Macrodiatonic and microdiatonic scales - Revision history

Dummy index: -obikhod (i intended it as an example of named chain-of-fifth nonoctave scale, now it is clearly wrong)

2025-04-19T15:55:33Z

-obikhod (i intended it as an example of named chain-of-fifth nonoctave scale, now it is clearly wrong)

← Older revision		Revision as of 15:55, 19 April 2025
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	'''Macrodiatonic scales'''{{idiosyncratic}} are [[nonoctave]] [[MOS scale]]s that have 5 large and 2 small steps like the diatonic scale, but have a period greater than 2/1, making them extremely [[stretched tuning\|stretched]] versions of the diatonic scale. The equivalent term for compressed diatonic scales (period < 2/1) is '''microdiatonic'''{{idiosyncratic}}. Macrodiatonic/microdiatonic scales typically sound completely unrecognizable due to the stretching/squishing, yet are structurally identical to diatonic (with it being possible to translate from diatonic to macrodiatonic/microdiatonic scales "on the fly"). Nonoctave [[regular temperament]]s assosciated with macrodiatonic/microdiatonic scales are sometimes termed as macro[[meantone]]/micromeantones. However, it is controversial to use the name of the temperament for things that only share a scale pattern rather than harmonic structure. [[User:CompactStar\|CompactStar]] suggests that the term macromeantone/micromeantone is only used for temperaments in which the "fifth" analogue is tuned flatter than its untempered interpretation.		'''Macrodiatonic scales'''{{idiosyncratic}} are [[nonoctave]] [[MOS scale]]s that have 5 large and 2 small steps like the diatonic scale, but have a period greater than 2/1, making them extremely [[stretched tuning\|stretched]] versions of the diatonic scale. The equivalent term for compressed diatonic scales (period < 2/1) is '''microdiatonic'''{{idiosyncratic}}. Macrodiatonic/microdiatonic scales typically sound completely unrecognizable due to the stretching/squishing, yet are structurally identical to diatonic (with it being possible to translate from diatonic to macrodiatonic/microdiatonic scales "on the fly"). Nonoctave [[regular temperament]]s assosciated with macrodiatonic/microdiatonic scales are sometimes termed as macro[[meantone]]/micromeantones. However, it is controversial to use the name of the temperament for things that only share a scale pattern rather than harmonic structure. [[User:CompactStar\|CompactStar]] suggests that the term macromeantone/micromeantone is only used for temperaments in which the "fifth" analogue is tuned flatter than its untempered interpretation.

	In a broader sense, a scale created by repeating one simple intonation ("fifth" analogue) and it has a low otonal limit triad (with "third" analogue which is but not always genspan +4.) But, if 3/2 is used as generator, such as [[angel]] and ~~[[User:Moremajorthanmajor~~/~~8L_3s_(perfect_twelfth-equivalent)#Relationship_to_the_Obikhod~~\|~~obikhod]]~~, another name should be considered. The terms longdiatonic and shortdiatonic have been proposed to refer to the latter, most likely by [[User:Dummy index\|Dummy index]].		In a broader sense, a scale created by repeating one simple intonation ("fifth" analogue) and it has a low otonal limit triad (with "third" analogue which is but not always genspan +4.) But, if 3/2 is used as generator, such as [[angel]] and {{mos scalesig\|8L 3s<3/1>\|link=1}}, another name should be considered. The terms longdiatonic and shortdiatonic have been proposed to refer to the latter, most likely by [[User:Dummy index\|Dummy index]].

	== Notation ==		== Notation ==
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	* [[Ed5/3\|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 8/7. 6:7:8 triad is homologous to minor triad on the known circle of fifths.		* [[Ed5/3\|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 8/7. 6:7:8 triad is homologous to minor triad on the known circle of fifths.
	=== Longdiatonic/shortdiatonic ===		=== Longdiatonic/shortdiatonic ===
	* ~~[[2L 1s (4/3-equivalent)\|~~2L 1s<4/3>]]		* 2L 1s<4/3>
	* [[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]		* [[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]
	* [[6L 1s (8/5-equivalent)\|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5.		* [[6L 1s (8/5-equivalent)\|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5.

