Yahoo Tuning Groups Ultimate Backup makemicromusic 53 tone equal temperament

I've been exploring algorithmic approaches to generate microtonal music
for a while, though making only occasional progress. So here is a small
step:

http://soundclick.com/share?songid=6094721

I am always looking for a nice balance between structure that I impose
directly and structure that emerges from the dynamics of the system
that I construct. I am interested in the potential of key shifts in 53
tone equal temperament. So here I arrange the system dynamics to see if
I can force a kind of Moebius twist to emerge.

Hope you get something positive out of it!

Jim

🔗Carl Lumma <carl@...>

I like it. I think it's maybe a bit long for the amount of
juice it packs.

-Carl

At 02:07 PM 12/21/2007, you wrote:
>I've been exploring algorithmic approaches to generate microtonal music
>for a while, though making only occasional progress. So here is a small
>step:
>
>http://soundclick.com/share?songid=6094721
>
>I am always looking for a nice balance between structure that I impose
>directly and structure that emerges from the dynamics of the system
>that I construct. I am interested in the potential of key shifts in 53
>tone equal temperament. So here I arrange the system dynamics to see if
>I can force a kind of Moebius twist to emerge.
>
>Hope you get something positive out of it!
>
>Jim

🔗Jim K <kukulaj@...>

--- In MakeMicroMusic@yahoogroups.com, "Jim K" <kukulaj@...> wrote:
>
> So here is a small step:
>
> http://soundclick.com/share?songid=6094721

Maybe if I say something more about what I am trying to do, the piece
might make more sense... and maybe folks can steer me toward more
effective methods!

The building blocks I am giving myself are the intervals a perfect
fifth and a major third, which would be 3/2 and 5/4 just tuned, or 31
and 17 steps in 53edo. No doubt one can use 53edo to explore rational
intervals involving factors of 7 or 11, but I am not trying to
explore that here.

I don't want to make music that could be better played in just
tuning. Nothing wrong with that, but I want to see what 53edo in
particular can do.

The difference between just and tempered tuning, as I see it, is in
what happens as one gradually moves, step by step, using the building
block intervals. In just tuning, the exponents on the prime factors
can just keep getting bigger and bigger, and the pitch space will
eventually get filled in by all the subtly different ratios.

In a tempered tuning, some of the subtlety is tempered out... so
paths that in just tuning would end at subtly different pitches, in
the tempered scale end up at the same place. The fun is to exploit
this.

My thinking about this is based on Easley Blackwood's _The Structure
of Recognizable Diatonic Tunings_. That's all way above my head. But
that's where I got the idea that lots of music isn't even trying to
be just tuned, but is in fact exploiting the temperament, i.e. the
ambiguity, how one tempered pitch stands for several just pitches.

In this piece, I am using the fact that, in 53edo, 8 perfect fifths
plus one major third brings one right back to where one started. I
impose a series of key shift to follow that path, to return to the
starting point in a non-trivial loop.

Another way to think about this... in just tuning, it's like the
harmonic universe is flat, with as many dimensions as the prime
numbers one is utilizing. This harmonic universe is also infinite.
But in the tempered world, the universe closes back on itself - it's
like a toroid of some kind. So, for example, in Pythagorean harmony
based on just the primes 2 and 3, temperament closes the series of
fifths into a circle. With the prime factor 5 tossed in the looping
possibilities get more complicated. So I just picked one such loop
that 53edo provides.

I realize that folks here have thought through these things far more
deeply and extensively than I can fathom... but still, by writing
from my elementary perspective, maybe I can trigger some suitably
elementary feedback!

Jim

🔗Herman Miller <hmiller@...>

Jim K wrote:

> My thinking about this is based on Easley Blackwood's _The Structure > of Recognizable Diatonic Tunings_. That's all way above my head. But > that's where I got the idea that lots of music isn't even trying to > be just tuned, but is in fact exploiting the temperament, i.e. the > ambiguity, how one tempered pitch stands for several just pitches.

I haven't read his book (I probably ought to look for a copy of it one of these days), but I've been inspired by his _Twelve Microtonal Etudes_, which apply those ideas to everthing from 13 to 24 equal steps to the octave.

> In this piece, I am using the fact that, in 53edo, 8 perfect fifths > plus one major third brings one right back to where one started. I > impose a series of key shift to follow that path, to return to the > starting point in a non-trivial loop.
> > Another way to think about this... in just tuning, it's like the > harmonic universe is flat, with as many dimensions as the prime > numbers one is utilizing. This harmonic universe is also infinite. > But in the tempered world, the universe closes back on itself - it's > like a toroid of some kind. So, for example, in Pythagorean harmony > based on just the primes 2 and 3, temperament closes the series of > fifths into a circle. With the prime factor 5 tossed in the looping > possibilities get more complicated. So I just picked one such loop > that 53edo provides.

We call those sorts of loops "comma pumps" -- whether that's any official sort of terminology I don't know, but it's useful to have something to call them. I wrote a harmonic progression with a closed loop like that in 15-ET once -- and after discussing it on the tuning list it turned out that it also worked in 22-ET. These days, we'd call it a comma pump in porcupine temperament. 53 is an interesting ET since it belongs to a number of useful temperaments -- in other words, it tempers out a number of small intervals. There's the well-known schisma (32805/32768) and the somewhat less familiar kleisma (15625/15552), along with combinations of those, but also the Bohlen-Pierce major diesis (3125/3087) and other 7-limit intervals (e.g. 225/224, 4375/4374) in case you ever have an interest in adding the prime factor 7.

🔗Jim K <kukulaj@...>

--- In MakeMicroMusic@yahoogroups.com, Herman Miller <hmiller@...>
wrote:
>
> There's the well-known schisma (32805/32768)

yes, this is exactly the comma I am pumping! (If I understand the
terminology here!)

Here is a diagram of the harmonic space and the notes used in the piece
with their frequency of occurance:

http://s140.photobucket.com/albums/r6/kukulaj/?
action=viewB$t=diagram.jpg

It's easy to see the loop here. One mystery is why note 18 occurs so
often - it lies off that main path. Perhaps some fluke of the algorithm
that generates the sequence. Anyway, mostly the behavior seems to make
sense.

Jim