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Equal tempered tuning

Equal tempered tuning may use any value for the standard interval. Dividing the octave into multiples of 12 units (12edo) is the most widely used system and dividing this further into 24edo, 48edo, 72edo and 96edo are in current use by some composers. Equal temperaments may also be named as cents per division (cET) Eg 88cET.

Many equal temperament tunings may be viewed and mapped in a similar way to LucyTuning, using Large and small intervals, as shown below:

Steps

per

octave

Cents

per

step

Steps/cents

per (L)

Large

Interval

Steps/cents

per (s)

small

interval

Steps/cents

per (3L+s) = Vth

LucyTuned Fifth = 695.493 cents

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

1420 0.8450704 226

190.99

145

122.54

823

695.49

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.
Related Pages
Just Intonation
Meantone Tunings
Pythagorean Tuning

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

Comparison of 22 and 88 equal division of the octave and LucyTuning intervals: Note names, positions and steps of fourths and fifths.