User:Moremajorthanmajor/5L 3s (15/7-equivalent) - Revision history

ArrowHead294 at 16:46, 3 March 2025

2025-03-03T16:46:44Z

← Older revision		Revision as of 16:46, 3 March 2025
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	{{Infobox MOS		{{Infobox MOS
	\|Tuning=5L 3s<15/7>}}{{MOS intro\|Scale Signature=5L 3s<15/7>}}		\|Tuning=5L 3s<15/7>
			}}
			{{MOS intro\|Scale Signature=5L 3s<15/7>}}

	Any ed15/7 with an interval between 494.8¢ and 527.8¢ has a 5L 3s scale. [[13ed15/7]] is the smallest ed15/7 with a (non-degenerate) 5L 3s scale and thus is the most commonly used 5L 3s tuning.		Any ed15/7 with an interval between 494.8¢ and 527.8¢ has a 5L 3s scale. [[13ed15/7]] is the smallest ed15/7 with a (non-degenerate) 5L 3s scale and thus is the most commonly used 5L 3s tuning.

	==Standing assumptions==		==Standing assumptions==
	The [[TAMNAMS]] system is used in this article to name 5L 3s<15/7> intervals and step size ratios and step ratio ranges.		The [[TAMNAMS]] system is used in this article to name 5L 3s<15/7> intervals and step size ratios and step ratio ranges.
Line 1,108:		Line 1,111:
	\|}		\|}
	==Scale tree==		==Scale tree==
	{{Scale ~~tree\|~~5L 3s<15/7>}}		{{MOS tuning spectrum\|Scale Signature=5L 3s<15/7>}}

Moremajorthanmajor: /* Intervals */

2024-12-29T18:29:13Z

Intervals

← Older revision		Revision as of 18:29, 29 December 2024
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	\|11\13, 1116.452		\|11\13, 1116.452
	\|15\18, 1099.536		\|15\18, 1099.536
	\|26\31, 1106.~~6295~~		\|26\31, 1106.629
	\|Ff		\|Ff
	\|11/6, 13/7, 15/8		\|11/6, 13/7, 15/8
Line 428:		Line 428:
	\|12\13, 1217.942		\|12\13, 1217.942
	\|17\18, 1246.140		\|17\18, 1246.140
	\|29\31, 1234.~~3175~~		\|29\31, 1234.317
	\|F		\|F
	\|2/1		\|2/1

Moremajorthanmajor: /* Parasoft to ultrasoft tunings */

2023-06-30T19:37:40Z

Parasoft to ultrasoft tunings

← Older revision		Revision as of 19:37, 30 June 2023
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	\|s (-5g + 2 minor 9ths)		\|s (-5g + 2 minor 9ths)
	\|3\29, 136.494		\|3\29, 136.494
	\|4\37, ~~[[Tel:~~142.~~6425\|142.6425]]~~		\|4\37, 142.642
	\|}		\|}
	====Intervals====		====Intervals====
Line 778:		Line 778:
	\| -8		\| -8
	\|}		\|}

	===Parahard===		===Parahard===
	23ed15/7 Neapolitan-oneiro combines the sound of the 15/7 minor ninth and the [[8/7]] whole tone. This is because 23ed15/7 Neapolitan-oneirotonic has a large step of 229.5¢.		23ed15/7 Neapolitan-oneiro combines the sound of the 15/7 minor ninth and the [[8/7]] whole tone. This is because 23ed15/7 Neapolitan-oneirotonic has a large step of 229.5¢.

Moremajorthanmajor at 00:21, 21 June 2023

2023-06-21T00:21:05Z

← Older revision		Revision as of 00:21, 21 June 2023
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	The chain of perfect 4ths becomes: ... Ef Af Qf Ff Bf Df G C E A Q F B D ...		The chain of perfect 4ths becomes: ... Ef Af Qf Ff Bf Df G C E A Q F B D ...

