10edf: Difference between revisions
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== Theory == | |||
{{ | 10edf is related to [[17edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is about 6.68 cents compressed. 10edf is [[consistent]] to the [[integer limit|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit. | ||
=== Harmonics === | |||
{{Harmonics in equal|10|3|2|intervals=integer|columns=11}} | |||
{{Harmonics in equal|10|3|2|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 10edf (continued)}} | |||
==Intervals== | ==Intervals== | ||
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|} | |} | ||
== | == Music == | ||
; [[Peter Kosmorsky]] | |||
* [https://www.archive.org/details/10Edf ''10 edf''] (archived 2011) | |||
== | == See also == | ||
* | * [[17edo]] – relative edo | ||
* [[27edt]] – relative edt | |||
* [[44ed6]] – relative ed6 | |||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 14:26, 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
| degree | Neptunian notation using 8\10edf | Neapolitan notation using 3/10edf | |
|---|---|---|---|
| 0 | C | F | |
| 1 | 70.1955 | ^C, vDb | F^, Gb |
| 2 | 140.391 | C#, Db | F#, Gd |
| 3 | 210.5865 | vD | G |
| 4 | 280.782 | D | G^, Ab |
| 5 | 350.9775 | ^D, vE | G#, Ad |
| 6 | 421.173 | E | A |
| 7 | 491.3685 | ^E, vF | A^, Hb |
| 8 | 561.564 | F | A#, Hd |
| 9 | 631.7595 | ^F, vC | H |
| 10 | 701.955 | C | B |
| 11 | 772.1505 | ^C, vDb | B^, Cb |
| 12 | 842.346 | C#, Db | B#, Cd |
| 13 | 912.5415 | vD | C |
| 14 | 982.737 | D | C^, Db |
| 15 | 1052.9325 | ^D, vE | C#, Dd |
| 16 | 1123.128 | E | D |
| 17 | 1193.3235 | ^E, vF | D^, Eb |
| 18 | 1263.519 | F | D#, Eb |
| 19 | 1333.7145 | ^F, vC | E |
| 20 | 1403.91 | C | F |
Music
- 10 edf (archived 2011)