2006-05-06)
Subject: Re: [tuning] Re: Struggling to find a practical tuning for my goals

On 5/6/06, Aaron Wolf <[email protected]> wrote:
[...]
> notes?  Really, I just wish I could have labels in the sequencer that
> could be ratios instead of letter names or MIDI note numbers.  Then
> I'd have no problem getting comfortable with any number of notes,
> because I'd follow everything by the ratio name.

I got fed up with forgetting which key was which ratio, so I got a
bunch of little removable stickers and stuck them on the keys as
labels.

Keenan

From: Graham Breed (2006-05-06)
Subject: Re: [tuning] Re: Struggling to find a practical tuning for my goals

Aaron Wolf wrote:

> Here's one point in a process.  Every time I go through it I feel like changing
> something.  I'm just not sure.  What I've saved at the moment:
> 
> 1/1
> 33/32
> 16/15 (was 17/16 yesterday)
> 35/32
> 9/8
> 7/6
> 11/9
> 5/4
> 9/7 (I'm not sure I'm into utonal 7s though)

You could use 14/11 instead, but perhaps utonal 11s are even more evil.

> 4/3
> 11/8
> 7/5
> 23/16
> 3/2
> 14/9
> 8/5
> 5/3
> 12/7
> 7/4
> 9/5
> 15/8
> 31/16
> [2/1]
> 
> Again, don't go with "Aaron requires a 24-note scale" or anything else
> like that.  I'm thinking that will be more practical when trying to learn
> to actually use this to make music within normal sequencer software.
> I'm wanting to know if people who've gotten into this stuff think that
> makes sense, or might there be other ways to learn to be comfortable
> composing and making sense of things with a different number of
> notes?  Really, I just wish I could have labels in the sequencer that
> could be ratios instead of letter names or MIDI note numbers.  Then
> I'd have no problem getting comfortable with any number of notes,
> because I'd follow everything by the ratio name.

24 notes is practical.  I used to use it so that the keyboard fingerings 
would be consistent.  Eventually I moved on to a Ztar to get more notes, 
but I was still doing fine with 24.  I didn't bother about the sequencer 
labels because I ignored them.  To find where a particular note was, I 
pressed the key and the power of MIDI made that note light up on the 
piano roll.  Spanning multiple channels to get more notes is that bit 
less practical.

A blackjack+3 mapping would almost fulfil your criteria.  It's within 
10% of the accuracy you'd have by only tempering out 225:224 (your 14/9 
- 25/16 kleisma) and the smallest scale step is around 33 cents.  It 
works well in the 7-prime limit and has some 11-limit approximations as 
well.  It doesn't have any innate 24-ness.  Perhaps it would do as a 
stop-gap while you find out what harmonies you end up using and how you 
want to use the pitch bending.  Then you can find a just scale that 
works with the music you've actually written, which I expect would be 
more to your liking than an abstractly derived one.

Here's a description:

http://www.microtonal.co.uk/miracle/keyboard.html


                  Graham

From: Carl Lumma (2006-05-06)
Subject: Re: Struggling to find a practical tuning for my goals

> Again, don't go with "Aaron requires a 24-note scale" or
> anything else like that.

Well then, the gloves are off.  Blackjack (21 tones) might
be worth a shot, as Graham suggests.  And myna[23] would be
a strong possibility.

> Really, I just wish I could have labels in the sequencer that
> could be ratios instead of letter names or MIDI note numbers.  Then
> I'd have no problem getting comfortable with any number of notes,
> because I'd follow everything by the ratio name.

You know, there's a lot of noise about 'going beyond the 12-tone
system', but people forget that most music isn't 12-tone, but
7-tone.  So for my first microtonal adventures, I'm thinking
I'll go to 10 tones.

-Carl

From: Petr Parízek (2006-05-06)
Subject: Re: [tuning] Re: Struggling to find a practical tuning for my goals

Hi Aaron.

Actually, I've been experimenting with similar interval properties recently.
Unfortunately, I've not come to any meaningful results yet. As far as my
older results are concerned, they are only 5-limit. If you'd like to know
more about them, you can tell me. And for my other even older results, you
may look at scales like "parizek_qmtp24.scl", which is an irregular meantone
system, or "parizek_epi2a.scl", which has lots of otonal chords. You'll find
both of them in Manuel's scale archive.

Petr

From: Aaron Wolf (2006-05-06)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Keenan Pepper" <keenanpepper@...> wrote:
>
> On 5/5/06, Aaron Wolf <backfromthesilo@...> wrote:
> [...]
> > I want to generally be near-just, and I also want a scale that is
> > even *enough* to play chromatically in a way that sounds relatively
> > smooth in direct ascent or descent.  In order to be manageable and
> > have a decent range, I want to limit myself to a smaller number of
> > notes.
> 
> Well, that about sums up the goals of "mainstream" tuning theory. You
> can't have all three at the same time, but you can have any two:
> 
> near-just intervals + even scale -> complex temperaments,
large-number edos
> near-just intervals + small number of notes -> pure JI: hexanies etc.
> even scale + small number of notes -> simple temperaments,
small-number edos
> 

Yeah, but the thing you left out about my idea:
I want to focus on having a pretty even scale, and
near-just, BUT, the small number of notes is just for
a modal otonal incomplete system, because my idea
is to use pitch bend to shift key.  In other words,
I'd pitch ben the whole system through progressions
like I-IV-V-bVI-bVII-I or lots of other possibilities,
and within each pitch bended key, I'd have my selected
system of notes relative to that temporary key center,
so overall, I'm willing to have TONS of notes.  I just
don't want to bog my mind and sequencer interface and lose
octaves by having too many notes in the inherent MIDI tuning.

-Aaron

From: Ozan Yarman (2006-05-06)
Subject: Re: [tuning] Re: Struggling to find a practical tuning for my goals

Why don't you pick as many notes as you like from my 79-tone tuning as
delineated in

www.ozanyarman.com\anonymous\79tone.xls

?

It is circular, it is near-just, it has commas and everything, plus it can
be custom-tailored.

Oz.

