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Notating Augmented and Tripletone

🔗Gene Ward Smith <genewardsmith@juno.com> <genewardsmith@juno.com>

1/10/2003 1:43:27 AM

"Augmented" is the name I've given the 7-limit linear temperament with wedgie [3, 0, 6, 14, -1, -7] and TM basis [36/35, 128/125]; and
"Tripletone" is my name for the system with wedgie
[3, 0, -6, -14, 18, -7] and TM basis [64/63, 126/125]. Unless we are in 12-et these are different systems and need different names; they cannot both be called "augmented".

Tripletone has a 7-limit poptimal generator of 2/27 and a 9-limit one
of 5/66. I would suggest 2/27. Augmented has 8/33 for a 7-limit poptimal and 11/45 in the 9-limit. The 33 et seems a reasonable choice to me, but 12 would be an alterative.

Any opinions on this?