16edf: Difference between revisions
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m add todo:expand, add harmonics, make table collapsible |
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Lookalikes: [[27edo]], [[43edt]] | Lookalikes: [[27edo]], [[43edt]] | ||
== Harmonics == | |||
{{Harmonics in equal|16|3|2}} | |||
{{Harmonics in equal|16|3|2|start=12|collapsed=1}} | |||
== Intervals == | == Intervals == | ||
{| class="wikitable right-2 mw-collapsible" | |||
{| class="wikitable right-2" | |+ Intervals of 16edf | ||
|- | |- | ||
! degree | ! degree | ||
| Line 216: | Line 220: | ||
== Music == | == Music == | ||
[https://www.youtube.com/watch?v=-RUeO6hJLBY schizophrenic lullaby fugue] by nationalsolipsism | * [https://www.youtube.com/watch?v=-RUeO6hJLBY schizophrenic lullaby fugue] by [[nationalsolipsism]] | ||
[https://www.youtube.com/watch?v=8YegsoiO1Co Neptune] by Nae Ayy | * [https://www.youtube.com/watch?v=8YegsoiO1Co Neptune] by [[Nae Ayy]] | ||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
{{todo|expand}} | |||
Revision as of 03:26, 21 December 2024
| ← 15edf | 16edf | 17edf → |
16EDF is the equal division of the just perfect fifth into 16 parts of 43.8722 cents each, corresponding to 27.3522 edo (similar to every third step of 82edo). 16edf contains good approximations of the 7th and 13th harmonics.
It serves as a good approximation to halftone temperament, containing the ~7/5 generator at 13 steps.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -15.5 | -15.5 | +13.0 | +21.5 | +13.0 | +9.3 | -2.5 | +13.0 | +6.1 | +16.5 | -2.5 |
| Relative (%) | -35.2 | -35.2 | +29.6 | +49.0 | +29.6 | +21.3 | -5.7 | +29.6 | +13.8 | +37.7 | -5.7 | |
| Steps (reduced) |
27 (11) |
43 (11) |
55 (7) |
64 (0) |
71 (7) |
77 (13) |
82 (2) |
87 (7) |
91 (11) |
95 (15) |
98 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -9.4 | -6.1 | +6.1 | -17.9 | +8.7 | -2.5 | -8.3 | -9.4 | -6.1 | +1.1 | +11.9 |
| Relative (%) | -21.5 | -13.9 | +13.8 | -40.9 | +19.9 | -5.7 | -19.0 | -21.4 | -13.9 | +2.5 | +27.1 | |
| Steps (reduced) |
101 (5) |
104 (8) |
107 (11) |
109 (13) |
112 (0) |
114 (2) |
116 (4) |
118 (6) |
120 (8) |
122 (10) |
124 (12) | |
Intervals
| degree | cents value | corresponding JI intervals |
Halftone[6] notation (using ups and downs) | comments |
|---|---|---|---|---|
| 0 | 0.0000 | 1/1 | C | |
| 1 | 43.8722 | 40/39, 39/38 | ^C | |
| 2 | 87.7444 | 20/19 | Db | |
| 3 | 131.6166 | 55/51, (27/25) | vD | |
| 4 | 175.4888 | (21/19) | D | |
| 5 | 219.3609 | vE | ||
| 6 | 263.2331 | (7/6) | E | |
| 7 | 307.1053 | Fb | ||
| 8 | 350.9775 | 60/49, 49/40 | vF | |
| 9 | 394.8497 | (44/35) | F | |
| 10 | 438.7219 | (9/7) | Ab | |
| 11 | 482.5941 | vA | ||
| 12 | 526.4663 | (19/14) | A | |
| 13 | 570.3384 | (25/18), 153/110, 112/81 | B | |
| 14 | 614.2106 | (10/7) | Cb | |
| 15 | 658.0828 | 19/13 | vC | |
| 16 | 701.9550 | 3/2 (exact) | C | just perfect fifth |
| 17 | 745.8272 | 20/13 | ||
| 18 | 789.6994 | 30/19 | ||
| 19 | 833.5716 | 55/34 | ||
| 20 | 877.4438 | |||
| 21 | 921.3159 | |||
| 22 | 965.1881 | 7/4 | ||
| 23 | 1009.0603 | |||
| 24 | 1052.9325 | 90/49, (11/6) | ||
| 25 | 1096.8047 | (66/35) | ||
| 26 | 1140.6769 | |||
| 27 | 1184.5491 | |||
| 28 | 1228.4213 | 128/63 | ||
| 29 | 1272.2934 | 25/12 | ||
| 30 | 1316.1656 | 15/7 | ||
| 31 | 1360.0378 | 57/26 | ||
| 32 | 1403.9100 | 9/4 (exact) | pythagorean ninth |