14edo - Revision history

Lucius Chiaraviglio: /* Music */ Update for new sub-page name

2026-05-13T15:59:40Z

Music: Update for new sub-page name

← Older revision		Revision as of 15:59, 13 May 2026
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	== Music ==		== Music ==
	{{Main\|Music ~~in 14edo~~}}		{{Main\|14edo/Music}}
	{{Catrel\|14edo tracks}}		{{Catrel\|14edo tracks}}

Fitzgerald Lee: /* Approximation to JI */Added interval mappings, 14 and 14c

2026-04-15T09:57:15Z

Approximation to JI: Added interval mappings, 14 and 14c

← Older revision		Revision as of 09:57, 15 April 2026
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	==== Selected 13-limit intervals ====		==== Selected 13-limit intervals ====
	[[File:14ed2-001.svg\|alt=alt : Your browser has no SVG support.]]		[[File:14ed2-001.svg\|alt=alt : Your browser has no SVG support.]]
			=== Interval mappings ===
			{{Q-odd-limit intervals\|14}}
			{{Q-odd-limit intervals\|13.95\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 14c val mapping}}

	== Regular temperament properties ==		== Regular temperament properties ==

Overthink: /* Theory */ the commas section actually assumes the patent val

2026-03-23T00:35:43Z

Theory: the commas section actually assumes the patent val

← Older revision		Revision as of 00:35, 23 March 2026
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	14edo is the double of [[7edo]], and thus contains its flat 686{{C}} fifth, while adding new intervals halfway between each 7edo step. The intervals of 14edo not found in 7edo are [[Backslash notation\|1\14]] = 86{{C}}, 3\14 = 257{{C}}, 5\14 = 429{{C}}, 7\14 = 600{{C}}, and their [[octave complement]]s. The 1\14 interval is a small semitone, and its inversion a major seventh, which is suitable for a {{w\|leading tone}}. The 3\14 interval can be considered a small [[subminor third]] (or inframinor third), thus bringing a new, distinct flavor from the [[neutral third]] of 7edo, which is 4 steps of 14edo. The 5\14 interval is the [[fifth complement]] of 3\14, and can be considered a [[supermajor third]], so that stacking 3\14 and 5\14 gives the triad 0–3–8 steps (0–257–686{{C}}). Finally, the 7\14 interval is the familiar [[tritone]] found in [[12edo]], as well as every even-numbered [[edo]].		14edo is the double of [[7edo]], and thus contains its flat 686{{C}} fifth, while adding new intervals halfway between each 7edo step. The intervals of 14edo not found in 7edo are [[Backslash notation\|1\14]] = 86{{C}}, 3\14 = 257{{C}}, 5\14 = 429{{C}}, 7\14 = 600{{C}}, and their [[octave complement]]s. The 1\14 interval is a small semitone, and its inversion a major seventh, which is suitable for a {{w\|leading tone}}. The 3\14 interval can be considered a small [[subminor third]] (or inframinor third), thus bringing a new, distinct flavor from the [[neutral third]] of 7edo, which is 4 steps of 14edo. The 5\14 interval is the [[fifth complement]] of 3\14, and can be considered a [[supermajor third]], so that stacking 3\14 and 5\14 gives the triad 0–3–8 steps (0–257–686{{C}}). Finally, the 7\14 interval is the familiar [[tritone]] found in [[12edo]], as well as every even-numbered [[edo]].

