Submerged - Revision history

Overthink: /* Tuning spectrum */ note val

2026-02-17T06:08:30Z

Tuning spectrum: note val

← Older revision		Revision as of 06:08, 17 February 2026
Line 116:		Line 116:
	\|		\|
	\| 373.333		\| 373.333
	\|		\| 45ef val
	\|-		\|-
	\|		\|

Fitzgerald Lee: added diamond monotone (7-odd-limit) for tuning spectrum, simplified interval chain

2026-02-13T15:14:48Z

added diamond monotone (7-odd-limit) for tuning spectrum, simplified interval chain

← Older revision		Revision as of 15:14, 13 February 2026
Line 131:		Line 131:
	\|		\|
	\| '''375.000'''		\| '''375.000'''
	\| '''~~Lower~~ bound of 7-odd-limit diamond monotone''', major thirds slightly sharper than this fall under [[magic]]		\| '''Upper bound of 7-odd-limit diamond monotone''', major thirds slightly sharper than this fall under [[magic]]
	\|}		\|}

Fitzgerald Lee at 15:12, 13 February 2026

2026-02-13T15:12:29Z

← Older revision		Revision as of 15:12, 13 February 2026
Line 28:		Line 28:
	\| 2		\| 2
	\| 745.2		\| 745.2
	\| [[32/21]], [[20/13]]		\| [[25/16]], [[32/21]]
	\|-		\|-
	\| 3		\| 3
	\| 1117.8		\| 1117.8
	\| [[40/21~~]], [[25/13~~]]		\| [[40/21]]
	\|-		\|-
	\| 4		\| 4
	\| 290.4		\| 290.4
	\| [[64/~~55]], [[13/11~~]]		\| [[25/21]]
	\|-		\|-
	\| 5		\| 5
	\| 663.0		\| 663.0
	\| '''[[16/11]]'''~~, [[22/15]]~~		\| '''[[16/11]]'''
	\|-		\|-
	\| 6		\| 6
	\| 1035.6		\| 1035.6
	\| [[20/11~~]], [[11/6~~]]		\| [[20/11]]
	\|-		\|-
	\| 7		\| 7
	\| 208.2		\| 208.2
	\| [[25~~/22]], [[55/48~~]]		\| [[28/25]]
	\|-		\|-
	\| 8		\| 8
	\| 580.8		\| 580.8
	\| [[7/5~~]], [[55/39~~]]		\| [[7/5]]
	\|-		\|-
	\| 9		\| 9
	\| 953.4		\| 953.4
	\| ~~[[26/15]],~~ '''[[7/4]]'''		\| '''[[7/4]]'''
	\|-		\|-
	\| 10		\| 10
	\| 126.0		\| 126.0
	\| '''[[16/15]]'''~~, [[14/13]]~~		\| '''[[16/15]]'''
	\|-		\|-
	\| 11		\| 11
	\| 498.6		\| 498.6
	\| '''[[4/3]]'''~~, [[35/26]]~~		\| '''[[4/3]]'''
	\|-		\|-
	\| 12		\| 12
	\| 871.2		\| 871.2
	\| ~~[[64/39]],~~ [[5/3]]		\| [[5/3]]
	\|-		\|-
	\| 13		\| 13
	\| 43.8		\| 43.8
	\| ~~[[40/39]],~~ [[25/24]]		\| [[25/24]]
	\|}		\|}
	<nowiki/>* In 5-limit CTE tuning		<nowiki/>* In 5-limit CTE tuning
Line 103:		Line 103:
	\| 1/10-comma		\| 1/10-comma
	\|-		\|-
	\| [[29edo\|8\29]]		\| '''[[29edo\|8\29]]'''
	\|
	~~\| 372.414~~
	\|		\|
			\| '''372.414'''
			\| '''Lower bound of 7-odd-limit diamond monotone'''
	\|-		\|-
	\|		\|
Line 128:		Line 128:
	\| 1/13-comma		\| 1/13-comma
	\|-		\|-
	\| [[16edo\|5\16]]		\| '''[[16edo\|5\16]]'''
	\|		\|
	\| 375.000		\| '''375.000'''
	\| ~~Major~~ thirds slightly sharper than this fall under [[magic]]		\| '''Lower bound of 7-odd-limit diamond monotone''', major thirds slightly sharper than this fall under [[magic]]
	\|}		\|}

FloraC: Review

2025-11-09T12:05:34Z

Review

Show changes

Fitzgerald Lee: /* Interval Chain */All of two now

2025-11-08T11:10:05Z

Interval Chain: All of two now

← Older revision		Revision as of 11:10, 8 November 2025
Line 27:		Line 27:
	\|3		\|3
	\|1117.8		\|1117.8
	\|[[40/21]]		\|[[40/21]], [[25/13]]
	\|-		\|-
	\|4		\|4
	\|290.4		\|290.4
	\|[[13/11]]		\|[[64/55]], [[13/11]]
	\|-		\|-
	\|5		\|5
Line 55:		Line 55:
	\|10		\|10
	\|126.0		\|126.0
	\|'''[[16/15]]''', [[14/13~~]], [[13/12~~]]		\|'''[[16/15]]''', [[14/13]]
	\|-		\|-
	\|11		\|11
	\|498.6		\|498.6
	\|'''[[4/3]]'''		\|'''[[4/3]]''', [[35/26]]
	\|-		\|-
	\|12		\|12

