J. Sundberg's Harmony and Tonality available on-line!

http://www.speech.kth.se/music/publications/kma/papers/kma54-ocr.pdf

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
> http://www.speech.kth.se/music/publications/kma/papers/kma54-ocr.pdf

Page 17 of this has ain interesting diagram, according to which the
closest key to C is a, then e, then c. You could try to measure this
and use it for a metric on the 5-limit lattice and the dual hexagonal
tiling of triads.

Ugh. Could someone translate this for non-scientists?

Joe

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
> http://www.speech.kth.se/music/publications/kma/papers/kma54-ocr.pdf
>

Kalle Aho wrote:
> http://www.speech.kth.se/music/publications/kma/papers/kma54-ocr.pdf

I'm looking at the second Krumhansl paper now. She gives a generator for the Bohlen-Pierce scale which gives the same rank 2 temperament currently in my (hopelessly out of date) catalog as originating with Dan Stearns. So presumably she has precedence and whoever's keeping track of these things now should take note.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Kalle Aho wrote:
> > http://www.speech.kth.se/music/publications/kma/papers/kma54-ocr.pdf
>
> I'm looking at the second Krumhansl paper now. She gives a generator
> for the Bohlen-Pierce scale which gives the same rank 2 temperament
> currently in my (hopelessly out of date) catalog as originating with
Dan
> Stearns. So presumably she has precedence and whoever's keeping track
> of these things now should take note.

I don't know if anyone is keeping track. However, since we have two
names, I propose the following: one name goes to the rank-two
temperament (and by inclusion, the rank-one no twos temperament)
tempering out 3125/3087, plus more in higher limits, and the other
goes to the 37&41 temperament. The latter has [14 11 9 -6 -7] as a
generator mapping/OE part of wedgie. It can be construed as having a
generator of 13/11 in the 13-limit, for which 25/21 has to make do in
the 7-limit.

The deep dark secret of BP stuff is that since 3 is 65 steps in 41-et,
and since that is divisible by 13, the BP scale and other BP
manifestations have an interpretation in 41-et, and this would be an
example.

Dan, would you object to having your name epoxied onto one of these?