----- Original Message -----
From: "Aaron Wolf" <[email protected]>
To: <[email protected]>
Sent: 06 May\ufffds 2006 Cumartesi 17:45
Subject: [tuning] Re: Struggling to find a practical tuning for my goals


> --- In [email protected], "Keenan Pepper" <keenanpepper@...> wrote:
> >
> > On 5/5/06, Aaron Wolf <backfromthesilo@...> wrote:
> > [...]
> > > I want to generally be near-just, and I also want a scale that is
> > > even *enough* to play chromatically in a way that sounds relatively
> > > smooth in direct ascent or descent.  In order to be manageable and
> > > have a decent range, I want to limit myself to a smaller number of
> > > notes.
> >
> > Well, that about sums up the goals of "mainstream" tuning theory. You
> > can't have all three at the same time, but you can have any two:
> >
> > near-just intervals + even scale -> complex temperaments,
> large-number edos
> > near-just intervals + small number of notes -> pure JI: hexanies etc.
> > even scale + small number of notes -> simple temperaments,
> small-number edos
> >
>
> Yeah, but the thing you left out about my idea:
> I want to focus on having a pretty even scale, and
> near-just, BUT, the small number of notes is just for
> a modal otonal incomplete system, because my idea
> is to use pitch bend to shift key.  In other words,
> I'd pitch ben the whole system through progressions
> like I-IV-V-bVI-bVII-I or lots of other possibilities,
> and within each pitch bended key, I'd have my selected
> system of notes relative to that temporary key center,
> so overall, I'm willing to have TONS of notes.  I just
> don't want to bog my mind and sequencer interface and lose
> octaves by having too many notes in the inherent MIDI tuning.
>
> -Aaron
>
>

From: Aaron Wolf (2006-05-06)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Keenan Pepper" <keenanpepper@...> wrote:
>
> On 5/6/06, Aaron Wolf <backfromthesilo@...> wrote:
> [...]
> > notes?  Really, I just wish I could have labels in the sequencer that
> > could be ratios instead of letter names or MIDI note numbers.  Then
> > I'd have no problem getting comfortable with any number of notes,
> > because I'd follow everything by the ratio name.
> 
> I got fed up with forgetting which key was which ratio, so I got a
> bunch of little removable stickers and stuck them on the keys as
> labels.
> 
> Keenan
>

Not a bad idea, but what about when going over recorded or
composed stuff on the computer screen?  I wish I could change
C2 to 4/3 or something and make that show up when I click
that note onscreen.

From: Carl Lumma (2006-05-06)
Subject: Re: Struggling to find a practical tuning for my goals

> Yeah, but the thing you left out about my idea:
> I want to focus on having a pretty even scale, and
> near-just, BUT, the small number of notes is just for
> a modal otonal incomplete system, because my idea
> is to use pitch bend to shift key.  In other words,
> I'd pitch ben the whole system through progressions
> like I-IV-V-bVI-bVII-I or lots of other possibilities,
> and within each pitch bended key, I'd have my selected
> system of notes relative to that temporary key center,
> so overall, I'm willing to have TONS of notes.  I just
> don't want to bog my mind and sequencer interface and lose
> octaves by having too many notes in the inherent MIDI tuning.

Why have 24 exposed, then?  Why not have 12 exposed and
bend from there?

-Carl

From: Keenan Pepper (2006-05-06)
Subject: Re: [tuning] Re: Struggling to find a practical tuning for my goals

On 5/6/06, Carl Lumma <[email protected]> wrote:
> You know, there's a lot of noise about 'going beyond the 12-tone
> system', but people forget that most music isn't 12-tone, but
> 7-tone.  So for my first microtonal adventures, I'm thinking
> I'll go to 10 tones.

This is a very good point. Everyone keeps talking about these giant
systems of hundreds or thousands of pitches, but I think a nice
consonant and melodically recognizable scale with 8, 9, or 10 pitches,
that can be perceived as a coherent unit as the diatonic scale can,
would go a lot farther towards comprehensible xenharmonic music.

A good test is how well you can sing it.

Keenan

From: Aaron Wolf (2006-05-06)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Carl Lumma" <clumma@...> wrote:
>
> > Yeah, but the thing you left out about my idea:
> > I want to focus on having a pretty even scale, and
> > near-just, BUT, the small number of notes is just for
> > a modal otonal incomplete system, because my idea
> > is to use pitch bend to shift key.  In other words,
> > I'd pitch ben the whole system through progressions
> > like I-IV-V-bVI-bVII-I or lots of other possibilities,
> > and within each pitch bended key, I'd have my selected
> > system of notes relative to that temporary key center,
> > so overall, I'm willing to have TONS of notes.  I just
> > don't want to bog my mind and sequencer interface and lose
> > octaves by having too many notes in the inherent MIDI tuning.
> 
> Why have 24 exposed, then?  Why not have 12 exposed and
> bend from there?
> 
> -Carl
>

That's not out of the question, but it's vastly more limiting.
What I'm going for is a system that will fulfill most of my
desires for various sorts of modal playing.
In other words, I want to get used to ONE system, that
might evolve over time, but doesn't change from piece
to piece.  And I'd like to have options to play modally
against a 1/1 drone, and select both 7/4 and 9/5, for
example.  And other issues like having something in
between 8/5 and 3/2 (likely 14/9).  24 exposed will allow
for a very large range once I then add the bending, and
allow for some shifting and exploring without bending.

See, it's similar to my barbershop studies...
It is very aurally clear when a shift away from tonic
occurs.  So when I want that effect, I can bend the
whole system.  But I want as much as I can practically
have of the notes that will not feel like a departure
from tonic.  So I guess emotionally, my goal is to
have my 24-note system include as much as possible
of notes that subjectively feel like tonic related
notes.  So I'm interested also in what anyone here
thinks that means to them.

To summarize (again, please criticize these parameters
if you think there's issues):

24 note system, somewhat consistent steps, focusing
on notes as closely related to 1/1 as possible, with
an otonal bias (but not strictly otonal).  Goal is
to then use pitch bend for harmonic movements that
intend to be felt as a departure from tonic.

Criticism I'm looking for could include statements
such as: "Don't be so concerned about equal steps,
you'll be happier including 7/4, 16/9, AND 9/5, all
three.  Try to use pitch bend as little as possible,
because it's annoying and non-intuitive"
or: "That sounds great, if you really get used to it,
having a few set pitch bend amounts for the whole system
could get very comfortable and natural"
Stuff like that from people who have been there before
me.  I appreciate all the feedback, thanks, everyone.

-Aaron

From: Aaron Wolf (2006-05-06)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Keenan Pepper" <keenanpepper@...> wrote:
>
> On 5/6/06, Carl Lumma <clumma@...> wrote:
> > You know, there's a lot of noise about 'going beyond the 12-tone
> > system', but people forget that most music isn't 12-tone, but
> > 7-tone.  So for my first microtonal adventures, I'm thinking
> > I'll go to 10 tones.
> 
> This is a very good point. Everyone keeps talking about these giant
> systems of hundreds or thousands of pitches, but I think a nice
> consonant and melodically recognizable scale with 8, 9, or 10 pitches,
> that can be perceived as a coherent unit as the diatonic scale can,
> would go a lot farther towards comprehensible xenharmonic music.
> 
> A good test is how well you can sing it.
> 
> Keenan
>

I agree fully.  My goal though is a system that I can
learn and get used to and not change all the time.
So one piece might use only 5 notes out of 24.  Another
might start like that and then shift to a different
set of 7 notes.  And I'd like to have lots of in-between
kinda passing notes.  It's like an unset instrument, like
voice or violin certainly does not stick to 5 or 7 set
notes ever.  But they might conceive of the notes as 5
basic notes that can be slightly sharper or flatter and
still be thought of as the same scale place.
Also, I want to be able to use consonant harmonies, a la
barbershop, such that even though 14/9 might not be a
perceived melodic note, I have access to it almost
in a way that will be perceived as a timbre change by
building up the harmony.

