"Choral" voice-leading with 13-intervals

Hello, everyone.

The recent discussion about "13-limit chorales" moves me to a few
remarks, with emphasis on some simple but possibly illustrative MIDI
examples of "choral" kinds of textures with lots of note-against-note
motion of three or four voices -- albeit in an historical European
style about four centuries earlier than the Bach query would imply.

However, please let me emphasize that there are various ways of
approaching 13-intervals, and Kyle, you have given us something very
original and beautiful, with that cadence using 13/9 and 13/7 indeed
special!

Also, George, I warmly agree that isoharmonic sonorities are a great
approach to these higher ratios, and might have special euphony when
one deals with densely saturated 13-limit harmonies. My ways of using
13-intervals are often not so dense (e.g. a simple 22:26:33 or
26:33:44), but even in such a style something like 7:9:11:13 can be
powerfully compelling and "different." One I find intriguing is
11:16:21:26. By the way, thank you for introducing me to these chords!

The first brief snippet is a three-voice texture in what is called
conductus style, popular around 1200, realized in JOT-17, a "Just
Octachord Tuning" where each each fourth is divided into seven steps,
and thus an "octachord" of eight notes, for example Bb-A#-B-C-Db-C#-D-Eb.
Here's the MIDI:

<http://www.bestii.com/~mschulter/jot17ex1.mid>

and here's the Scala file for JOT-17 (if you have Scala, try the

KEY 14

command to see the scale in a Bb-Bb range revealing the largely
superparticular step structure of the octachords based on the
arithmetic or subharmonic series of 28:27:26 and 24:23:22:21):

! jot17.scl
!
Just octachord tuning -- 9:8-4:3-9:8 division, 17 steps (7 + 3 + 7), C-C
17
!
91/88
273/253
273/242
13/11
364/297
14/11
117/88
91/66
63/44
3/2
273/176
819/506
819/484
39/22
182/99
21/11
2/1

Here's something a bit freer in mixing old and new elements: a piece
called _For Kathleen Schlesinger: Forms of Tonality_, again realized
in a MIDI version in JOT-17. Actually I originally composed this in
another just scale, but it "ports" easily to JOT-17.

<http://www.bestii.com/~mschulter/kathton3a.mid>

Another mostly note-against-note piece, _Cantilena for George Secor_,
has four-voice harmony, featuring some suspension idioms which might
be taken as mixing 14th-century and 16th-century idioms (a creative
process which unfolded as part of a delightful dialogue with George on
his 17-tone well-temperament or 17-WT, from whom I have learned much
indeed).

<http://www.bestii.com/~mschulter/cantigsj.mid>

Please let me caution that the two versions of the three-voice _O
Europae_ which follow are in the tempered Peppermint system rather
than a just tuning: however, I would consider many of the
approximations of just ratios, including those of 11 and 13, as close
enough to illustrate many of the qualities of the just versions also.
The opening and closing portions draw on typical voice-leading
techniques around 1400, while the middle is more "xenharmonic."

<http://www.bestii.com/~mschulter/o_europ09.mid>
<http://www.bestii.com/~mschulter/o_europ09.mid>

Here's the Peppermint tuning:

! peprmint.scl
!
Peppermint 24: Wilson/Pepper apotome/limma=Phi, 2 chains spaced for pure 7:6
24
!
58.679693 cents
128.669246 cents
187.348938 cents
208.191213 cents
7/6
287.713180 cents
346.392873 cents
416.382426 cents
475.062119 cents
495.904393 cents
554.584086 cents
624.573639 cents
683.253332 cents
704.095607 cents
762.775299 cents
832.764852 cents
891.444545 cents
912.286820 cents
970.966512 cents
991.808787 cents
1050.488479 cents
1120.478033 cents
1179.157725 cents
2/1

In peace and love,

Margo
mschulter@...

Thank you, that was wonderful and informative. I've long been a fan of
prebaroque vocal music like that, _Cantilena for George Secor_ and
_For Kathleen Schlesinger: Forms of Tonality_ especially, in the way
that they seem to move in and out of familiar consonances. It sounds
like the limit moves from 3 up to 13 and back, am I right?

--
~Tristan Parker
http://www.myspace.com/rozencrantz
"Western music is fast because it's out of tune"
-- Terry Riley

> Please let me caution that the two versions of the three-voice _O
> Europae_ which follow are in the tempered Peppermint system rather
> than a just tuning: however, I would consider many of the
> approximations of just ratios, including those of 11 and 13, as close
> enough to illustrate many of the qualities of the just versions also.
> The opening and closing portions draw on typical voice-leading
> techniques around 1400, while the middle is more "xenharmonic."