	Thus the [[~~13edIX\|~~13ed15/7]] gamut is as follows:		Thus the [[13ed15/7]] gamut is as follows:

	'''G/F#''' G#/Af '''A''' A#/Bf '''B/Cf''' '''C/B#''' C#/Qf '''Q''' Q#/Df '''D/Ef E/D#''' E#/Ff '''F/Gf G'''		'''G/F#''' G#/Af '''A''' A#/Bf '''B/Cf''' '''C/B#''' C#/Qf '''Q''' Q#/Df '''D/Ef E/D#''' E#/Ff '''F/Gf G'''
Line 110:		Line 110:
	\|1L + 2s		\|1L + 2s
	\|-		\|-
	\| colspan="8" \|The chromatic 13-note MOS (either [[5L 8s (15/7-equivalent)\|5L 8s]], [[8L 5s (15/7-equivalent)\|8L 5s]], or [[~~13edIX\|~~13ed15/7]]) also has the following intervals (from some root):		\| colspan="8" \|The chromatic 13-note MOS (either [[5L 8s (15/7-equivalent)\|5L 8s]], [[8L 5s (15/7-equivalent)\|8L 5s]], or [[13ed15/7]]) also has the following intervals (from some root):
	\|-		\|-
	\|8		\|8
Line 163:		Line 163:
	\|-		\|-
	! class="unsortable" \|Degree		! class="unsortable" \|Degree
	!Size in [[~~13edIX\|~~13ed15/7]] (basic)		!Size in [[13ed15/7]] (basic)
	!Size in [[18ed15/7]] (hard)		!Size in [[18ed15/7]] (hard)
	!Size in [[21ed15/7]] (soft)		!Size in [[21ed15/7]] (soft)
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	**The large step is near the Pythagorean 9/8 whole tone, somewhere between as in [[12edo]] and as in [[17edo]].		**The large step is near the Pythagorean 9/8 whole tone, somewhere between as in [[12edo]] and as in [[17edo]].
	**The major 3rd (made of two large steps) is a near-[[Pythagorean]] to [[Neogothic]] major third.		**The major 3rd (made of two large steps) is a near-[[Pythagorean]] to [[Neogothic]] major third.
	EDIXs that are in the hypohard range include [[~~13edIX\|~~13ed15/7]], [[18ed15/7]], and 31ed15/7.		EDIXs that are in the hypohard range include [[13ed15/7]], [[18ed15/7]], and 31ed15/7.

	The sizes of the generator, large step and small step of Neapolitan-oneirotonic are as follows in various hypohard Neapolitan-oneiro tunings.		The sizes of the generator, large step and small step of Neapolitan-oneirotonic are as follows in various hypohard Neapolitan-oneiro tunings.
Line 284:		Line 284:
	\|-		\|-
	!		!
	![[~~13edIX\|~~13ed15/7]] (basic)		![[13ed15/7]] (basic)
	![[18ed15/7]] (hard)		![[18ed15/7]] (hard)
	!31ed15/7 (semihard)		!31ed15/7 (semihard)
Line 308:		Line 308:
	\|-		\|-
	! class="unsortable" \|Degree		! class="unsortable" \|Degree
	!Size in [[~~13edIX\|~~13ed15/7]] (basic)		!Size in [[13ed15/7]] (basic)
	!Size in [[18ed15/7]] (hard)		!Size in [[18ed15/7]] (hard)
	!Size in 31ed15/7 (semihard)		!Size in 31ed15/7 (semihard)
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	===Hyposoft===		===Hyposoft===
	[[Hyposoft]] Neapolitan-oneirotonic tunings (with generator between 8\21 and 5\13) have step ratios between 3/2 and 2/1. The 8\21-to-5\13 range of Neapolitan-oneirotonic tunings can be considered "meantone Neapolitan-oneirotonic”. This is because these tunings share the following features with meantone diatonic tunings:		[[Hyposoft]] Neapolitan-oneirotonic tunings (with generator between 8\21 and 5\13) have step ratios between 3/2 and 2/1. The 8\21-to-5\13 range of Neapolitan-oneirotonic tunings can be considered "meantone Neapolitan-oneirotonic”. This is because these tunings share the following features with meantone diatonic tunings:
	*The large step is between near the meantone and near the Pythagorean 9/8 whole tone, somewhere between as in [[19edo]] and as in [[~~17edo\|~~12edo]].		*The large step is between near the meantone and near the Pythagorean 9/8 whole tone, somewhere between as in [[19edo]] and as in [[12edo]].
	*The major 3rd (made of two large steps) is a near-[[Just intonation\|just]] to near-[[Pythagorean]] major third.		*The major 3rd (made of two large steps) is a near-[[Just intonation\|just]] to near-[[Pythagorean]] major third.
	The sizes of the generator, large step and small step of Neapolitan-oneirotonic are as follows in various hyposoft Neapolitan-oneiro tunings ([[~~13edIX\|~~13ed15/7]] not shown).		The sizes of the generator, large step and small step of Neapolitan-oneirotonic are as follows in various hyposoft Neapolitan-oneiro tunings ([[13ed15/7]] not shown).
	{\| class="wikitable right-2 right-3 right-4 right-5"		{\| class="wikitable right-2 right-3 right-4 right-5"
	\|-		\|-
Line 1,024:		Line 1,024:
	\|15\38, 520.833		\|15\38, 520.833
	\|21\53, 522.798		\|21\53, 522.798
	\|25\63, 523.~~58’~~		\|25\63, 523.588
	\|484.07		\|484.07
	\|C		\|C