I think the main issue is my desire to get one "this
works for now" system for a number of pieces.
Just as an ET piano player or guitarist could stick to
a 7 note scale for one piece, when they are exploring
and composing it is meaningful to know that the other
notes are there and accessible.  That's what I am
hesitant to give up.  I just really don't want to have
a different tuning system for each piece.  At this point
in my life, I want to devise something I can accept, with
it's pros and cons both, and then make music and put all
the thinking about devising the system behind me and not
decide a new tuning all the time for each piece.

-Aaron

From: Gene Ward Smith (2006-05-07)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Carl Lumma" <clumma@...> wrote:
>
> Hi Aaron,
> 
> If Gene can get his e-mail trouble sorted out, I'm sure he'll
> give you some great solutions.  In the meantime...

Except I wasn't clear on what he really wanted.

> The way I understand it, you want 24 notes/octave, as
> evenly-spaced as possible (hopefully no steps smaller than
> 30 cents), with accurate 7-limit otonal harmony and possibly
> 225:224 tempered out.
> 
> That's a tall order.

It doesn't sound that bad. Blackjack, for instance, is a little
irregular in step size but otherwise seems to fit. Garibaldi[24] has
similar issues. There are a lot of good choices that stem from
tempering 5-limit JI via 225/224, however. It would be nice to have a
better idea what we're aiming at.

> Anyway, assuming you do want to stick to 24 for piano-roll
> purposes, the "hemifourths" and "decimal" temperaments have
> MOSs of 24 notes.  Hemifourths tempers out 81:80 (like
> meantone) and 49:48.  I don't think that gets you 225:224,
> but maybe Gene can correct me on this. 

It only does if you use 19-et for it, which isn't a bad plan. But
isn't this way too inaccurate for what he wants?

> Another option would be a non-MOS "marvel" scale, I think.
> Gene's the go-to man for that.
 
And I'd recommend it, but I want to know what, exactly, is wanted.

From: Yahya Abdal-Aziz (2006-05-07)
Subject: Re: Struggling to find a practical tuning for my goals

Hi all,

On Sat May 6, 2006, Keenan Pepper wrote: 
> 
> On 5/6/06, Carl Lumma wrote:
> > You know, there's a lot of noise about 'going beyond the 12-tone
> > system', but people forget that most music isn't 12-tone, but
> > 7-tone.  So for my first microtonal adventures, I'm thinking
> > I'll go to 10 tones.
> 
> This is a very good point. Everyone keeps talking about these giant
> systems of hundreds or thousands of pitches, but I think a nice
> consonant and melodically recognizable scale with 8, 9, or 10 pitches,
> that can be perceived as a coherent unit as the diatonic scale can,
> would go a lot farther towards comprehensible xenharmonic music.
> 
> A good test is how well you can sing it.
> 
> Keenan


Hear, hear!  (Please, Carl?)

I often play with 4-, 5-, or 6-note scales, since
I really do believe that "less is more".  Such 
small scales lend an immediate tonal coherence
to (what can be) otherwise fairly complex
rhythmic play.

Today, I've knocked up a small piano piece
based on a motif that came to me yesterday,
using an 8-note scale harmonised in perfect 
fourths.  The choice of scale notes is (somewhat) 
constrained by those fourths.  At present, it's 
only realised in 12-EDO, but just wait till I start 
bending those notes ...!

On Aaron's original question - I doubt that I'd
ever settle on "a" tuning that would meet all my 
goals.  But I really don't see why, today, we 
can't have the exact tuning we want for each 
and every piece.  (Setting aside, of course, trivial 
questions like *paying* for the instruments that
can implement them.)

Regards, 
Yahya


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From: Yahya Abdal-Aziz (2006-05-07)
Subject: Re: Struggling to find a practical tuning for my goals

Hi all,

Aaron Wolf wrote on Sat May 6, 2006: 
> 
> --- In [email protected], "Carl Lumma" <clumma@...> wrote:
> >
> > > Yeah, but the thing you left out about my idea:
> > > I want to focus on having a pretty even scale, and
> > > near-just, BUT, the small number of notes is just for
> > > a modal otonal incomplete system, because my idea
> > > is to use pitch bend to shift key.  In other words,
> > > I'd pitch ben the whole system through progressions
> > > like I-IV-V-bVI-bVII-I or lots of other possibilities,
> > > and within each pitch bended key, I'd have my selected
> > > system of notes relative to that temporary key center,
> > > so overall, I'm willing to have TONS of notes.  I just
> > > don't want to bog my mind and sequencer interface and lose
> > > octaves by having too many notes in the inherent MIDI tuning.
> > 
> > Why have 24 exposed, then?  Why not have 12 exposed and
> > bend from there?
> > 
> > -Carl
> >
> 
> That's not out of the question, but it's vastly more limiting.
> What I'm going for is a system that will fulfill most of my
> desires for various sorts of modal playing.
> In other words, I want to get used to ONE system, that
> might evolve over time, but doesn't change from piece
> to piece.  And I'd like to have options to play modally
> against a 1/1 drone, and select both 7/4 and 9/5, for
> example.  And other issues like having something in
> between 8/5 and 3/2 (likely 14/9).  24 exposed will allow
> for a very large range once I then add the bending, and
> allow for some shifting and exploring without bending.

Offhand, I'd say that exposing 22 srutis,
all just ratios, should about do it.  Unless,
of course, you intend to use many more 
than seven essential notes per octave in 
your scales.

 
> See, it's similar to my barbershop studies...
> It is very aurally clear when a shift away from tonic
> occurs.  So when I want that effect, I can bend the
> whole system.  But I want as much as I can practically
> have of the notes that will not feel like a departure
> from tonic.  So I guess emotionally, my goal is to
> have my 24-note system include as much as possible
> of notes that subjectively feel like tonic related
> notes.  So I'm interested also in what anyone here
> thinks that means to them.

To me, that means using notes that *are 
closely related* to the tonic.  F'rinstance,
I can just about hack an F# in C, considered
as the major third above a fourth below a 
fifth above the tonic.  But a C#, being the
major third above a fourth below a fourth 
below a fifth above the tonic, is getting 
remote.  When I'm playing a against a drone
on C, that is.  However, if the F# and C# are
chord notes that coincide with harmonics of
the more closely related D and A, they're
cool.


