# 1ed33/32

(Redirected from 33/32 equal step tuning)
 ← 0ed33/32 1ed33/32 2ed33/32 →
Prime factorization n/a
Step size 53.2729¢
Octave 23\1ed33/32 (1225.28¢)
(convergent)
Twelfth 36\1ed33/32 (1917.83¢)
(convergent)
Consistency limit 3
Distinct consistency limit 1
Special properties

1 equal division of 33/32 (1ed33/32), also known as ambitonal sequence of 33/32 (AS33/32) or 33/32 equal-step tuning, is an equal multiplication of 33/32 (the Alpharabian quarter-tone), and results in a nonoctave tuning equivalent to 22.5255 EDO.

Lookalikes: 5ed7/6, 45ed4

## Theory

Approximation of prime harmonics in 1ed33/32
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +25.3 +15.9 -16.1 -12.6 +4.0 -18.9 -3.8 +16.7 +5.6 -22.8 +21.5
Relative (%) +47.4 +29.8 -30.3 -23.7 +7.5 -35.4 -7.2 +31.3 +10.4 -42.8 +40.4
Step 23 36 52 63 78 83 92 96 102 109 112

In this tuning, 2 steps by definition correspond to the parapotome 1089/1024.

Intervals with excellent approximation in this tuning are: 7/6 (5), 20/13 (14), 18/11 (16). Other intervals with good approximation are: 6/5, 7/5, 9/5, 13/7, 13/9, 11/10, 19/12, 17/16, 17/15, 16/15.

In the 5-limit, 1ed33/32 tempers out the syntonic comma 81/80, making it meantone.

In the 7-limit, as a consequence of representing 6/5 and 7/6 well, it's great at representing the 5:6:7 otonal tetrad. This means that 385/384 is tempered out.

## Regular temperament properties

"Normal" subgroups calculated using the 23edo val that matches 33/32 equal step tuning patent val.

Subgroup Comma list Mapping
2.3.5 81/80, 15625/12288 23 36 52
2.3.5.7 35/32, 175/162, 625/588 23 36 52 63
33/32.7/6 117440512/117406179 1 5