Moremajorthanmajor at 00:16, 21 June 2023

2023-06-21T00:16:22Z

← Older revision		Revision as of 00:16, 21 June 2023
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	{{Infobox MOS		{{Infobox MOS
	\|Tuning=5L 3s<15/7>}}~~The minor ninth of a diatonic scale has a '''~~5L 3s''' [[MOS]] structure with generators ranging from 2\5 (two degrees of [[5ed15/7]] = 527.8¢) to 3\8 (three degrees of [[8ed15/7]] = 494.8¢). In the case of 8edo, L and s are the same size; in the case of 5ed15/7~~, s becomes so small it disappears (and all that remains are the five equal L's).~~		\|Tuning=5L 3s<15/7>}}{{MOS intro\|Scale Signature=5L 3s<15/7>}}

	Any ed15/7 with an interval between 494.8¢ and 527.8¢ has a 5L 3s scale. [[13ed15/7]] is the smallest ~~edIX~~ with a (non-degenerate) 5L 3s scale and thus is the most commonly used 5L 3s tuning.		Any ed15/7 with an interval between 494.8¢ and 527.8¢ has a 5L 3s scale. [[13ed15/7]] is the smallest ed15/7 with a (non-degenerate) 5L 3s scale and thus is the most commonly used 5L 3s tuning.
	==Standing assumptions==		==Standing assumptions==
	The [[TAMNAMS]] system is used in this article to name 5L 3s<15/7> intervals and step size ratios and step ratio ranges.		The [[TAMNAMS]] system is used in this article to name 5L 3s<15/7> intervals and step size ratios and step ratio ranges.
Line 192:		Line 192:
	\|minor 3rd		\|minor 3rd
	\|3\13, 304.487		\|3\13, 304.487
	\|4\18, 293.~~2095~~		\|4\18, 293.210
	\|5\21, 314.153		\|5\21, 314.153
	\|Bf		\|Bf
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	\| rowspan="2" \|9\13, 913.460		\| rowspan="2" \|9\13, 913.460
	\|13\18, 952.931		\|13\18, 952.931
	\|14\21, 879.~~6285~~		\|14\21, 879.629
	\|D		\|D
	\| +7		\| +7
	\|- bgcolor="#eaeaff"		\|- bgcolor="#eaeaff"
	\|minor 7th		\|minor 7th
	\|12\18, 879.~~6285~~		\|12\18, 879.629
	\|15\21, 942.459		\|15\21, 942.459
	\|Ef		\|Ef
Line 341:		Line 341:
	\|minor 3rd		\|minor 3rd
	\|3\13, 304.487		\|3\13, 304.487
	\|4\18, 293.~~2095~~		\|4\18, 293.210
	\|7\31, 297.939		\|7\31, 297.939
	\|Bf		\|Bf
Line 403:		Line 403:
	\|- bgcolor="#eaeaff"		\|- bgcolor="#eaeaff"
	\|minor 7th		\|minor 7th
	\|12\18, 879.~~6285~~		\|12\18, 879.629
	\|21\31, 893.816		\|21\31, 893.816
	\|Ef		\|Ef
Line 525:		Line 525:
	\|perfect 5th		\|perfect 5th
	\|11\31, 691.137		\|11\31, 691.137
	\|18\34, 698.~~5285~~		\|18\34, 698.529
	\|Q		\|Q
	\|3/2		\|3/2
Line 538:		Line 538:
	\|- bgcolor="#eaeaff"		\|- bgcolor="#eaeaff"
	\|major 6th		\|major 6th
	\|14\21, 879.~~6285~~		\|14\21, 879.629
	\|23\34, 892.564		\|23\34, 892.564
	\|D		\|D
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	\|minor 7th		\|minor 7th
	\|15\21, 942.459		\|15\21, 942.459