> To summarize (again, please criticize these parameters
> if you think there's issues):
> 
> 24 note system, somewhat consistent steps, focusing
> on notes as closely related to 1/1 as possible, with
> an otonal bias (but not strictly otonal).  Goal is
> to then use pitch bend for harmonic movements that
> intend to be felt as a departure from tonic.

Define closely related?  Eg, which is closer to C: 
 - B considered as the major third on the fifth, or 
 - B considered as five fifths?

Again, which is closer to C: 
 - Bb considered as the reduced seventh harmonic, or
 - Bb considered as the minor third above the fifth?

I think a lot depends on your feeling for what
is harmonically close.  Given that you enjoy using 
V - bVI - bVII - I, I'd say you have a reasonable
tolerance for utonalities.  Perhaps you'd have half
as much utonality as otonality, as many people do;
in that case, one would extend one's interval chains
further upwards than downwards.


> Criticism I'm looking for could include statements
> such as: "Don't be so concerned about equal steps,
> you'll be happier including 7/4, 16/9, AND 9/5, all
> three.  Try to use pitch bend as little as possible,
> because it's annoying and non-intuitive"

I suspect you're right on both counts!  
You do like pure harmonies, and IME pitch 
bend is only useful for (a) monophonic live 
playing or (b) automatic playing of complex 
textures.  (Unless you've got enough gear 
to bend only one line while playing the rest 
straight.)


> or: "That sounds great, if you really get used to it,
> having a few set pitch bend amounts for the whole system
> could get very comfortable and natural"

Don't see this.


> Stuff like that from people who have been there before
> me.  I appreciate all the feedback, thanks, everyone.
 
Aaron,

The more I read of your requirements, the 
more I'm convinced that only you have the 
actual answers you need.  But I do hope my 
thoughts may help a little.  The least I can 
do, in return for the pleasure your music 
has given me, is to offer those thoughts to 
you.

Regards, 
Yahya


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From: Gene Ward Smith (2006-05-07)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Keenan Pepper" <keenanpepper@...> wrote:

> Actually 41-edo does this very well. It's a pity, 41 is a really nice
> temperament, but I can't remember a single piece written in it.

I wrote one of my least memorable pieces in it. Anyone else?

From: Gene Ward Smith (2006-05-07)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Keenan Pepper" <keenanpepper@...> wrote:

> This is a very good point. Everyone keeps talking about these giant
> systems of hundreds or thousands of pitches, but I think a nice
> consonant and melodically recognizable scale with 8, 9, or 10 pitches,
> that can be perceived as a coherent unit as the diatonic scale can,
> would go a lot farther towards comprehensible xenharmonic music.

I don't think more notes makes it incomprehensible, it just makes you
lose your sense of a scale, since notes get merged together as
variations of the same note. If the harmony makes sense, the rest of
it will.

From: Aaron Wolf (2006-05-07)
Subject: Re: Struggling to find a practical tuning for my goals

> On Aaron's original question - I doubt that I'd
> ever settle on "a" tuning that would meet all my 
> goals.  But I really don't see why, today, we 
> can't have the exact tuning we want for each 
> and every piece.  (Setting aside, of course, trivial 
> questions like *paying* for the instruments that
> can implement them.)
> 
> Regards, 
> Yahya
> 

I realize that having "a" tuning isn't really a very reasonable idea in
some respects.  However, I'm concerned about two factors:

1. Being able to improvise and play around in order to determine
where I want a piece to go, and what notes I want to focus on for
that piece.  So I want a big enough range to allow for some exploration.

2. I want to get comfortable with a system so that I don't confuse which
notes are which from piece to piece.  If I really KNOW that I want a certain
set of notes for a piece, of course I'll just do that, and there's no question.
I'm looking for something where I'll create the system, play around, write
some piece and feel that even if I could imagine something else in the
piece that my system doesn't allow, I instead focus on what is possible
within my system, so I learn and get comfortable with the placement of
notes overall.  Hence, I want the system to be broad enough to be
satisfactory for lots of different modes, even if it doesn't cover everything.

It's similar to getting a custom-fretted instrument.  You get the setup
figured out, and then try to make as much music as you can on it.

I know I may change to something else later, but I'm looking for something
I can play with and get comfortable with for a long time.

-Aaron

From: Aaron Wolf (2006-05-07)
Subject: Re: Struggling to find a practical tuning for my goals

> Offhand, I'd say that exposing 22 srutis,
> all just ratios, should about do it.  Unless,
> of course, you intend to use many more 
> than seven essential notes per octave in 
> your scales.
> 

That's a good thought...

> To me, that means using notes that *are 
> closely related* to the tonic.  F'rinstance,
> I can just about hack an F# in C, considered
> as the major third above a fourth below a 
> fifth above the tonic.  But a C#, being the
> major third above a fourth below a fourth 
> below a fifth above the tonic, is getting 
> remote.  When I'm playing a against a drone
> on C, that is.  However, if the F# and C# are
> chord notes that coincide with harmonics of
> the more closely related D and A, they're
> cool.
> 

I think whereas MOST of my notes are to be harmonically related,
stuff like 33/32 and any not in between 7/5 and 3/2 are really
more of melodic function.  I like the idea of having some melodic
passing/leading tones that are dissonant on the way to the harmony.
This is really just to substitute for sliding a la what pitch bend is
normally used for.  I'm not as sure about this part, which is a lot of
the reason for the somewhat equal steps.  This is my least certain
aspect.

> Define closely related?  Eg, which is closer to C: 
>  - B considered as the major third on the fifth, or 
>  - B considered as five fifths?
> 

Definitely 15/8 not the bunch of fifths pythagorean one.

> Again, which is closer to C: 
>  - Bb considered as the reduced seventh harmonic, or
>  - Bb considered as the minor third above the fifth?
> 

In most cases the harmonic seventh.

> I think a lot depends on your feeling for what
> is harmonically close.  Given that you enjoy using 
> V - bVI - bVII - I, I'd say you have a reasonable
> tolerance for utonalities.  Perhaps you'd have half
> as much utonality as otonality, as many people do;
> in that case, one would extend one's interval chains
> further upwards than downwards.
> 

Oh, I love utonal PROGRESSIONS.  Meaning I like the idea of having
a high 1/1 and moving the bass to redefine the 1/1 as a different part
of the harmony, such as in the progression above.  But I don't like
utonal chords, like 8/7-4/3-8/5-1/1.  My thinking was to use pitch
bend on the whole system to create these utonally based PROGRESSIONS
and keep the note system that otherwise exists primarily otonal.
That make sense?

