re 19, 22, etc

>
> > Regarding 19TET in particular, perhaps it is the last temperment which
> > preserves "sameness" of the "big" and "small" major seconds (9:8, 10:9).
>
> 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.
>

The next line in my mail was, "but is this a good thing?", to which I
don't know the answer.

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.

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.

(a few examples T M3 P5
12 4 7
19 6 11
31 10 18)

Is there a special word for tunings defined by

4 * P5 - M3 - 1 = T / 2?

(a few examples T M3 P5
22 7 13
34 11 20
53 17 31)

thanks, and by the way, what does 88cet mean? Each tone having 88 cents?

Bob Valentine



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