back to list

Vicentino #2

🔗Gene Ward Smith <gwsmith@svpal.org>

3/10/2004 6:25:15 PM

It occurs to me there is at least one other temperament family one
might want to tack Vicentino's name onto. In the 5-limit, it would be
the temperament deriving from the comma 2^72/5^31. As a temperamnet
this isn't much, but out of it you get something which looks like
Vicentino's adaptive tuning scheme, with two meantones separated by
1/4 comma--the mapping being [<31 49 72|, <0 1 0|]. The extensions to
the 7 and 11 limits seem better; the 11-limit mapping would be
[<31 49 72 87 107|, <0 1 0 0 2|], with commas 441/440, 3136/3125, and
41503/41472. In the 7-limit one has 3136/3125 and 823543/819200.
Either gives something which is supported by 186, 217 or 248 and which
is the temperament related to using 217-et for Vicentino-style
adaptive tuning. The TOP generators are not exactly the same for 5, 7,
or 11 limits so you'd take your pick. Does anyone care to suggest a
name before I go and call it "adaptive"?