12edt - Revision history

Dummy index: /* Theory */ fix link

2025-09-29T13:09:21Z

Theory: fix link

← Older revision		Revision as of 13:09, 29 September 2025
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	=== Macrodiatonic and macromeantone ===		=== Macrodiatonic and macromeantone ===
	12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[~~macrodiatonic and microdiatonic\|~~macrodiatonic]] {{mos scalesig\|5L 2s<3/1>}} scale. This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable, since, for example, the [[generator]] is now the size of a major seventh instead of a perfect fifth. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 [[subgroup]], equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).		12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic]] {{mos scalesig\|5L 2s<3/1>}} scale. This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable, since, for example, the [[generator]] is now the size of a major seventh instead of a perfect fifth. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 [[subgroup]], equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).

	Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.		Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.

Fredg999 category edits: Removing from Category:Edonoi using Cat-a-lot

2025-08-01T19:20:37Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:20, 1 August 2025
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	[http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3 Tritave in 12] by [http://www.chrisvaisvil.com Chris Vaisvil]		[http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3 Tritave in 12] by [http://www.chrisvaisvil.com Chris Vaisvil]
	~~[[Category:edonoi]]~~
	[[Category:listen]]		[[Category:listen]]
	[[category:macrotonal]]		[[category:macrotonal]]

Fredg999 category edits: Removing from Category:Edt using Cat-a-lot

2025-07-31T15:31:26Z

Removing from Category:Edt using Cat-a-lot

← Older revision		Revision as of 15:31, 31 July 2025
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	[http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3 Tritave in 12] by [http://www.chrisvaisvil.com Chris Vaisvil]		[http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3 Tritave in 12] by [http://www.chrisvaisvil.com Chris Vaisvil]
	[[Category:edonoi]]		[[Category:edonoi]]
	~~[[Category:edt]]~~
	[[Category:listen]]		[[Category:listen]]
	[[category:macrotonal]]		[[category:macrotonal]]

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

2025-03-08T00:26:02Z

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

← Older revision		Revision as of 00:26, 8 March 2025
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	=== Macrodiatonic and macromeantone ===		=== Macrodiatonic and macromeantone ===
	12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic\|macrodiatonic]] {{sl\|5L 2s}} scale. This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable, since, for example, the [[generator]] is now the size of a major seventh instead of a perfect fifth. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 [[subgroup]], equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).		12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic\|macrodiatonic]] {{mos scalesig\|5L 2s<3/1>}} scale. This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable, since, for example, the [[generator]] is now the size of a major seventh instead of a perfect fifth. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 [[subgroup]], equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).

	Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.		Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.

ArrowHead294 at 20:48, 4 March 2025

2025-03-04T20:48:22Z

← Older revision		Revision as of 20:48, 4 March 2025
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	{{Infobox ET}}		{{Infobox ET}}
	12edt divides 3, the tritave, into 12 equal parts of 158.496 cents each, corresponding to 7.571 edo, and can be used as a generator chain for [[Kleismic_family#Hemikleismic\|hemikleismic temperament]]. From a no-twos point of view, it tempers out 49/45 and 27/25 in the 7-limit, and 1331/1125 and 1331/1225 in the 11-limit.		{{ED intro}}

	~~== Interval table ==~~		12edt corresponds to 7.571 edo, and can be used as a generator chain for [[Kleismic_family#Hemikleismic\|hemikleismic temperament]]. From a no-twos point of view, it tempers out 49/45 and 27/25 in the 7-limit, and 1331/1125 and 1331/1225 in the 11-limit.
	~~{{Interval table}}~~

	== Prime harmonics ==		== Prime harmonics ==
	{{Harmonics in equal\|12\|3\|1\|intervals=prime}}		{{Harmonics in equal\|12\|3\|1\|intervals=prime}}

			== Theory ==
			In octave land, 12edo handles the 2.3.5 subgroup and [[11edo]] handles the 2.7.11 subgroup—ie. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (Bohlen–Pierce) and 12edt handles the 2.3.5.13.17.19—and, it is a multiple of 4edt which is the simplest BP equal temperament.

			=== Macrodiatonic and macromeantone ===
			12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic\|macrodiatonic]] {{sl\|5L 2s}} scale. This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable, since, for example, the [[generator]] is now the size of a major seventh instead of a perfect fifth. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 [[subgroup]], equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).

			Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.

			== Interval table ==
			{{Interval table}}

	== Scala file ==		== Scala file ==
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	3/1		3/1
	</pre>		</pre>

	~~== Theory ==~~
	In octave land, 12edo handles the 2.3.5 subgroup and [[11edo]] handles the 2.7.11 subgroup—ie. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (Bohlen–Pierce) and 12edt handles the 2.3.5.13.17.19—and, it is a multiple of 4edt which is the simplest BP equal temperament.

	~~=== Macrodiatonic and macromeantone ===~~
	12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic\|macrodiatonic]] scale ([[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]). This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable—for example, the "perfect fifth" is inflated to the size of a major seventh. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 subgroup, equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).

	~~Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.~~

	== Compositions ==		== Compositions ==

ArrowHead294 at 18:26, 25 February 2025

2025-02-25T18:26:17Z

← Older revision		Revision as of 18:26, 25 February 2025
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	{{Harmonics in equal\|12\|3\|1\|intervals=prime}}		{{Harmonics in equal\|12\|3\|1\|intervals=prime}}

	==Scala file==		== Scala file ==

	<pre>		<pre>
	! C:\Cakewalk\scales\tritave-in-12.scl		! C:\Cakewalk\scales\tritave-in-12.scl
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	</pre>		</pre>

	==Theory==		== Theory ==
	In octave land, 12edo handles the 2.3.5 subgroup and [[11edo]] handles the 2.7.11 ~~subgroup - ie~~. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (~~Bohlen-Pierce~~) and 12edt handles the 2.3.5.13.17.~~19 -- AND!~~ it is a multiple of 4edt which is the simplest BP equal temperament.		In octave land, 12edo handles the 2.3.5 subgroup and [[11edo]] handles the 2.7.11 subgroup—ie. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (Bohlen–Pierce) and 12edt handles the 2.3.5.13.17.19—and, it is a multiple of 4edt which is the simplest BP equal temperament.

	===Macrodiatonic and macromeantone===		=== Macrodiatonic and macromeantone ===
	12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic\|macrodiatonic]] scale ([[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]). This scale has an identical structure to diatonic, but with everything stretched out to be ~~unrecognizable-for~~ example, the "perfect fifth" is inflated to the size of a major seventh. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 subgroup, equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).		12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic\|macrodiatonic]] scale ([[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]). This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable—for example, the "perfect fifth" is inflated to the size of a major seventh. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 subgroup, equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).

	Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.		Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.

	==Compositions==		== Compositions ==
	[https://archive.org/details/InstantGamelan Instant Gamelan] by [[Carlo_Serafini\|Carlo Serafini]]		[https://archive.org/details/InstantGamelan Instant Gamelan] by [[Carlo_Serafini\|Carlo Serafini]]

Lériendil: /* Theory */

2024-08-15T03:34:38Z

Theory

← Older revision		Revision as of 03:34, 15 August 2024
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	===Macrodiatonic and macromeantone===		===Macrodiatonic and macromeantone===
	12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic\|macrodiatonic]] scale ([[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]). This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable-for example, the "perfect fifth" is inflated to the size of a major seventh. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 subgroup, equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/]] octave-reduced (although this is not a completely exact stretching of ~~mentone~~, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).		12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic\|macrodiatonic]] scale ([[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]). This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable-for example, the "perfect fifth" is inflated to the size of a major seventh. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 subgroup, equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).

	Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.		Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.

CompactStar: Moved this paragraph which I think makes llittle sense anyways

2024-03-01T17:50:39Z

Moved this paragraph which I think makes llittle sense anyways

← Older revision		Revision as of 17:50, 1 March 2024
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	</pre>		</pre>

	==Macrodiatonic and macromeantone==		==Theory==
			In octave land, 12edo handles the 2.3.5 subgroup and [[11edo]] handles the 2.7.11 subgroup - ie. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (Bohlen-Pierce) and 12edt handles the 2.3.5.13.17.19 -- AND! it is a multiple of 4edt which is the simplest BP equal temperament.