> 
> The more I read of your requirements, the 
> more I'm convinced that only you have the 
> actual answers you need.  But I do hope my 
> thoughts may help a little.  The least I can 
> do, in return for the pleasure your music 
> has given me, is to offer those thoughts to 
> you.
> 
> Regards, 
> Yahya
> 

Oh, I think you're certainly right.  I would say my goal in discussion is
to get criticism for my whole attitude and ideas so I question them, and
to be exposed to possibilities I hadn't known about or thought of.  In the
end, I think I do know what I want.  I just want to make sure my ideas
stand up to criticism and questioning, so I can solidify them and really
make some of these tough decisions.  Thanks for all the comments and
help, Yahya!

-Aaron

From: Aaron Wolf (2006-05-07)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Gene Ward Smith" <genewardsmith@...> wrote:
>
> --- In [email protected], "Keenan Pepper" <keenanpepper@> wrote:
> 
> > This is a very good point. Everyone keeps talking about these giant
> > systems of hundreds or thousands of pitches, but I think a nice
> > consonant and melodically recognizable scale with 8, 9, or 10 pitches,
> > that can be perceived as a coherent unit as the diatonic scale can,
> > would go a lot farther towards comprehensible xenharmonic music.
> 
> I don't think more notes makes it incomprehensible, it just makes you
> lose your sense of a scale, since notes get merged together as
> variations of the same note. If the harmony makes sense, the rest of
> it will.
>

Mainly, everything just needs to have clarity as having a place in the
order of things.  If you sense that a note is a return to a previous
"place" or that a sound has a function as going from one place to
another, then the music has clarity.  This is obviously a tonal attitude
(vs atonal perspectives).  Since these things are subjective, there's a
lot of leway as to how to acheive them.  Certainly a small number
of notes helps keep everything clear to the listener, but isn't the only
way.

From: Carl Lumma (2006-05-07)
Subject: Re: Struggling to find a practical tuning for my goals

> > To me, that means using notes that *are 
> > closely related* to the tonic.

Aaron, don't know how useful this will be, but I once
spent some time listening to intervals above a drone,
and came up with...

!
 Intervals of attraction, trial and error, Pennsburg 1999.
 22
!
 11/10 !.......165
 9/8 !.........204
 8/7 !.........231
 7/6 !.........267 ) 4
 6/5 !.........316
 11/9 !........347
 5/4 !.........386 ) 7
 9/7 !.........435
 4/3 !.........498
 11/8 !........551
 7/5 !.........583
 3/2 !.........702 ) 12
 11/7 !........783
 8/5 !.........814
 13/8 !........841
 5/3 !.........884
 12/7 !........933
 7/4 !.........969
 9/5 !........1018
 11/6 !.......1049
 15/8 !.......1088
 2/1 !........1200
!

-Carl

From: Aaron Wolf (2006-05-07)
Subject: Re: Struggling to find a practical tuning for my goals

Carl, that's awesome.  I am very interested in hearing about this sort
of thing.  That's exactly the sort of stuff I was hoping other experienced
microtonalists could share.  Hmm, 11/10... Yeah, that's worth considering...

-Aaron

--- In [email protected], "Carl Lumma" <clumma@...> wrote:
>
> > > To me, that means using notes that *are 
> > > closely related* to the tonic.
> 
> Aaron, don't know how useful this will be, but I once
> spent some time listening to intervals above a drone,
> and came up with...
> 
> !
>  Intervals of attraction, trial and error, Pennsburg 1999.
>  22
> !
>  11/10 !.......165
>  9/8 !.........204
>  8/7 !.........231
>  7/6 !.........267 ) 4
>  6/5 !.........316
>  11/9 !........347
>  5/4 !.........386 ) 7
>  9/7 !.........435
>  4/3 !.........498
>  11/8 !........551
>  7/5 !.........583
>  3/2 !.........702 ) 12
>  11/7 !........783
>  8/5 !.........814
>  13/8 !........841
>  5/3 !.........884
>  12/7 !........933
>  7/4 !.........969
>  9/5 !........1018
>  11/6 !.......1049
>  15/8 !.......1088
>  2/1 !........1200
> !
> 
> -Carl
>

From: Gene Ward Smith (2006-05-07)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Carl Lumma" <clumma@...> wrote:
>
> > > To me, that means using notes that *are 
> > > closely related* to the tonic.
> 
> Aaron, don't know how useful this will be, but I once
> spent some time listening to intervals above a drone,
> and came up with...

Interesting subset of the 15-limit diamond. 15/8, the overtone, makes
it in from the 15-limit, and nothing else, which makes sense, and the
same happens again with 13. The 11-limit diamond is missing 12/11,
10/9, 14/11, 10/7, 16/11, 14/9, 18/11, 16/9, 20/11, all of which have
an inversion in the octave which is is lower in Tenney height, and
which is included. It's sad to see 14/11 doesn't make your cut, as it
is a useful interval to have be attractive, and I am surprised 10/7
doesn't hold any attraction, and mystified as to why 11/10 is
attractive and 10/9 isn't. Maybe it's just more otonal.

The greatest Tenney height in the scale is 120, for 15/8. If we take
all rational numbers 1<=q<2 with Tenney height less than 121, we get a 
26 note scale. By reducing that figure down to less than 111, we get
the scale cons21.scl, already in the Scala archives because of a
different height measure, numerator+denominator < 21.

From: Carl Lumma (2006-05-08)
Subject: Re: Struggling to find a practical tuning for my goals

> The greatest Tenney height in the scale is 120, for 15/8. If we take
> all rational numbers 1<=q<2 with Tenney height less than 121, we get
> a 26 note scale. By reducing that figure down to less than 111, we
> get the scale cons21.scl, already in the Scala archives because of a
> different height measure, numerator+denominator < 21.

Good work, Gene.  Aaron, that (24-tone) scale is

! cons21.scl
!
 Set of intervals with num + den <= 21 not exceeding 2/1
 24
!
 11/10
 10/9
 9/8
 8/7
 7/6
 6/5
 11/9
 5/4
 9/7
 4/3
 11/8
 7/5
 10/7
 3/2
 11/7
 8/5
 13/8
 5/3
 12/7
 7/4
 9/5
 11/6
 13/7
 2/1
!

-Carl

From: Carl Lumma (2006-05-08)
Subject: Re: Struggling to find a practical tuning for my goals

Aaron,

Here's the "blackjack" FYI

! blackjack.scl
!
 21-note MOS of "MIRACLE" temperament, TL 2-5-2001
 21
!             G
 83.33333   ! G#v
 116.66667  ! Ab^
 200.00000  ! A
 233.33333  ! A>
 316.66667  ! Bb^
 350.00000  ! B[
 383.33333  ! Bv
 466.66667  ! C<
 500.00000  ! C
 583.33333  ! C#v
 616.66667  ! Db^
 700.00000  ! D
 733.33333  ! D>
 816.66667  ! Eb^
 850.00000  ! E[
 933.33333  ! E>
 966.66667  ! F<
 1050.00000 ! F]
 1083.33333 ! F#v
 1166.66667 ! G<
 2/1        ! G
!

