source file: m1399.txt Date: Tue, 28 Apr 1998 23:34:10 -0500 Subject: Re: JI Tuning Resolution From: "jloffink" > From: Daniel Wolf > Perhaps you misunderstood me. If the tuning resolution is, for example, 1 > Hz, in lower registers there is going to be good intonation for the > harmonic series above 1 Hz, and all else will be rough approximations. I > think that the contrast between the exact and approximate tunings would be > musically unacceptable (with a resolution of 1 Hz, try modulating from the > key of 80 Hz to its subdominant!). If I can't have a tuning with the > accuracy of the Rayna, then I would like the potential deviation from Just > to be spread around as much as possible in a temperament that represents > harmonic identities consistently. As long as you are not working with > sustained textures that really require something like the Rayna, I think > that absolute frequency resolution will be secondary to consistency. I made > the suggestion that equal-tempered division of the octave divisible by 12 > be considered because, MIDI standard or not, tuning tables seem to be > expressed at the software level most often in terms of unit deviations from > 12tet pitch classes, not in terms of octave divisions alone, and > manufacturers will probably be interested in supporting microtonal capacity > only when that does not eliminate an accurate 12tet. From my experience, > 768tet and 1200tet are not good choices but there are ET of this magnitude > that would be better. > No, I understood you perfectly. The MIDI Tuning Standard has a maximum resolution of 100 cents / 2^14 = .0061 cents. Only 768TET, 1536 TET, 3072TET, etc. fit within that standard. Trying to achieve some other nTET with better consistency will have several problems from a practical standpoint: 1. The MIDI Tuning Standard, while currently implemented by only three manufacturers (Emu, Ensoniq and Turtle Beach), is the only standard we've got. To propose some division of the semitone other than its 2^n divisions would set back the little progress it has made. I know some list members are disappointed over the lack of response to the MIDI Tuning Standard, but this is to be expected given the design life cycles of these instrument lines that amount to 3-8 years on average. 2. Division of the octave or semitone by other than binary multiples is not likely to be accepted by manufacturers. They have no margin timewise for anything more complicated than binary multiplication/division in calculating pitch. Remember that they are using microprocessors like the 68000, 68340 (68020 comparible), or 68020 running at 16 to 25 MHz, not the latest Pentium or RISC processor. While this situation will improve in the future, the increase in voice count is likely to eat up any processing speed improvements. 3. My impression is that instruments with "1 cent resolution" actually map some 100 cent / 2^n division to the 1 cent value. The Ensoniq EPS/16Plus/ASR-10 certainly do this. I believe Roland does it as well. The actual scale is stored as 100 / 2^n divisions, usually 768TET, not 1 cent. This could explain why some list members have worse results with these instruments since the conversion errors are not consistent. For instance, if you want to adjust a pitch by +0.6 cents, you would round up to 1 cent. The 1 cent value on your synth display is closest to 1.5625 cents, so now your pitch is adjusted by +1.5625 cents, instead of 0 cents which would have been closer. Perhaps one request should be to show the actual cents values to several decimal places, not roughly translated values or hard to decipher tuning units. John Loffink jloffink@pdq.net