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Jorgensen Temperament

🔗Mike Battaglia <battaglia01@...>

3/3/2012 1:25:13 PM

This was a conversation from XA:

Melle Weijters I don't know if I follow that language. I'll go over to
the xenharmonic wiki and read some of the grammar and do my homework.
In the book, he writes about the Jorgensen comma and how it
distributes among the intervals, but I don't get how it works in
combination of your answer. In the end, the 5 and 7 temperament is a
selection of twelve tones taken from the 70 equal tones to the octave
about an hour ago · Like

Melle Weijters ‎(oops, entered too early...) and then the word scale
might be the best way to describe it. But, reading the whole chapter,
he was quite serious about it.
about an hour ago · Like

Paul Erlich What is the Jorgensen comma??
about an hour ago via mobile · Like

Melle Weijters and I quote: "the Jorgensen comma is the excess of 41
octaves over 70 fifths. <insert math> 1.03715 which in rounded numbers
is 63.15 cents in size. The fourths F Bb and F# B are each narrowed by
exactly 1/70 Jorgensen comma, and the fifths Bb F and B F# are each
widened by exactly 1/70 Jorgensen comma. Thus the ratio of the fifths
Bb F and B F# is <insert match> The effect of the latter fourths and
fifths is similar to that of Just Intonation. All the white key fifths
are narrowed by a little more than 1/4 Jorgensen comma and all the
black key fifths are widened by approximately 57/200 Jorgensen comma."
about an hour ago · Like

------------

So the "Jorgensen comma" could perhaps be said to correspond to the
val <70 111|, or to this 5-limit temperament then, which I suppose
should be "Jorgensen temperament":

http://x31eq.com/cgi-bin/rt.cgi?ets=140_70&limit=5

It tempers out 2596148429267413814265248164610048/2503155504993241601315571986085849.

I doubt it's practically useful in any meaningful sense, but I suppose
historically interesting.

-Mike