Here's a JI version of the same scale

! blackjack_r.scl
!
 Rational "Wilson/Grady"-style version, Paul Erlich, TL 28-11-2001
 21
!
 21/20
 15/14
 9/8
 8/7
 6/5
 11/9
 5/4
 21/16
 4/3
 7/5
 10/7
 3/2
 32/21
 8/5
 18/11
 12/7
 7/4
 11/6
 15/8
 63/32
 2/1
!

-Carl

From: Carl Lumma (2006-05-08)
Subject: Re: Struggling to find a practical tuning for my goals

Last but not least, here's myna[23]

!
 myna[23], 7-limit TOP tuning (Paul Erlich).
 23
!
 40.73
 81.46
 187.7
 228.43
 269.16
 309.89
 350.62
 391.35
 497.59
 538.32
 579.05
 619.78
 880.51
 701.24
 807.48
 848.21
 888.94
 929.67
 970.4
 1011.13
 1117.37
 1158.1
 1198.83
!

Now if Gene cooks you a marvel[24], that'll wrap it up.
Then you just have to play with these and pick your fav!

-Carl

From: Carl Lumma (2006-05-08)
Subject: Re: Struggling to find a practical tuning for my goals

[I wrote...]
> Last but not least, here's myna[23]
> 
> !
>  myna[23], 7-limit TOP tuning (Paul Erlich).
>  23
> !
>  40.73
>  81.46
>  187.7
>  228.43
>  269.16
>  309.89
>  350.62
>  391.35
>  497.59
>  538.32
>  579.05
>  619.78
>  880.51
>  701.24
>  807.48
>  848.21
>  888.94
>  929.67
>  970.4
>  1011.13
>  1117.37
>  1158.1
>  1198.83
> !

Note the octaves here are just over 1 cent flat.

-Carl

From: Aaron Wolf (2006-05-08)
Subject: Re: Struggling to find a practical tuning for my goals

Carl,

Thanks for all the scales, I'll let you know  where I end up after I explore a bit.

-Aaron

From: Carl Lumma (2006-05-08)
Subject: Re: Struggling to find a practical tuning for my goals

> [I wrote...]
> > Last but not least, here's myna[23]
> > 
> > !
> >  myna[23], 7-limit TOP tuning (Paul Erlich).
> >  23
> > !
> >  40.73
> >  81.46
> >  187.7
> >  228.43
> >  269.16
> >  309.89
> >  350.62
> >  391.35
> >  497.59
> >  538.32
> >  579.05
> >  619.78
> >  880.51
> >  701.24
> >  807.48
> >  848.21
> >  888.94
> >  929.67
> >  970.4
> >  1011.13
> >  1117.37
> >  1158.1
> >  1198.83
> > !
> 
> Note the octaves here are just over 1 cent flat.
> 
> -Carl

Aaron - there's a typo above.  The thing below the 5th
should be 680.51 not 880.51.  A corrected version appears
below for easy cutting-and-pasting.

! myna[23].scl
!
 23 notes of myna temperament, 7-limit TOP tuning (Paul Erlich).
 23
!
 40.73
 81.46
 187.7
 228.43
 269.16
 309.89
 350.62
 391.35
 497.59
 538.32
 579.05
 619.78
 680.51
 701.24
 807.48
 848.21
 888.94
 929.67
 970.4
 1011.13
 1117.37
 1158.1
 1198.83
!

-Carl

From: Carl Lumma (2006-05-08)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Carl Lumma" <clumma@...> wrote:
>
> > [I wrote...]
> > > Last but not least, here's myna[23]
> > > 
> > > !
> > >  myna[23], 7-limit TOP tuning (Paul Erlich).
> > >  23
> > > !
> > >  40.73
> > >  81.46
> > >  187.7
> > >  228.43
> > >  269.16
> > >  309.89
> > >  350.62
> > >  391.35
> > >  497.59
> > >  538.32
> > >  579.05
> > >  619.78
> > >  880.51
> > >  701.24
> > >  807.48
> > >  848.21
> > >  888.94
> > >  929.67
> > >  970.4
> > >  1011.13
> > >  1117.37
> > >  1158.1
> > >  1198.83
> > > !
> > 
> > Note the octaves here are just over 1 cent flat.
> > 
> > -Carl
> 
> Aaron - there's a typo above.  The thing below the 5th
> should be 680.51 not 880.51.  A corrected version appears
> below for easy cutting-and-pasting.

$@#!&%&, make that 660.51.

! myna[23].scl
!
 23 notes of myna temperament, 7-limit TOP tuning (Paul Erlich).
 23
!
 40.73
 81.46
 187.7
 228.43
 269.16
 309.89
 350.62
 391.35
 497.59
 538.32
 579.05
 619.78
 660.51
 701.24
 807.48
 848.21
 888.94
 929.67
 970.4
 1011.13
 1117.37
 1158.1
 1198.83
!

-Carl

From: Kraig Grady (2006-05-08)
Subject: Re: Struggling to find a practical tuning for my goals

The scale that Erv uses the most for his everyday exploration of 
traditional type melody and harmonies (being his own ear extension of 
the results of boomliter and creel is).
 http://anaphoria.com/evangelina.PDF
if more interested in utonality scales one can use the inverse of this.
 boomsliter and creel basically resulted in the 22 shutis as being what 
the western ear wants to hear
>
>
>   

-- 
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

From: Carl Lumma (2006-05-08)
Subject: Re: Struggling to find a practical tuning for my goals

[Kraig wrote...]
> The scale that Erv uses the most for his everyday exploration of 
> traditional type melody and harmonies (being his own ear
> extension of the results of boomliter and creel is).
>  http://anaphoria.com/evangelina.PDF
> if more interested in utonality scales one can use the inverse
> of this.

Here's a Scala file for convenience

! evangelina.scl
!
 Erv Wilson's everyday go-to scale (Kraig Grady, T66325).
 22
!
 135/128
 13/12
 10/9
 9/8
 7/6
 11/9
 5/4
 81/64
 4/3
 11/8
 45/32
 17/12
 3/2
 405/256
 13/8
 5/3
 27/16
 7/4
 11/6
 15/8
 243/128
 2
!

Except I noticed that the tubulong and uath settings differ
by a single note.  Above is the tubulong version, which
has 243/128 instead of 23/12.  Kraig, know anything about
this?

