2777edo

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Prime factorization 2777 (prime)
Step size 0.432121¢ 
Fifth 1624\2777 (701.764¢)
Semitones (A1:m2) 260:211 (112.4¢ : 91.18¢)
Dual sharp fifth 1625\2777 (702.197¢)
Dual flat fifth 1624\2777 (701.764¢)
Dual major 2nd 472\2777 (203.961¢)
Consistency limit 7
Distinct consistency limit 7

2777 equal divisions of the octave (abbreviated 2777edo or 2777ed2), also called 2777-tone equal temperament (2777tet) or 2777 equal temperament (2777et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2777 equal parts of about 0.432 ¢ each. Each step represents a frequency ratio of 21/2777, or the 2777th root of 2.

Theory

2777edo is consistent to the 7-odd-limit and its harmonic 3 is about halfway its steps. Using the 2.9.5.7.11.13.17.23.29.31 subgroup it tempers out 12376/12375, 14400/14399, 25025/25024, 123201/123200, 20736/20735, 194481/194480, 16445/16443, 27625/27621 and 23716/23715. It supports joshuavoic.

Odd harmonics

Approximation of odd harmonics in 2777edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.191 +0.002 -0.011 +0.051 +0.068 -0.052 -0.188 +0.050 -0.214 -0.201 +0.030
Relative (%) -44.1 +0.6 -2.5 +11.8 +15.8 -12.1 -43.5 +11.6 -49.5 -46.5 +6.8
Steps
(reduced)
4401
(1624)
6448
(894)
7796
(2242)
8803
(472)
9607
(1276)
10276
(1945)
10849
(2518)
11351
(243)
11796
(688)
12197
(1089)
12562
(1454)

Subsets and supersets

2777edo is the 404th prime EDO. 5554edo, which doubles it, gives a good correction to the harmonic 3.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [8803 -2777 [2777 8803]] -0.0081 0.0081 1.87
2.9.5 [146 -38 -11, [-89 -21 67 [2777 8803 6448]] -0.0057 0.0074 1.71
2.9.5.7 [2 -10 14 -1, [-1 -9 -3 13, [-48 0 11 8 [2777 8803 6448 7796]] -0.0033 0.0076 1.76
2.9.5.7.11 151263/151250, 184549376/184528125, 35156250/35153041, 3487704605/3486784401 [2777 8803 6448 7796 9607]] -0.0066 0.0095 2.20
2.9.5.7.11.13 123201/123200, 6656/6655, 151263/151250, 8859375/8859136, 43061200/43046721 [2777 8803 6448 7796 9607 10276]] -0.0032 0.0116 2.68
2.9.5.7.11.13.17 12376/12375, 14400/14399, 123201/123200, 194481/194480, 4685824/4685625, 81331250/81310473 [2777 8803 6448 7796 9607 10276 11351]] -0.0045 0.0112 2.59