19edo - Revision history

FloraC: /* Subsets and supersets */ restore certain info (I don't see why it should be removed)

2026-08-03T18:24:55Z

Subsets and supersets: restore certain info (I don't see why it should be removed)

← Older revision		Revision as of 18:24, 3 August 2026
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	19edo is the 8th [[prime edo]], following [[17edo]] and preceding [[23edo]].		19edo is the 8th [[prime edo]], following [[17edo]] and preceding [[23edo]]. As such, it does not contain any nontrivial subset edos, though it contains [[19ed4]].

	[[38edo]], which doubles 19edo, provides an approximation of harmonic 11 that works well with the flat tendency of its 5-limit mapping. [[57edo]] effectively corrects the harmonic 7 to just, although it is [[76edo]] that fits the best.		[[38edo]], which doubles 19edo, provides an approximation of harmonic 11 that works well with the flat tendency of its 5-limit mapping. [[57edo]] effectively corrects the harmonic 7 to just, although it is [[76edo]] that fits the best.

Eliora: /* Subsets and supersets */ expand in general what 19edo can do, not just undevigintone and meanmag as these are covered in 19th-octave temps.

2026-08-03T14:36:12Z

Subsets and supersets: expand in general what 19edo can do, not just undevigintone and meanmag as these are covered in 19th-octave temps.

← Older revision		Revision as of 14:36, 3 August 2026
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	19edo is the 8th [[prime edo]], following [[17edo]] and preceding [[23edo~~]]. As such, it does not contain any nontrivial subset edos, though it contains [[19ed4~~]].		19edo is the 8th [[prime edo]], following [[17edo]] and preceding [[23edo]].

	[[38edo]], which doubles 19edo, provides an approximation of harmonic 11 that works well with the flat tendency of its 5-limit mapping~~. See [[undevigintone]]~~. [[57edo]] effectively corrects the harmonic 7 to just, although it is [[76edo]] that fits the best. See [[~~meanmag~~]].		[[38edo]], which doubles 19edo, provides an approximation of harmonic 11 that works well with the flat tendency of its 5-limit mapping. [[57edo]] effectively corrects the harmonic 7 to just, although it is [[76edo]] that fits the best.

			Large edos like [[190edo]], [[494edo]], [[665edo]], [[836edo]], [[1178edo]], and many others, contain 19edo and also exhibit high consistency in higher limits. These are also notable because they still temper out the [[enneadeca]], which preserves the precise [[6/5]] mapping 19edo has while improving upon it with microtemperaments.

			See [[19th-octave temperaments]] for a detailed overview.

	=== Miscellaneous properties ===		=== Miscellaneous properties ===

Overthink: /* Intervals */ simple note names

2026-06-06T03:13:03Z

Intervals: simple note names

Show changes

Overthink: /* Theory */ grammar

2026-06-02T00:42:52Z

Theory: grammar

← Older revision		Revision as of 00:42, 2 June 2026
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	== Theory ==		== Theory ==
	19edo is the second edo, after [[12edo]] which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]], which has a 18-[[cent]]-sharp fifth). Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, it serves as a good tuning for [[meantone]]. Unlike 12edo, where [[enharmonic]] notes are conflated, 19edo distinguishes them, and differs from [[17edo]] in that its [[diatonic semitone]] is wider than the [[chromatic semitone]], rather than narrower. In fact, it is nearly identical to the enharmonic scale of [[1/3-comma meantone]], and can be considered a closed form thereof.		19edo is the second edo, after [[12edo]], which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]], which has a 18-[[cent]]-sharp fifth). Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, it serves as a good tuning for [[meantone]]. Unlike 12edo, where [[enharmonic]] notes are conflated, 19edo distinguishes them, and differs from [[17edo]] in that its [[diatonic semitone]] is wider than the [[chromatic semitone]], rather than narrower. In fact, it is nearly identical to the enharmonic scale of [[1/3-comma meantone]], and can be considered a closed form thereof.

	It is less successful in the [[7-limit]] as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]), but it is still better than 12edo overall.		It is less successful in the [[7-limit]] as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]), but it is still better than 12edo overall.

