19edo - Revision history

Naren: Add link to Mandelbaum thesis

2026-09-24T22:24:20Z

Add link to Mandelbaum thesis

← Older revision		Revision as of 22:24, 24 September 2026
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	== Further reading ==		== Further reading ==
			* [[Mandelbaum, Joel]]. ''[https://anaphoria.com/mandelbaum.html Multiple Division of the Octave and the Tonal Resources of 19-tone Temperament]''. 1961.
	* [[Darreg, Ivor]]. ''[http://www.tonalsoft.com/sonic-arts/darreg/case.htm A Case for Nineteen]''. 1982.		* [[Darreg, Ivor]]. ''[http://www.tonalsoft.com/sonic-arts/darreg/case.htm A Case for Nineteen]''. 1982.
	* Darreg, Ivor. ''[https://microstick.net/nineteen-for-the-nineties-by-ivor-darreg/ Nineteen for the Nineties]''. (Unknown date of publication).		* Darreg, Ivor. ''[https://microstick.net/nineteen-for-the-nineties-by-ivor-darreg/ Nineteen for the Nineties]''. (Unknown date of publication).

Naren: Fix dead links, archive link for Yasser, link to pdf for Bucht and Huovinen paper.

2026-09-24T20:25:36Z

Fix dead links, archive link for Yasser, link to pdf for Bucht and Huovinen paper.

Naren: Fix dead link

2026-09-24T20:02:20Z

Fix dead link

← Older revision		Revision as of 20:02, 24 September 2026
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	== Further reading ==		== Further reading ==
	* [[Darreg, Ivor]]. ''[http://www.tonalsoft.com/sonic-arts/darreg/case.htm A Case for Nineteen]''. 1982.		* [[Darreg, Ivor]]. ''[http://www.tonalsoft.com/sonic-arts/darreg/case.htm A Case for Nineteen]''. 1982.
	* Darreg, Ivor. ''[~~http~~://~~www.~~microstick.net/~~nineteenarticle.htm~~ Nineteen for the Nineties]''~~{{dead link}}~~. (Unknown date of publication).		* Darreg, Ivor. ''[https://microstick.net/nineteen-for-the-nineties-by-ivor-darreg/ Nineteen for the Nineties]''. (Unknown date of publication).
	* Howe, Hubert S., Jr. [http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html 19-Tone Theory and Applications]. c. 2004.		* Howe, Hubert S., Jr. [http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html 19-Tone Theory and Applications]. c. 2004.
	* [[Sethares, William A]]. [http://sethares.engr.wisc.edu/tet19/guitarchords19.html Tunings for 19 Tone Equal Tempered Guitar]. 1991.		* [[Sethares, William A]]. [http://sethares.engr.wisc.edu/tet19/guitarchords19.html Tunings for 19 Tone Equal Tempered Guitar]. 1991.

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 ===

← Older revision		Revision as of 20:25, 24 September 2026
Line 1,182:		Line 1,182:
	* [[Darreg, Ivor]]. ''[http://www.tonalsoft.com/sonic-arts/darreg/case.htm A Case for Nineteen]''. 1982.		* [[Darreg, Ivor]]. ''[http://www.tonalsoft.com/sonic-arts/darreg/case.htm A Case for Nineteen]''. 1982.
	* Darreg, Ivor. ''[https://microstick.net/nineteen-for-the-nineties-by-ivor-darreg/ Nineteen for the Nineties]''. (Unknown date of publication).		* Darreg, Ivor. ''[https://microstick.net/nineteen-for-the-nineties-by-ivor-darreg/ Nineteen for the Nineties]''. (Unknown date of publication).
	* Howe, Hubert S., Jr. [~~http~~://~~qcpages~~.~~qc.edu~~/~~%7Ehowe~~/~~articles/19-Tone%20Theory.html~~ 19-Tone Theory and Applications]. c. 2004.		* Howe, Hubert S., Jr. [https://huberthowe.org/tone-theory/ 19-Tone Theory and Applications]. c. 2004.
	* [[Sethares, William A]]. [http://sethares.engr.wisc.edu/tet19/guitarchords19.html Tunings for 19 Tone Equal Tempered Guitar]. 1991.		* [[Sethares, William A]]. [http://sethares.engr.wisc.edu/tet19/guitarchords19.html Tunings for 19 Tone Equal Tempered Guitar]. 1991.
	* [[Sword, Ron]]. ''[http://www.metatonalmusic.com/books.html Enneadecaphonic Scales for Guitar: A Repository of Scales, Chord-Scales, Notations and Techniques for Nineteen Equal Divisions of the Octave]''. 2010.		* [[Sword, Ron]]. ''[http://www.metatonalmusic.com/books.html Enneadecaphonic Scales for Guitar: A Repository of Scales, Chord-Scales, Notations and Techniques for Nineteen Equal Divisions of the Octave]''. 2010.
	* Yasser, Joseph. ''[https://~~www.worldcat~~.org/~~fr/title~~/~~726192994~~ Theory of Evolving Tonality]''. 1932.		* Yasser, Joseph. ''[https://archive.org/details/theoryofevolving0000jose Theory of Evolving Tonality]''. 1932.

	== External links ==		== External links ==
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	* [http://www.n-ism.org/Projects/microtonalism.php Microtonalism] by Ingrid Pearson, Graham Hair, Dougie McGilvray, Nick Bailey, Amanda Morrison and Richard Parncutt (from n-ISM, the Network for Interdisciplinary Studies in Science, Technology, and Music)		* [http://www.n-ism.org/Projects/microtonalism.php Microtonalism] by Ingrid Pearson, Graham Hair, Dougie McGilvray, Nick Bailey, Amanda Morrison and Richard Parncutt (from n-ISM, the Network for Interdisciplinary Studies in Science, Technology, and Music)
	* [http://mtg.redkeylabs.com/index.php?topic=6.0 Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar].		* [http://mtg.redkeylabs.com/index.php?topic=6.0 Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar].
	* [[Bostjan Zupancic]]'s [https://sites.google.com/site/bostjanzupancickhereb/~~home~~/bostjan/microtones/19edo 19-EDO pages]		* [[Bostjan Zupancic]]'s [https://sites.google.com/site/bostjanzupancickhereb/khereb/bostjan/microtones/19edo 19-EDO pages]
	* [https://sites.google.com/view/19edoscales Catalog of all 19edo heptatonic scales]		* [https://sites.google.com/view/19edoscales Catalog of all 19edo heptatonic scales]

	=== References ===		=== References ===
	* Bucht, Saku and Huovinen, Erkki, ''Perceived consonance of harmonic intervals in 19-tone equal temperament'', CIM04_proceedings.		* Bucht, Saku and Huovinen, Erkki, [https://www.parncutt.org/CIM04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf ''Perceived consonance of harmonic intervals in 19-tone equal temperament''], CIM04_proceedings.
	* Levy, Kenneth J., ''Costeley's Chromatic Chanson'', Annales Musicologues: Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.		* Levy, Kenneth J., ''Costeley's Chromatic Chanson'', Annales Musicologues: Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.