Re: 72-tet

I agree that Aristoxenos was not really proposing equal temperament and AFAIK no Greek theorist ever thought he did. The doctrine of 30 parts to the fourth, 12 to the tone, 6 to the semitone, etc. is due to a later writer, Cleonides--Aristoxenos spoke just of parts of a tone. Eratosthenes clearly mistook these parts for parts of a real string and Ptolemy repeated the error in the Harmonics.

BTW, Julian Carrillo had a 72-tone piano built, but as far as know never wrote any music specifically for it or analysed the tuning for its harmonic properties.

--John

--- In tuning@yahoogroups.com, "John H. Chalmers" <JHCHALMERS@...> wrote:
>
> I agree that Aristoxenos was not really proposing equal temperament and
> AFAIK no Greek theorist ever thought he did.

Evidence? If he didn't mean to divide the tone evenly, then what did he mean? He certainly didn't mean chopping it up using rational intervals!

The doctrine of 30 parts to
> the fourth, 12 to the tone, 6 to the semitone, etc. is due to a later
> writer, Cleonides--Aristoxenos spoke just of parts of a tone.

From what Aristoxenos wrote, you can immediately deduce the 30 parts to the fourth, 12 to the tone, 6 to the semitone. But that's hardly relevant, since now you seem to be saying Cleonides invented 72 equal. Is that what you are saying, and if not, what are you saying?

> Eratosthenes clearly mistook these parts for parts of a real string and
> Ptolemy repeated the error in the Harmonics.

Which seems to have no relevance.

> BTW, Julian Carrillo had a 72-tone piano built, but as far as know never
> wrote any music specifically for it or analysed the tuning for its
> harmonic properties.

Did Haba try to analyze it?