Fredg999: Manually link to MMTM's user page for obikhod (for reference)

2025-04-19T15:15:35Z

Manually link to MMTM's user page for obikhod (for reference)

← Older revision		Revision as of 15:15, 19 April 2025
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	'''Macrodiatonic scales'''{{idiosyncratic}} are [[nonoctave]] [[MOS scale]]s that have 5 large and 2 small steps like the diatonic scale, but have a period greater than 2/1, making them extremely [[stretched tuning\|stretched]] versions of the diatonic scale. The equivalent term for compressed diatonic scales (period < 2/1) is '''microdiatonic'''{{idiosyncratic}}. Macrodiatonic/microdiatonic scales typically sound completely unrecognizable due to the stretching/squishing, yet are structurally identical to diatonic (with it being possible to translate from diatonic to macrodiatonic/microdiatonic scales "on the fly"). Nonoctave [[regular temperament]]s assosciated with macrodiatonic/microdiatonic scales are sometimes termed as macro[[meantone]]/micromeantones. However, it is controversial to use the name of the temperament for things that only share a scale pattern rather than harmonic structure. [[User:CompactStar\|CompactStar]] suggests that the term macromeantone/micromeantone is only used for temperaments in which the "fifth" analogue is tuned flatter than its untempered interpretation.		'''Macrodiatonic scales'''{{idiosyncratic}} are [[nonoctave]] [[MOS scale]]s that have 5 large and 2 small steps like the diatonic scale, but have a period greater than 2/1, making them extremely [[stretched tuning\|stretched]] versions of the diatonic scale. The equivalent term for compressed diatonic scales (period < 2/1) is '''microdiatonic'''{{idiosyncratic}}. Macrodiatonic/microdiatonic scales typically sound completely unrecognizable due to the stretching/squishing, yet are structurally identical to diatonic (with it being possible to translate from diatonic to macrodiatonic/microdiatonic scales "on the fly"). Nonoctave [[regular temperament]]s assosciated with macrodiatonic/microdiatonic scales are sometimes termed as macro[[meantone]]/micromeantones. However, it is controversial to use the name of the temperament for things that only share a scale pattern rather than harmonic structure. [[User:CompactStar\|CompactStar]] suggests that the term macromeantone/micromeantone is only used for temperaments in which the "fifth" analogue is tuned flatter than its untempered interpretation.

	In a broader sense, a scale created by repeating one simple intonation ("fifth" analogue) and it has a low otonal limit triad (with "third" analogue which is but not always genspan +4.) But, if 3/2 is used as generator, such as [[angel]] and [[obikhod]], another name should be considered. The terms longdiatonic and shortdiatonic have been proposed to refer to the latter, most likely by [[User:Dummy index\|Dummy index]].		In a broader sense, a scale created by repeating one simple intonation ("fifth" analogue) and it has a low otonal limit triad (with "third" analogue which is but not always genspan +4.) But, if 3/2 is used as generator, such as [[angel]] and [[User:Moremajorthanmajor/8L_3s_(perfect_twelfth-equivalent)#Relationship_to_the_Obikhod\|obikhod]], another name should be considered. The terms longdiatonic and shortdiatonic have been proposed to refer to the latter, most likely by [[User:Dummy index\|Dummy index]].

	== Notation ==		== Notation ==

Dummy index: /* Examples of macrodiatonic and microdiatonic scales */ +tetrahanson

