Equal tempered tuning may use any value for the standard interval. Dividing the octave into multiples of 12 units is fairly common with 24tET, 48tET, and 72tET having been widely used. Equal temperaments are usually described as tones per octave (tET), or cents per tone (cET) Eg 88cET.

Many equal temperament tunings may also be viewed and mapped in a similar way to LucyTuning with Large and small intervals.

Steps

per

octave

Cents

per

step

Steps/cents

per (L)

Large

Interval

Steps & cents

per (s)

small

interval

Steps/cents

per (3L+s)

Fifth (V)

12 100 2

200

1

100

7

700

19 63.16 3

189.47

2

126.32

11

694.74

31 38.71 5

193.553

3

116.13

18

696.77

53 22.64 9

203.77

4

90.57

31

701.89

79 15. 13

197.4719

7

106.33

46

698.73

88 13.64 14

190.91

9

122.73

51

695.45

Wendy Carlos has experimented with and published information on three equal tunings

name Intervals

per Octave

cents per interval Number of

steps per Fifth

Alpha 15.385 78.0 9
Beta 18.809 63.8 11
Gamma 34.188 35.1 20

The possibilities are endless.

Get Microsoft Works 4.0 adjustable spreadsheet of fretting positions, and cent + ratio values for any meantone and most xtET tunings. (worksfret.zip)

Other tuning systems

LucyTuning homepage