Re: Dan's over / under scales - non octave generalisation

HI Dan,

Try 4 for the non octave
and the best value for x is 2,
and all the scales are symmetrical.

1/1 2/1 4/1

1/1 8/5 5/2 4/1

1/1 10/7 2/1 14/5 4/1

1/1 4/3 7/4 16/7 3/1 4/1

1/1 14/11 8/5 2/1 5/2 22/7 4/1

1/1 14/11 8/5 2/1 5/2 22/7 4/1
...

14 note scale:
1/1 10/9 16/13 34/25 3/2 38/23 20/11 2/1 11/5 46/19 8/3 50/17 13/4 18/5 4/1

24 note scale:
1/1 50/47 26/23 6/5 14/11 58/43 10/7 62/41 8/5 22/13 34/19 70/37 2/1
74/35 38/17 26/11 5/2 82/31 14/5 86/29 22/7 10/3 46/13 94/25 4/1

Same thing will happen whenever the scale repeat is the square
of a rational, e.g. 9/4 will give symmetrical scales
with x = 3 such as this 8 note scale:

1/1 51/46 27/22 19/14 3/2 63/38 11/6 69/34 9/4

Robert