[ktbwrestler]

This is really interesting and creative! Did you deliberately make some notes sit outside of the standard 440hz diatonic scale? Even when I click your Debussy demo, you’re hitting some notes outside of the normal 440hz scale!

[slaymaker1907]

With the design of this keyboard, only one note (maximum) can be in tune with the 440Hz equal temperament tuning, at least apart from octaves. No complicated proof of this is necessary since the ratio between any two notes in equal temperament is irrational and every note combination on this keyboard is rational. The irrationality of equal temperament is likely part of the reason why equal temperament was no common until relatively recently in human history.

I think the example also highlights why equal temperament is pretty good if you can't change tuning on the fly. Certain keys (the musical theory kind, not the keyboard kind) will sound completely different. At least equal temperament is equally out of tune from just intonation (how singers and instruments with variable pitch tune chords) for every key.

Something from the well-tempered clavier by Bach would likely work a lot better as a demonstration because it doesn't stray nearly as far from the home key. You could also make it work better by maybe adding in some keybindings to adjust the key like harps use. You probably wouldn't even need to add in 12 modes for it since harmonically related keys still work pretty well. Keys like F and Bb work well together because they are close on the circle of fifths, but F and B (natural) will not since they are basically as far apart as possible.

[ad8e]

So, there are two things currently going on with the Debussy example.

The first is, yes, some of the notes from Debussy are actually poorly playable on the piano. One is this: https://i.imgur.com/K0Wuu3Q.png. This is a visualization I built (and which can't be ported to web easily, so unfortunately it's just something I have for now). It's like a scrolling player piano with rising notes, and the numbers next to the bars are what the numerators are. Note there are two 7s in the middle, and pianos are not good at 7s. I've verified these numbers are correct manually, so it's supposed to sound like that and the piano has an inaccurate approximation. This corresponds to this location in the score: https://i.imgur.com/24XY8vR.png

The second is, I suspect there is a mistake near the end. This visualization overlaps the original with the twelve-tone version: https://i.imgur.com/tS7WzRg.png. Note how some of the bars are separated from each other. I'm currently in the process of checking these notes. My original 12ET -> Just Intonation conversion was automatic and I fixed up all the errors I could find, but I could have missed one. EDIT: yes, there was. I fixed it now.

The third doesn't happen in this example, but sometimes composers want to deliberately round, such as in the Circle of Fifths. That would create unpleasant commas. I'm kind of lucky that it didn't happen in the demo I chose. The Circle of Fifths is not actually an issue; first, you can't keep old notes persistent across the whole circle; they will interfere. And second, thanks to Diana Deutsch's experiments on pitch memory, we know that if there are more than 16 notes between the old and new note, you shouldn't be able to discern the comma. However, although the Circle is not a big deal, other rounding intervals can become an issue, like 63/64, where the composer would like the rounding to occur somewhere other than the exact pitch repeat. Listeners are effective at detecting when an exact pitch repeat is slightly inexact, while they have a harder time discerning slightly-off harmonies.

[ktbwrestler]

To specify, the pitch gets wonky on the first melodic phrase after you introduce the first 4 chords. It’s the second note of the melody E A B… A is not tempered at 440hz to the scale!

[ad8e]

I'm not sure we're looking at the same thing, but I fixed an issue with the just intonation transcription. Now, the largest non-transient deviation from 440 Hz scale is 0.14 semitones, caused by Debussy modulating by a third (5/4).

[ktbwrestler]

To clearly show you what sounds off, replicate this

Reload the page

Type .,;m

You’ll notice that m is not the “right” temperament as the dom7 in that arpegio