1700edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 1699edo1700edo1701edo →
Prime factorization 22 × 52 × 17
Step size 0.705882¢
Fifth 994\1700 (701.647¢) (→497\850)
Semitones (A1:m2) 158:130 (111.5¢ : 91.76¢)
Dual sharp fifth 995\1700 (702.353¢) (→199\340)
Dual flat fifth 994\1700 (701.647¢) (→497\850)
Dual major 2nd 289\1700 (204¢) (→17\100)
Consistency limit 5
Distinct consistency limit 5

1700 equal divisions of the octave (1700edo), or 1700-tone equal temperament (1700tet), 1700 equal temperament (1700et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1700 equal parts of about 0.706 ¢ each.

Theory

1700edo is consistent in the 5-odd-limit, although there is a large relative delta on the 3rd harmonic. From a regular temperament theory perspective, it's best usage is as a 2.9.11.21.23.31 subgroup tuning because all other harmonics up to 29th have more than 25% error. Nonetheless, it tunes the 323 & 2023 temperament leaves in the 17-limit on the patent val.

One step of 1700edo is the relative cent for 17edo. It has been named iota by Margo Schulter and George Secor.

Odd harmonics

Approximation of odd harmonics in 1700edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) -0.308 -0.196 +0.351 +0.090 -0.024 +0.178 +0.202 +0.221 -0.337 +0.043 -0.039
relative (%) -44 -28 +50 +13 -3 +25 +29 +31 -48 +6 -6
Steps
(reduced)
2694
(994)
3947
(547)
4773
(1373)
5389
(289)
5881
(781)
6291
(1191)
6642
(1542)
6949
(149)
7221
(421)
7467
(667)
7690
(890)

Regular temperament properties

Rank-2 temperaments

Periods

per 8ve

Generator

(Reduced)

Cents

(Reduced)

Associated

Ratio

Temperament
17 121\1700
(21\1700)
85.412
(14.824)
1024/975
(8192/8125)
Leaves