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Beep, orwell, and schismic

🔗Gene Ward Smith <gwsmith@svpal.org>

7/4/2004 10:28:10 PM

Beep is the temperament with wedgie <<2 3 1 0 -4 -6||, the 5-limit
comma of which is 27/25. This 5-limit temperament and 7-limit beep
overlap, with 7/31 as a common poptimal generator. A 7-limit
temperament with generator 7/31 representing a 7/6 sounds like orwell,
however. In fact, if you run beep out very far it will run into the
orwell range, and we have the phenomenon we've discussed where a
temperament gets out of its applicable range, so to speak. Evidently
this happens pretty soon for 7-limit beep.

Meanwhile, the 9-limit version of beep is completely different so far
as poptimal tuning goes, with 3/14 a poptimal generator.

A very different example is provided by schismic. Here the 5-limit
temperament has 169/289 as a poptimal generator; the fifth in question
is very slightly flatter than the range for 7 or 9 limit schismic, by
which I mean the temperament adding 4375/4374 to the schisma, which
171-et does well, but not so well as to give us a poptimal generator.
To get one for 7 and 9 limit schismic, we need to go to 1031/1763,
1131/1934, etc. You could name it after famous people associated to
the year in question, if you didn't like using "schismic" for a
7-limit temperament with a different TOP tuning, even if only slightly
different, than its 5-limit reduction. In that case I would suggest
using pontiac, for 1763, rather than hitler, for the year in which he
became the German Fuehrer. But that's just me.

Meanwhile, garibaldi is quite happy, for both the 7 and 9 limits, with
94-equal.