Voicing jazz chords in JI and 41/53/72 ET for dummies?

I should've learned this long ago, but is there a guide to voicing and tuning complex chords in a non-meantone tuning? I'm experimenting and doing calculations right now, but I'm sure someone's already did work on this topic.

An example: the major 6/9 chord, and I'll use 72 equal temperament here. The major triad a no-brainer if you want 4:5:6 - 0:23:42, or in C, C Ev G in ASCIIzed Richter-Herf notation as used by Scala. The major sixth would be best voiced as 0:23:42:53, or C E\ G A\, A-54 would give you a wolf fifth.

And the ninth (D) could be either 83 or 84, but D-83 gives you a wolf fifth (G-D\) and D-84 gives you a wolf fourth (A\-D). Which major ninth to chose would depend on what chord you're progressing towards or out of, but the best bet would seem to be D-84, if you compare the ninth to the other three notes in the chord. C-D is equivalent to 9/4 while C-D\ is to 20/9. E\-D is equivalent to 9/5 while E\-D\ is to 16/9. G-D is 3/4 while G-D\ is a wolf fifth (40/27). A\-D\ is a perfect fourth (4/3) while A\-D is a wolf fourth (27/20). D is more stable with three of the four other notes while D\ is more stable with only one - so my recommended voicing is 0:23:46:57:84.

I tested the chords with both the 83 and 84-comma ninths in Scala and the 84-comma one sounded smoother. But that's just one example. I still need to test all the other chords, and then do chords with neutral, subminor and supermajor intervals that can't be played in 12-tone tuning.

By the way, I voice the so-called "Hendrix chord", 7#9no5, as 0:23:58:88, which can also be an Italian sixth with an added augmented ninth. One of my favorite chords is the same chord plus an augmented fourth, 0:23:35:58:88 - that would be a French sixth plus augmented ninth, or Wagner's "Tristan chord" plus major third.

~D.

Hey Danny,

I am by no means an authority on this, but I've been tackling the same
question myself for the past few months. Here's what I've arrived at:

Chords like C E G Bb D F# (C7#11) can be voiced a few different ways
in JI, and all are equally valid, and all sound slightly different.
Just like a C7 can be voiced as 4:5:6 with the 7 at 7/4 or voiced as
4:5:6 with the 7 at 9/5, there are different ways to voice C7#11.

1) You can do 4:5:6:7:9:11
2) You can make the D-F# dyad a 5/4
3) You can make the D-F# dyad a 9/7

The last one has a very bright and almost sad quality to it.
Furthermore, when you hear these chords played in a big band (say in a
brass section), they will often adjust the intonation to one or more
of these. Sometimes I hear the #11 played as an 11/4, and sometimes I
hear it as a 5/4 over a 9/8, and sometimes I hear it as a 9/7 over a
9/8. Subtle microtonal inflections bring out different feelings, and
since no such authority exists right now, you sort of get to invent
it.

The other thing, and the one that I find infinitely more interesting,
is that even within the context of 12-tet (say on a piano), I've heard
a huge range of JI chords IMPLIED by the same 12-tet voicing. So in
our C7#11 example, there are ways to play that chord on a piano and
hear it as a mistuned version of 4:5:6:7:9:11, or the 5/4 over 9/8 on
top, or any of the other options up there. The way the chord is
voiced, the surrounding chords, the voice leading, and sometimes even
the musical context and thematic setting all contribute to how you'll
perceive that chord as functioning or existing.

I can't speak for anyone else about that last bit, but that is how it
appears to me. Hope this helps you out.

