14edf: Difference between revisions
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== Theory == | |||
14edf is related to [[24edo]], but with the perfect fifth rather than the [[2/1|octave]] being just, which stretches the octave by about 3.35 cents. The [[patent val]] has a generally sharp tendency for harmonics up to 22, with the exception for [[7/1|7]], [[14/1|14]], and [[21/1|21]]. | |||
=== Harmonics === | |||
{{Harmonics in equal|14|3|2|intervals=integer|columns=11}} | |||
{{Harmonics in equal|14|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 14edf (continued)}} | |||
== | === Subsets and supersets === | ||
Since 14 factors into primes as {{nowrap| 2 × 7 }}, 14edf contains subset edfs [[2edf]] and [[7edf]]. | |||
{{ | |||
== Intervals == | == Intervals == | ||
| Line 106: | Line 108: | ||
|} | |} | ||
== See also == | |||
* [[24edo]] – relative edo | |||
[[ | * [[38edt]] – relative edt | ||
* [[56ed5]] – relative ed5 | |||
* [[62ed6]] – relative ed6 | |||
* [[86ed12]] – relative ed12 | |||
Revision as of 10:08, 27 May 2025
| ← 13edf | 14edf | 15edf → |
14 equal divisions of the perfect fifth (abbreviated 14edf or 14ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 14 equal parts of about 50.1 ¢ each. Each step represents a frequency ratio of (3/2)1/14, or the 14th root of 3/2.
Theory
14edf is related to 24edo, but with the perfect fifth rather than the octave being just, which stretches the octave by about 3.35 cents. The patent val has a generally sharp tendency for harmonics up to 22, with the exception for 7, 14, and 21.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.4 | +3.4 | +6.7 | +21.5 | +6.7 | -9.5 | +10.1 | +6.7 | +24.9 | +10.3 | +10.1 |
| Relative (%) | +6.7 | +6.7 | +13.4 | +42.9 | +13.4 | -18.9 | +20.1 | +13.4 | +49.6 | +20.5 | +20.1 | |
| Steps (reduced) |
24 (10) |
38 (10) |
48 (6) |
56 (0) |
62 (6) |
67 (11) |
72 (2) |
76 (6) |
80 (10) |
83 (13) |
86 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +21.9 | -6.1 | +24.9 | +13.4 | +8.7 | +10.1 | +16.7 | -21.9 | -6.1 | +13.6 | -13.2 | +13.4 |
| Relative (%) | +43.7 | -12.2 | +49.6 | +26.7 | +17.4 | +20.1 | +33.4 | -43.7 | -12.2 | +27.2 | -26.3 | +26.7 | |
| Steps (reduced) |
89 (5) |
91 (7) |
94 (10) |
96 (12) |
98 (0) |
100 (2) |
102 (4) |
103 (5) |
105 (7) |
107 (9) |
108 (10) |
110 (12) | |
Subsets and supersets
Since 14 factors into primes as 2 × 7, 14edf contains subset edfs 2edf and 7edf.
Intervals
| Degree | Cents |
|---|---|
| 0 | 0 |
| 1 | 50.1396 |
| 2 | 100.2793 |
| 3 | 150.4189 |
| 4 | 200.5586 |
| 5 | 250.6982 |
| 6 | 300.8379 |
| 7 | 350.9775 |
| 8 | 401.1171 |
| 9 | 451.2568 |
| 10 | 501.3964 |
| 11 | 551.536 |
| 12 | 601.6757 |
| 13 | 651.8154 |
| 14 | 701.955 |
| 15 | 752.0946 |
| 16 | 802.2343 |
| 17 | 852.3739 |
| 18 | 902.5136 |
| 19 | 952.6532 |
| 20 | 1002.7929 |
| 21 | 1052.9235 |
| 22 | 1103.0721 |
| 23 | 1153.2118 |
| 24 | 1203.3514 |
| 25 | 1253.4911 |
| 26 | 1303.6307 |
| 27 | 1353.7704 |
| 28 | 1403.91 |