10edf: Difference between revisions
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{{Harmonics in equal|10|3|2|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 10edf (continued)}} | {{Harmonics in equal|10|3|2|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 10edf (continued)}} | ||
==Intervals== | == Intervals == | ||
{| class="wikitable" | {| class="wikitable center-all right-2" | ||
! | ! # | ||
! | ! Cents | ||
![[1L 3s (fifth-equivalent)|Neptunian]] notation using 8\10edf | ! [[1L 3s (fifth-equivalent)|Neptunian]] notation<br>using 8\10edf | ||
![[Ed9/4|Neapolitan]] notation using 3/10edf | ! [[Ed9/4|Neapolitan]] notation<br>using 3/10edf | ||
|- | |- | ||
| 0 | |||
|C | | 0.0 | ||
|F | | C | ||
| F | |||
|- | |- | ||
| 1 | | 1 | ||
|70. | | 70.2 | ||
|^C, vDb | | ^C, vDb | ||
|F^, Gb | | F^, Gb | ||
|- | |- | ||
|2 | | 2 | ||
|140. | | 140.4 | ||
|C#, Db | | C#, Db | ||
|F#, Gd | | F#, Gd | ||
|- | |- | ||
|3 | | 3 | ||
|210. | | 210.6 | ||
|vD | | vD | ||
|G | | G | ||
|- | |- | ||
|4 | | 4 | ||
|280. | | 280.8 | ||
|D | | D | ||
|G^, Ab | | G^, Ab | ||
|- | |- | ||
|5 | | 5 | ||
| | | 351.0 | ||
|^D, vE | | ^D, vE | ||
|G#, Ad | | G#, Ad | ||
|- | |- | ||
|6 | | 6 | ||
|421. | | 421.2 | ||
|E | | E | ||
|A | | A | ||
|- | |- | ||
|7 | | 7 | ||
|491. | | 491.4 | ||
|^E, vF | | ^E, vF | ||
|A^, Hb | | A^, Hb | ||
|- | |- | ||
| 8 | | 8 | ||
|561. | | 561.6 | ||
|F | | F | ||
|A#, Hd | | A#, Hd | ||
|- | |- | ||
|9 | | 9 | ||
|631. | | 631.8 | ||
|^F, vC | | ^F, vC | ||
|H | | H | ||
|- | |- | ||
|10 | | 10 | ||
| | | 702.0 | ||
|C | | C | ||
|B | | B | ||
|- | |- | ||
|11 | | 11 | ||
|772. | | 772.2 | ||
|^C, vDb | | ^C, vDb | ||
|B^, Cb | | B^, Cb | ||
|- | |- | ||
|12 | | 12 | ||
|842. | | 842.3 | ||
|C#, Db | | C#, Db | ||
|B#, Cd | | B#, Cd | ||
|- | |- | ||
|13 | | 13 | ||
|912. | | 912.5 | ||
|vD | | vD | ||
|C | | C | ||
|- | |- | ||
|14 | | 14 | ||
|982. | | 982.7 | ||
|D | | D | ||
|C^, Db | | C^, Db | ||
|- | |- | ||
|15 | | 15 | ||
|1052. | | 1052.9 | ||
|^D, vE | | ^D, vE | ||
|C#, Dd | | C#, Dd | ||
|- | |- | ||
|16 | | 16 | ||
|1123. | | 1123.1 | ||
|E | | E | ||
|D | | D | ||
|- | |- | ||
|17 | | 17 | ||
|1193. | | 1193.3 | ||
|^E, vF | | ^E, vF | ||
|D^, Eb | | D^, Eb | ||
|- | |- | ||
|18 | | 18 | ||
|1263. | | 1263.5 | ||
|F | | F | ||
|D#, Eb | | D#, Eb | ||
|- | |- | ||
|19 | | 19 | ||
|1333. | | 1333.7 | ||
|^F, vC | | ^F, vC | ||
|E | | E | ||
|- | |- | ||
|20 | | 20 | ||
|1403. | | 1403.9 | ||
|C | | C | ||
|F | | F | ||
|} | |} | ||
Revision as of 14:30, 21 May 2025
| ← 9edf | 10edf | 11edf → |
(semiconvergent)
(semiconvergent)
10 equal divisions of the perfect fifth (abbreviated 10edf or 10ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 10 equal parts of about 70.2 ¢ each. Each step represents a frequency ratio of (3/2)1/10, or the 10th root of 3/2.
Theory
10edf is related to 17edo, but with the perfect fifth rather than the octave being just. The octave is about 6.68 cents compressed. 10edf is consistent to the 7-integer-limit, but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -6.7 | -6.7 | -13.4 | +21.5 | -13.4 | +0.6 | -20.0 | -13.4 | +14.8 | -9.8 | -20.0 |
| Relative (%) | -9.5 | -9.5 | -19.0 | +30.6 | -19.0 | +0.8 | -28.5 | -19.0 | +21.1 | -13.9 | -28.5 | |
| Steps (reduced) |
17 (7) |
27 (7) |
34 (4) |
40 (0) |
44 (4) |
48 (8) |
51 (1) |
54 (4) |
57 (7) |
59 (9) |
61 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -18.2 | -6.1 | +14.8 | -26.7 | +8.7 | -20.0 | +26.8 | +8.2 | -6.1 | -16.5 | -23.2 | -26.7 |
| Relative (%) | -25.9 | -8.7 | +21.1 | -38.0 | +12.4 | -28.5 | +38.1 | +11.6 | -8.7 | -23.4 | -33.1 | -38.0 | |
| Steps (reduced) |
63 (3) |
65 (5) |
67 (7) |
68 (8) |
70 (0) |
71 (1) |
73 (3) |
74 (4) |
75 (5) |
76 (6) |
77 (7) |
78 (8) | |
Intervals
| # | Cents | Neptunian notation using 8\10edf |
Neapolitan notation using 3/10edf |
|---|---|---|---|
| 0 | 0.0 | C | F |
| 1 | 70.2 | ^C, vDb | F^, Gb |
| 2 | 140.4 | C#, Db | F#, Gd |
| 3 | 210.6 | vD | G |
| 4 | 280.8 | D | G^, Ab |
| 5 | 351.0 | ^D, vE | G#, Ad |
| 6 | 421.2 | E | A |
| 7 | 491.4 | ^E, vF | A^, Hb |
| 8 | 561.6 | F | A#, Hd |
| 9 | 631.8 | ^F, vC | H |
| 10 | 702.0 | C | B |
| 11 | 772.2 | ^C, vDb | B^, Cb |
| 12 | 842.3 | C#, Db | B#, Cd |
| 13 | 912.5 | vD | C |
| 14 | 982.7 | D | C^, Db |
| 15 | 1052.9 | ^D, vE | C#, Dd |
| 16 | 1123.1 | E | D |
| 17 | 1193.3 | ^E, vF | D^, Eb |
| 18 | 1263.5 | F | D#, Eb |
| 19 | 1333.7 | ^F, vC | E |
| 20 | 1403.9 | C | F |
Music
- 10 edf (archived 2011)