-Mike

On Mon, Sep 22, 2008 at 4:35 PM, Danny Wier <dawiertx@...> wrote:
> I should've learned this long ago, but is there a guide to voicing and
> tuning complex chords in a non-meantone tuning? I'm experimenting and
> doing calculations right now, but I'm sure someone's already did work on
> this topic.
>
> An example: the major 6/9 chord, and I'll use 72 equal temperament here.
> The major triad a no-brainer if you want 4:5:6 - 0:23:42, or in C, C Ev
> G in ASCIIzed Richter-Herf notation as used by Scala. The major sixth
> would be best voiced as 0:23:42:53, or C E\ G A\, A-54 would give you a
> wolf fifth.
>
> And the ninth (D) could be either 83 or 84, but D-83 gives you a wolf
> fifth (G-D\) and D-84 gives you a wolf fourth (A\-D). Which major ninth
> to chose would depend on what chord you're progressing towards or out
> of, but the best bet would seem to be D-84, if you compare the ninth to
> the other three notes in the chord. C-D is equivalent to 9/4 while C-D\
> is to 20/9. E\-D is equivalent to 9/5 while E\-D\ is to 16/9. G-D is 3/4
> while G-D\ is a wolf fifth (40/27). A\-D\ is a perfect fourth (4/3)
> while A\-D is a wolf fourth (27/20). D is more stable with three of the
> four other notes while D\ is more stable with only one - so my
> recommended voicing is 0:23:46:57:84.
>
> I tested the chords with both the 83 and 84-comma ninths in Scala and
> the 84-comma one sounded smoother. But that's just one example. I still
> need to test all the other chords, and then do chords with neutral,
> subminor and supermajor intervals that can't be played in 12-tone tuning.
>
> By the way, I voice the so-called "Hendrix chord", 7#9no5, as
> 0:23:58:88, which can also be an Italian sixth with an added augmented
> ninth. One of my favorite chords is the same chord plus an augmented
> fourth, 0:23:35:58:88 - that would be a French sixth plus augmented
> ninth, or Wagner's "Tristan chord" plus major third.
>
> ~D.
>
>

Or, to drive the point home even further, consider this chord:

C Eb G Bb D F A C

If you have each minor third dyad in there as 6/5 and each major third
as 5/4, the C you arrive at on top will actually be 81/80 sharp of
2/1. If you put 2/1 in there, it will give a different sound -- a much
more restful character for the C-c dyad but a little bit more
dissonance between the A and C. The first one sounds like a chord
extension (continuing the 7th-9th-11th-13th progression to the 15th)
and the second one sounds like a benign doubling of the root note by
two octaves.

In the same way, if you're playing the following chord:

C Eb F Bb

If the C-Eb is a 6/5, and the Eb-Bb is a 3/2, then where do we put the
F? We could make C-F a 4/3, or F-Bb a 4/3 - but not both. And they're
both valid - the two simply sound different. The C-F as 4/3 sounds
much more placid and relaxed, and the F-Bb sounds more excited and
maybe even a bit agitated or tense to my ears -- as if it is a chord
forcefully extruding out into some direction.

What we're doing by getting used to the different qualities of sound
of intervals that might be wider or narrower by a comma is analogous
to what Bach did by getting used to the sound of the tritone, imo.