			===Macrodiatonic and macromeantone===
	12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic\|macrodiatonic]] scale ([[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]). This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable-for example, the "perfect fifth" is inflated to the size of a major seventh. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 subgroup, equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/]] octave-reduced (although this is not a completely exact stretching of mentone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).		12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic\|macrodiatonic]] scale ([[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]). This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable-for example, the "perfect fifth" is inflated to the size of a major seventh. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 subgroup, equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/]] octave-reduced (although this is not a completely exact stretching of mentone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).

	Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.		Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.

	In octave land, 12edo handles the 2.3.5 subgroup and [[11edo]] handles the 2.7.11 subgroup - ie. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (Bohlen-Pierce) and 12edt handles the 2.3.5.13.17.19 -- AND! it is a multiple of 4edt which is the simplest BP equal temperament.

	==Compositions==		==Compositions==

BudjarnLambeth: /* Macrodiatonic and macromeantone */ Added link to 11edo

2024-01-30T08:50:35Z

Macrodiatonic and macromeantone: Added link to 11edo

← Older revision		Revision as of 08:50, 30 January 2024
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	Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.		Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.

	In octave land, 12edo handles the 2.3.5 subgroup and 11edo handles the 2.7.11 subgroup - ie. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (Bohlen-Pierce) and 12edt handles the 2.3.5.13.17.19 -- AND! it is a multiple of 4edt which is the simplest BP equal temperament.		In octave land, 12edo handles the 2.3.5 subgroup and [[11edo]] handles the 2.7.11 subgroup - ie. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (Bohlen-Pierce) and 12edt handles the 2.3.5.13.17.19 -- AND! it is a multiple of 4edt which is the simplest BP equal temperament.

	==Compositions==		==Compositions==

CompactStar: /* Macrodiatonic and macromeantone */Rework this section (I'm keeping the original information I removed at the bottom in case it's useful)

2024-01-30T02:58:42Z

Macrodiatonic and macromeantone: Rework this section (I'm keeping the original information I removed at the bottom in case it's useful)

← Older revision		Revision as of 02:58, 30 January 2024
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	</pre>		</pre>

	==~~Exactly analogous to meantone~~==		==Macrodiatonic and macromeantone==
	~~In octave land,~~ 12edo ~~handles the 2.~~3~~.5 subgroup~~ and ~~11edo handles the 2~~.~~7.11 subgroup~~ - ~~ie. meantone and orgone temperaments. In tritave land however~~, ~~13edt handles~~ the 3.~~5.7 territory (Bohlen-Pierce)~~ and ~~12edt handles~~ the 2.3.5.13.17~~.19 -- AND! it is a multiple of 4edt which is the simplest BP equal temperament. Now~~, ~~exactly analogous~~ to ~~meantone~~, ~~in which (~~3/2~~)^4=~~5/1, ~~here (17/9)^4=(19/10)^~~4~~=13~~/1~~, tempering out the 171/170, 85293/83521 and 130321/130000 commas. In fact, even the MOS pattern is the same for this higher limit meantone! Relish the sweet 9:13:17 and 20:27:38 chords~~.		12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1\|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic\|macrodiatonic]] scale ([[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]). This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable-for example, the "perfect fifth" is inflated to the size of a major seventh. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 subgroup, equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/]] octave-reduced (although this is not a completely exact stretching of mentone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).

	Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which ~~is found in~~ the fifth harmonic and is based on the 5:9:13:(17):(21) chord.		Another example of a macrodiatonic scale is [[17ed5\|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.

			In octave land, 12edo handles the 2.3.5 subgroup and 11edo handles the 2.7.11 subgroup - ie. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (Bohlen-Pierce) and 12edt handles the 2.3.5.13.17.19 -- AND! it is a multiple of 4edt which is the simplest BP equal temperament.

	==Compositions==		==Compositions==