18ed7/3
Jump to navigation
Jump to search
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
← 17ed7/3 | 18ed7/3 | 19ed7/3 → |
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
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) |
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) |