back to list

Arithmetic Series Scale: modified version

🔗Michael <djtrancendance@...>

6/3/2009 9:30:48 AM

    I have been trying to find a new version of the arithmetic series scale which optimizes for critical band, further separating anything too close to the semi-tone
*****************************************
The original scale is
1.5 (1/2)^1 + 1      AKA 3/2
1.4117 (1.5/1.0625)   AKA 24/17
1.25    (1/2)^2 + 1 AKA  5/4
1.125  (1/2)^3 + 1  AKA 9/8
1.0625 (1/2)^4 + 1 AKA 17/16
1
*****************************************
The new version attempts to solve/space-out the rough/overly areas between 1.41 and 1.5...and between 1,1.0625, and 1.125 by slightly altering the ratios used to make the minimum distance between notes closer to 1.07 than 1.055 (IE the semitone). .

    The new (hopefully improved) version of the scale is

1.5           AKA 3/2

1.35        (23/17 CHANGED from 24/17)     

1.25        (5/4)

1.142857 (8/7 CHANGED from 9/8)  

1.066666 (16/15 CHANGED from 17/16)

1

    I think this gives a more relaxed sound while keeping the same feel as the original arithmetic series scale...but what do you think?

-Michael