any ideas?

A Tribonacci parallel to Kornerup's "Golden Meantone" Fibonacci tuning
could be derived from the following series where the proportion of the
fifth to the third would equal the Tribonacci constant (as,
logarithmically speaking, the numerator of the previous fraction is
the third of the denominator of the fraction that follows it, and the
numerator of each fraction is the fifth of its denominator... L/s
gives the Tribonacci constant here as well):

1 1 2 4
---, ---, ---, ---, ...
2 2 3 7

Here's the rotation of scales (in rounded cents):

0 208 383 496 704 879 1087 1200
0 175 288 496 671 879 992 1200
0 113 321 496 704 817 1025 1200
0 208 383 591 704 912 1087 1200
0 175 383 496 704 879 992 1200
0 208 321 529 704 817 1025 1200
0 113 321 496 609 817 992 1200

Any suggestions for an apropos "Golden Meantone" like name for this
scale?

--Dan Stearns

Dan wrote,

>as,
>logarithmically speaking, the numerator of the previous fraction is
>the third of the denominator of the fraction that follows it, and the
>numerator of each fraction is the fifth of its denominator...

What does that mean?

Paul,

I mean it in the same sense as Yasser's Fibonacci series (1/2, 3/5,
4/7, ...) where the numerator is the fifth of the denominator. Except
that in the Tribonacci series I gave (1/2, 1/2, 2/3, 4/7, ...), I'm
also taking the numerator of the preceding fraction as the third...

So if the series is carried out to 22-tET:

1/2, 1/2, 2/3, 4/7, 7/12, 13/22

1:2^(13/22) would be the fifth and 1:2^(7/22) would be the third. And
the Tribonacci series is working the proportion of the thirds and the
fifths so that the product of the third and the Tribonacci constant
equals the fifth. This also makes the large step the product of the
small step and the Tribonacci constant.

--Dan Stearns

Dan wrote,

>I mean it in the same sense as Yasser's Fibonacci series (1/2, 3/5,
>4/7, ...) where the numerator is the fifth of the denominator.

That's not true: the series continues 7/12, 12/19, 19/31, but the fifth of
19 is 11 and the fifth of 31 is 18.

I wrote,

<<I mean it in the same sense as Yasser's Fibonacci series (1/2, 3/5,
4/7, ...) where the numerator is the fifth of the denominator.>>

Paul Erlich wrote,

<<That's not true: the series continues 7/12, 12/19, 19/31, but the
fifth of 19 is 11 and the fifth of 31 is 18.>>

Not the series I gave (1/2, 3/5, 4/7, ...). This gives both the Yasser
and the Kornerup interpretation that you mention... it's all in how
you read it I suppose, but it's really only the Kornerup type parallel
that I'm interested in here anyway, as the Yasser series of MOS
m-out-of-n scales would not work the same way in the Tribonacci
example, I just used the Yasser example to hopefully better illustrate
what I was doing... anyway, did you get what I was trying to get at
before any better now?

--Dan Stearns

I wrote,

><<That's not true: the series continues 7/12, 12/19, 19/31, but the
>fifth of 19 is 11 and the fifth of 31 is 18.>>

>Not the series I gave (1/2, 3/5, 4/7, ...). This gives both the Yasser
>and the Kornerup interpretation that you mention...

Can you show how?

Oh, never mind, Dan, I was looking at this wrong . . . anyway, let me think
about it . . .