5edf: Difference between revisions
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Adopt template: ED intro; +harmonics table; misc. cleanup |
Rework interval table, including removing irrelevant stuff |
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== Intervals == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable center-1 right-2" | ||
|- | |- | ||
! | ! # | ||
! | ! Cents | ||
! | ! Approximate Ratios | ||
! colspan="2"| [[1L 3s (fifth-equivalent)|Neptunian]] Notation | |||
!colspan="2"|[[1L 3s (fifth-equivalent)|Neptunian]] | |||
|- | |- | ||
| 0 | |||
| | | 0.0 | ||
|[[1/1]] | | [[1/1]] | ||
|perfect unison | | perfect unison | ||
|C | | C | ||
|- | |- | ||
|1 | | 1 | ||
|140. | | 140.4 | ||
| [[13/12]], [[49/45]] | |||
|[[13/12]], [[49/45]] | | augmented unison, minor second | ||
|augmented unison, minor second | | C#, Db | ||
|C#, Db | |||
|- | |- | ||
|2 | | 2 | ||
|280. | | 280.8 | ||
| [[75/64]], [[20/17]], [[13/11]] | |||
|[[75/64]], [[20/17]], [[13/11]] | | major second, minor third | ||
|major second, minor third | | D, Eb | ||
|D, Eb | |||
|- | |- | ||
|3 | | 3 | ||
|421. | | 421.2 | ||
| [[14/11]], [[23/18]] | |||
|[[14/11]], [[23/18]] | | major third, diminished fourth | ||
|major third, diminished fourth | | E, Fb | ||
|E, Fb | |||
|- | |- | ||
|4 | | 4 | ||
|561. | | 561.6 | ||
| [[11/8]], [[18/13]], [[25/18]] | |||
|[[11/8]], [[18/13]], [[25/18]] | | perfect fourth | ||
|perfect fourth | | F | ||
|F | |||
|- | |- | ||
|5 | | 5 | ||
| | | 702.0 | ||
| [[3/2]] | |||
|[[3/2]] | | perfect fifth | ||
|perfect fifth | | C | ||
|C | |||
|- | |- | ||
|6 | | 6 | ||
|842. | | 842.3 | ||
| [[21/13]], [[13/8]], [[18/11]] | |||
|[[21/13]], [[13/8]], [[18/11]] | | augmented fifth, minor sixth | ||
|augmented fifth, minor sixth | | C#, Db | ||
|C#, Db | |||
|- | |- | ||
|7 | | 7 | ||
|982. | | 982.7 | ||
| [[7/4]], [[30/17]] | |||
|[[7/4]], [[30/17]] | | major sixth, minor seventh | ||
|major sixth, minor seventh | | D, Eb | ||
|D, Eb | |||
|- | |- | ||
|8 | | 8 | ||
|1123. | | 1123.1 | ||
| | |||
| | | major seventh, minor octave | ||
|major seventh, minor octave | | E, Fb | ||
|E, Fb | |||
|- | |- | ||
|9 | | 9 | ||
|1263. | | 1263.5 | ||
| | | | ||
|major octave | | major octave | ||
|F | | F | ||
|- | |- | ||
|10 | | 10 | ||
|1403. | | 1403.9 | ||
| | |||
| | | | ||
| | | C | ||
|C | |||
|- | |- | ||
|11 | | 11 | ||
|1544. | | 1544.3 | ||
| | |||
| | | | ||
| | | C#, Db | ||
|C#, Db | |||
|- | |- | ||
|12 | | 12 | ||
|1684. | | 1684.7 | ||
| | |||
| | | | ||
| | | D, Eb | ||
|D, Eb | |||
|- | |- | ||
|13 | | 13 | ||
|1825. | | 1825.1 | ||
| | |||
| | | | ||
| | | E | ||
|E | |||
|- | |- | ||
|14 | | 14 | ||
|1965. | | 1965.5 | ||
| | |||
| | | | ||
| | | F | ||
|F | |||
|- | |- | ||
|15 | | 15 | ||
|2105. | | 2105.9 | ||
| | | | ||
|C | | | ||
| C | |||
|- | |- | ||
|16 | | 16 | ||
|2246. | | 2246.3 | ||
| | | | ||
| | | | ||
|C#, Db | | C#, Db | ||
|- | |- | ||
|17 | | 17 | ||
|2386. | | 2386.6 | ||
| | |||
| | | | ||
| | | D | ||
|D | |||
|} | |} | ||
Revision as of 06:14, 10 May 2024
| ← 4edf | 5edf | 6edf → |
5 equal divisions of the perfect fifth (abbreviated 5edf or 5ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 5 equal parts of about 140 ¢ each. Each step represents a frequency ratio of (3/2)1/5, or the 5th root of 3/2. It corresponds to 8.5476 edo.
Theory
5edf is close to the bleu generator chain and every second step of 17edo. 4 steps of 5edf is a fraction of a cent away to the seventh harmonic (which is 112/81 instead of 7/4 since the equave is 3/2), which is an extremely accurate approximation for the size of this scale.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +63.5 | +63.5 | -13.4 | +21.5 | -13.4 | +0.6 | +50.2 | -13.4 | -55.4 | +60.4 | +50.2 |
| Relative (%) | +45.2 | +45.2 | -9.5 | +15.3 | -9.5 | +0.4 | +35.7 | -9.5 | -39.4 | +43.0 | +35.7 | |
| Steps (reduced) |
9 (4) |
14 (4) |
17 (2) |
20 (0) |
22 (2) |
24 (4) |
26 (1) |
27 (2) |
28 (3) |
30 (0) |
31 (1) | |
Intervals
| # | Cents | Approximate Ratios | Neptunian Notation | |
|---|---|---|---|---|
| 0 | 0.0 | 1/1 | perfect unison | C |
| 1 | 140.4 | 13/12, 49/45 | augmented unison, minor second | C#, Db |
| 2 | 280.8 | 75/64, 20/17, 13/11 | major second, minor third | D, Eb |
| 3 | 421.2 | 14/11, 23/18 | major third, diminished fourth | E, Fb |
| 4 | 561.6 | 11/8, 18/13, 25/18 | perfect fourth | F |
| 5 | 702.0 | 3/2 | perfect fifth | C |
| 6 | 842.3 | 21/13, 13/8, 18/11 | augmented fifth, minor sixth | C#, Db |
| 7 | 982.7 | 7/4, 30/17 | major sixth, minor seventh | D, Eb |
| 8 | 1123.1 | major seventh, minor octave | E, Fb | |
| 9 | 1263.5 | major octave | F | |
| 10 | 1403.9 | C | ||
| 11 | 1544.3 | C#, Db | ||
| 12 | 1684.7 | D, Eb | ||
| 13 | 1825.1 | E | ||
| 14 | 1965.5 | F | ||
| 15 | 2105.9 | C | ||
| 16 | 2246.3 | C#, Db | ||
| 17 | 2386.6 | D | ||