	In terms of [[just intonation]], 14edo contains the approximation of [[3/2]] from 7edo. 14edo does not do well in the [[5-limit]], with [[5/4]] being close to halfway between its steps, so that 14edo does not approximate the [[4:5:6]] major triad or the [[10:12:15\|1/(6:5:4)]] minor triad accurately. The closest approximation of [[7/4]] is very flat at 11\14 (943{{C}}), so that two of them stack to [[3/1]], ~~thus tempering out~~ [[49/48]], ~~and supporting~~ [[semaphore]] temperament. However, since the 3rd harmonic is flat, the [[7/6]] and [[9/7]] intervals are approximated much more accurately, so that the 0–3–8 steps triad is a usable approximation of [[6:7:9]], and the 0–5–8 steps (0–429–686{{C}}) triad approximates [[14:18:21\|1/(9:7:6)]]. The semaphore temperament notably generates the [[mos scale]] with pattern [[5L 4s]] (named ''semiquartal''), which contains many [[~]]6:7:9 and ~1/(9:7:6) triads. In the [[11-limit]], the [[11/8]] interval is tuned very flat and equated with [[4/3]]. However, [[11/9]] is tuned rather accurately, being represented with the 4\14 interval (343{{C}}), so that the [[Neutral (interval quality)\|neutral]] triad formed by dividing the perfect fifth in two can be interpreted as a stack of two [[11/9]]'s, thus tempering out [[243/242]]. The neutral third can also be stacked on the supermajor third to get a ~[[7:9:11]] chord.		In terms of [[just intonation]], 14edo contains the approximation of [[3/2]] from 7edo. 14edo does not do well in the [[5-limit]], with [[5/4]] being close to halfway between its steps, so that 14edo does not approximate the [[4:5:6]] major triad or the [[10:12:15\|1/(6:5:4)]] minor triad accurately. The closest approximation of [[7/4]] is very flat at 11\14 (943{{C}}), so that two of them stack to [[3/1]], meaning that [[49/48]] is [[tempering out\|tempered out]], so that 14edo [[support]]s the [[semaphore]] temperament. However, since the 3rd harmonic is flat, the [[7/6]] and [[9/7]] intervals are approximated much more accurately, so that the 0–3–8 steps triad is a usable approximation of [[6:7:9]], and the 0–5–8 steps (0–429–686{{C}}) triad approximates [[14:18:21\|1/(9:7:6)]]. The semaphore temperament notably generates the [[mos scale]] with pattern [[5L 4s]] (named ''semiquartal''), which contains many [[~]]6:7:9 and ~1/(9:7:6) triads. In the [[11-limit]], the [[11/8]] interval is tuned very flat and equated with [[4/3]]. However, [[11/9]] is tuned rather accurately, being represented with the 4\14 interval (343{{C}}), so that the [[Neutral (interval quality)\|neutral]] triad formed by dividing the perfect fifth in two can be interpreted as a stack of two [[11/9]]'s, thus tempering out [[243/242]]. The neutral third can also be stacked on the supermajor third to get a ~[[7:9:11]] chord.

	While prime [[5/1\|5]] is poorly approximated, the [[7/5]] and [[11/10]] intervals are approximated fairly well. If we accept these approximations in addition to the ones described earlier, then we end up with a low-complexity, high-damage full [[11-limit]] temperament where ~~the~~ [[comma]]s ~~listed in the [[#Commas]] section~~ are [[tempered out]]. This leads to some of the bizarre equivalences described in the second "Approximate ratios" column in the table. This mapping uses the (barely) second-best mapping of prime 5, so it is notated with [[wart notation]] as "14c", where c is the 3rd letter of the alphabet, and 5 is the 3rd prime number. While not very accurate as a temperament, this mapping can be used to classify 11-limit intervals, which conveniently tempers out the [[square superparticular]]s of odds 5, 7, 9, and 11, and is the unique mapping to do so.		While prime [[5/1\|5]] is poorly approximated, the [[7/5]] and [[11/10]] intervals are approximated fairly well. If we accept these approximations in addition to the ones described earlier, then we end up with a low-complexity, high-damage full [[11-limit]] temperament where many rather large [[comma]]s are tempered out. This leads to some of the bizarre equivalences described in the second "Approximate ratios" column in the table. This mapping uses the (barely) second-best mapping of prime 5, so it is notated with [[wart notation]] as "14c", where c is the 3rd letter of the alphabet, and 5 is the 3rd prime number. While not very accurate as a temperament, this mapping can be used to classify 11-limit intervals, which conveniently tempers out the [[square superparticular]]s of odds 5, 7, 9, and 11, and is the unique mapping to do so.

	14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo\|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. The 5L 4s mos scale is rich in triads, wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.		14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo\|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. The 5L 4s mos scale is rich in triads, wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.

