Scale and composition in 5.11.31 subgroup

Here's a new composition in honor of tomorrow, May 31, 2011. (I probably won't get the leisure time to release it tomorrow, so the timing is what it is.) It's just a little under three minutes long, and under 3 MB to download.

http://www.freivald.org/~jake/documents/May 31, 2011.mp3

It's slow and mellow, even languorous, so don't listen to it if you're not in that sort of mood.

What follows is a mix of the tuning and compositional aspects of the piece, since this is crossposted to MMM and Tuning.

----

If you're like me, once you start to obsess over something, you see it everywhere: $3.86-per-gallon gas makes you think of a major third, that sort of thing.

A few weeks ago, I noticed that the end of may was 5/31/11, so I noodled around with the 5.11.31 subgroup and derived the following scale. I don't see any relevant subsets or supersets of it in the Scala archive, so perhaps it's essentially unused.

! C:\Program Files (x86)\Scala22\2011-may-31.scl
!
May 31, 2011 scale -- based on 5.11.31 subgroup
12
!
125/121
33275/29791
34375/29791
31/25
155/121
1331/961
1375/961
961/625
961/605
1331/775
55/31
29791/15625

Note that it's actually three chords of 125/121, 33275/29791, 34375/29791, and 31/25, stacked with an intervening 125/121. Clearly, as a non-octave scale, you could split it up at any chord boundary, but I found it convenient to keep it to twelve notes.

It's strictly proper, and Scala's SHOW DATA function shows a bunch of other stuff I don't know much about. (Vogel's harmonic complexity is too high to compute? Should that intimidate me? What about the fact that the Rothenberg Stability is 1, but the Lumma Stability is only 0.55?) I figured that, since it contains tones with Tenney Heights as high as 1024065625, I shouldn't worry about the theoretical calculations much if I were going to try to compose with it.

It has three interval sizes, but I figured I shouldn't temper them, for three reasons: First, because people with golden ears might miss the 31-ness of it all, instead hearing 7-based ratios or some other interval; second, because I couldn't find any advantage to tempering, though perhaps someone else could see something worthwhile; third, because I think the different interval sizes add something to the character of the scale.

I started writing a few faster pieces using bongy-gongy inharmonic timbres, since people talk about those being useful for this for high-prime scales, but I didn't like anything I was doing. I started over, this time with a Warm Pad slowly playing the most harmonious chords I could find. Those include things like two stacked 31/25ths, a 55/31 split by a 31/25 on the bottom, and an 11/5 split by a 55/31 on the bottom. Since they have crazy ratios like 15625:19375:29791 (the two 31/25ths), I didn't bother to compute them.

I set up chord progressions in an A-B-A structure, and I decided to give a theme to a saxophone (A) and a somewhat rambling solo to a nylon-string guitar (B). I also doubled the Warm Pad with strings and added tubular bells as an accent.

The Warm Pad might be a cheat -- it sounds deeper than the string sample I have, so I'm guessing it doubles down an octave -- but I like it, so I'm keeping it. After all, every timbre has some tones in it that aren't part of the scale, right? :)

I wrote it using LilyPond and rendered it with Timidity++.

Regards,
Jake

P.S. Yes, I know 5/29/11 was just yesterday, but I thought of 31 first, and didn't think I'd have time to write something for 5/29. I did try to generate a scale for it, but I didn't like it as much as this one anyway.

Just a lil' fyi if you should ever want to explore this subgroup in the context of an EDO, 22 tunes the 31st harmonic near-Just, misses the 11th by a mere 6 or so cents, and the 5th harmonic by about the same. I wonder how close your scale is to the intervals in 22?

-Igs

--- In tuning@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:
>
> Here's a new composition in honor of tomorrow, May 31, 2011. (I probably
> won't get the leisure time to release it tomorrow, so the timing is what
> it is.) It's just a little under three minutes long, and under 3 MB to
> download.
>
> http://www.freivald.org/~jake/documents/May 31, 2011.mp3
>
> It's slow and mellow, even languorous, so don't listen to it if you're
> not in that sort of mood.
>
> What follows is a mix of the tuning and compositional aspects of the
> piece, since this is crossposted to MMM and Tuning.
>
> ----
>
> If you're like me, once you start to obsess over something, you see it
> everywhere: $3.86-per-gallon gas makes you think of a major third, that
> sort of thing.
>
> A few weeks ago, I noticed that the end of may was 5/31/11, so I noodled
> around with the 5.11.31 subgroup and derived the following scale. I
> don't see any relevant subsets or supersets of it in the Scala archive,
> so perhaps it's essentially unused.
>
> ! C:\Program Files (x86)\Scala22\2011-may-31.scl
> !
> May 31, 2011 scale -- based on 5.11.31 subgroup
> 12
> !
> 125/121
> 33275/29791
> 34375/29791
> 31/25
> 155/121
> 1331/961
> 1375/961
> 961/625
> 961/605
> 1331/775
> 55/31
> 29791/15625
>
> Note that it's actually three chords of 125/121, 33275/29791,
> 34375/29791, and 31/25, stacked with an intervening 125/121. Clearly, as
> a non-octave scale, you could split it up at any chord boundary, but I
> found it convenient to keep it to twelve notes.
>
> It's strictly proper, and Scala's SHOW DATA function shows a bunch of
> other stuff I don't know much about. (Vogel's harmonic complexity is too
> high to compute? Should that intimidate me? What about the fact that the
> Rothenberg Stability is 1, but the Lumma Stability is only 0.55?) I
> figured that, since it contains tones with Tenney Heights as high as
> 1024065625, I shouldn't worry about the theoretical calculations much if
> I were going to try to compose with it.
>
> It has three interval sizes, but I figured I shouldn't temper them, for
> three reasons: First, because people with golden ears might miss the
> 31-ness of it all, instead hearing 7-based ratios or some other
> interval; second, because I couldn't find any advantage to tempering,
> though perhaps someone else could see something worthwhile; third,
> because I think the different interval sizes add something to the
> character of the scale.
>
> I started writing a few faster pieces using bongy-gongy inharmonic
> timbres, since people talk about those being useful for this for
> high-prime scales, but I didn't like anything I was doing. I started
> over, this time with a Warm Pad slowly playing the most harmonious
> chords I could find. Those include things like two stacked 31/25ths, a
> 55/31 split by a 31/25 on the bottom, and an 11/5 split by a 55/31 on
> the bottom. Since they have crazy ratios like 15625:19375:29791 (the two
> 31/25ths), I didn't bother to compute them.
>
> I set up chord progressions in an A-B-A structure, and I decided to give
> a theme to a saxophone (A) and a somewhat rambling solo to a
> nylon-string guitar (B). I also doubled the Warm Pad with strings and
> added tubular bells as an accent.
>
> The Warm Pad might be a cheat -- it sounds deeper than the string sample
> I have, so I'm guessing it doubles down an octave -- but I like it, so
> I'm keeping it. After all, every timbre has some tones in it that aren't
> part of the scale, right? :)
>
> I wrote it using LilyPond and rendered it with Timidity++.
>
> Regards,
> Jake
>
> P.S. Yes, I know 5/29/11 was just yesterday, but I thought of 31 first,
> and didn't think I'd have time to write something for 5/29. I did try to
> generate a scale for it, but I didn't like it as much as this one anyway.
>

> I wonder how close your scale is to the intervals in 22?

Thanks, Igs. I was thinking that I should look at 22-EDO.

That said, 22 EDO would miss this by a lot. For one thing, there's no 2, hence no "O" to make an ED of. :) But the rest of it misses pretty widely, too:

125/121 = 56.305
22 EDO = 54.545

33275/29791 = 191.475
22 EDO = 163.636 or 218.182

34375/29791 = 247.780
22 EDO = 218.182 or 272.727

31/25 = 372.408
22 EDO = 381.818

155/121 = 428.713
22 EDO = 436.364

1331/961 = 563.883
22 EDO = 545.455

1375/961 = 620.188
22 EDO = 600.000 or 654.545

961/625 = 744.816
22 EDO = 763.636

961/605 = 801.122
22 EDO = 818.182

1331/775 = 936.291
22 EDO = 927.273

55/31 = 992.596
22 EDO = 981.818

29791/15625 = 1117.224
22 EDO = 1090.909 or 1145.455

Regards,
Jake

--- In tuning@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:

> http://www.freivald.org/~jake/documents/May 31, 2011.mp3

http://tinyurl.com/3mppv7t

Interesting. Here's a non-broken link to it.

> A few weeks ago, I noticed that the end of may was 5/31/11, so I noodled
> around with the 5.11.31 subgroup and derived the following scale. I
> don't see any relevant subsets or supersets of it in the Scala archive,
> so perhaps it's essentially unused.

Hardly likely that a non-octave 2.11.31 subgroup scale would be anything else.

Thanks for the listens and comments, Igs, Chris, Gene, and Carl.

Thanks for fixing the link, Gene. That was a "duh" moment.

Carl said:

> If all music is reposted on tuning, what's the point of MMM?

Beats me. I'm not quite sure what the protocol is. Personally, if I had written something in a tuning that had any kind of history -- 22 EDO, Canton, etc. -- then I wouldn't have posted to Tuning. If I were talking about the tuning, but without a piece of music (more than just an example, that is), then I wouldn't have posted it to MMM. In my mind, the Vogel's Harmonic Complexity talk is more of a Tuning-list thing, while the A-B-A and LilyPond / Timidity stuff is more of an MMM thing. But that's just me.

Regards,
Jake