Tuning the Dorian Mode

A couple of weeks ago, several people posted about the tuning of the
Dorian mode. I don't think the tuning is absolute, but here's one way
to derive a tuning for it.

Begin with a scale in just intonation:

C D E F G A B C
1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1
9/8 10/9 16/15 9/8 10/9 9/8 16/15

Start the Dorian scale on the second scale degree of the just scale, and
make the new starting pitch 1/1:

D E F G A B C D
9/8 5/4 4/3 3/2 5/3 15/8 2/1 9/8
becomes
1/1 10/9 32/27 4/3 40/27 5/3 16/9 2/1
10/9 16/15 9/8 10/9 9/8 16/15 9/8

In this new scale, the fifth, minor third and major second are all flat,
so retune these pitches for this scale as follows:

D E F G A B C D
1/1 9/8 6/5 4/3 3/2 5/3 16/9 2/1
9/8 16/15 10/9 10/9 9/8 16/15 9/8

Using this tuning for the original scale (in case you can't move your 1/1)
gives the following pitches:

C D E F G A B C D
1/1 9/8 81/64 27/20 3/2 27/16 15/8 2/1 9/4
9/8 9/8 16/15 10/9 10/9 9/8 16/15 9/8

Best,

Lydia Ayers

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