Overthink: /* Theory */ expand explanation

2026-03-23T00:28:39Z

Theory: expand explanation

← Older revision		Revision as of 00:28, 23 March 2026
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	== Theory ==		== Theory ==
	~~The character~~ of ~~14edo does not well serve those seeking low-~~[[~~limit~~]] ~~JI approaches~~, ~~with the exception~~ of [[~~Subgroup~~\|~~5:7:9:11:17:19~~]] ~~(which is quite well approximated~~, ~~relative to other JI approximations of the low-numbered edos). However~~, ~~the~~ [[~~ratio~~]]s ~~7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9~~, and ~~11/10 are all recognizably approximated~~, ~~and if you accept that 14edo offers approximations of these intervals, you end up with~~ a ~~low-complexity, high-damage~~ [[~~11-limit~~]] ~~temperament where~~ the [[~~comma~~]]~~s listed later in this page are~~ [[~~tempered out~~]]~~. This leads to some~~ of ~~the bizarre equivalences described in the second "Approximate ratios" column in the table. While not very accurate as a temperament~~, ~~14edo in the 14c val~~ can ~~provide~~ a ~~mapping~~ that ~~can be used to classify intervals~~, ~~which conveniently tempers out~~ the ~~square superparticulars of odds 5,~~ 7, ~~9, and 11~~.		14edo is the double of [[7edo]], and thus contains its flat 686{{C}} fifth, while adding new intervals halfway between each 7edo step. The intervals of 14edo not found in 7edo are [[Backslash notation\|1\14]] = 86{{C}}, 3\14 = 257{{C}}, 5\14 = 429{{C}}, 7\14 = 600{{C}}, and their [[octave complement]]s. The 1\14 interval is a small semitone, and its inversion a major seventh, which is suitable for a {{w\|leading tone}}. The 3\14 interval can be considered a small [[subminor third]] (or inframinor third), thus bringing a new, distinct flavor from the [[neutral third]] of 7edo, which is 4 steps of 14edo. The 5\14 interval is the [[fifth complement]] of 3\14, and can be considered a [[supermajor third]], so that stacking 3\14 and 5\14 gives the triad 0–3–8 steps (0–257–686{{C}}). Finally, the 7\14 interval is the familiar [[tritone]] found in [[12edo]], as well as every even-numbered [[edo]].

	~~14et has quite a bit~~ of [[~~xenharmonic~~]] ~~appeal~~, in ~~a similar way~~ to [[~~17edo~~\|~~17et~~]], ~~on account of having three types~~ of 3rd ~~and three types of 6th~~, ~~rather than~~ the ~~usual two of~~ [[~~12et~~]]~~. Since 14et also has a recognizable 4th~~ and ~~5th~~, ~~this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses~~ a [[triad]]~~-rich 9-note~~ [[mos scale]] of [[5L~~ ~~4s]], ~~wherein~~ 7 of 9 ~~notes are~~ [[~~tonic~~]] ~~to a subminor~~, ~~supermajor~~, ~~and~~/or neutral triad.		In terms of [[just intonation]], 14edo contains the approximation of [[3/2]] from 7edo. 14edo does not do well in the [[5-limit]], with [[5/4]] being close to halfway between its steps, so that 14edo does not approximate the [[4:5:6]] major triad or the [[10:12:15\|1/(6:5:4)]] minor triad accurately. The closest approximation of [[7/4]] is very flat at 11\14 (943{{C}}), so that two of them stack to [[3/1]], thus tempering out [[49/48]], and supporting [[semaphore]] temperament. However, since the 3rd harmonic is flat, the [[7/6]] and [[9/7]] intervals are approximated much more accurately, so that the 0–3–8 steps triad is a usable approximation of [[6:7:9]], and the 0–5–8 steps (0–429–686{{C}}) triad approximates [[14:18:21\|1/(9:7:6)]]. The semaphore temperament notably generates the [[mos scale]] with pattern [[5L 4s]] (named ''semiquartal''), which contains many [[~]]6:7:9 and ~1/(9:7:6) triads. In the [[11-limit]], the [[11/8]] interval is tuned very flat and equated with [[4/3]]. However, [[11/9]] is tuned rather accurately, being represented with the 4\14 interval (343{{C}}), so that the [[Neutral (interval quality)\|neutral]] triad formed by dividing the perfect fifth in two can be interpreted as a stack of two [[11/9]]'s, thus tempering out [[243/242]]. The neutral third can also be stacked on the supermajor third to get a ~[[7:9:11]] chord.

	14edo contains an [[omnidiatonic]] scale that can replace the standard diatonic scale, allowing for recognizable triadic harmony using the chords [[6:7:9]] and [[14:18:21]], as well as a neutral chord which can be seen as [[2:sqrt(6):3]].		While prime [[5/1\|5]] is poorly approximated, the [[7/5]] and [[11/10]] intervals are approximated fairly well. If we accept these approximations in addition to the ones described earlier, then we end up with a low-complexity, high-damage full [[11-limit]] temperament where the [[comma]]s listed in the [[#Commas]] section are [[tempered out]]. This leads to some of the bizarre equivalences described in the second "Approximate ratios" column in the table. This mapping uses the (barely) second-best mapping of prime 5, so it is notated with [[wart notation]] as "14c", where c is the 3rd letter of the alphabet, and 5 is the 3rd prime number. While not very accurate as a temperament, this mapping can be used to classify 11-limit intervals, which conveniently tempers out the [[square superparticular]]s of odds 5, 7, 9, and 11, and is the unique mapping to do so.