	\|24\34, 931.~~3713~~		\|24\34, 931.371
	\|Ef		\|Ef
	\|12/7		\|12/7
Line 592:		Line 592:
	\|s (-5g + 2 minor 9ths)		\|s (-5g + 2 minor 9ths)
	\|3\29, 136.494		\|3\29, 136.494
	\|4\37, 142.6425		\|4\37, [[Tel:142.6425\|142.6425]]
	\|}		\|}
	====Intervals====		====Intervals====
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	\|- bgcolor="#eaeaff"		\|- bgcolor="#eaeaff"
	\|diminished 6th		\|diminished 6th
	\|17\29, 773.~~4665~~		\|17\29, 773.466
	\|Dff		\|Dff
	\|[[11/7]], [[14/9]]		\|[[11/7]], [[14/9]]
Line 713:		Line 713:
	\|-		\|-
	\|minor 6th		\|minor 6th
	\|18\29, 818.~~9645~~		\|18\29, 818.965
	\|Df		\|Df
	\|[[13/8]], [[8/5]]		\|[[13/8]], [[8/5]]
Line 719:		Line 719:
	\|-		\|-
	\|major 6th		\|major 6th
	\|19\29, 864.~~4625~~		\|19\29, 864.463
	\|D		\|D
	\|[[5/3]], [[224/135]]		\|[[5/3]], [[224/135]]
Line 840:		Line 840:
	\|-		\|-
	\|dim. 4th		\|dim. 4th
	\|6\23, 344.~~2025~~		\|6\23, 344.202
	\|Cf		\|Cf
	\|6/5		\|6/5
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	\|L (3g - minor 9th)		\|L (3g - minor 9th)
	\|7/38, 243.055		\|7/38, 243.055
	\|10/53, 248.~~9515~~		\|10/53, 248.951
	\|12/63, 251.322		\|12/63, 251.322
	\|231.51		\|231.51
Line 977:		Line 977:
	\|1/38, 34.722		\|1/38, 34.722
	\|1/53, 24.895		\|1/53, 24.895
	\|1/63, 20.~~9345~~		\|1/63, 20.934
	\|21.05		\|21.05
	\|50/49 81/80 91/90		\|50/49 81/80 91/90
Line 1,005:		Line 1,005:
	\|2		\|2
	\|7/38, 243.055		\|7/38, 243.055
	\|10/53, 248.~~9515~~		\|10/53, 248.951
	\|12/63, 251.322		\|12/63, 251.322
	\|231.51		\|231.51
Line 1,013:		Line 1,013:
	\|-		\|-
	\|3		\|3
	\|14\38, 486.~~1105~~		\|14\38, 486.111
	\|20\53, 497.903		\|20\53, 497.903
	\|24\63, 502.645		\|24\63, 502.645

Moremajorthanmajor at 04:57, 12 June 2023

2023-06-12T04:57:27Z

Show changes

Moremajorthanmajor at 05:00, 1 June 2023

2023-06-01T05:00:38Z

Show changes

Moremajorthanmajor at 03:54, 27 May 2023

2023-05-27T03:54:24Z

← Older revision		Revision as of 03:54, 27 May 2023
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	~~{{delete}}~~
	{{Infobox MOS		{{Infobox MOS
	\| Name =		\| Name =

Moremajorthanmajor at 20:01, 15 May 2023

2023-05-15T20:01:11Z

← Older revision		Revision as of 20:01, 15 May 2023
Line 1:		Line 1:
			{{delete}}
	{{Infobox MOS		{{Infobox MOS
	\| Name =		\| Name =

Inthar at 10:10, 17 August 2022

2022-08-17T10:10:49Z

← Older revision		Revision as of 10:10, 17 August 2022
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	\| nSmallSteps = 3		\| nSmallSteps = 3
	\| Equalized = 3		\| Equalized = 3
	\| ~~Paucitonic~~ = 2		\| Collapsed = 2
	\| Pattern = LLsLLsLs		\| Pattern = LLsLLsLs
	\| Neutral = 2L 6s		\| Neutral = 2L 6s