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A mythical non-octave scale?

🔗Gene Ward Smith <gwsmith@svpal.org>

8/17/2004 4:30:52 PM

The scale with generator (7/5)^(1/15) is presented on nonoctave.com as
a nonoctave scale

http://www.nonoctave.com/tuning/LilMissScaleOven/gallery.html#octave

However, the most obvious way to interpret it is as a stretched-octave
tuning of 31-equal. It stretches the octave by 3.86 cents, which is
quite a bit more than the TOP tuning of 1.48 cents. I imagine it would
be more than the zeta tuning also if I took the trouble to find what
that is, but it is *not* more than the errors of some of the listed
approximations; we have a 5/3 off by 8.8 cents, for instance. The only
reason the octave is not on the list is that it's not on the list, but
strangely, many other intervals with 2 as a factor are.

I've mentioned before that the 88 cent NO scale is suspicously like
octacot where you ignore the octaves, but at least if you take a
generator of 5/68 you don't run into an octave. It's therefore a true
NO scale even if it is loaded to the gills with intervals containing
2. In fact, the generator looks like a 21/20, two generators giving a
10/9, three a 7/6, and only when we get to five do we have 9/7.

Incidentally, an interesting 88 generator to try would be Golden 88:

6/62 - sqrt(5)/310; 13, 14, 27, 41, 68, 109, 177, 286 ...

It has a cents value of 88.118 cents, which you might compare to the
(7/4)^(1/11) value of 88.075 cents Scott recommends. Of course a
golden value makes sense only if you intend to reduce to the octave!