-Mike

On Mon, Sep 22, 2008 at 7:23 PM, Mike Battaglia <battaglia01@...> wrote:
> Hey Danny,
>
> I am by no means an authority on this, but I've been tackling the same
> question myself for the past few months. Here's what I've arrived at:
>
> Chords like C E G Bb D F# (C7#11) can be voiced a few different ways
> in JI, and all are equally valid, and all sound slightly different.
> Just like a C7 can be voiced as 4:5:6 with the 7 at 7/4 or voiced as
> 4:5:6 with the 7 at 9/5, there are different ways to voice C7#11.
>
> 1) You can do 4:5:6:7:9:11
> 2) You can make the D-F# dyad a 5/4
> 3) You can make the D-F# dyad a 9/7
>
> The last one has a very bright and almost sad quality to it.
> Furthermore, when you hear these chords played in a big band (say in a
> brass section), they will often adjust the intonation to one or more
> of these. Sometimes I hear the #11 played as an 11/4, and sometimes I
> hear it as a 5/4 over a 9/8, and sometimes I hear it as a 9/7 over a
> 9/8. Subtle microtonal inflections bring out different feelings, and
> since no such authority exists right now, you sort of get to invent
> it.
>
> The other thing, and the one that I find infinitely more interesting,
> is that even within the context of 12-tet (say on a piano), I've heard
> a huge range of JI chords IMPLIED by the same 12-tet voicing. So in
> our C7#11 example, there are ways to play that chord on a piano and
> hear it as a mistuned version of 4:5:6:7:9:11, or the 5/4 over 9/8 on
> top, or any of the other options up there. The way the chord is
> voiced, the surrounding chords, the voice leading, and sometimes even
> the musical context and thematic setting all contribute to how you'll
> perceive that chord as functioning or existing.
>
> I can't speak for anyone else about that last bit, but that is how it
> appears to me. Hope this helps you out.
>
> -Mike
>
> On Mon, Sep 22, 2008 at 4:35 PM, Danny Wier <dawiertx@...> wrote:
>> I should've learned this long ago, but is there a guide to voicing and
>> tuning complex chords in a non-meantone tuning? I'm experimenting and
>> doing calculations right now, but I'm sure someone's already did work on
>> this topic.
>>
>> An example: the major 6/9 chord, and I'll use 72 equal temperament here.
>> The major triad a no-brainer if you want 4:5:6 - 0:23:42, or in C, C Ev
>> G in ASCIIzed Richter-Herf notation as used by Scala. The major sixth
>> would be best voiced as 0:23:42:53, or C E\ G A\, A-54 would give you a
>> wolf fifth.
>>
>> And the ninth (D) could be either 83 or 84, but D-83 gives you a wolf
>> fifth (G-D\) and D-84 gives you a wolf fourth (A\-D). Which major ninth
>> to chose would depend on what chord you're progressing towards or out
>> of, but the best bet would seem to be D-84, if you compare the ninth to
>> the other three notes in the chord. C-D is equivalent to 9/4 while C-D\
>> is to 20/9. E\-D is equivalent to 9/5 while E\-D\ is to 16/9. G-D is 3/4
>> while G-D\ is a wolf fifth (40/27). A\-D\ is a perfect fourth (4/3)
>> while A\-D is a wolf fourth (27/20). D is more stable with three of the
>> four other notes while D\ is more stable with only one - so my
>> recommended voicing is 0:23:46:57:84.
>>
>> I tested the chords with both the 83 and 84-comma ninths in Scala and
>> the 84-comma one sounded smoother. But that's just one example. I still
>> need to test all the other chords, and then do chords with neutral,
>> subminor and supermajor intervals that can't be played in 12-tone tuning.
>>
>> By the way, I voice the so-called "Hendrix chord", 7#9no5, as
>> 0:23:58:88, which can also be an Italian sixth with an added augmented
>> ninth. One of my favorite chords is the same chord plus an augmented
>> fourth, 0:23:35:58:88 - that would be a French sixth plus augmented
>> ninth, or Wagner's "Tristan chord" plus major third.
>>
>> ~D.
>>
>>
>

