14edo

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

Approximation of prime harmonics in 14edo

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)

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 quality may be omitted. The most stable chords are [0 3 8] and [0 4 8], including extensions with the 11th and 12th steps.