Xenllium at 10:44, 3 May 2026

2026-05-03T10:44:03Z

← Older revision		Revision as of 10:44, 3 May 2026
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	\| 23		\| 23
	\| [[70/69]]		\| [[70/69]]
	\| {{monzo\| 1 -1 1 1 0 0 0 0 -}}		\| {{monzo\| 1 -1 1 1 0 0 0 0 -1 }}
	\| 24.91		\| 24.91
	\| Twethuzoyo		\| Twethuzoyo
Line 1,037:		Line 1,037:
	\| M2		\| M2
	\| [[1L 5s]], [[6L 1s]], [[6L 7s]]		\| [[1L 5s]], [[6L 1s]], [[6L 7s]]
	\| [[Deutone]]<br>[[Spell]]		\| [[Deutone]] <br>[[Xenial]] / [[Sensamagic clan #Xenia\|Xenia]] <br>[[Spell]]
	\|-		\|-
	\| 4		\| 4
Line 1,043:		Line 1,043:
	\| A2, d3		\| A2, d3
	\| [[1L 3s]], [[4L 1s]], <br>[[5L 4s]], [[5L 9s]]		\| [[1L 3s]], [[4L 1s]], <br>[[5L 4s]], [[5L 9s]]
	\| [[Godzilla]]		\| [[Godzilla]] / [[Helayo]]
	\|-		\|-
	\| 5		\| 5
Line 1,073:		Line 1,073:
	\| A4		\| A4
	\| [[2L 3s]], [[2L 5s]], [[2L 7s]], <br>[[2L 9s]], [[2L 11s]], [[2L 13s]], <br>[[2L 15s]]		\| [[2L 3s]], [[2L 5s]], [[2L 7s]], <br>[[2L 9s]], [[2L 11s]], [[2L 13s]], <br>[[2L 15s]]
	\| [[Liese]] / [[~~pycnic~~]]~~<br>~~[[~~Triton~~]]		\| [[Liese]] <br>[[Triton]] / [[pycnic]]
	\|}		\|}

FloraC: /* Intervals */ don't see why there needs to be a column width contraint. Better go with left-align for varing-width columns

2026-03-28T10:38:15Z

Intervals: don't see why there needs to be a column width contraint. Better go with left-align for varing-width columns

← Older revision		Revision as of 10:38, 28 March 2026
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	== Intervals ==		== Intervals ==
	{\| class="wikitable right-1 right-2 ~~center-3~~"		{\| class="wikitable right-1 right-2"
	\|-		\|-
	! [[Degree\|#]]		! [[Degree\|#]]
	! [[Cent]]s		! [[Cent]]s
	! ~~style="width: 140px;" \|~~ [[Interval category\|Interval categories]]		! [[Interval category\|Interval categories]]
	! Approximated ratios<ref group="note">As a [[2.3.5.7.13 subgroup\|2.3.5.7.13-subgroup]] temperament.</ref>		! Approximated ratios<ref group="note">As a [[2.3.5.7.13 subgroup\|2.3.5.7.13-subgroup]] temperament.</ref>
	\|-		\|-
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	\| 4		\| 4
	\| 252.6		\| 252.6
	\| Augmented second<br />Diminished third		\| Augmented second<br>Diminished third
	\| [[7/6]], [[8/7]], [[15/13]]		\| [[7/6]], [[8/7]], [[15/13]]
	\|-		\|-

Overthink: /* Theory */ link cent; better language

2026-03-27T22:08:32Z

Theory: link cent; better language

← Older revision		Revision as of 22:08, 27 March 2026
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	== Theory ==		== Theory ==
	19edo is the second edo, after [[12edo]] which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]], which has a 18-cent-sharp fifth). Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, it serves as a good tuning for [[meantone]]. Unlike 12edo, where [[enharmonic]] notes are conflated, 19edo distinguishes them, and differs from [[17edo]] in that its [[diatonic semitone]] is wider than the [[chromatic semitone]], rather than narrower. In fact, it is nearly identical to the enharmonic scale of [[1/3-comma meantone]], and can be considered a closed form thereof.		19edo is the second edo, after [[12edo]] which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]], which has a 18-[[cent]]-sharp fifth). Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, it serves as a good tuning for [[meantone]]. Unlike 12edo, where [[enharmonic]] notes are conflated, 19edo distinguishes them, and differs from [[17edo]] in that its [[diatonic semitone]] is wider than the [[chromatic semitone]], rather than narrower. In fact, it is nearly identical to the enharmonic scale of [[1/3-comma meantone]], and can be considered a closed form thereof.

