# 1ed33/32

← 0ed33/32 | 1ed33/32 | 2ed33/32 → |

(convergent)

(convergent)

**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

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 | +30 | -30 | -24 | +7 | -35 | -7 | +31 | +10 | -43 | +40 | |

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 |