19edt - Revision history

Overthink: /* Theory */ more tritave-reduced harmonics

2025-11-14T22:53:10Z

Theory: more tritave-reduced harmonics

← Older revision		Revision as of 22:53, 14 November 2025
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	== Theory ==		== Theory ==
	19edt is not a truly [[xenharmonic]] tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo\|12-tone scale]]. Although it is really just the normal 12edo framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in [[accuracy]], with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]].		19edt is not a truly [[xenharmonic]] tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo\|12-tone scale]]. Although it is really just the normal 12edo framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in [[accuracy]], with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]]. It also misses [[13/9]], but its [[17/9]] is nearly pure, being only 0.1 cents sharp of just, and [[19/9]] can be considered usable as well.

	This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0–600–1000 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a "macro-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{mos scalesig\|5L 4s<3/1>\|link=1}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic {{mos scalesig\|8L 3s<3/1>\|link=1}} scale.		This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0–600–1000 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a "macro-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{mos scalesig\|5L 4s<3/1>\|link=1}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic {{mos scalesig\|8L 3s<3/1>\|link=1}} scale.

ArrowHead294: /* See also */

2025-06-10T13:26:47Z

ArrowHead294: /* See also */

2025-06-10T13:25:55Z

ArrowHead294 at 13:06, 10 June 2025

2025-06-10T13:06:58Z

← Older revision		Revision as of 13:06, 10 June 2025
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	* [[Bernhard Stopper]]'s [https://piano-stopper.de/?page_id=107&lang=en OnlyPure tuning]{{dead link}}		* [[Bernhard Stopper]]'s [https://piano-stopper.de/?page_id=107&lang=en OnlyPure tuning]{{dead link}}

			[[Category:12edo]]
	[[Category:Macrotonal]]		[[Category:Macrotonal]]

ArrowHead294: Replace {{scale link}} with {{mos scalesig}}

2025-03-08T00:26:58Z

Replace {{scale link}} with {{mos scalesig}}

← Older revision		Revision as of 00:26, 8 March 2025
Line 9:		Line 9:
	19edt is not a truly [[xenharmonic]] tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo\|12-tone scale]]. Although it is really just the normal 12edo framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in [[accuracy]], with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]].		19edt is not a truly [[xenharmonic]] tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo\|12-tone scale]]. Although it is really just the normal 12edo framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in [[accuracy]], with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]].

	This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0–600–1000 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a "macro-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{sl\|5L 4s}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic [[8L 3s (3/1~~-equivalent)~~\|~~8L 3s]]~~ scale.		This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0–600–1000 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a "macro-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{mos scalesig\|5L 4s<3/1>\|link=1}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic {{mos scalesig\|8L 3s<3/1>\|link=1}} scale.

	=== Harmonics ===		=== Harmonics ===

BudjarnLambeth: /* Theory */ added links

2025-03-04T02:11:30Z

Theory: added links

← Older revision		Revision as of 02:11, 4 March 2025
Line 7:		Line 7:

	== Theory ==		== Theory ==
	19edt is not a truly xenharmonic tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo\|12-tone scale]]. Although it is really just the normal 12edo framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in accuracy, with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]].		19edt is not a truly [[xenharmonic]] tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo\|12-tone scale]]. Although it is really just the normal 12edo framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in [[accuracy]], with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]].

	This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0–600–1000 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a "macro-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{sl\|5L 4s}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic [[8L 3s (3/1-equivalent)\|8L 3s]] scale.		This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0–600–1000 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a "macro-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{sl\|5L 4s}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic [[8L 3s (3/1-equivalent)\|8L 3s]] scale.

Jerdle: /* Theory */9:5 is ~1000¢, not ~1100.

2025-02-16T05:25:28Z

Theory: 9:5 is ~1000¢, not ~1100.

← Older revision		Revision as of 05:25, 16 February 2025
Line 9:		Line 9:
	19edt is not a truly xenharmonic tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo\|12-tone scale]]. Although it is really just the normal 12edo framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in accuracy, with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]].		19edt is not a truly xenharmonic tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo\|12-tone scale]]. Although it is really just the normal 12edo framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in accuracy, with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]].

	This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as ~~0–600–1100~~ cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a "macro-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{sl\|5L 4s}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic [[8L 3s (3/1-equivalent)\|8L 3s]] scale.		This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0–600–1000 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a "macro-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{sl\|5L 4s}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic [[8L 3s (3/1-equivalent)\|8L 3s]] scale.

