Re: [tuning] Strictly Proper/All Prime Scale Correction

Jacky,

"Guide tone" (Du: gidstoon) is Fokker's term for the lowest common
multiple; the opposite of "fundamental", i.e. greatest common divisor.
If a chord contains these two tones as well as all tones in between
which are both a submultiple resp. multiple of them, then you have a
chord which Euler called a "complete chord". An example is 1:3:5:15.
For your scale the guide tone is a very high number. Because it's
higher than 2^31, Scala doesn't compute it. Such a high number is
meaningless.

Rothenberg's stability is defined as the portion of the intervals
which are unique to one interval class, out of all possible intervals.
For example the major scale in 12-tET has a stability of 20/21,
because there are 2 occurrences of the 600 cents tritone, one for
interval class 3 and one for 4 (do SHOW INTERVALS or SHOW/TOTAL
INTERVALS to see this). There are 6*7 intervals so the stability is
(42-2)/42.

The odd number limit listed in your post is wrong. It should be 841
(O: 841 U: 713) for your scale. This bug will be fixed in the next
release.

Manuel Op de Coul coul@ezh.nl