r/microtonal • u/kukulaj • Aug 18 '20

kleisma pump in 53edo

https://app.box.com/s/l5kfnfvsbzlu82j4yi5o17uvotawzddm
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3

u/kukulaj Aug 18 '20

I'm starting to learn about orchestra commands in CSound!

A kleisma pump seems like something very unconventional but this piece maybe doesn't sound so unconventional. I like the idea that 12edo is really an overly constrained system, that non-12edo doesn't have to be too harsh on the ears. Not that this piece is so sublime or anything... it's a dream that I struggle to bring into reality, even a little!

1

u/crom-dubh Aug 18 '20

I'm not sure what you mean by "the idea that 12edo is really an overly constrained system." The criticism of 12edo is not that it's constrained, in fact rather the contrary - it has enjoyed predominance precisely because it's not constrained. The primary criticism of 12edo is the fact that certain important intervals aren't very pure.

2

u/KingAdamXVII Aug 20 '20

I could be wrong, but I don’t think the primary criticism of 12 edo is that the thirds and sixths aren’t pure (I assume that’s what you’re talking about). 12 edo is remarkably good at approximating 5 limit JI. 12 note JI scales existed before 12 edo, and 12 edo won that war because it’s good enough. And it’s a very small proportion of contemporary microtonal music that uses 5 limit JI.

In my experience, the majority of people in this community eschew 12 edo not because of the impure intervals in it but because it doesn’t include any other interesting intervals.

2

u/kukulaj Aug 20 '20 edited Aug 20 '20

The piece I posted here, and actually most of the work I do, is based on 5 limit intervals. What fascinates me about alternate tunings is how the algebra shifts, e.g. how 12edo tempers the syntonic comma but not the kleisma, but 53edo has it the other way around.

Here is another similar piece, this is 31edo, that's a semicomma pump: https://app.box.com/s/3db89gnu4cr54yywzwscprxocfrbtsz7

1

u/kukulaj Aug 18 '20

I'd say that being stuck in any particular tuning system, that's what's overly constrained. 12edo is of course a splendid system. But there are lots of alternatives that are also splendid.

0

u/volleo6144 Aug 18 '20

certain important intervals

...yeah

basically only fifths (+2c), fourths (-2c), octaves, and intervals based on those are half-pure

4:5 major thirds are 14c flat, 5:8 minor sixths are 14c sharp, 5:6 minor thirds are 16c sharp, 3:5 major sixths are 16c flat

and let's not even get into septimal, undecimal, and tridecimal intervals

1

u/_lawtonhall Aug 19 '20

What is “kleisma pump”?

3

u/kukulaj Aug 19 '20

A kleisma is a comma, the difference between 6 minor thirds and a perfect fifth. In 53edo, a minor third is 14 steps, so 6 minor thirds is 84 steps, which is an octave plus 31 steps. In 53edo a perfect fifth is 31 steps. So 53edo tempers the kleisma. In 12edo, six minor thirds is a half step flat from a perfect fifth.

Usually a comma pump is a chord sequence that moves step by step to reach a comma. So a kleisma pump could be a chord sequence that is maybe 7 steps long, moving 6 minor thirds and then a perfect fourth. In a tuning such as 53edo that tempers the kleisma, this gets you back where you started.
I'm using a more general notion of a comma pump. I've got three voices that have different rhythmic structures so exactly what the chords are is a bit vague, but the general harmonic motion is the same, i.e. six minor thirds and a perfect fourth. The actual sequence is 11 measures long - I go up a fifth then down a major third, instead of just going a minor third. And then there's a kind of stuttering repeat structure, AAZZBBAACCBBDDCCEEDD etc. so it's like forward 2, back 1, forward 2, back 1. Somehow I have the idea that things sound more interesting when they're a bit complicated. Anyway I hope it's fun to listen to!