	=== Harmonics ===		=== Harmonics ===

FloraC: -redundant categories

2025-01-15T13:47:59Z

-redundant categories

← Older revision		Revision as of 13:47, 15 January 2025
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	[[Category:Macrotonal]]		[[Category:Macrotonal]]
	~~[[Category:Edonoi]]~~
	~~[[Category:Edt]]~~

FloraC: /* Theory */ +subsets and supersets

2025-01-15T13:42:36Z

Theory: +subsets and supersets

← Older revision		Revision as of 13:42, 15 January 2025
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	{{Harmonics in equal\|steps=19\|num=3\|denom=1\|intervals=integer}}		{{Harmonics in equal\|steps=19\|num=3\|denom=1\|intervals=integer}}
	{{Harmonics in equal\|steps=19\|num=3\|denom=1\|intervals=integer\|start=12\|columns=12\|collapsed=1\|title=Approximation of harmonics in 19edt (continued)}}		{{Harmonics in equal\|steps=19\|num=3\|denom=1\|intervals=integer\|start=12\|columns=12\|collapsed=1\|title=Approximation of harmonics in 19edt (continued)}}

			=== Subsets and supersets ===
			19edt is the 8th [[prime equal division\|prime edt]], following [[17edt]] and before [[23edt]].

	== Intervals ==		== Intervals ==

FloraC: Cleanup

2025-01-15T13:39:25Z

Cleanup

← Older revision		Revision as of 13:39, 15 January 2025
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	{{interwiki		{{interwiki
	\|en = 19ed3		\| en = 19ed3
	\|de = ~~Bernhard_Stopper~~		\| de = Bernhard Stopper
	}}		}}
	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}} It is also known as '''Stopper tuning'''.		{{ED intro}} It is also known as '''Stopper tuning'''.

	== ~~Properties~~ ==		== Theory ==
	~~19 equal divisions of the tritave~~ is not a ~~"real"~~ xenharmonic tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo\|12-tone scale]]. Although it is really just the normal 12edo ~~tuning~~ framed in a ~~tritave equivalence~~, it can still be used as a temperament with no twos like other tritave tunings, although limited accuracy, with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]].		19edt is not a truly xenharmonic tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo\|12-tone scale]]. Although it is really just the normal 12edo framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in accuracy, with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]].

	This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0–600–1100 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a ~~“macro~~-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{sl\|5L 4s}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic [[8L 3s (3/1-equivalent)\|~~Obikhod~~]] scale.		This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0–600–1100 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a "macro-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{sl\|5L 4s}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic [[8L 3s (3/1-equivalent)\|8L 3s]] scale.

	== Harmonics ==		=== Harmonics ===
	{{Harmonics in equal		{{Harmonics in equal\|steps=19\|num=3\|denom=1\|intervals=integer}}
	\| steps = 19		{{Harmonics in equal\|steps=19\|num=3\|denom=1\|intervals=integer\|start=12\|columns=12\|collapsed=1\|title=Approximation of harmonics in 19edt (continued)}}
	\| num = 3
	\| denom = 1
	\| intervals = integer
	}}
	{{Harmonics in equal
	\| steps = 19
	\| num = 3
	\| denom = 1
	\| start = 12
	\| collapsed = 1
	\| ~~intervals~~ = ~~integer~~
	}}

	== Intervals ==		== Intervals ==
Line 31:		Line 19:

	== See also ==		== See also ==
	* [[7edf~~\|7EDF~~]] ~~–~~ relative ~~ED3/2~~		* [[7edf]] – relative edf
	* [[12edo~~\|12EDO~~]] ~~–~~ relative ~~EDO~~		* [[12edo]] – relative edo
	* [[28ed5~~\|28ED5~~]] ~~–~~ relative ~~ED5~~		* [[28ed5]] – relative ed5
	* [[31ed6~~\|31ED6~~]] ~~–~~ relative ~~ED6~~		* [[31ed6]] – relative ed6
	* [[34ed7~~\|34ED7~~]] ~~–~~ relative ~~ED7~~		* [[34ed7]] – relative ed7
	* [[40ed10~~\|40ED10~~]] ~~–~~ relative ~~ED10~~		* [[40ed10]] – relative ed10
	* [[43ed12~~\|43ED12~~]] ~~–~~ relative ~~ED12~~		* [[43ed12]] – relative ed12

	== External links ==		== External links ==

← Older revision		Revision as of 13:26, 10 June 2025
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	* [[43ed12]] – relative ed12		* [[43ed12]] – relative ed12
	* [[76ed80]] – close to the zeta-optimized tuning for 12edo		* [[76ed80]] – close to the zeta-optimized tuning for 12edo
			* [[1ed18/17\|AS18/17]] – relative [[AS\|ambitonal sequence]]

	== External links ==		== External links ==

← Older revision		Revision as of 13:25, 10 June 2025
Line 29:		Line 29:
	* [[40ed10]] – relative ed10		* [[40ed10]] – relative ed10
	* [[43ed12]] – relative ed12		* [[43ed12]] – relative ed12
			* [[76ed80]] – close to the zeta-optimized tuning for 12edo

	== External links ==		== External links ==