From Paul Erlich

Paul asked me to post his reply to my "Old Bone" post, while he tries to
sort out his MIME problem...


>>But there is something special about JI as far as modulatory effects
>>go: its consistency level is infinite. 72tET is only level 2 consistent at
>>the 11 limit. Any modulation in JI following a chain of 3 or more 11/8's
>>will no longer be represented consistently in 72tET.

I don't think a chain of 3 (or even 2) 11/8s results in an acoustically
recognizable interval; if the individual 11/8s are tuned well enough,
that's all that can matter. And even if the resultant interval were
acoustically recognizable, we're talking about the case of modulation
where the interval occurs not as a simultaneity but with the tones
seperated over quite a span of time. So level 3 consistency in the
context of modulation is a double irrelevancy.

The 11/8 in 72tET is 1 cent off. If you really think this discrepancy
makes certain modulation effects impossible, you should (a) perform some
listening experiments and (b) remember that it was Partch himself who,
when told that JI made ordinary modulations impossible, allowed the
22-cent syntonic comma "correction" which would not be noticeable enough
to impede the sense of modulation.

>>I must confess I do not know if such a modulation appears in Partch's
>>music. Careful listening would tell. Such a modulation is not
>>possible in the 11 limit tonality diamond as such. But Partch was not
tied >>to the diamond as such. He added secondary tonalities as he needed
them, >>and I'm sure he would have no problem with modulating the entire
diamond by
>>some interval.

Sure, but as far as strictly defined notated pitches, didn't he stick to
43? No room for transposed tonality diamonds on 11 identities.


Third irrelevancy: I consider plain old, simultanoeus-sounding, level-1
consistency to be important for ETs up to 34, and possibly 69. Beyond
that, the tones are less than 1% different from one another, so in most
musical circumstances what you have is tantamount to a continuous
spectrum of pitch.