14edo - Revision history

Vector at 02:57, 7 April 2026

2026-04-07T02:57:39Z

← Older revision		Revision as of 02:57, 7 April 2026
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	\|}		\|}

			== Notation ==
	{{Navbox EDO}}		It makes the most sense in 14edo to use 7edo as the nominals ABCDEFG, and ups and downs (or some other equivalent inflection) to raise/lower by an edostep. This is consistent with standard ups and downs notation.{{Navbox EDO}}
	{{Cat\|Edos}}		{{Cat\|Edos}}

Iniðil: /* Intrvals */ typo

2026-03-04T20:13:31Z

Intrvals: typo

← Older revision		Revision as of 20:13, 4 March 2026
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	14edo can also support Western functional harmony. The most stable chords are [0 3 8] and [0 4 8], including extensions with the 11th and 12th steps.		14edo can also support Western functional harmony. The most stable chords are [0 3 8] and [0 4 8], including extensions with the 11th and 12th steps.

	== ~~Intrvals~~ ==		== Intervals ==
	Here is a table of 14edo's intervals:		Here is a table of 14edo's intervals:
	{\| class="wikitable"		{\| class="wikitable"

Iniðil: add interval table

2026-03-04T16:58:37Z

add interval table

@@ Line 1: / Line 1: @@
 '''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, [[Delta-rational chord|DR]]-based approaches may be more practically useful.
 == Theory ==
@@ Line 16: / Line 11: @@
 === JI approximation ===
 {{Harmonics in ED|14|31|0}}
@@ Line 37: / Line 33: @@
 ==== Chords ====
-edo 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.
+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.
 {{Navbox EDO}}
 {{Cat|Edos}}

Iniðil: /* Edostep interpretations */ language

2026-03-04T16:21:01Z

Edostep interpretations: language

← Older revision		Revision as of 16:21, 4 March 2026
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	== Theory ==		== Theory ==
	=== Edostep interpretations ===		=== Edostep interpretations ===
	The edostep of 14edo ~~admits~~ several interpretations within the [[19-limit]]:		The edostep of 14edo allows several interpretations within the [[19-limit]]:
	* 20/19 (the third part of dividing 7/6)		* 20/19 (the third part of dividing 7/6)
	* 21/20 (the difference between 4/3 and 7/5)		* 21/20 (the difference between 4/3 and 7/5)

Iniðil: /* Chords */

2026-03-04T16:20:12Z

Chords

← Older revision		Revision as of 16:20, 4 March 2026
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	==== Chords ====		==== 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.		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.

	{{Navbox EDO}}		{{Navbox EDO}}
	{{Cat\|Edos}}		{{Cat\|Edos}}

Iniðil: provide more information

2026-03-04T16:18:41Z

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.
 {{Navbox EDO}}
 {{Cat|Edos}}

Inthar at 04:59, 23 February 2026

2026-02-23T04:59:19Z

← Older revision		Revision as of 04:59, 23 February 2026
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	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.

			{{Navbox EDO}}
	{{Cat\|Edos}}		{{Cat\|Edos}}

Lériendil: deploying cat

2026-02-10T01:08:04Z

deploying cat

← Older revision		Revision as of 01:08, 10 February 2026
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.

			{{Cat\|Edos}}

Vector at 02:38, 4 February 2026

2026-02-04T02:38:15Z

← Older revision		Revision as of 02:38, 4 February 2026
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	'''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, [[Delta-rational chord\|DR]]-based approaches may be more practically useful.		'''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, [[Delta-rational chord\|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.		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.

Calvera: fix

2026-02-03T17:46:50Z

fix

← Older revision		Revision as of 17:46, 3 February 2026
Line 1:		Line 1:
	'''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\|~~Delta-rational chord]]-based approaches may be more practically useful.		'''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, [[Delta-rational chord\|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.		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.