TIA Perceptual Tuning

+thegoldenband · October 22, 2020

5 hours ago, bizarrostormy said:

Sorry for the necrobump, but I would like to register my disagreement. In song form!

Pretty cool, and very nice work! You're quite right, the VCS does surprisingly well here. Only in the closing measures do the intonation difficulties become a problem, particularly around the second and fourth scale degrees (G and Bb), which seems to match up with G4 and Bb4 being marked as well out-of-tune on your spreadsheet.

Bach's idiom makes it easy to ignore the changing timbres. Applying a harpsichord-like envelope to each note -- so that it has a strong attack and quick decay -- would make that even less noticeable, and would be stylistically appropriate too. Not sure if Slocum's drivers allow for that.

For some reason I'm getting a bunch of divide by zero errors on the F Major tab of your spreadsheet when I view it in-browser, but when I download it, those go away. Probably an issue on my end?

+Pat Brady · October 23, 2020

22 minutes ago, thegoldenband said:

Pretty cool, and very nice work! You're quite right, the VCS does surprisingly well here. Only in the closing measures do the intonation difficulties become a problem, particularly around the second and fourth scale degrees (G and Bb), which seems to match up with G4 and Bb4 being marked as well out-of-tune on your spreadsheet.

Bach's idiom makes it easy to ignore the changing timbres. Applying a harpsichord-like envelope to each note -- so that it has a strong attack and quick decay -- would make that even less noticeable, and would be stylistically appropriate too. Not sure if Slocum's drivers allow for that.

For some reason I'm getting a bunch of divide by zero errors on the F Major tab of your spreadsheet when I view it in-browser, but when I download it, those go away. Probably an issue on my end?

Thanks!

As written, there are a bunch of G4s and Bb4s, and my first attempt sounded fairly awful. I nearly gave up, intending to find another piece/song better suited to this tuning. Instead I shifted most of the right-hand (treble clef) part down an octave, and the last measure up an octave, to avoid those notes. I didn't get rid of all of them, as you noticed. I've attached a revision that's more interventionist with octave shifts, but avoids G4 and Bb4 altogether (and some other slight changes).

Agree about the changing timbres. It also helps to take care in adjusting the volume per waveform. I don't see any way in this driver to set envelopes.

The spreadsheet formulas are complicated enough that most of them are in a script. The script generates all of the TIA frequencies, all the POKEY values, and all the POKEY frequencies for 8 different POKEY settings. It shows DIV0 and other errors while waiting for the script to return. Sometimes that happens quickly, sometimes it takes a while.

To delve into the math a bit: frequency-division synthesis is in tune when the period of the tonic is an integer multiple of the numerator of the frequency ratio.

For just intonation, if TIA AUDF = $1D is the tonic, the period is decimal 30. The major second (10/9 frequency ratio), minor third (6/5), major third (5/4), fifth (3/2), major sixth (5/3), and major seventh (15/8), and the tonic and several other notes an octave up will all be in tune. But the fourth (4/3) and minor sixth (8/5) are not.

OTOH if TIA AUDF = $17 is the tonic, as in the A major scale recommended by RevEng and also shown in my A major (15 kHz basis) table, the period is decimal 24. The minor third, fourth, fifth, minor sixth and octave are in tune, and the major third is sharp but usable, but major and minor seconds, major sixths, and major and minor sevenths are all way off.

In this particular F major tuning, the tonic is available at both AUDF = $1D (with AUDC = $0C) and AUDF = $17 (with AUDC = $01), so at the cost of switching waveforms, for tuning we get the best of both worlds, including every note in the scale from F3 to F4, several of the accidentals, and many notes in other octaves.

bwv856p.bin