			14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo\|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. The 5L 4s mos scale is rich in triads, wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.

			14edo also contains an [[omnidiatonic]] scale that can replace the standard diatonic scale, allowing for recognizable triadic harmony using the chords [[6:7:9]] and [[14:18:21]], as well as a neutral chord which can be seen as [[2:sqrt(6):3]].

	=== Prime harmonics ===		=== Prime harmonics ===

Lucius Chiaraviglio: /* Instruments */ Fxi typo

2026-01-20T07:12:06Z

Instruments: Fxi typo

← Older revision		Revision as of 07:12, 20 January 2026
Line 449:		Line 449:

	== Instruments ==		== Instruments ==
	[[Lumatone mapping for 14edo]\|Lumatone mappings for 14edo] are available.		[[Lumatone mapping for 14edo\|Lumatone mappings for 14edo]] are available.

	== Music ==		== Music ==

Lucius Chiaraviglio: /* See also */ Move Lumatone mapping for 14edo above Music section for consistency with most other EDO pages.

2026-01-20T07:11:30Z

See also: Move Lumatone mapping for 14edo above Music section for consistency with most other EDO pages.

← Older revision		Revision as of 07:11, 20 January 2026
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	[[File:14edo_mus2.jpg\|thumb]]		[[File:14edo_mus2.jpg\|thumb]]

			== Instruments ==
			[[Lumatone mapping for 14edo]\|Lumatone mappings for 14edo] are available.

	== Music ==		== Music ==
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	== See also ==		== See also ==
	* [[Lumatone mapping for 14edo]]
	* [[MisterShafXen’s take on 14edo harmony]]		* [[MisterShafXen’s take on 14edo harmony]]

Tristanbay: /* Sagittal notation */ Switched to template

2025-10-24T02:09:43Z

Sagittal notation: Switched to template

← Older revision		Revision as of 02:09, 24 October 2025
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	This notation uses the same sagittal sequence as [[9edo#Sagittal notation\|9-EDO]], is a subset of the notations for EDOs [[28edo#Sagittal notation\|28]] and [[42edo#Second-best fifth notation\|42b]], and is a superset of the notation for [[7edo#Sagittal notation\|7-EDO]].		This notation uses the same sagittal sequence as [[9edo#Sagittal notation\|9-EDO]], is a subset of the notations for EDOs [[28edo#Sagittal notation\|28]] and [[42edo#Second-best fifth notation\|42b]], and is a superset of the notation for [[7edo#Sagittal notation\|7-EDO]].

	~~<imagemap>~~		{{Sagittal chart\|}}
	~~File:14-EDO_Sagittal.svg~~
	~~desc none~~
	~~rect 80 0 300 50 [[Sagittal_notation]]~~
	~~rect 423 0 583 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]~~
	~~rect 20 80 423 106 [[Fractional_3-limit_notation#Bad-fifths_limma-fraction_notation~~ \| ~~limma-fraction notation]]~~
	~~default [[File:14-EDO_Sagittal.svg]]~~
	~~</imagemap>~~

	=== Ivor Darreg's notation ===		=== Ivor Darreg's notation ===

Overthink: /* Theory */

2025-09-30T03:57:40Z

Theory

← Older revision		Revision as of 03:57, 30 September 2025
Line 9:		Line 9:

	== Theory ==		== Theory ==
	The character of 14edo does not well serve those seeking low-[[limit]] JI approaches, with the exception of [[Subgroup\|5:7:9:11:17:19]] (which is quite well approximated, relative to other JI approximations of the low-numbered edos). However, the [[ratio]]s 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage [[11-limit]] temperament where the [[comma]]s listed later in this page are [[tempered out]]. This leads to some of the bizarre equivalences described in the second "Approximate ratios" column in the table.		The character of 14edo does not well serve those seeking low-[[limit]] JI approaches, with the exception of [[Subgroup\|5:7:9:11:17:19]] (which is quite well approximated, relative to other JI approximations of the low-numbered edos). However, the [[ratio]]s 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage [[11-limit]] temperament where the [[comma]]s listed later in this page are [[tempered out]]. This leads to some of the bizarre equivalences described in the second "Approximate ratios" column in the table. While not very accurate as a temperament, 14edo in the 14c val can provide a mapping that can be used to classify intervals, which conveniently tempers out the square superparticulars of odds 5, 7, 9, and 11.