<http://www.bestii.com/~mschulter/o_europ09.mid>
<http://www.bestii.com/~mschulter/o_europ08.mid>

Hi, everyone, and here I've corrected the second link so that it points to
a version with a different registration than the first, rather than again
to the same file. My apologies for this small glitch in the previous post.

Peace and love,

Margo

> Message: 2
> Date: Mon, 21 Nov 2005 16:04:06 -0800
> From: Rozencrantz the Sane <rozencrantz@...>
> Subject: Re: "Choral" voice-leading with 13-intervals
>
> Thank you, that was wonderful and informative. I've long been a fan of
> prebaroque vocal music like that, _Cantilena for George Secor_ and
> _For Kathleen Schlesinger: Forms of Tonality_ especially, in the way
> that they seem to move in and out of familiar consonances. It sounds
> like the limit moves from 3 up to 13 and back, am I right?

Hi, there, and thank you for this feedback: you have indeed picked up on
what I might call an "alternation" of stable 3-limit sonorities and
various "relatively-concordant-but-unstable" sonorities often involving
13-intervals.

This fits a pre-Baroque, and more specifically 13th-14th century, pattern
of using octaves, fifths, and fourths as stable concords, but alternating
with more complex and unstable sonorities, which are sometimes explained
in theory as "neither perfectly consonant nor perfectly (i.e. "acutely")
dissonant," but alluringly in between. As it happens, I find that ratios
of 11 and 13 often nicely fill this kind of role for a "neo-medieval"
style.

What I'll try to do is to record and post some more music which might
illustrate this kind of texture and some of the techniques -- thanks for
the encouragement and appreciation, and for your perceptive comment
pointing to an important aspect of style.

Peace and love,

Margo
mschulter@...

On Tue, 22 Nov 2005, Margo Schulter wrote:

> > Message: 2
> > Date: Mon, 21 Nov 2005 16:04:06 -0800
> > From: Rozencrantz the Sane <rozencrantz@...>
> > Subject: Re: "Choral" voice-leading with 13-intervals
> >
> > Thank you, that was wonderful and informative. I've long been a fan of
> > prebaroque vocal music like that, _Cantilena for George Secor_ and
> > _For Kathleen Schlesinger: Forms of Tonality_ especially, in the way
> > that they seem to move in and out of familiar consonances. It sounds
> > like the limit moves from 3 up to 13 and back, am I right?
>
> Hi, there, and thank you for this feedback: you have indeed picked up on
> what I might call an "alternation" of stable 3-limit sonorities and
> various "relatively-concordant-but-unstable" sonorities often involving
> 13-intervals.
>
> This fits a pre-Baroque, and more specifically 13th-14th century, pattern
> of using octaves, fifths, and fourths as stable concords, but alternating
> with more complex and unstable sonorities, which are sometimes explained
> in theory as "neither perfectly consonant nor perfectly (i.e. "acutely")
> dissonant," but alluringly in between. As it happens, I find that ratios
> of 11 and 13 often nicely fill this kind of role for a "neo-medieval"
> style.

Margo,
Thanks for the explanation - it makes it a little clearer
what your aims were. The style is SO different form
what we usually hear, that the unprepared listener may
well be confused as to how that kind of music proceeds.

> What I'll try to do is to record and post some more music which might
> illustrate this kind of texture and some of the techniques -- thanks for
> the encouragement and appreciation, and for your perceptive comment
> pointing to an important aspect of style.

My one complaint about the pieces you posted is that
they were too short! And now I know why - I was
enjoying them, but didn't hear enough of them to be
able to understand why ...

> Peace and love,
> Margo

Likewise!
Yahya

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Please let me make this response to Yahya

> Thanks for the explanation - it makes it a little clearer
> what your aims were. The style is SO different form
> what we usually hear, that the unprepared listener may
> well be confused as to how that kind of music proceeds.

Thank you for this reminder that different people hear things differently
-- and I'd suspect that your response might be representative. This might
be in part because while taking basic 13th-14th century European
techniques and adding some elements like neutral intervals has become
"common practice" for me, the basic style as well as the additions might
not be as familiar as Bach, say.

> My one complaint about the pieces you posted is that
> they were too short! And now I know why - I was
> enjoying them, but didn't hear enough of them to be
> able to understand why ...

This is an interesting point, and maybe ties with a remark I've heard from
people like Brian McLaren that after a few minutes listeners start to get
acclimated to almost any tuning system or scale. Thus a piece which
provides a bit of time for "orientation" might help.

By the way, I'll respond off-group to your question about Pythagorean and
meantone tuning and intonation.

Peace and love,

Margo