Monday, December 31, 2007

Shortspeak for Intervals of 31tET

I expect at least (& probably at most) one reader to have interest in this:

Shortspeak for Intervals of 31tET

scale degreecentslongnameshortname
00perfect unisonprsu
139greater unisongosu
277lesser toneleto
3116minor tonemito
4155neutral tonenuto
5194major tonejato
6232greater tonegoto
7271lesser thirdledi
8310minor thirdmidi
9348neutral thirdnudi
10387major thirdjadi
11426greater thirdgodi
12465lesser fourthlefo
13503perfect fourthprfo
14542greater fourthgofo
15581lesser tritoneletr
16619greater tritonegotr
17658lesser fifthlefi
18697perfect fifthprfi
19735greater fifthgofi
20774lesser sixthlexa
21813minor sixthmixa
22852neutral sixthnuxa
23890major sixthjaxa
24929greater sixthgoxa
25968lesser seventhlevu
261006minor seventhmivu
271045neutral seventhnuvu
281084major seventhjavu
291123greater seventhgovu
301161lesser octaveleco
311200perfect octaveprco

Some explanation: Here I have tried to create a logical, internally consistent way to refer to th various intervals of th microtonal division of th octave into 31 steps (as opposed to th more common 12 steps), 31-tone equal temperament, or 31tET.

Each interval "shortname" I've devised has exactly two simple syllables of two letters to facilitate its easy & speedy utterance. I have taken a set of common names for th intervals already in existence & used them as a jumping-off point. You'll notice I've done away with th words subminor, supermajor, diminished, & augmented in favor of th more consistent lesser & greater. In a system with more notes, those types of distinctions could prove important, but I believe it gets in th way here, so I've simplified.

Below I have listed th two-letter particle words. In each case, at least one prominent letter (often two) of th original word you will find in its particle. You'll notice that I've changed some vowels from th original words. I did this to ensure that th particles sound distinct from one another. I have made sure that all five vowels appear in th suffixes & prefixes. You'll also notice that I've reversed th order of letters from some of th original words. I did this to put each particle in consonant-vowel form, to allow it to function cooperatively with th other particles to aid pronunciation.

le- :: lesser.
mi- :: minor.
nu- :: neutral.
ja- :: major. Note letter reversal. You could pronounce it jah or jay, altho I prefer th former.
go- :: greater. I changed th vowel for variety.
pr- :: perfect. Pronounce it like per.

-su :: unison. Note letter reversal.
-to :: tone, as in second.
-di :: third. Note letter reversal.
-fo :: fourth.
-tr :: tritone. Altho it's three letters, tri also works very well, & may sound better to you.
-fi :: fifth. Pronounce like fee.
-xa :: sixth. I changed th vowel for variety.
-vu :: seventh. I changed th vowel for variety.
-co :: octave. Note letter reversal.


Anonymous said...


Having two syllables is perfect for practicing singing melodic intervals. Would your permit switching the order of syllables? It would be neat for one ordering to mean the interval travelling in the upwards direction, and the other, down. But also, and unrelatedly, I tend to imagine two-syllable words with the first syllable accented - how have you been saying them to yourself? - and I want the shortname to "stress" the interval-class before the inflection; it's analogous to languages that put the noun before the adjective.

As to the particles themselves...brilliant. I kind of wish that "third" was -dr, a phonetic reversal. Whayou think?

Andrew Aaron Heathwaite said...


It pleases me that you find value in this system. I came up with something very similar a while ago for 17tET, so it didn't take much to apply it to 31.

I hadn't thought of switching th order of th syllables. I have no opposition, & it makes sense to distinguish between ascending & descending intervals. However, doing so would contradict your statement, "I want the shortname to "stress" the interval-class before the inflection."

I say them as you do, with accent on th first syllable - a trochee.

Making thirds "-dr" does not bother me except that, generally speaking, I tend to enjoy singing "i" more than "r". According to classical singing diction, "r" counts as a vowel, so "-dr" works.

(However, it might negatively affect th unconscious sexiness of th system when th "neutral third" sounds more like "neuter" than "nudie". Hee hee.)

Th "i" exists already in "fi" for fifth. So "dr" probably makes more sense, fitting better with th English & providing variety.

¤ ¤ ¤

I thought of a possible downside to using this system. By giving one name to some of th more ambiguous intervals, like, say, th 465 cent interval I've labelled "lesser fourth, lefo," it unconsciously implies & thus limits their function. In practice these past few days, I've found that "lefo" can sound very much like a third, rather than a fourth. (Admittedly, an extremely wide third.)

I don't know if we could remove this bias in dealing with ambiguous intervals, nor whether it really matters. It does not bother me to use something called "lesser fourth" as a third in appropriate contexts.

~a th nn