	14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo\|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a [[triad]]-rich 9-note [[mos scale]] of [[5L 4s]], wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.		14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo\|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a [[triad]]-rich 9-note [[mos scale]] of [[5L 4s]], wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.

BudjarnLambeth: /* Octave stretch or compression */

2025-09-23T02:24:22Z

Octave stretch or compression

@@ Line 410: / Line 410: @@
 == Octave stretch or compression ==
 edo benefits from [[octave stretch]] as harmonics 3, 7, and 11 are all tuned flat. [[22edt]], [[ed6|36ed6]] and [[42zpi]] are among the possible choices.
 == Scales ==

BudjarnLambeth: /* Octave stretch or compression */

2025-08-28T00:35:53Z

Octave stretch or compression

← Older revision		Revision as of 00:35, 28 August 2025
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	{{Harmonics in cet\|85.842\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 14et, 11-limit WE tuning (continued)}}		{{Harmonics in cet\|85.842\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 14et, 11-limit WE tuning (continued)}}

	; [[36ed6]]		; [[ed6\|36ed6]]
	* Step size: 86.165{{c}}, octave size: 1206.3{{c}}		* Step size: 86.165{{c}}, octave size: 1206.3{{c}}
	Stretching the octave of 14edo by around NNN{{c}} results in improved primes 3, 7 and 11, but a worse prime 2 and completely unusable prime 13. This approximates all no-13s harmonics up to 16 within 35.3{{c}}. The tuning 36ed6 does this.		Stretching the octave of 14edo by around NNN{{c}} results in improved primes 3, 7 and 11, but a worse prime 2 and completely unusable prime 13. This approximates all no-13s harmonics up to 16 within 35.3{{c}}. The tuning 36ed6 does this.

← Older revision		Revision as of 00:35, 23 March 2026
Line 11:		Line 11:
	14edo is the double of [[7edo]], and thus contains its flat 686{{C}} fifth, while adding new intervals halfway between each 7edo step. The intervals of 14edo not found in 7edo are [[Backslash notation\|1\14]] = 86{{C}}, 3\14 = 257{{C}}, 5\14 = 429{{C}}, 7\14 = 600{{C}}, and their [[octave complement]]s. The 1\14 interval is a small semitone, and its inversion a major seventh, which is suitable for a {{w\|leading tone}}. The 3\14 interval can be considered a small [[subminor third]] (or inframinor third), thus bringing a new, distinct flavor from the [[neutral third]] of 7edo, which is 4 steps of 14edo. The 5\14 interval is the [[fifth complement]] of 3\14, and can be considered a [[supermajor third]], so that stacking 3\14 and 5\14 gives the triad 0–3–8 steps (0–257–686{{C}}). Finally, the 7\14 interval is the familiar [[tritone]] found in [[12edo]], as well as every even-numbered [[edo]].		14edo is the double of [[7edo]], and thus contains its flat 686{{C}} fifth, while adding new intervals halfway between each 7edo step. The intervals of 14edo not found in 7edo are [[Backslash notation\|1\14]] = 86{{C}}, 3\14 = 257{{C}}, 5\14 = 429{{C}}, 7\14 = 600{{C}}, and their [[octave complement]]s. The 1\14 interval is a small semitone, and its inversion a major seventh, which is suitable for a {{w\|leading tone}}. The 3\14 interval can be considered a small [[subminor third]] (or inframinor third), thus bringing a new, distinct flavor from the [[neutral third]] of 7edo, which is 4 steps of 14edo. The 5\14 interval is the [[fifth complement]] of 3\14, and can be considered a [[supermajor third]], so that stacking 3\14 and 5\14 gives the triad 0–3–8 steps (0–257–686{{C}}). Finally, the 7\14 interval is the familiar [[tritone]] found in [[12edo]], as well as every even-numbered [[edo]].

