751edo

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← 750edo 751edo 752edo →
Prime factorization 751 (prime)
Step size 1.59787¢ 
Fifth 439\751 (701.465¢)
Semitones (A1:m2) 69:58 (110.3¢ : 92.68¢)
Consistency limit 3
Distinct consistency limit 3

751 equal divisions of the octave (abbreviated 751edo or 751ed2), also called 751-tone equal temperament (751tet) or 751 equal temperament (751et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 751 equal parts of about 1.6 ¢ each. Each step represents a frequency ratio of 21/751, or the 751st root of 2.

Theory

751edo is inconsistent in the 5-odd-limit, with rather large errors in the harmonics 3, 7 and 17. It has two mappings possible for the 7-limit:

  • 751 1190 1744 2108] (patent val)
  • 751 1190 1743 2108] (751c val)

Using the patent val, it tempers out 2460375/2458624 (breeze comma), 26873856/26796875 and [-14 7 -6 6 in the 7-limit.

Using the 751c val, it tempers out 420175/419904, 2109375/2097152 and 1640558367/1638400000 in the 7-limit, supporting quinwell.

Odd harmonics

Approximation of odd harmonics in 751edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.490 +0.371 -0.517 +0.617 -0.053 -0.048 -0.120 +0.504 -0.309 +0.591 -0.312
Relative (%) -30.7 +23.2 -32.4 +38.6 -3.3 -3.0 -7.5 +31.5 -19.4 +37.0 -19.5
Steps
(reduced)
1190
(439)
1744
(242)
2108
(606)
2381
(128)
2598
(345)
2779
(526)
2934
(681)
3070
(66)
3190
(186)
3299
(295)
3397
(393)

Subsets and supersets

751edo is the 133rd prime edo. 1502edo, which doubles it, gives a good correction to the harmonic 5.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-1190 751 [751 1190]] 0.1547 0.1547 9.68


Icon-Todo.png Todo: explain its xenharmonic value