RE: 19, 22, etc

Firstly, I want to order Neil Haverstick's new CD as well as "Beethoven
in the Temperaments". Will you guys send me the ordering info?

>Bob Valentine wrote,
>}> > Regarding 19TET in particular, perhaps it is the last temperment which
>}> > preserves "sameness" of the "big" and "small" major seconds (9:8, 10:9).
>
>To which Gary Morrison replied,
>
>}> Perhaps this isn't very important (or maybe it is), but this strikes me
>}> as a strange way to think of it. The historical and probably
>}> psychoacoustic basis of Western tuning is Ptolemaic JI, which has two
>}> different sizes of whole step. There is therefore no meaning to
>preserving
>}> an abstraction that represents those two intervals identically. You can't
>}> preserve something ahistorical.
>
>Gary, Bob didn't mean "last" and "preserve" in a historical sense, he meant
>it in a counting sense, going from 12TET up to higher and higher ETs. Of
>course he was not correct, as 31, 43, 50, and 55 demonstrate.
>
>By the way, Gary is incorrect that modern Western musical practice is
>historically derived from Graeco-Roman practice, a point Johnny Reinhard has
>made before. I dispute the psychoacoustic connection as well. Ptolemy
>described many scales, and the reason moderns have for focusing on just one,
>when ascribed to Ptolemy, is a complete distortion of history. If anything,
>the West started with Pythagorean tuning, and progressed from there through
>schismatic to meantone and finally to 12TET (could've been 19 or 31 but for
>convenience and expense).
>
>}The next line in my mail was, "but is this a good thing?", to which I
>}don't know the answer.
>
>I tried to make the case that it is a good thing.
>
>}It was since explained to me that "sameness of the big and small major
>}seconds" is another way of saying "meantone" and there is
>}a historic precedence suggesting that for Western, harmonically oriented
>}music, meantone will result in less (or no) "drift" vs. a non-meantone
>}tuning.
>
>Meantone results in no drift. A C is a C is a C. Other tunings will drift, C
>will often end up around where B used to be. Ben Johnston, a JI composer, has
>used this fact in writing Beethoven-style passages, which he follows with
>other passages that cause the music to drift back up.
>
>Also the equal sizes of whole step are easier to hear, to sing, and make
>modulation much easier. I don't buy that 9:8 and 10:9 are easier to sing as
>purely melodic steps than any mean-whole-tone. Johnny Reinhard will agree
>that the ability to accurately produce melodic intervals acoustically more
>complex than a perfect fourth is a function of rote learning.
>
>}let
>} P5 = number of tempered units per perfect fifth
>} M3 = number of tempered units per major third
>} T = temperment, number of notes per octave
>
>}If I was correct in my understanding, a succinct definition of
>}meantone is that
>
>} 4 * P5 - M3 = T / 2.
>
>T*2, not T/2. Otherwise you are correct.
>
>}Is there a special word for tunings defined by
>
>} 4 * P5 - M3 - 1 = T / 2?
>
>If you mean T*2 instead of T/2, I believe the term "having a syntonic comma
>of one degree" is the most concise description out there. The only such
>tunings I find interesting are 15 and 22. JI is interesting as well, and 34,
>41, 46, and 53 are HASCOOD approximations to JI, which make them second-order
>interesting :) 27 is HASCOOD as well.


SMTPOriginator: tuning@eartha.mills.edu
From: mr88cet@texas.net (Gary Morrison)
Subject: Re: PLANCK CONSTANT
PostedDate: 30-12-97 03:30:09
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