	In terms of [[just intonation]], 14edo contains the approximation of [[3/2]] from 7edo. 14edo does not do well in the [[5-limit]], with [[5/4]] being close to halfway between its steps, so that 14edo does not approximate the [[4:5:6]] major triad or the [[10:12:15\|1/(6:5:4)]] minor triad accurately. The closest approximation of [[7/4]] is very flat at 11\14 (943{{C}}), so that two of them stack to [[3/1]], ~~thus tempering out~~ [[49/48]], ~~and supporting~~ [[semaphore]] temperament. However, since the 3rd harmonic is flat, the [[7/6]] and [[9/7]] intervals are approximated much more accurately, so that the 0–3–8 steps triad is a usable approximation of [[6:7:9]], and the 0–5–8 steps (0–429–686{{C}}) triad approximates [[14:18:21\|1/(9:7:6)]]. The semaphore temperament notably generates the [[mos scale]] with pattern [[5L 4s]] (named ''semiquartal''), which contains many [[~]]6:7:9 and ~1/(9:7:6) triads. In the [[11-limit]], the [[11/8]] interval is tuned very flat and equated with [[4/3]]. However, [[11/9]] is tuned rather accurately, being represented with the 4\14 interval (343{{C}}), so that the [[Neutral (interval quality)\|neutral]] triad formed by dividing the perfect fifth in two can be interpreted as a stack of two [[11/9]]'s, thus tempering out [[243/242]]. The neutral third can also be stacked on the supermajor third to get a ~[[7:9:11]] chord.		In terms of [[just intonation]], 14edo contains the approximation of [[3/2]] from 7edo. 14edo does not do well in the [[5-limit]], with [[5/4]] being close to halfway between its steps, so that 14edo does not approximate the [[4:5:6]] major triad or the [[10:12:15\|1/(6:5:4)]] minor triad accurately. The closest approximation of [[7/4]] is very flat at 11\14 (943{{C}}), so that two of them stack to [[3/1]], meaning that [[49/48]] is [[tempering out\|tempered out]], so that 14edo [[support]]s the [[semaphore]] temperament. However, since the 3rd harmonic is flat, the [[7/6]] and [[9/7]] intervals are approximated much more accurately, so that the 0–3–8 steps triad is a usable approximation of [[6:7:9]], and the 0–5–8 steps (0–429–686{{C}}) triad approximates [[14:18:21\|1/(9:7:6)]]. The semaphore temperament notably generates the [[mos scale]] with pattern [[5L 4s]] (named ''semiquartal''), which contains many [[~]]6:7:9 and ~1/(9:7:6) triads. In the [[11-limit]], the [[11/8]] interval is tuned very flat and equated with [[4/3]]. However, [[11/9]] is tuned rather accurately, being represented with the 4\14 interval (343{{C}}), so that the [[Neutral (interval quality)\|neutral]] triad formed by dividing the perfect fifth in two can be interpreted as a stack of two [[11/9]]'s, thus tempering out [[243/242]]. The neutral third can also be stacked on the supermajor third to get a ~[[7:9:11]] chord.

	While prime [[5/1\|5]] is poorly approximated, the [[7/5]] and [[11/10]] intervals are approximated fairly well. If we accept these approximations in addition to the ones described earlier, then we end up with a low-complexity, high-damage full [[11-limit]] temperament where ~~the~~ [[comma]]s ~~listed in the [[#Commas]] section~~ are [[tempered out]]. This leads to some of the bizarre equivalences described in the second "Approximate ratios" column in the table. This mapping uses the (barely) second-best mapping of prime 5, so it is notated with [[wart notation]] as "14c", where c is the 3rd letter of the alphabet, and 5 is the 3rd prime number. While not very accurate as a temperament, this mapping can be used to classify 11-limit intervals, which conveniently tempers out the [[square superparticular]]s of odds 5, 7, 9, and 11, and is the unique mapping to do so.		While prime [[5/1\|5]] is poorly approximated, the [[7/5]] and [[11/10]] intervals are approximated fairly well. If we accept these approximations in addition to the ones described earlier, then we end up with a low-complexity, high-damage full [[11-limit]] temperament where many rather large [[comma]]s are tempered out. This leads to some of the bizarre equivalences described in the second "Approximate ratios" column in the table. This mapping uses the (barely) second-best mapping of prime 5, so it is notated with [[wart notation]] as "14c", where c is the 3rd letter of the alphabet, and 5 is the 3rd prime number. While not very accurate as a temperament, this mapping can be used to classify 11-limit intervals, which conveniently tempers out the [[square superparticular]]s of odds 5, 7, 9, and 11, and is the unique mapping to do so.

	14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo\|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. The 5L 4s mos scale is rich in triads, wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.		14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo\|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. The 5L 4s mos scale is rich in triads, wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad.