19edt - Revision history

Hotcrystal0 at 23:17, 20 September 2026

2026-09-20T23:17:48Z

← Older revision		Revision as of 23:17, 20 September 2026
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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 [[12edo]], the predominant tuning in Western music.. 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.		19edt is not a truly [[xenharmonic]] tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of [[12edo]], the predominant tuning in Western music. 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.

Hotcrystal0: This

2026-09-20T23:17:41Z

This

← Older revision		Revision as of 23:17, 20 September 2026
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]]. 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.		19edt is not a truly [[xenharmonic]] tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of [[12edo]], the predominant tuning in Western music.. 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.

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
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]]. 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
Line 33:		Line 33:
	* [[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
Line 34:		Line 34:

	[[Category:Macrotonal]]		[[Category:Macrotonal]]
	~~[[Category:Edonoi]]~~
	~~[[Category:Edt]]~~

← Older revision		Revision as of 13:26, 10 June 2025
Line 30:		Line 30:
	* [[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 ==