An interesting aspects of Bach spacings of chords often were not what Helmholtz concluded would be the most 'consonant' in his counterpuntal music. Context will always decide more than such a priori decisions. But we still like to have somethings to start with. I did quite a few pieces on different inversions of 4 note chords out of the first 12 harmonics and ran across much unexpected material that i found useful. To play through all the inversions will get to allot of things that theory will not. The down fall of this method is one is always influenced by what one played before and after which merely supports the influence of context.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> Or, to drive the point home even further, consider this chord:
>
> C Eb G Bb D F A C
>
> If you have each minor third dyad in there as 6/5 and each major third
> as 5/4, the C you arrive at on top will actually be 81/80 sharp of
> 2/1. If you put 2/1 in there, it will give a different sound -- a much
> more restful character for the C-c dyad but a little bit more
> dissonance between the A and C. The first one sounds like a chord
> extension (continuing the 7th-9th-11th-13th progression to the 15th)
> and the second one sounds like a benign doubling of the root note by
> two octaves.
>
> In the same way, if you're playing the following chord:
>
> C Eb F Bb
>
> If the C-Eb is a 6/5, and the Eb-Bb is a 3/2, then where do we put the
> F? We could make C-F a 4/3, or F-Bb a 4/3 - but not both. And they're
> both valid - the two simply sound different. The C-F as 4/3 sounds
> much more placid and relaxed, and the F-Bb sounds more excited and
> maybe even a bit agitated or tense to my ears -- as if it is a chord
> forcefully extruding out into some direction.
>
> What we're doing by getting used to the different qualities of sound
> of intervals that might be wider or narrower by a comma is analogous
> to what Bach did by getting used to the sound of the tritone, imo.
>
> -Mike
>
> On Mon, Sep 22, 2008 at 7:23 PM, Mike Battaglia <battaglia01@... > <mailto:battaglia01%40gmail.com>> wrote:
> > Hey Danny,
> >
> > I am by no means an authority on this, but I've been tackling the same
> > question myself for the past few months. Here's what I've arrived at:
> >
> > Chords like C E G Bb D F# (C7#11) can be voiced a few different ways
> > in JI, and all are equally valid, and all sound slightly different.
> > Just like a C7 can be voiced as 4:5:6 with the 7 at 7/4 or voiced as
> > 4:5:6 with the 7 at 9/5, there are different ways to voice C7#11.
> >
> > 1) You can do 4:5:6:7:9:11
> > 2) You can make the D-F# dyad a 5/4
> > 3) You can make the D-F# dyad a 9/7
> >
> > The last one has a very bright and almost sad quality to it.
> > Furthermore, when you hear these chords played in a big band (say in a
> > brass section), they will often adjust the intonation to one or more
> > of these. Sometimes I hear the #11 played as an 11/4, and sometimes I
> > hear it as a 5/4 over a 9/8, and sometimes I hear it as a 9/7 over a
> > 9/8. Subtle microtonal inflections bring out different feelings, and
> > since no such authority exists right now, you sort of get to invent
> > it.
> >
> > The other thing, and the one that I find infinitely more interesting,
> > is that even within the context of 12-tet (say on a piano), I've heard
> > a huge range of JI chords IMPLIED by the same 12-tet voicing. So in
> > our C7#11 example, there are ways to play that chord on a piano and
> > hear it as a mistuned version of 4:5:6:7:9:11, or the 5/4 over 9/8 on
> > top, or any of the other options up there. The way the chord is
> > voiced, the surrounding chords, the voice leading, and sometimes even
> > the musical context and thematic setting all contribute to how you'll
> > perceive that chord as functioning or existing.
> >
> > I can't speak for anyone else about that last bit, but that is how it
> > appears to me. Hope this helps you out.
> >
> > -Mike
> >
> > On Mon, Sep 22, 2008 at 4:35 PM, Danny Wier <dawiertx@... > <mailto:dawiertx%40sbcglobal.net>> wrote:
> >> I should've learned this long ago, but is there a guide to voicing and
> >> tuning complex chords in a non-meantone tuning? I'm experimenting and
> >> doing calculations right now, but I'm sure someone's already did > work on
> >> this topic.
> >>
> >> An example: the major 6/9 chord, and I'll use 72 equal temperament > here.
> >> The major triad a no-brainer if you want 4:5:6 - 0:23:42, or in C, C Ev
> >> G in ASCIIzed Richter-Herf notation as used by Scala. The major sixth
> >> would be best voiced as 0:23:42:53, or C E\ G A\, A-54 would give you a
> >> wolf fifth.
> >>
> >> And the ninth (D) could be either 83 or 84, but D-83 gives you a wolf
> >> fifth (G-D\) and D-84 gives you a wolf fourth (A\-D). Which major ninth
> >> to chose would depend on what chord you're progressing towards or out
> >> of, but the best bet would seem to be D-84, if you compare the ninth to
> >> the other three notes in the chord. C-D is equivalent to 9/4 while C-D\
> >> is to 20/9. E\-D is equivalent to 9/5 while E\-D\ is to 16/9. G-D > is 3/4
> >> while G-D\ is a wolf fifth (40/27). A\-D\ is a perfect fourth (4/3)
> >> while A\-D is a wolf fourth (27/20). D is more stable with three of the
> >> four other notes while D\ is more stable with only one - so my
> >> recommended voicing is 0:23:46:57:84.
> >>
> >> I tested the chords with both the 83 and 84-comma ninths in Scala and
> >> the 84-comma one sounded smoother. But that's just one example. I still
> >> need to test all the other chords, and then do chords with neutral,
> >> subminor and supermajor intervals that can't be played in 12-tone > tuning.
> >>
> >> By the way, I voice the so-called "Hendrix chord", 7#9no5, as
> >> 0:23:58:88, which can also be an Italian sixth with an added augmented
> >> ninth. One of my favorite chords is the same chord plus an augmented
> >> fourth, 0:23:35:58:88 - that would be a French sixth plus augmented
> >> ninth, or Wagner's "Tristan chord" plus major third.
> >>
> >> ~D.
> >>
> >>
> >
>
>

