18ed7/3

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← 17ed7/318ed7/319ed7/3 →
Prime factorization 2 × 32
Step size 81.4928¢ 
Octave 15\18ed7/3 (1222.39¢) (→5\6ed7/3)
Twelfth 23\18ed7/3 (1874.34¢)
Consistency limit 2
Distinct consistency limit 2

18 equal divisions of 7/3 (abbreviated 18ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 18 equal parts of about 81.5 ¢ each. Each step represents a frequency ratio of (7/3)1/18, or the 18th root of 7/3.

This scale is a neutral Dorian mode of the Middletown relative of Whitewood temperament, or the White Oak scale. The Middletown Valley relatives of Blackwood temperament are:

Fair Terra Rubra: bi-equal tetrad

Fair Tritetrachordal: Middletown Valley Double Augmented

Fair Montrose: Vesuvius Marcodiminished

Unfair Montrose: Annapolis~Oriole Macro-Blackwood

Unfair Tritetrachordal: Mt. Airy

Unfair Terra Rubra: Westminster

Intervals

Degrees Enneatonic Dodecatonic ed7/3
1 FG G 1#/2b 81.4928
2 G J A J A 2 162.9856
3 GJ GA J^/Ab A^/Bb Jv/A\\ Av/B\\ 3 244.4785
4 J A J^^/Aw A^^/Bw Jw/A^^ Aw/B^^ 3#/4b 325.9713
5 JA AB J#/Av A#/Bv Jp/A^ Ap/B^ 4 407.46415
6 A B A B A B 5 488.957
7 AB BH B H B H 5#/6b 570.45
8 B H H C H C 6 651.9426
9 BH HC H^/Cb C^/Db Hv/C\\ Cv/D\\ 7 733.43545
10 H C H^^/Cw C^^/Dw Hw/C^^ Cw/D^^ 7#/8b 814.9283
11 HC CD H#/Cv C#/Dv Hp/C^ Cp/D^ 8 896.4211
12 C D C D C D 9 977.9139
13 CD DS D S D S 9#/Xb 1059.4068
14 D S E X 1140.8996
15 DE SE E^/Fb Ev/F\\ E 1222.3924
16 E E^^/Fw Ew/F^^ E#/0b 1303.8852
17 EF E#/Fv Ep/F^ 0 1385.3781
18 F 1 1466.8709

Harmonics

Approximation of harmonics in 18ed7/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +22.4 -27.6 -36.7 -15.6 -5.2 -27.6 -14.3 +26.3 +6.8 +4.8 +17.2
Relative (%) +27.5 -33.9 -45.0 -19.1 -6.4 -33.9 -17.6 +32.2 +8.4 +5.9 +21.1
Steps
(reduced)
15
(15)
23
(5)
29
(11)
34
(16)
38
(2)
41
(5)
44
(8)
47
(11)
49
(13)
51
(15)
53
(17)
Approximation of harmonics in 18ed7/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -39.9 -5.2 +38.3 +8.1 -15.4 -32.8 +36.5 +29.2 +26.3 +27.2 +31.7
Relative (%) -49.0 -6.4 +47.0 +9.9 -18.9 -40.3 +44.8 +35.9 +32.2 +33.4 +39.0
Steps
(reduced)
54
(0)
56
(2)
58
(4)
59
(5)
60
(6)
61
(7)
63
(9)
64
(10)
65
(11)
66
(12)
67
(13)