Re: Digest Number 447

> Dave Hill wrote,
>
>>One music professor told me that he
>>had always been told that the deviations in pitches
>>introduced by equal temperament were so small that
>>they had a negligible effect on the way the music
>>sounded. When he heard side by side piano performances
>>of simple pieces in equal temperament and mean tone
>>temperament he said that to his surprise he found that
>>there was a big difference and that to him the mean
>>tone version sounded better than did the equal tempered
>>version. After having heard the comparison, his reaction
>>was that it seemed to him difficult to understand how
>>equal temperament could have been universally adopted
>>by the music world.
>
And Paul Erlich replied:

> Good work Dave! We need to expose all music professors to this!

Some of us are trying--and occasionally finding a ready and receptive
audience. A few years ago I presented a lecture/demonstration on "acoustic
tuning" (for lack of a better name) to the National Convention of the
American Choral Directors Association. It was largely an attempt to
demonstrate the difference between piano pitches and aural tuning and that
listening to keyboard "models" of vocal "parts" would not likely lead to
stunning performances. Some of those folks had never heard the difference,
so needless to say it started some worthwhile conversation.

On the other hand, when I brought up the subject in regard to ear-training
classes in our own department meeting, the chairman said, in effect, "Jerry,
why do you persist in this crusade; our music system is firmly based on
twelve-tone equal temperament." Do you suppose the fact that he has authored
a music fundamentals book based on that premise has anything to do with his
position?

It ain't gonna be easy.

Gerald Eskelin

From Paul Erlich:
>
> 730-tET can be found in Paul Hahn's
> http://library.wustl.edu/~manynote/consist2.txt
> (This chart only shows those ETs which have a higher consistency level at
> some harmonic limit than all lower-numbered ETs, and goes up to 10000TET.)
>
> In Paul Hahn's terminology, 730-tET is consistent at the 5-limit to level
> 22, meaning that any interval constructed of any combination of up to 22
> consonant 5-limit intervals (minor thirds, major thirds, perfect fourths)
> will be represented the same way whether the interval is first computed in
> JI and then rounded to 730-tET, or if the consonant intervals are rounded to
> 730-tET first and then combined. By comparison, 12-tET is consistent at the
> 5-limit only to level 3: the ratio 648:625 (often called the greater
> diesis) can be constructed from four 6:5 minor thirds; while four minor
> thirds (minus an octave) add up to a unison in 12-tET, the actual size of
> 648:625 in JI is 62.565 cents, so it rounds up to one step in 12-tET. 53-tET
> is consistent at the 5-limit to level 8.
>
> Bosanquet's 612-tET is almost as good, as it is consistent at the 5-limit to
> level 21. In order to improve on the consistency level of 730-tET in the
> 5-limit, one would have to go up to 1783-tET, which is consistent to level
> 42 (heh, I just said level 42), and then to improve on that, 4296-tET is
> 5-limit consistent to level 119. Note that 4296 is a multiple of 12. So if
> you wanted to get a 12-tET-based synthesizer to provide ridiculously exact
> JI (5-limit consonances within 0.002 cents of just), you could design it to
> divide the semitone into 4296/12 = 358 equal parts . . . Being a little more
> realistic, note that 612 is also divisible by 12 and gives 5-limit
> consonances within 0.093 cents of just . . .
>
Jis 1 questshun. Duz ah need ta no dis stuff tah sang da blues? :-)

(No disrespect, Paul; just couldn't resist.)

GRE