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another Pythagorean question...

🔗D.Stearns <STEARNS@CAPECOD.NET>

6/12/2000 12:52:38 AM

Is there any historical, musical precedent for 7-limit extended
Pythagorean similes? In other words some occurrence of a Pythagorean
mapping that utilizes both the 32805/32768 and the 33554432/33480783
where "enharmonic" spellings represent differences of the syntonic and
septimal comma (e.g., F = 4/3, E# = 27/20, and Gbb = 21/16, etc.) and
shared schismatic spellings absorb the 225/224 (e.g., C# = 16/15 and
15/14, etc.):

---Bbb-----Fb------Cb------Gb---
/ \ F# / \ C# / \ G# /
/ \ / \ / \ /
/ Fbb\ / Cbb\ / Gbb\ /
----F-------C-------G-------D----
/ \ Cx / \ Gx / \ Dx /
/ \ / \ / \ /
/ Cb \ / Gb \ / Db \ /
---C#------G#------D#------A#---

thanks,
Dan