User:MisterShafXen/Sandbox: Difference between revisions
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Prime factorization
2 × 17
Step size
99.0831 ¢
Octave
12\34ed7 (1189 ¢) (→ 6\17ed7)
Twelfth
19\34ed7 (1882.58 ¢)
Consistency limit
11
Distinct consistency limit
6
Created page with "{{Sandbox}}" Tags: Visual edit Mobile edit Mobile web edit Advanced mobile edit |
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{{ | == 34ed7 == | ||
{{Infobox ET|34ed7}} | |||
{{ED intro|34ed7}} This tuning is a compressed [[12edo]]. | |||
{{Interval table|34ed7|additional=12edo note names; 9\109-based note names | |||
C | |||
C#/Db; ^^Db | |||
D; vD | |||
D#/Eb; ^Eb | |||
E; vvE | |||
F | |||
F#/Gb; ^^Gb | |||
G; vG | |||
G#/Ab; ^Ab | |||
A; vvA | |||
A#/Bb; Bb | |||
B; vvvB | |||
C; vC | |||
C#/Db; ^Db | |||
D; vvD | |||
D#/Eb; Eb | |||
E; vvvE | |||
F; vF | |||
F#/Gb; ^Gb | |||
G; vvG | |||
G#/Ab; Ab | |||
A; vvvA | |||
A#/Bb; vBb | |||
B; vvvvB | |||
C; vvC | |||
C#/Db; Db | |||
D; vvvD | |||
D#/Eb; vEb | |||
E; vvvvE | |||
F; vvF | |||
F#/Gb; Gb | |||
G; vvvG | |||
G#/Ab; vAb | |||
A; vvvvA | |||
A#/Bb; vvBb}}{{Harmonics in equal|steps=34|num=7}} | |||
== 50ed4/3 == | |||
Revision as of 18:36, 1 August 2025
34ed7
| ← 33ed7 | 34ed7 | 35ed7 → |
34 equal divisions of the 7th harmonic (abbreviated 34ed7) is a nonoctave tuning system that divides the interval of 7/1 into 34 equal parts of about 99.1 ¢ each. Each step represents a frequency ratio of 71/34, or the 34th root of 7. This tuning is a compressed 12edo.
| Steps | Cents | Approximate ratios | 12edo note names | 9\109-based note names |
|---|---|---|---|---|
| 0 | 0 | 1/1 | C | |
| 1 | 99.1 | 19/18 | C#/Db | ^^Db |
| 2 | 198.2 | 9/8, 28/25 | D | vD |
| 3 | 297.2 | 13/11, 19/16, 25/21 | D#/Eb | ^Eb |
| 4 | 396.3 | 24/19 | E | vvE |
| 5 | 495.4 | 4/3 | F | |
| 6 | 594.5 | F#/Gb | ^^Gb | |
| 7 | 693.6 | 3/2 | G | vG |
| 8 | 792.7 | 19/12 | G#/Ab | ^Ab |
| 9 | 891.7 | 5/3 | A | vvA |
| 10 | 990.8 | 16/9, 23/13 | A#/Bb | Bb |
| 11 | 1089.9 | 15/8 | B | vvvB |
| 12 | 1189 | C | vC | |
| 13 | 1288.1 | 19/9, 21/10 | C#/Db | ^Db |
| 14 | 1387.2 | 20/9 | D | vvD |
| 15 | 1486.2 | 26/11 | D#/Eb | Eb |
| 16 | 1585.3 | 5/2 | E | vvvE |
| 17 | 1684.4 | F | vF | |
| 18 | 1783.5 | 14/5 | F#/Gb | ^Gb |
| 19 | 1882.6 | G | vvG | |
| 20 | 1981.7 | 22/7 | G#/Ab | Ab |
| 21 | 2080.7 | 10/3 | A | vvvA |
| 22 | 2179.8 | A#/Bb | vBb | |
| 23 | 2278.9 | 26/7 | B | vvvvB |
| 24 | 2378 | C | vvC | |
| 25 | 2477.1 | 21/5, 25/6 | C#/Db | Db |
| 26 | 2576.2 | D | vvvD | |
| 27 | 2675.2 | 14/3 | D#/Eb | vEb |
| 28 | 2774.3 | E | vvvvE | |
| 29 | 2873.4 | 21/4 | F | vvF |
| 30 | 2972.5 | F#/Gb | Gb | |
| 31 | 3071.6 | G | vvvG | |
| 32 | 3170.7 | 25/4 | G#/Ab | vAb |
| 33 | 3269.7 | A | vvvvA | |
| 34 | 3368.8 | 7/1 | A#/Bb | vvBb |
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.0 | -19.4 | -22.0 | -12.0 | -30.4 | +0.0 | -33.0 | -38.8 | -23.0 | +10.2 | -41.4 |
| Relative (%) | -11.1 | -19.6 | -22.2 | -12.1 | -30.7 | +0.0 | -33.3 | -39.1 | -23.2 | +10.3 | -41.8 | |
| Steps (reduced) |
12 (12) |
19 (19) |
24 (24) |
28 (28) |
31 (31) |
34 (0) |
36 (2) |
38 (4) |
40 (6) |
42 (8) |
43 (9) | |