18ed5/2
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Prime factorization
2 × 32
Step size
88.1285¢
Octave
14\18ed5/2 (1233.8¢) (→7\9ed5/2)
Twelfth
22\18ed5/2 (1938.83¢) (→11\9ed5/2)
Consistency limit
3
Distinct consistency limit
2
| ← 17ed5/2 | 18ed5/2 | 19ed5/2 → |
18 equal divisions of 5/2 (abbreviated 18ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 18 equal parts of about 88.1 ¢ each. Each step represents a frequency ratio of (5/2)1/18, or the 18th root of 5/2.
This scale is a neutral Mixolydian 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 | Cents | |||||
|---|---|---|---|---|---|---|---|---|
| 1 | FG | G | 1#/2b | 88.1285 | ||||
| 2 | G | J | A | J | A | 2 | 176.257 | |
| 3 | GJ | GA | J^/Ab | A^/Bb | Jv/A\\ | Av/B\\ | 3 | 264.386 |
| 4 | J | A | J^^/Aw | A^^/Bw | Jw/A^^ | Aw/B^^ | 3#/4b | 352.514 |
| 5 | JA | AB | J#/Av | A#/Bv | Jp/A^ | Ap/B^ | 4 | 440.643 |
| 6 | A | B | A | B | A | B | 5 | 528.771 |
| 7 | AB | BH | B | H | B | H | 5#/6b | 616.9 |
| 8 | B | H | H | C | H | C | 6 | 705.028 |
| 9 | BH | HC | H^/Cb | C^/Db | Hv/C\\ | Cv/D\\ | 7 | 793.157 |
| 10 | H | C | H^^/Cw | C^^/Dw | Hw/C^^ | Cw/D^^ | 7#/8b | 881.285 |
| 11 | HC | CD | H#/Cv | C#/Dv | Hp/C^ | Cp/D^ | 8 | 969.414 |
| 12 | C | D | C | D | C | D | 9 | 1057.5425 |
| 13 | CD | DS | D | S | D | S | 9#/Xb | 1145.671 |
| 14 | D | S | E | X | 1233.8 | |||
| 15 | DE | SE | E^/Fb | Ev/F\\ | E | 1321.928 | ||
| 16 | E | E^^/Fw | Ew/F^^ | E#/0b | 1410.0566 | |||
| 17 | EF | E#/Fv | Ep/F^ | 0 | 1498.185 | |||
| 18 | F | 1 | 1586.314 | |||||
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +33.8 | +36.9 | -20.5 | +33.8 | -17.5 | -19.9 | +13.3 | -14.4 | -20.5 | -9.3 | +16.3 |
| Relative (%) | +38.4 | +41.8 | -23.3 | +38.4 | -19.8 | -22.6 | +15.1 | -16.3 | -23.3 | -10.5 | +18.5 | |
| Steps (reduced) |
14 (14) |
22 (4) |
27 (9) |
32 (14) |
35 (17) |
38 (2) |
41 (5) |
43 (7) |
45 (9) |
47 (11) |
49 (13) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -34.1 | +13.9 | -17.5 | -41.1 | +30.2 | +19.4 | +13.9 | +13.3 | +16.9 | +24.5 | +35.7 |
| Relative (%) | -38.7 | +15.7 | -19.8 | -46.6 | +34.3 | +22.0 | +15.8 | +15.1 | +19.2 | +27.8 | +40.5 | |
| Steps (reduced) |
50 (14) |
52 (16) |
53 (17) |
54 (0) |
56 (2) |
57 (3) |
58 (4) |
59 (5) |
60 (6) |
61 (7) |
62 (8) | |