	It is less successful in the [[7-limit]] as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]), but it is still better than 12edo ~~on average~~.		It is less successful in the [[7-limit]] as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]), but it is still better than 12edo overall.

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

Overthink: /* Interval quality and chord names in color notation */ formatting

2026-03-20T18:59:56Z

Interval quality and chord names in color notation: formatting

← Older revision		Revision as of 18:59, 20 March 2026
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	\|-		\|-
	\| gu (5-under)		\| gu (5-under)
	\| 12:10:8:7<br>~~or 1:6~~/~~5:3~~/~~2:12~~/7		\| 1/(12:10:8:7)<br>(1–6/5–3/2–12/7)
	\| 0–5–11–15		\| 0–5–11–15
	\| C–E♭–G–A♯		\| C–E♭–G–A♯

Overthink: /* Intervals */ Formatting; MOS:SEAOFBLUE

2026-03-20T18:57:16Z

Intervals: Formatting; MOS:SEAOFBLUE

← Older revision		Revision as of 18:57, 20 March 2026
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	== Intervals ==		== Intervals ==
	{\| class="wikitable right-1 right-2 center-~~5 center-8~~"		{\| class="wikitable right-1 right-2 center-3"
	\|-		\|-
	! [[Degree\|#]]		! [[Degree\|#]]
	! [[Cent]]s		! [[Cent]]s
	! [[Interval category\|Interval categories]]		! style="width: 140px;" \| [[Interval category\|Interval categories]]
	! Approximated ratios<ref group="note">As a [[2.3.5.7.13 subgroup\|2.3.5.7.13-~~]][[~~subgroup]] temperament.</ref>		! Approximated ratios<ref group="note">As a [[2.3.5.7.13 subgroup\|2.3.5.7.13-subgroup]] temperament.</ref>
	\|-		\|-
	\| 0		\| 0
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	\|-		\|-
	\| gu (5-under)		\| gu (5-under)
	\| 12:10:8:7 or 1:6/5:3/2:12/7		\| 12:10:8:7<br>or 1:6/5:3/2:12/7
	\| 0–5–11–15		\| 0–5–11–15
	\| C–E♭–G–A♯		\| C–E♭–G–A♯

Overthink: /* History */ comma and formatting

2026-03-20T18:47:48Z

History: comma and formatting

← Older revision		Revision as of 18:47, 20 March 2026
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	Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson [[Seigneur Dieu ta pitié]] of 1558. Costeley understood and desired the circulating aspect of this tuning, which he defined as dividing the just major second into three approximately equal parts. Costeley had other compositions that made use of intervals, such as the diminished third, which have a meaningful context in 19edo, but not in other tuning systems contemporary with the work.		Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson [[Seigneur Dieu ta pitié]] of 1558. Costeley understood and desired the circulating aspect of this tuning, which he defined as dividing the just major second into three approximately equal parts. Costeley had other compositions that made use of intervals, such as the diminished third, which have a meaningful context in 19edo, but not in other tuning systems contemporary with the work.

	In 1577 music theorist Francisco de Salinas proposed [[1/3~~-comma meantone\|{{frac\|1\|3}}~~-comma meantone]], in which the fifth is 694.786{{c}}; the fifth of 19edo is 694.737{{c}}, which is only a twentieth of a cent flatter. Salinas suggested tuning nineteen tones to the octave to this tuning, which comes within less than one cent of closing exactly, so that his suggestion is effectively 19edo.		In 1577, music theorist Francisco de Salinas proposed [[1/3-comma meantone]], in which the fifth is 694.786{{c}}; the fifth of 19edo is 694.737{{c}}, which is only a twentieth of a cent flatter. Salinas suggested tuning nineteen tones to the octave to this tuning, which comes within less than one cent of closing exactly, so that his suggestion is effectively 19edo.

	In 1835, mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone tunings he regarded as better, such as [[50edo\|50 equal temperament]] ([http://www.tonalsoft.com/sonic-arts/monzo/woolhouse/essay.htm summary of Woolhouse's essay]).		In 1835, mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone tunings he regarded as better, such as [[50edo\|50 equal temperament]] ([http://www.tonalsoft.com/sonic-arts/monzo/woolhouse/essay.htm summary of Woolhouse's essay]).