Mike Battaglia wrote:
> Hey Danny,
>
> I am by no means an authority on this, but I've been tackling the same
> question myself for the past few months. Here's what I've arrived at:
>
> Chords like C E G Bb D F# (C7#11) can be voiced a few different ways
> in JI, and all are equally valid, and all sound slightly different.
> Just like a C7 can be voiced as 4:5:6 with the 7 at 7/4 or voiced as
> 4:5:6 with the 7 at 9/5, there are different ways to voice C7#11.
>
> 1) You can do 4:5:6:7:9:11
> That's written in Richter-Herf (Scala version) as: C E\ G BbL D F#v, or in Extended Tartini-Couper which I use: C Ev G Bdb^ D F+. I'd call that a "resolved eleventh chord", since it's as consonant as it could possibly be. It would be best at the end of a tune or phrase.
> 2) You can make the D-F# dyad a 5/4
> My "normal" tuning for C7#11 might be 0:23:42:60:84:107 in 72et, representing 1/1:5/4:3/2:16/9:14/5.

> 3) You can make the D-F# dyad a 9/7
>
> The last one has a very bright and almost sad quality to it.
> I treat 9/7 as a diminished fourth, so I would consider that a "sad" chord. Or a tense and confused one, since it would be C E G Bb D Gb.

> Furthermore, when you hear these chords played in a big band (say in a
> brass section), they will often adjust the intonation to one or more
> of these. Sometimes I hear the #11 played as an 11/4, and sometimes I
> hear it as a 5/4 over a 9/8, and sometimes I hear it as a 9/7 over a
> 9/8. Subtle microtonal inflections bring out different feelings, and
> since no such authority exists right now, you sort of get to invent
> it.
> Hey, do you mean 9/7 over 9/8 or over 10/9? Because I like your chord, but I'd leave out the perfect fifth and tune it 1/1:5/4:16/9:20/9:20/7 (0:23:60:83:109). It would actually be a C9b5, with the diminished fifth actually being a twelfth. Or leave in the perfect fifth if you want something ultra-dissonant and borderline disgusting, which is okay with me.

> The other thing, and the one that I find infinitely more interesting,
> is that even within the context of 12-tet (say on a piano), I've heard
> a huge range of JI chords IMPLIED by the same 12-tet voicing. So in
> our C7#11 example, there are ways to play that chord on a piano and
> hear it as a mistuned version of 4:5:6:7:9:11, or the 5/4 over 9/8 on
> top, or any of the other options up there. The way the chord is
> voiced, the surrounding chords, the voice leading, and sometimes even
> the musical context and thematic setting all contribute to how you'll
> perceive that chord as functioning or existing.
> Well yeah, the mind knows how to compensate somehow. Altering a pitch by a single comma just smooths out the sound; it might make it easier on the brain too.

I am to the point that I hear the F sharp and F half-sharp (7/5 vs. 11/8) as two different pitches; likewise B flat and B flat-and-a-half (16/9 or 9/5 vs. 7/4). So I'll need at least 24-equal.

> I can't speak for anyone else about that last bit, but that is how it
> appears to me. Hope this helps you out.
>
> -Mike
>
> On Mon, Sep 22, 2008 at 4:35 PM, Danny Wier <dawiertx@...> wrote:
> >> An example: the major 6/9 chord, and I'll use 72 equal temperament here.
>> The major triad a no-brainer if you want 4:5:6 - 0:23:42, or in C, C Ev
>> G in ASCIIzed Richter-Herf notation as used by Scala. The major sixth
>> would be best voiced as 0:23:42:53, or C E\ G A\, A-54 would give you a
>> wolf fifth.
>> P.S.: I meant C E\ G, not C Ev G; that would be a neutral or "Rast" triad, 0:21:42. ~D.

Mike Battaglia wrote:
> Or, to drive the point home even further, consider this chord:
>
> C Eb G Bb D F A C
>
> If you have each minor third dyad in there as 6/5 and each major third
> as 5/4, the C you arrive at on top will actually be 81/80 sharp of
> 2/1. If you put 2/1 in there, it will give a different sound -- a much
> more restful character for the C-c dyad but a little bit more
> dissonance between the A and C. The first one sounds like a chord
> extension (continuing the 7th-9th-11th-13th progression to the 15th)
> and the second one sounds like a benign doubling of the root note by
> two octaves.
> Well, one of my rules *is* that a 32/27 minor third is preferable to a 81/64 major third. But since you'll inevitably end up with a wolf interval (even if it's a wolf fifteenth, 81/20), it would be wise to omit a few notes. It's a similar situation to having to leave notes out to avoid the "comma pump"

> In the same way, if you're playing the following chord:
>
> C Eb F Bb
>
> If the C-Eb is a 6/5, and the Eb-Bb is a 3/2, then where do we put the
> F? We could make C-F a 4/3, or F-Bb a 4/3 - but not both. And they're
> both valid - the two simply sound different. The C-F as 4/3 sounds
> much more placid and relaxed, and the F-Bb sounds more excited and
> maybe even a bit agitated or tense to my ears -- as if it is a chord
> forcefully extruding out into some direction.

Or use the Pythagorean minor third for Eb, 32/27 again.

But I tried C:Eb/:F/:Bb/, and I think I like that's best. In JI, that's 1/1:6/5:27/20:9/5 (1:19:31:61); in harmonics, 20:24:27:36. So a wolf is not always a bad thing, at least the fourth.

Well I better get back to work on all these chords before I claim to be an expert. ~D.

> That's written in Richter-Herf (Scala version) as: C E\ G BbL D F#v, or
> in Extended Tartini-Couper which I use: C Ev G Bdb^ D F+. I'd call that
> a "resolved eleventh chord", since it's as consonant as it could
> possibly be. It would be best at the end of a tune or phrase.
>> 2) You can make the D-F# dyad a 5/4

I always liked HEWM notation, so I'd write it as C E- G Bb< D F^. And
when using it as a I chord it definitely sounds resolved, but if you
put that chord over something than the root it starts to sound as
resolved as say the V chord, which is an otonal chord as well.

> I treat 9/7 as a diminished fourth, so I would consider that a "sad"
> chord. Or a tense and confused one, since it would be C E G Bb D Gb.

It could be treated as a septimal meantone diminished fourth as well.
I've been messing around with scales like C D E> F G A> B> C, though,
so you can also hear it as a large major third.

> Hey, do you mean 9/7 over 9/8 or over 10/9? Because I like your chord,
> but I'd leave out the perfect fifth and tune it 1/1:5/4:16/9:20/9:20/7
> (0:23:60:83:109). It would actually be a C9b5, with the diminished fifth
> actually being a twelfth. Or leave in the perfect fifth if you want
> something ultra-dissonant and borderline disgusting, which is okay with me.

Scale wise I still hear that top note as a #11, because it still just
sounds like a lydian dominant-ish chord to me. If you want to build a
scale that puts it at the fifth scale step, you'd have the following
notes in the scale right off the bat:

1/1, 10/9, 5/4, (something), 10/7, (something), 16/9, 2/1

Maybe you could put 4/3 in there to make it a more even scale, but who
knows. I see that you were going for having the 10/7 dyad (or 20/7) in
there, which is why you put it over 10/9? I was hearing it as a 5/4
extension on top of the 9th, but yours sounds good as well.

> Well yeah, the mind knows how to compensate somehow. Altering a pitch by
> a single comma just smooths out the sound; it might make it easier on
> the brain too.

Sometimes it roughens out the sound in a good way as well. Try C-Eb-F,
where C-Eb is 6/5 and Eb-F is 9/8 (20:24:27). Sounds much brighter
than making Eb-F 10/9, which would make C-F 4/3 (15:18:20). They're
both valid, just slightly different chords. The first one carries more
"information" to my ears.

> I am to the point that I hear the F sharp and F half-sharp (7/5 vs.
> 11/8) as two different pitches; likewise B flat and B flat-and-a-half
> (16/9 or 9/5 vs. 7/4). So I'll need at least 24-equal.

Definitely. I have a quarter tone setup in my room where two keyboards
play the same patch a quarter tone apart -- while it's not the holy
72-tone grail of music, it's still definitely enough to get started.
You can sort of approximate 7/6 by playing 2 and a half steps -- given
the right context sometimes your brain just seems to hear it that way.

-Mike

> Well, one of my rules *is* that a 32/27 minor third is preferable to a
> 81/64 major third. But since you'll inevitably end up with a wolf
> interval (even if it's a wolf fifteenth, 81/20), it would be wise to
> omit a few notes. It's a similar situation to having to leave notes out
> to avoid the "comma pump"

Well, I know it's supposedly a microtonal faux pas to have a
comma-augmented double octave in there, but that chord sounds good to
my ears. I'm trying to hear when a comma-augmented octave by itself
might sound good in a chord voicing, or a comma-augmented fifth or a
fourth. Everyone abandoned those intervals as being out of tune
"wolf-intervals" a long time ago, but I think chords like this prove
that they can jigsaw into chord voicings just like any other interval,
imo.

Another thing I've been experimenting with are chords that have notes
in them that are one comma apart. Not for some kind of beating effect,
but to actually hear what it sounds like if you want to build a chord
such as C Eb+ F F+ Bb+, where the C-F is in there and the F+-Bb+ as
well. I find they sound better if the volume of the comma dyad is
lowered a bit, but still apparent.

-Mike

Mike wrote:

>C Eb F Bb
>
>If the C-Eb is a 6/5, and the Eb-Bb is a 3/2, then where do we put the
>F? We could make C-F a 4/3, or F-Bb a 4/3 - but not both.

You probably know that in 22-ET, you can have both. Just stating
it for the record.

-C.

>Definitely. I have a quarter tone setup in my room where two keyboards
>play the same patch a quarter tone apart -- while it's not the holy
>72-tone grail of music, it's still definitely enough to get started.
>You can sort of approximate 7/6 by playing 2 and a half steps -- given
>the right context sometimes your brain just seems to hear it that way.
>
>-Mike

Two 12-ET keyboards a 1/4-tone apart? That would give 24-ET...
For a subset of 72, it's been suggested to tune two 12-ET keyboards
a 1/6-tone apart...

-Carl

Mike wrote:

>The other thing, and the one that I find infinitely more interesting,
>is that even within the context of 12-tet (say on a piano), I've heard
>a huge range of JI chords IMPLIED by the same 12-tet voicing. So in
>our C7#11 example, there are ways to play that chord on a piano and
>hear it as a mistuned version of 4:5:6:7:9:11, or the 5/4 over 9/8 on
>top, or any of the other options up there. The way the chord is
>voiced, the surrounding chords, the voice leading, and sometimes even
>the musical context and thematic setting all contribute to how you'll
>perceive that chord as functioning or existing.

One way to tackle microtonal voicing / voice leading is with
algorithms -- "adaptive JI", but the approach can be used not only
for JI but in any case where one draws harmonic intervals from a
small bag while drawing melodic intervals from a bigger bag.

Some of these algorithms -- Hermode tuning for example -- interpret
each notated harmony first (e.g. C-E-G = 4:5:6) and then slide the
roots around to minimize voice leading distance or whatever. But
my (unimplemented) adaptive JI algorithm actually chooses the
harmonic interpretation which minimizes voice leading distance from
the previous chord, and then adjusts roots to further reduce it,
as in Hermode tuning. (And now that I have a way to measure the
strength of arbitrary chord changes in just intonation, one could
chose harmonic interpretations on that basis also.)

I realize that you and Danny are interested in learning to do these
kinds of things as a musical skill rather than automatically. And
that will afford much greater expressive power than any algorithm.
But it's something to think about.

-Carl

Mike Battaglia wrote:
> Another thing I've been experimenting with are chords that have notes
> in them that are one comma apart. Not for some kind of beating effect,
> but to actually hear what it sounds like if you want to build a chord
> such as C Eb+ F F+ Bb+, where the C-F is in there and the F+-Bb+ as
> well. I find they sound better if the volume of the comma dyad is
> lowered a bit, but still apparent.

First of all, sorry I dropped out of the discussion all a sudden, and on a topic I started too. I got busy with things, including a new composition. Something for an imaginary video game, you could say.

I need to experiment with chords like what you got. One I want to use is a type of quarter chord: C F F+ Bb+ (1/1 4/3 27/20 9/5). I can see it fitting in a chord progression like C7sus4 to Cm7(no5). The two chords in their "normal" voicing would be C:F:Bb and C:Eb+:Bb+, so replace the first chord with C:F:F+:Bb+ and you not only avoid a comma slide on the B-flat, but you emphasize the fourth by doubling and detuning it.

But I got a lot of work to do on this subject. Maybe I /should/ write a book.

(Also, I forgot about HEWM, as you mentioned in another e-mail, and I like it for ASCII messages in particular.)

~D.

Correction to my last reply:

> I need to experiment with chords like what you got. One I want to use is > a type of quarter chord: C F F+ Bb+ (1/1 4/3 27/20 9/5). I can see it That should be "quartal chord", in case you're wondering. ~D.

81/40 is a cool interval as well. Takes some getting used to at first,
but eventually starts to have a character all of its own.

The aforementioned C Eb+ G Bb+ D F+ A C+ has it. So does this one: C
Eb+ F+ G Bb+ C+ (or 40:48:54:60:72:81). Then try switching the 81 back
and forth to 80 and hear the difference.
I love that the emancipation of the dissonance continues by finding
the harmonic function of so-called "wolf intervals."

-Mike

On Thu, Sep 25, 2008 at 6:36 PM, Danny Wier <dawiertx@...> wrote:
> Correction to my last reply:
>
>> I need to experiment with chords like what you got. One I want to use is
>> a type of quarter chord: C F F+ Bb+ (1/1 4/3 27/20 9/5). I can see it
>
> That should be "quartal chord", in case you're wondering. ~D.
>

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> >Definitely. I have a quarter tone setup in my room where two
> >keyboards play the same patch a quarter tone apart -- while it's not
> >the holy 72-tone grail of music, it's still definitely enough to get
> >started.
> >You can sort of approximate 7/6 by playing 2 and a half steps --
> >given the right context sometimes your brain just seems to hear it
> >that way.
> >
> >-Mike
>
> Two 12-ET keyboards a 1/4-tone apart? That would give 24-ET...
> For a subset of 72, it's been suggested to tune two 12-ET keyboards
> a 1/6-tone apart...
>

And THAT would give 36-ET...

I would like to know more about this, because two keyboards with 12
tones each is the lineup that my keyboard with its split mode can
handle...
--
Hans Straub

At 09:29 AM 10/20/2008, you wrote:
>--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>>
>> >Definitely. I have a quarter tone setup in my room where two
>> >keyboards play the same patch a quarter tone apart -- while it's not
>> >the holy 72-tone grail of music, it's still definitely enough to get
>> >started.
>> >You can sort of approximate 7/6 by playing 2 and a half steps --
>> >given the right context sometimes your brain just seems to hear it
>> >that way.
>> >
>> >-Mike
>>
>> Two 12-ET keyboards a 1/4-tone apart? That would give 24-ET...
>> For a subset of 72, it's been suggested to tune two 12-ET keyboards
>> a 1/6-tone apart...
>
>And THAT would give 36-ET...

2 * 12 != 36

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> At 09:29 AM 10/20/2008, you wrote:
> >--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@> wrote:
> >>
> >> Two 12-ET keyboards a 1/4-tone apart? That would give 24-ET...
> >> For a subset of 72, it's been suggested to tune two 12-ET keyboards
> >> a 1/6-tone apart...
> >
> >And THAT would give 36-ET...
>
> 2 * 12 != 36
>

Alright, a subset of 36-ET, then. Still no more reasons to call that
72-ET than two 12-ET keyboards a 1/4-tone apart.
Now how about my questions?
And who suggested it?
--
Hans Straub

>> >> Two 12-ET keyboards a 1/4-tone apart? That would give 24-ET...
>> >> For a subset of 72, it's been suggested to tune two 12-ET keyboards
>> >> a 1/6-tone apart...
>> >
>> >And THAT would give 36-ET...
>>
>> 2 * 12 != 36
>
> Alright, a subset of 36-ET, then.

Did I say 1/6-tone? I meant 1/12-tone. Thanks for catching
that, Hans.

>Now how about my questions?

Which? Sorry.

>And who suggested it?

Paul Erlich.

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> >> >> Two 12-ET keyboards a 1/4-tone apart? That would give 24-
ET...
> >> >> For a subset of 72, it's been suggested to tune two 12-ET
keyboards
> >> >> a 1/6-tone apart...
> >> >
> >> >And THAT would give 36-ET...
> >>
> >> 2 * 12 != 36
> >
> > Alright, a subset of 36-ET, then.
>
> Did I say 1/6-tone? I meant 1/12-tone. Thanks for catching
> that, Hans.
>

Now that makes much more sense. Thanks!
Yeah, it's a 1/6 SEMItone...
--
Hans Straub