-Carl

From: Aaron Wolf (2006-05-08)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], Kraig Grady <kraiggrady@...> wrote:
>
> The scale that Erv uses the most for his everyday exploration of 
> traditional type melody and harmonies (being his own ear extension of 
> the results of boomliter and creel is).
>  http://anaphoria.com/evangelina.PDF
> if more interested in utonality scales one can use the inverse of this.
>  boomsliter and creel basically resulted in the 22 shutis as being what 
> the western ear wants to hear
> >
> >
> >   
> 
> -- 
> Kraig Grady
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
> The Wandering Medicine Show
> KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles
>

Thanks!

From: George D. Secor (2006-05-08)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Aaron Wolf" <backfromthesilo@...> 
wrote:
>
> Greetings everyone,
> 
> While I continue to plan for ways to realize an acoustically based 
> instrument that will meet my goals, I'm starting to experiment with 
> synth tuning stuff.  I recently got Max Magic Microtuner and I'm 
> trying to find a balanced, compromised tuning that will be a useful 
> compositional field to explore and reach the goals I have.
> 
> Here's where I'm at:
> 
> I want to generally be near-just, and I also want a scale that is 
> even *enough* to play chromatically in a way that sounds relatively 
> smooth in direct ascent or descent.  In order to be manageable and 
> have a decent range, I want to limit myself to a smaller number of 
> notes.

Hi Aaron,

I've been away from the lists for a few days, so I didn't see this 
until today.  What you're seeking sounds quite similar to something I 
was trying to achieve in 1975.  My 13-limit high-tolerance 
temperament (HTT) supplies multiple otonal ogdoads, i.e., very close 
approximations of 8:9:10:11:12:13:14:15, on various starting tones.  
For details see:

http://groups.yahoo.com/group/MakeMicroMusic/messages/6847
which references another message with .scl data:
http://groups.yahoo.com/group/tuning-math/message/7574
A later message gives some information about the tempering:
http://groups.yahoo.com/group/tuning-math/message/10586

> ...
> Additionally, simply to keep everything straight and work with 
> standard sequencers layouts, I figured that using exactly 24 notes 
> would be a good balance because I'd have much more to work with 
> than using only 12, but I can still easily realte things in terms 
of the 
> names and positions they will be in a standard sequencer piano roll.

As it turned out I didn't end up with 24 tones/octave, but how about 
17 and 29-tone subsets of a 41-tone superset (all of which are 
constant structures)?

In the 29-tone HTT subset, the starting tones on which the ogdoads 
occur are Bb, F, C, G, D, and A, so you can modulate quite a bit 
without having to resort to pitch-changing on the fly (which leaves 
the door open for acoustic instruments).  The tones are reasonably 
spaced for melodic purposes, and there are multiple pairs of tones 
separated by the 80:81 comma.

I have the 29-HTT subset as one of the six hard-wired tunings in my 
generalized-keyboard Scalatron.  In the fall of 1975 I performed an 
improvisation on that instrument in this tuning, which I shared on 
MMM:
http://groups.yahoo.com/group/MakeMicroMusic/message/6889
The .mp3 file is no longer at the link indicated, but if you're 
interested in hearing it, I could put it back for a few days.

> I'm looking for constructive criticism.  I want to end up with a 
balance 
> where I know what I've compromised, but I have a decent little 
universe
>  of music to explore, especially using the idea of pitch bending to 
> any new key.

In a 17-tone subset (which I also call the "triple delight") the 
starting tones for ogdoads are in a chain of neutral 3rds (F, A-
semiflat, and C) -- yes, that's 3 otonal ogdoads in 17-tones/octave!  
This subset can be transposed in a manner similar to your idea of 
pitch-bending:  Changing only 3 of the 17 pitches will transpose the 
tuning up a neutral 3rd (new starting tones A-semiflat, C, and E-
semiflat).  Change 3 more pitches to transpose up a fifth above the 
starting set (C, E-semiflat, and G), or 3 more pitches to transpose a 
neutral 6th above the starting set (E-semiflat, G, and B-semiflat), 
etc., etc.  Although there are no two pitches differing by ~80:81 
within a 17-tone subset, changing the pitches by threes will result 
in comma-shifts.  In addition, since there are a lot of neutral 3rds 
in a 17-tone subset, it's possible to come up with some very 
unconventional chord progressions.

I have a 2-2/3-octave set of aluminum tubulongs (tubular bells) in 
the 17-tone triple delight that I made in 1979 (not permanently 
mounted, however), which will make the point that HTT doesn't limit 
me to electronics.

One drawback I have found with the 17-tone subsets is that the 
melodic spacing of the tones is not as uniform as I would like.

> If I were to temper, I really don't want it to be too dramatic.  
About 
> the only thing I'd like to temper out is the 14/9 - 25/16 kleisma.  
> And I'm leaning toward using simple fixed JI.

The tempering in HTT is so slight that you would be hard pressed to 
tell that it's not JI!

> I'd absolutely minimally have 7-prime-limit and have decent focus 
on 
> 9 and 15.  Overall, I'm wanting to go essentially otonal.  I'd like 
to 
> explore 11 and 13, though I'm less confident with them.  

HTT treats 11's and 13's as being in a single sequence of fifths, 
e.g., 11/8 of F is the same pitch as 13/8 of D, where the F and D are 
in the same sequence of fifths.  Likewise, 7's are also in the same 
sequence of fifths as the 11's and 13's, so that 7/4 of Bb is the 
same pitch as 11/8 of D.  Thus, there are quite a few possibilities 
for common-tone modulations.

> I'd even like 
> to have 17 or 19, but I'm leaning towards making those the 
exception 
> that I'd have to do extra junk to get to, and not have them in my 
> normal system.  

The 29-HTT has an Eb that's almost exactly 19/16 of C (purely by 
accident).  Anything else above the 13 limit would have to be 
approximated.

> ...
> While I'd like to have 7/4, 16/9, and 9/5, they are too close 
together to 
> sound evenly sequential without filling in 50+ total notes per 
octave.  
> I'd like to see every step in the scale be around 30-75 cents, 
ideally closer 
> to 50 to make the scale even.  My thinking was to use 7/4 and 9/5, 
and 
> leave 16/9 as a note I would get to by pitch bending the whole 
system to 
> 4/3 or 16/9 or something else where 16/9 would then exist relative 
to 
> the original 1/1.  

Since HTT is basically otonal, it has close approximations of both 
7/4 and 16/9, but not 9/5.  If you want a just minor 7th chord, you 
would need to use 5/3, 1/1, 5/4, 3/2.

The smallest intervals in 29-HTT are 24 cents, and the smallest ones 
in the 41-tone superset are around 19 cents.

