Re : Re: 13 note just intonation

Muenda qwa sahure wrote:

----------

> i believe that the following tuning system yields just intonation in all
> twelve keys, each key being unique, and a plausible circularity of fifths.
>
> C = 1/1
>
> C# = 16/15
>
> D = 9/8
>
> D# = 32/27
>
> E = 5/4
>
> F = 4/3
>
> F# = (45/32 64/45)
>
> G = 3/2
>
> G# = 8/5
>
> A = 27/16
>
> A# = 16/9
>
> B = 15/8

This makes a circle of virtually perfect 3/2s from Gb to F#, except A/E and
Ab/Eb which are almost 22 cents too small. The use of the 13th step only
'corrects' the difference between F# and Gb. To obtain a (5-limit)just
intonation for all twelve keys,too many 5/4s will be out of tune. I agree
with Paul Ehrlich:
most harmonies will not deserve the label 'just intonation'. I think that if
a piece of music deliberately limits itself to thirds and fifths and
never uses any 7ths in an harmonic way, it's more practical to fixe the
quality of each interval within the piece itself. I do play a lot of
renaissance music like this, ajusting moveable frets on the guitar for each
piece, many times choosing different values on different strings. E.g. a low
F# on the 6th string and a high F# on the 1st string.

Wim Hoogewerf, Paris