14edo: Difference between revisions
mNo edit summary |
provide more information |
||
| Line 5: | Line 5: | ||
Its equally-spaced [[MOS]] [[diatonic]] scale (equivalent to 7edo) allows all intervals to have a "minor", "neutral/perfect", and "major" variant, wherein (for instance) a minor third is the same pitch as a major second. [[21edo]] provides distinctions between these categories. | Its equally-spaced [[MOS]] [[diatonic]] scale (equivalent to 7edo) allows all intervals to have a "minor", "neutral/perfect", and "major" variant, wherein (for instance) a minor third is the same pitch as a major second. [[21edo]] provides distinctions between these categories. | ||
== Theory == | |||
=== Edostep interpretations === | |||
The edostep of 14edo admits several interpretations within the [[19-limit]]: | |||
* 20/19 (the third part of dividing 7/6) | |||
* 21/20 (the difference between 4/3 and 7/5) | |||
* 256/243 (the difference between 4/3 and two 9/8) | |||
* 28/27 (the difference between 15/14 and 10/9) | |||
* 22/21 (the difference between 12/11 and 8/7) | |||
=== JI approximation === | |||
{{Harmonics in ED|14|31|0}} | |||
{| class="wikitable" | |||
|+Thirds in 14edo | |||
!Quality | |||
|'''Subminor''' | |||
|'''Neutral''' | |||
|'''Supermajor''' | |||
|- | |||
!Cents | |||
|'''257.143''' | |||
|'''342.857''' | |||
|'''428.571''' | |||
|- | |||
!Just interpretation | |||
|'''22/19''' | |||
|'''17/14''' | |||
|'''22/17''' | |||
|} | |||
==== Chords ==== | |||
14edo can support Western functional harmony. Intervals may be named using “up” and “down” notation, and, as each is considered perfect, the minor-major-neutral qualification may be omitted. The most stable chords are [0 3 8] and [0 4 8], including extensions with the 11th and 12th steps. | |||
{{Navbox EDO}} | {{Navbox EDO}} | ||
{{Cat|Edos}} | {{Cat|Edos}} | ||
Revision as of 16:18, 4 March 2026
14edo, or 14 equal divisions of the octave, is the equal tuning featuring steps of (1200/14) ~≃ 85.714 cents, 14 of which stack to the perfect octave 2/1. While it approximates the 5:7:9:11:17:19 harmony relatively well for its size, it lacks a convincing realization of other low-complexity just intervals. Consequently, DR-based approaches may be more practically useful.
As a superset of the popular 7edo scale, it offers recognizable triadic harmonies built on subminor, neutral, and supermajor thirds; however, its poor approximation of perfect fourths and fifths gives it a distinctly xenharmonic character.
Its equally-spaced MOS diatonic scale (equivalent to 7edo) allows all intervals to have a "minor", "neutral/perfect", and "major" variant, wherein (for instance) a minor third is the same pitch as a major second. 21edo provides distinctions between these categories.
Theory
Edostep interpretations
The edostep of 14edo admits several interpretations within the 19-limit:
- 20/19 (the third part of dividing 7/6)
- 21/20 (the difference between 4/3 and 7/5)
- 256/243 (the difference between 4/3 and two 9/8)
- 28/27 (the difference between 15/14 and 10/9)
- 22/21 (the difference between 12/11 and 8/7)
JI approximation
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | -16.2 | +42.3 | -26.0 | -37.0 | +16.6 | -19.2 | -40.4 | -28.3 | -1.0 | -30.7 |
| Relative (%) | 0.0 | -18.9 | +49.3 | -30.3 | -43.2 | +19.4 | -22.4 | -47.1 | -33.0 | -1.2 | -35.9 | |
| Steps (reduced) |
14 (0) |
22 (8) |
33 (5) |
39 (11) |
48 (6) |
52 (10) |
57 (1) |
59 (3) |
63 (7) |
68 (12) |
69 (13) | |
| Quality | Subminor | Neutral | Supermajor |
|---|---|---|---|
| Cents | 257.143 | 342.857 | 428.571 |
| Just interpretation | 22/19 | 17/14 | 22/17 |
Chords
14edo can support Western functional harmony. Intervals may be named using “up” and “down” notation, and, as each is considered perfect, the minor-major-neutral qualification may be omitted. The most stable chords are [0 3 8] and [0 4 8], including extensions with the 11th and 12th steps.