> ...
> So in addition to help on the specifics, I'm hoping to get feedback 
on 
> whether people think my approach and attitude is reasonable.

It's indeed a struggle to find the one tuning that will "do it all" 
for you, so I hope that the above information may be helpful to you 
in some way.

Best,

--George

From: Gene Ward Smith (2006-05-09)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Carl Lumma" <clumma@...> wrote:
>
> Last but not least, here's myna[23]
> 
> !
>  myna[23], 7-limit TOP tuning (Paul Erlich).
>  23
> !
>  40.73
>  81.46
>  187.7
>  228.43
>  269.16
>  309.89
>  350.62
>  391.35
>  497.59
>  538.32
>  579.05
>  619.78
>  880.51
>  701.24
>  807.48
>  848.21
>  888.94
>  929.67
>  970.4
>  1011.13
>  1117.37
>  1158.1
>  1198.83
> !
> 
> Now if Gene cooks you a marvel[24], that'll wrap it up.
> Then you just have to play with these and pick your fav!

Here ya go:

! miracle24.scl
Miracle[24] in 72-et tuning
24
!
33.333333
83.333333
116.666667
150.000000
233.333333
266.666667
350.000000
383.333333
466.666667
500.000000
583.333333
616.666667
700.000000
733.333333
816.666667
850.000000
933.333333
966.666667
1000.000000
1050.000000
1083.333333
1116.666667
1166.666667
1200.000000

Let's not forget Garibaldi[24]. This is already in the Scala archives
as 24-94.scl, but here is a transposed version with otonal tetrads
moved to the 1/1 region:

! garibaldi24.scl
Garibaldi[24] in 94-et tuning
24
!
63.829787
89.361702
178.723404
204.255319
268.085106
293.617021
382.978723
408.510638
472.340426
497.872340
561.702128
587.234043
676.595745
702.127660
765.957447
791.489362
880.851064
906.382979
970.212766
995.744681
1085.106383
1110.638298
1174.468085
1200.000000

People who want less tempering might consider Hemiwuerschmidt[24].
Hemiweurschmidt has a 25-note MOS, so this has a single anomalous
larger step, but that doesn't seem like much of a reason to worry.

! hemiwuer24.scl
Hemiwurschmidt[24] in 229-et tuning
24
!
83.842795
120.524017
157.205240
193.886463
277.729258
314.410480
351.091703
387.772926
508.296943
544.978166
581.659389
618.340611
702.183406
738.864629
775.545852
812.227074
896.069869
932.751092
969.432314
1006.113537
1089.956332
1126.637555
1163.318777
1200.000000

From: Gene Ward Smith (2006-05-09)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Carl Lumma" <clumma@...> wrote:

> Here's a Scala file for convenience
> 
> ! evangelina.scl
> !
>  Erv Wilson's everyday go-to scale (Kraig Grady, T66325).
>  22

If we aren't sticking to exactly 24 notes, here's another one to
consider. Loads of harmony.

! dwarf25marv.scl
Marvelous Dwarf: 1/4 kleismic dwarf(<25 40 58|) = genus(15^4)
25
!
68.744546
115.587047
184.331593
253.076139
268.798786
299.918640
315.641287
384.385833
453.130379
499.972880
568.717426
615.559927
653.184619
684.304473
700.027120
768.771666
815.614167
884.358713
953.103259
999.945760
1068.690306
1084.412953
1115.532807
1153.157499
1200.000000
! eighteen tetrads/pentads representible by
! [[0, 0, 2], [1, -1, -1], [2, -2, 1], [0, -1, 1], [1, -1, 0], [1, -2, 0],
! [1, -2, 1], [1, -1, 1], [0, -2, -1], [0, -2, 0], [0, 0, 1], [0, -1, 0], 
! [0, -1, -1], [1, -2, -2], [0, -1, -2], [1, -2, -1], [2, -2, 2], [1,
-1, 2]]

From: Carl Lumma (2006-05-09)
Subject: Re: Struggling to find a practical tuning for my goals

> > Now if Gene cooks you a marvel[24], that'll wrap it up.
> > Then you just have to play with these and pick your fav!
> 
> Here ya go:
> 
> ! miracle24.scl
> Miracle[24] in 72-et tuning
> 24
> !
> 33.333333
> 83.333333
> 116.666667
> 150.000000
> 233.333333
> 266.666667
> 350.000000
> 383.333333
> 466.666667
> 500.000000
> 583.333333
> 616.666667
> 700.000000
> 733.333333
> 816.666667
> 850.000000
> 933.333333
> 966.666667
> 1000.000000
> 1050.000000
> 1083.333333
> 1116.666667
> 1166.666667
> 1200.000000

Is 72 the best marvel tuning?

> Let's not forget Garibaldi[24].

Did this ever have another name?

-C.

From: Carl Lumma (2006-05-09)
Subject: Re: Struggling to find a practical tuning for my goals

> > Now if Gene cooks you a marvel[24], that'll wrap it up.
> > Then you just have to play with these and pick your fav!
> 
> Here ya go:
> 
> ! miracle24.scl
> Miracle[24] in 72-et tuning
> 24
> !
> 33.333333
> 83.333333
> 116.666667
> 150.000000
> 233.333333
> 266.666667
> 350.000000
> 383.333333
> 466.666667
> 500.000000
> 583.333333
> 616.666667
> 700.000000
> 733.333333
> 816.666667
> 850.000000
> 933.333333
> 966.666667
> 1000.000000
> 1050.000000
> 1083.333333
> 1116.666667
> 1166.666667
> 1200.000000

Is 72 the best marvel tuning?

> Let's not forget Garibaldi[24].

Did this ever have another name?

-C.

From: Gene Ward Smith (2006-05-09)
Subject: Re: Struggling to find a practical tuning for my goals

--- In [email protected], "Carl Lumma" <clumma@...> wrote:

> Is 72 the best marvel tuning?

If you are only interested in the 7-limit you might prefer 175-et;
I've used it for that purpose. Woolhouse's 730-et is not only a great
5-limit tuning, it's a great miracle tuning for 11-limit miracle.

> > Let's not forget Garibaldi[24].
> 
> Did this ever have another name?

It formerly got called 7-limit schismic.

From: Kraig Grady (2006-05-09)
Subject: Re: Struggling to find a practical tuning for my goals

True Erv had me make this tubes a couple of years ago and alternates 
between the two.
 He has found he like the sound of the 23 harmonic as apart of his 
cadences (saying that he finds people use different ratios in different 
contexts.

Message 5 From: "Carl Lumma" 
Except I noticed that the tubulong and uath settings differ by a single 
note. Above is the tubulong version, which has 243/128 instead of 23/12. 
Kraig, know anything about this?
-- 
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles