Ch 36: 31 Spirits; 31-EDO Tuning

~
(David)

I’ve been feeling creatively stifled. The problem is that I’ve been trying to create a style of music I don’t really know.

Gryffe is encouraging me on live comms.

“I listened to some of your other stuff, Dee. Hope you don’t mind, Finn sent it over. It’s more underground, with this nice off-kilter sound. The intervals are almost like — are you using non-standard tuning?”

I have no idea what he’s talking about.

“Uh, I don’t know, I just bend the pitch around until it sounds good to me. I don’t even pay attention to what the notes are. Except for the bass, you know, I just make sure it’s in that 40 Hz to 130 Hz range, depending on the style.”

Gryffe says, “Right, of course. Okay, it just sort of sounds like such small intervals, like it’s 31-EDO tuning.”

Thirty-one. “Did you say thirty-one?”

“Yeah, 31. Does that ring a bell for you?”

I stammer. “Uh, well I just thought, um, no. I don’t even know what that means. Can you explain it?”

“Oh. Ok, well, there’s a system of tuning instruments that some guy invented a long time ago, I mean a really long time ago, way before there were computers or anything, and what it does is it divides each octave—you know what an octave is right?”

“Yes! I know that. Twelve semitones or notes up or down, that’s an octave, and it’s called an octave because, um, like scales, I guess they’re called? —have eight notes.” God I sound like an idiot. “The first and last note are the same note, but like, an octave apart, and if you include all the notes in between that are like, you know, half steps or semitones, or like, not in the scale? - then that is 12 notes. Sorry, I don’t know the terminology.”

“No, no, that’s exactly right! You got it. Twelve semitones or steps in every octave. First and last note are the same, but an octave apart, which just means the higher octave is twice the frequency of the lower one in terms of hertz. It doesn’t matter what terminology you use. And believe me, some of the most popular music is made by people who don’t know theory and all that. In my opinion, theory sometimes gets applied to music after the fact, you know what I mean? It’s really useful but some people don’t need to know it to be creative.”

I feel slightly less fraudulent. “Ok, yeah, octaves, what does it have to do with thirty-one, again?”

“So 31-EDO means ‘31 Equal Division of the Octave’. The octave is divided into 31 notes instead of 12. So there’s a lot more notes to work with. You can get these weird melodies. I don’t know much more about it. But you should look into it. You can set all your synths and sequencers to stick to that tuning if you want.”

“Wow, ok, I’ll try it.”

“But hey, you don’t have to,” Gryffe says quickly. “Like, don’t do it if it changes your workflow. I mean, I used your other melody as-is, I didn’t want to change it. But especially the bass in your more underground stuff, it has this kind of disturbed vibe that sounds honestly a bit mental. You’re giving me an underground revival experience over here.”

“Disturbed, mental — thanks!” We’re laughing again.

Gryffe adds, “Actually, you know, Those would be useful sounds late in the set when it’s really popping off. There might be some contraband going around by the later hours if you know what I mean.”

“Yes, I get it. So we’ll do that instead of the poppier sound. More underground. I can try for something like that.”

Gryffe agrees. Thank God.

I’m sitting in front of the SRI display. Blank canvas. I spoke to Gryffe as if I know what I’m doing. Now I have to come up with something. I don’t know where to start.

I want to learn about this 31-note tuning system, 31-EDO, as quickly as I can.

It’s curious, that number, “31”. It strangely corresponds to the number of “spirits” or chapters in Book I of Trithemius’s Steganographia, the T-1499 text.

Thirty-one chapters, and the 32nd chapter is a kind of summary.

Thirty-one notes, and the 32nd note brings you back around to the first note, one octave up.

Research.

31-EDO tuning has also been called “Tricesimoprimal” tuning. Tri. Trithemius. Another weird coincidence.

Nicola Vicentino (1511 to 1575) is credited with creating 31-EDO tuning. He was an Italian Renaissance-era music theorist and composer, known as a progressive musician. He invented a microtonal harpsichord with a sufficient number of keys to play the 31-note system. The keyboard actually had 5 extra keys beyond the 31 — necessary for practical playability, and allowing ancient Greek “genera” and different temperaments and microtonal intervals to be played with extreme precision.

Vicentino lived from 1511 to 1575. Trithemius died in 1516. I check for any historical references to some connection between them. Did Vicentino ever mention Trithemius? I find no such connection. As far as I can tell, no one has ever even commented on it. But I must say it’s fun to think about this “31” coincidence.

But why 31 notes per octave?

Vicentino was trying to recreate the perfection he believed had been achieved in the music of ancient Greece. He believed the ancient music had extraordinary psychological effects on listeners because of its use of just intonation, a tuning system in which every note’s frequency relates to every other note’s frequency through perfect whole-number ratios, like 3:2 for a perfect fifth or 5:4 for a major third. These mathematically pure intervals produce clean consonant harmonies, without the slight audible “beating” or dissonance one hears when the ratios are slightly off.

The problem with just intonation is that it’s mathematically impossible to create a complete closed system of perfect tuning. Ancient tuning systems tried to do it, but they had to allow for one major unavoidable imperfection.

The medieval-era Pythagorean system of tuning was one example. It prioritized mathematically perfect fifth (3:2) intervals at the cost of harsh sounding thirds. This worked for 11 of the 12 steps in the circle of fifths, but the 12th step inevitably produced a badly out-of-tune fifth interval because of the unavoidable mathematical error that accumulates. If you start with a note, then step up through all the fifth intervals in the octave — the circle of fifths — using this mathematically perfect fifth ratio, you unavoidably run into this badly out-of-tune interval on the last step. It came to be known as the “wolf” interval, so named for its dissonant sound.

Another example was quarter-comma meantone, used in the Renaissance era. It used slightly narrow, slightly “off” fifth intervals to allow perfect major third intervals. It was sort of the same idea as Pythagorean tuning, but to better suit the tastes of the era’s composers, the emphasis was on perfect thirds instead of fifths. But the same out-of-tune “wolf” interval occurred, even worse than Pythagorean, at that 12th step in the circle of fifths.

Music of these eras had to be composed in such a way that the wolf interval was avoided. This meant limiting the number of notes of an octave that were available for composing.

The modern-day approach, 12-EDO tuning, addresses the problem by tuning each of the 12 steps of the octave with a precisely equal interval. Each note is said to be 100 “cents” in tuning away from the next note. And 1200 cents is an octave. This system is a compromise. It accepts the cost of slightly mathematically imperfect intervals to gain the benefit of all intervals being musically useful. No wolf interval. Modern ears are so accustomed to the sound of 12-EDO intervals that we perceive it as perfectly tuned.

But Vicentino dealt with these tuning issues in a totally different way. He abandoned the 12-note framework entirely. His 31-EDO system divided the octave into 31 equally-spaced steps instead of 12. Whereas in 12-EDO each note is a standard 100 cents apart in tuning, in 31-EDO each note is 38.7 cents apart. This tuning distributed the mathematical error so thinly across so many notes that no single interval became a “wolf”. And within all these extra notes, fifth and third intervals could be found that were so close to mathematical perfection, no human could hear the difference.

This tuning approached the mythical Greek ideal as closely as practically possible without creating an unmanageable number of notes to the octave.

But despite all this musical and mathematical theory about pure thirds and fifths, the main attraction of Vicentino’s tuning system was the availability of all these extra notes for creating melodies and harmonies. Even in Vicentino’s own compositions, the main attraction of the music was the possibility of a strange, unfamiliar sound, if desired. The sound of the small intervals was arguably more important than just the perfect tuning.

And when I listen to examples, I have to agree. The achievement of almost-perfect intervals pales in comparison to the interest created by these odd, narrow melodic and harmonic intervals between the notes.

Most interesting of all, to me, is that this 31-EDO tuning creates a sound that reminds me of the old 21st century classical “underground” style of Drum & Bass or some dark or minimal techno production. 31-EDO seems to encourage the sound of those melodies — always deliberately odd-sounding, or “off kilter” as Gryffe put it. And that sound became conventional in that music. It just didn’t sound right if the melodies used standard intervals. Honestly, if you put a conventional melody over a 174 bpm beat, it often sounds stupid.

For years I’ve been imitating that sound just by moving the continuous pitch controller around, finding those random “in-between” pitches until I like the sound.

I mean, it usually sounds shit when I do it, but sometimes it randomly turns out good.

But now it seems I can achieve the same sound by hitting specific notes in the 31-EDO tuning system. Maybe this will let me work faster. Maybe I’ll get some kind of theoretical understanding of it, and I can use it systematically.

So I set up my SRI system for 31-EDO tuning. When I generate notes, they’ll all stick to the 31-EDO intervals.

As soon as I start playing around with sounds, I notice that interesting things are happening.

I’m immediately preoccupied by thoughts of how this tuning might interact with the SRI’s “language effect”.

It would be funny, wouldn’t it, if somehow the 31 notes made it easier to control the language effect. I know that realistically this is a fantasy, but it’s entertaining to think about.

Just like some of the conspiracy theories, or all this stuff about Trithemius — entertaining, but that doesn’t mean you believe it.

I’ll just try it. I’ll have to create some snippets of music, then listen as plain audio as I did in my earlier experiments.