meantone wolves and subsemitones

>>>[Paul Erlich/Brett Barbaro, TD 140.5:]
>>> The septimal comma is then the meantone "wolf", as is the 36/35.
>>
>> [Dave Keenan, TD 142.10:]
>> I think this is an abuse of the term "wolf". I noticed the same
>> mistake in Edward Dunne's article
>> http://www.math.okstate.edu/~dunne/students/Temperament.html
>>
>> I understand a "wolf" (without qualification) to be a fifth
>> where the error is considered intolerable. It's the meantone
>> G# to Eb that is the wolf, not the G# to Ab (if it existed).
>> Of course one can also speak of a "wolf third" or other
>> badly-tuned normally-consonant interval.
>
> [Paul Erlich/Brett Barbaro, TD 143.4:]
> You are correct. G# to Ab did exist on many Renaissance and
> Baroque keyboards -- perhaps we should call it the meantone
> "subsemitone".

I realize that several different meantones are under consideration
here, but in 1/4-comma meantone, this 'subsemitone' is exactly
the same as the 5-limit JI 'Great Diesis': 125:128 = ~ 41.06 �.

It is defined as such by Ellis in Helmholtz _On the Sensations
of Tone_, in his 'Table of Intervals not exceeding one Octave',
p 453:

[Ellis:]
> "Great Diesis, the defect of 3 major Thirds from an Octave,
> the interval between C# and Db in the meantone temperament,
> 3 Td"

'3 Td' is Ellis's shorthand for 3 '3rds' down, which is the same
as saying 5^-3 in the 'octave'-equivalent prime-factor notation
I use.

-monz

Joseph L. Monzo....................monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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