2025-02-17T13:02:35Z

Examples of macrodiatonic and microdiatonic scales: +tetrahanson

← Older revision		Revision as of 13:02, 17 February 2025
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	* [[Ed7/4\|5L 2s<7/4>]]: Generator is approximately 7/5 (dark generator is approximately 5/4).		* [[Ed7/4\|5L 2s<7/4>]]: Generator is approximately 7/5 (dark generator is approximately 5/4).
	* [[Ed9/5\|5L 2s<9/5>]]: Generator is approximately 7/5.		* [[Ed9/5\|5L 2s<9/5>]]: Generator is approximately 7/5.
	* [[5L 2s (12/5-equivalent)\|5L 2s<12/5>]]: Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5).		* [[5L 2s (12/5-equivalent)\|5L 2s<12/5>]]: Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5). This is made by cutting off the 5/3 interval range of the tetratave scale of [[tetrahanson]] [[8L 3s (4/1-equivalent)\|8L 3s<4/1>]].
	* [[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]: Generator is approximately [[17/9]], and 4 generators is vaguely equivalent to [[13/9]]. This relates this scale to the no-twos macromeantone temperament (or rather more like macroarchy, with the 17/9 being stretched) [[tempering out]] 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for [[12edt]]. Harder varieties of the scale can instead be interpreted where the generator is a sharp [[21/11]], and 3 generators is equivalent to [[7/3]], tempering out [[1331/1323]] and producing [[Mintaka]] temperament.		* [[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]: Generator is approximately [[17/9]], and 4 generators is vaguely equivalent to [[13/9]]. This relates this scale to the no-twos macromeantone temperament (or rather more like macroarchy, with the 17/9 being stretched) [[tempering out]] 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for [[12edt]]. Harder varieties of the scale can instead be interpreted where the generator is a sharp [[21/11]], and 3 generators is equivalent to [[7/3]], tempering out [[1331/1323]] and producing [[Mintaka]] temperament.
	* [[5L 2s (13/4-equivalent)\|5L 2s<13/4>]]: Generator is approximately [[2/1]]. This may be suitable for stretching 4:5:6 into 2:3:4, but the "[[3/2]]" in this chord is not very accurate and [[mavila]]-like in size.		* [[5L 2s (13/4-equivalent)\|5L 2s<13/4>]]: Generator is approximately [[2/1]]. This may be suitable for stretching 4:5:6 into 2:3:4, but the "[[3/2]]" in this chord is not very accurate and [[mavila]]-like in size.

Lériendil: /* Examples of macrodiatonic and microdiatonic scales */

2024-08-22T07:18:29Z

Examples of macrodiatonic and microdiatonic scales

← Older revision		Revision as of 07:18, 22 August 2024
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	* [[Ed9/5\|5L 2s<9/5>]]: Generator is approximately 7/5.		* [[Ed9/5\|5L 2s<9/5>]]: Generator is approximately 7/5.
	* [[5L 2s (12/5-equivalent)\|5L 2s<12/5>]]: Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5).		* [[5L 2s (12/5-equivalent)\|5L 2s<12/5>]]: Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5).
	* [[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]: Generator is approximately [[17/9]], and 4 generators is vaguely equivalent to [[13/9]]. This relates this scale to the no-twos macromeantone temperament (or rather more like macroarchy, with the 17/9 being stretched) [[tempering out]] 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for [[12edt]].		* [[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]: Generator is approximately [[17/9]], and 4 generators is vaguely equivalent to [[13/9]]. This relates this scale to the no-twos macromeantone temperament (or rather more like macroarchy, with the 17/9 being stretched) [[tempering out]] 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for [[12edt]]. Harder varieties of the scale can instead be interpreted where the generator is a sharp [[21/11]], and 3 generators is equivalent to [[7/3]], tempering out [[1331/1323]] and producing [[Mintaka]] temperament.
	* [[5L 2s (13/4-equivalent)\|5L 2s<13/4>]]: Generator is approximately [[2/1]]. This may be suitable for stretching 4:5:6 into 2:3:4, but the "[[3/2]]" in this chord is not very accurate and [[mavila]]-like in size.		* [[5L 2s (13/4-equivalent)\|5L 2s<13/4>]]: Generator is approximately [[2/1]]. This may be suitable for stretching 4:5:6 into 2:3:4, but the "[[3/2]]" in this chord is not very accurate and [[mavila]]-like in size.
	* [[5L 2s (4/1-equivalent)\|5L 2s<4/1>]]: This is precisely a 200% stretched diatonic scale. Generator is approximately [[9/4]] ([[3/2]]<sup>2</sup>). This can very clearly be interpreted as a temperament tempering out [[6561/6400]] ([[81/80]]<sup>2</sup>) in 4.9.25 for the meantone equivalent or 4096/3969 ([[64/63]]<sup>2</sup>) in 4.9.49 for the archy equivalent. This scale is extremely widely spaced, so it may preferable to use the macrochromatic scales [[7L 5s (4/1-equivalent)\|7L 5s<4/1>]] and [[5L 7s (4/1-equivalent)\|5L 7s<4/1>]] instead.		* [[5L 2s (4/1-equivalent)\|5L 2s<4/1>]]: This is precisely a 200% stretched diatonic scale. Generator is approximately [[9/4]] ([[3/2]]<sup>2</sup>). This can very clearly be interpreted as a temperament tempering out [[6561/6400]] ([[81/80]]<sup>2</sup>) in 4.9.25 for the meantone equivalent or 4096/3969 ([[64/63]]<sup>2</sup>) in 4.9.49 for the archy equivalent. This scale is extremely widely spaced, so it may preferable to use the macrochromatic scales [[7L 5s (4/1-equivalent)\|7L 5s<4/1>]] and [[5L 7s (4/1-equivalent)\|5L 7s<4/1>]] instead.

Dummy index: /* Longdiatonic/shortdiatonic */

2024-05-17T14:33:07Z

Longdiatonic/shortdiatonic

← Older revision		Revision as of 14:33, 17 May 2024
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	* [[7L 2s (5/2-equivalent)\|7L 2s<5/2>]]: Dark generator is approximately 3/2 and 5 generators is 6/5.		* [[7L 2s (5/2-equivalent)\|7L 2s<5/2>]]: Dark generator is approximately 3/2 and 5 generators is 6/5.
	* [[8L 3s (3/1-equivalent)\|8L 3s<3/1>]]: Generator is approximately 3/2 and 6 generators is 5/4.		* [[8L 3s (3/1-equivalent)\|8L 3s<3/1>]]: Generator is approximately 3/2 and 6 generators is 5/4.
			* [[7L 3s (4/1-equivalent)\|7L 3s<4/1>]]

	== See also ==		== See also ==

CompactStar: /* Longdiatonic/shortdiatonic */

2024-05-06T22:23:15Z

Longdiatonic/shortdiatonic

← Older revision		Revision as of 22:23, 6 May 2024
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	* [[Ed5/3\|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 8/7. 6:7:8 triad is homologous to minor triad on the known circle of fifths.		* [[Ed5/3\|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 8/7. 6:7:8 triad is homologous to minor triad on the known circle of fifths.
	=== Longdiatonic/shortdiatonic ===		=== Longdiatonic/shortdiatonic ===
	* (2L 1s<4/3>)		* [[2L 1s (4/3-equivalent)\|2L 1s<4/3>]]
	* [[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]		* [[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]
	* [[6L 1s (8/5-equivalent)\|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5.		* [[6L 1s (8/5-equivalent)\|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5.

CompactStar: /* Longdiatonic/shortdiatonic */

2024-05-06T22:23:00Z

Longdiatonic/shortdiatonic

← Older revision		Revision as of 22:23, 6 May 2024
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	=== Longdiatonic/shortdiatonic ===		=== Longdiatonic/shortdiatonic ===
	* (2L 1s<4/3>)		* (2L 1s<4/3>)
	* (~~xL ys~~<3/2>)		* [[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]
	* [[~~Ed8~~/5\|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5.		* [[6L 1s (8/5-equivalent)\|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5.
	* 4L 1s<5/3>: = 7L 2s<5/2> - 3L 1s<3/2>.		* 4L 1s<5/3>: = 7L 2s<5/2> - 3L 1s<3/2>.
	* [[3L 4s (7/4-equivalent)\|3L 4s<7/4>]]: Dark generator is just 3/2 and 2 generators is just 9/7. Merely this is a lattice by 9/7 and 7/6.		* [[3L 4s (7/4-equivalent)\|3L 4s<7/4>]]: Dark generator is just 3/2 and 2 generators is just 9/7. Merely this is a lattice by 9/7 and 7/6.

CompactStar at 22:21, 6 May 2024

2024-05-06T22:21:19Z

← Older revision		Revision as of 22:21, 6 May 2024
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	== Examples of macrodiatonic and microdiatonic scales ==		== Examples of macrodiatonic and microdiatonic scales ==
	* [[5L 2s (4/3-equivalent)\|5L 2s<4/3>]]: Generator is a neogothic minor third.		* [[5L 2s (4/3-equivalent)\|5L 2s<4/3>]]: Generator is a neogothic minor third.
			* [[10L 4s]] (5L 2s<1\2>): Generator is a neutral third. Includes the octave by virtue of its half-octave period.
	* [[5L 2s (3/2-equivalent)\|5L 2s<3/2>]]: Generator is a neogothic major third near [[81/64]] and [[14/11]]. In the [[half-prime subgroup]] paradigm it may be interpreted as [[63/50]] (relating to the 3/2.5/2.7/2 subgroup version of [[sirius]] temperament).		* [[5L 2s (3/2-equivalent)\|5L 2s<3/2>]]: Generator is a neogothic major third near [[81/64]] and [[14/11]]. In the [[half-prime subgroup]] paradigm it may be interpreted as [[63/50]] (relating to the 3/2.5/2.7/2 subgroup version of [[sirius]] temperament).
	* [[Ed7/4\|5L 2s<7/4>]]: Generator is approximately 7/5 (dark generator is approximately 5/4).		* [[Ed7/4\|5L 2s<7/4>]]: Generator is approximately 7/5 (dark generator is approximately 5/4).

Dummy index: /* In broader sense */ overcorrection

2024-04-28T05:21:29Z

In broader sense: overcorrection

← Older revision		Revision as of 05:21, 28 April 2024
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	=== Macrodiatonic/microdiatonic ===		=== Macrodiatonic/microdiatonic ===
	* [[EDF\|9L 2s<3/2>]]: Generator is approximately 5/4 and 6 generators is 9/8.		* [[EDF\|9L 2s<3/2>]]: Generator is approximately 5/4 and 6 generators is 9/8.
	* [[Ed5/3\|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 7/6. 6:7:8 triad is homologous to minor triad on the known circle of fifths.		* [[Ed5/3\|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 8/7. 6:7:8 triad is homologous to minor triad on the known circle of fifths.
	=== Longdiatonic/shortdiatonic ===		=== Longdiatonic/shortdiatonic ===
	* (2L 1s<4/3>)		* (2L 1s<4/3>)

Dummy index: /* In broader sense */

2024-04-28T04:39:51Z

In broader sense

← Older revision		Revision as of 04:39, 28 April 2024
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	=== Macrodiatonic/microdiatonic ===		=== Macrodiatonic/microdiatonic ===
	* [[EDF\|9L 2s<3/2>]]: Generator is approximately 5/4 and 6 generators is 9/8.		* [[EDF\|9L 2s<3/2>]]: Generator is approximately 5/4 and 6 generators is 9/8.
	* [[Ed5/3\|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 8/7.		* [[Ed5/3\|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 7/6. 6:7:8 triad is homologous to minor triad on the known circle of fifths.
	=== Longdiatonic/shortdiatonic ===		=== Longdiatonic/shortdiatonic ===
			* (2L 1s<4/3>)
			* (xL ys<3/2>)
	* [[Ed8/5\|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5.		* [[Ed8/5\|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5.
			* 4L 1s<5/3>: = 7L 2s<5/2> - 3L 1s<3/2>.
	* [[3L 4s (7/4-equivalent)\|3L 4s<7/4>]]: Dark generator is just 3/2 and 2 generators is just 9/7. Merely this is a lattice by 9/7 and 7/6.		* [[3L 4s (7/4-equivalent)\|3L 4s<7/4>]]: Dark generator is just 3/2 and 2 generators is just 9/7. Merely this is a lattice by 9/7 and 7/6.
	* [[3L 4s (9/5-equivalent)\|3L 4s<9/5>]]: Dark generator is just 3/2 and 2 generators is just 5/4. Merely this is a lattice by 5/4 and 6/5. The minor triad are more affinity for equave (10:12:15:18) than the major triad (20:25:30:36).		* [[3L 4s (9/5-equivalent)\|3L 4s<9/5>]]: Dark generator is just 3/2 and 2 generators is just 5/4. Merely this is a lattice by 5/4 and 6/5. The minor triad are more affinity for equave (10:12:15:18) than the major triad (20:25:30:36).

← Older revision		Revision as of 13:02, 17 February 2025
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	* [[Ed7/4\|5L 2s<7/4>]]: Generator is approximately 7/5 (dark generator is approximately 5/4).		* [[Ed7/4\|5L 2s<7/4>]]: Generator is approximately 7/5 (dark generator is approximately 5/4).
	* [[Ed9/5\|5L 2s<9/5>]]: Generator is approximately 7/5.		* [[Ed9/5\|5L 2s<9/5>]]: Generator is approximately 7/5.
	* [[5L 2s (12/5-equivalent)\|5L 2s<12/5>]]: Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5).		* [[5L 2s (12/5-equivalent)\|5L 2s<12/5>]]: Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5). This is made by cutting off the 5/3 interval range of the tetratave scale of [[tetrahanson]] [[8L 3s (4/1-equivalent)\|8L 3s<4/1>]].
	* [[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]: Generator is approximately [[17/9]], and 4 generators is vaguely equivalent to [[13/9]]. This relates this scale to the no-twos macromeantone temperament (or rather more like macroarchy, with the 17/9 being stretched) [[tempering out]] 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for [[12edt]]. Harder varieties of the scale can instead be interpreted where the generator is a sharp [[21/11]], and 3 generators is equivalent to [[7/3]], tempering out [[1331/1323]] and producing [[Mintaka]] temperament.		* [[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]: Generator is approximately [[17/9]], and 4 generators is vaguely equivalent to [[13/9]]. This relates this scale to the no-twos macromeantone temperament (or rather more like macroarchy, with the 17/9 being stretched) [[tempering out]] 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for [[12edt]]. Harder varieties of the scale can instead be interpreted where the generator is a sharp [[21/11]], and 3 generators is equivalent to [[7/3]], tempering out [[1331/1323]] and producing [[Mintaka]] temperament.
	* [[5L 2s (13/4-equivalent)\|5L 2s<13/4>]]: Generator is approximately [[2/1]]. This may be suitable for stretching 4:5:6 into 2:3:4, but the "[[3/2]]" in this chord is not very accurate and [[mavila]]-like in size.		* [[5L 2s (13/4-equivalent)\|5L 2s<13/4>]]: Generator is approximately [[2/1]]. This may be suitable for stretching 4:5:6 into 2:3:4, but the "[[3/2]]" in this chord is not very accurate and [[mavila]]-like in size.

← Older revision		Revision as of 07:18, 22 August 2024
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	* [[Ed9/5\|5L 2s<9/5>]]: Generator is approximately 7/5.		* [[Ed9/5\|5L 2s<9/5>]]: Generator is approximately 7/5.
	* [[5L 2s (12/5-equivalent)\|5L 2s<12/5>]]: Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5).		* [[5L 2s (12/5-equivalent)\|5L 2s<12/5>]]: Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5).
	* [[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]: Generator is approximately [[17/9]], and 4 generators is vaguely equivalent to [[13/9]]. This relates this scale to the no-twos macromeantone temperament (or rather more like macroarchy, with the 17/9 being stretched) [[tempering out]] 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for [[12edt]].		* [[5L 2s (3/1-equivalent)\|5L 2s<3/1>]]: Generator is approximately [[17/9]], and 4 generators is vaguely equivalent to [[13/9]]. This relates this scale to the no-twos macromeantone temperament (or rather more like macroarchy, with the 17/9 being stretched) [[tempering out]] 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for [[12edt]]. Harder varieties of the scale can instead be interpreted where the generator is a sharp [[21/11]], and 3 generators is equivalent to [[7/3]], tempering out [[1331/1323]] and producing [[Mintaka]] temperament.
	* [[5L 2s (13/4-equivalent)\|5L 2s<13/4>]]: Generator is approximately [[2/1]]. This may be suitable for stretching 4:5:6 into 2:3:4, but the "[[3/2]]" in this chord is not very accurate and [[mavila]]-like in size.		* [[5L 2s (13/4-equivalent)\|5L 2s<13/4>]]: Generator is approximately [[2/1]]. This may be suitable for stretching 4:5:6 into 2:3:4, but the "[[3/2]]" in this chord is not very accurate and [[mavila]]-like in size.
	* [[5L 2s (4/1-equivalent)\|5L 2s<4/1>]]: This is precisely a 200% stretched diatonic scale. Generator is approximately [[9/4]] ([[3/2]]<sup>2</sup>). This can very clearly be interpreted as a temperament tempering out [[6561/6400]] ([[81/80]]<sup>2</sup>) in 4.9.25 for the meantone equivalent or 4096/3969 ([[64/63]]<sup>2</sup>) in 4.9.49 for the archy equivalent. This scale is extremely widely spaced, so it may preferable to use the macrochromatic scales [[7L 5s (4/1-equivalent)\|7L 5s<4/1>]] and [[5L 7s (4/1-equivalent)\|5L 7s<4/1>]] instead.		* [[5L 2s (4/1-equivalent)\|5L 2s<4/1>]]: This is precisely a 200% stretched diatonic scale. Generator is approximately [[9/4]] ([[3/2]]<sup>2</sup>). This can very clearly be interpreted as a temperament tempering out [[6561/6400]] ([[81/80]]<sup>2</sup>) in 4.9.25 for the meantone equivalent or 4096/3969 ([[64/63]]<sup>2</sup>) in 4.9.49 for the archy equivalent. This scale is extremely widely spaced, so it may preferable to use the macrochromatic scales [[7L 5s (4/1-equivalent)\|7L 5s<4/1>]] and [[5L 7s (4/1-equivalent)\|5L 7s<4/1>]] instead.