Fitzgerald Lee: /* Interval Chain */Added links

2025-11-08T11:06:20Z

Interval Chain: Added links

← Older revision		Revision as of 11:06, 8 November 2025
Line 15:		Line 15:
	\|0		\|0
	\|0.0		\|0.0
	\|'''1/1'''		\|'''[[1/1]]'''
	\|-		\|-
	\|1		\|1
	\|372.6		\|372.6
	\|'''5/4''', '''16/13'''		\|'''[[5/4]]''', '''[[16/13]]'''
	\|-		\|-
	\|2		\|2
	\|745.2		\|745.2
	\|20/13		\|[[32/21]], [[20/13]]
	\|-		\|-
	\|3		\|3
	\|1117.8		\|1117.8
	\|40/21		\|[[40/21]]
	\|-		\|-
	\|4		\|4
	\|290.4		\|290.4
	\|13/11		\|[[13/11]]
	\|-		\|-
	\|5		\|5
	\|663.0		\|663.0
	\|'''16/11''', 22/15		\|'''[[16/11]]''', [[22/15]]
	\|-		\|-
	\|6		\|6
	\|1035.6		\|1035.6
	\|20/11, 11/6		\|[[20/11]], [[11/6]]
	\|-		\|-
	\|7		\|7
	\|208.2		\|208.2
	\|25/22		\|[[25/22]], [[55/48]]
	\|-		\|-
	\|8		\|8
	\|580.8		\|580.8
	\|7/5		\|[[7/5]], [[55/39]]
	\|-		\|-
	\|9		\|9
	\|953.4		\|953.4
	\|26/15, '''7/4'''		\|[[26/15]], '''[[7/4]]'''
	\|-		\|-
	\|10		\|10
	\|126.0		\|126.0
	\|'''16/15''', 14/13, 13/12		\|'''[[16/15]]''', [[14/13]], [[13/12]]
	\|-		\|-
	\|11		\|11
	\|498.6		\|498.6
	\|'''4/3'''		\|'''[[4/3]]'''
	\|-		\|-
	\|12		\|12
	\|871.2		\|871.2
	\|5/3		\|[[64/39]], [[5/3]]
	\|-		\|-
	\|13		\|13
	\|43.8		\|43.8
	\|40/39		\|[[40/39]], [[25/24]]
	\|}		\|}
	<nowiki/>* In 5-limit CTE tuning		<nowiki/>* In 5-limit CTE tuning

Fitzgerald Lee: /* Interval Chain */

2025-11-08T10:50:47Z

Interval Chain

← Older revision		Revision as of 10:50, 8 November 2025
Line 23:		Line 23:
	\|2		\|2
	\|745.2		\|745.2
	\|77/50		\|20/13
	\|-		\|-
	\|3		\|3

Fitzgerald Lee: /* Interval Chain */Fixed interval chain, sorry :(

2025-11-08T10:19:37Z

Interval Chain: Fixed interval chain, sorry :(

← Older revision		Revision as of 10:19, 8 November 2025
Line 23:		Line 23:
	\|2		\|2
	\|745.2		\|745.2
	\|20/~~13, 14/9~~		\|77/50
	\|-		\|-
	\|3		\|3
	\|1117.8		\|1117.8
	\|40/21~~, 21/11~~		\|40/21
	\|-		\|-
	\|4		\|4
	\|290.4		\|290.4
	\|13/11~~, 32/27~~		\|13/11
	\|-		\|-
	\|5		\|5
Line 39:		Line 39:
	\|6		\|6
	\|1035.6		\|1035.6
	\|~~9/5,~~ 20/11, 11/6		\|20/11, 11/6
	\|-		\|-
	\|7		\|7
	\|208.2		\|208.2
	\|~~44/39,~~ 25/22		\|25/22
	\|-		\|-
	\|8		\|8
	\|580.8		\|580.8
	\|~~18/13,~~ 7/5		\|7/5
	\|-		\|-
	\|9		\|9
	\|953.4		\|953.4
	\|~~12/7,~~ 26/15, '''7/4'''		\|26/15, '''7/4'''
	\|-		\|-
	\|10		\|10
	\|126.0		\|126.0
	\|'''16/15'''~~, 15/14~~, 14/13, 13/12		\|'''16/15''', 14/13, 13/12
	\|-		\|-
	\|11		\|11
Line 63:		Line 63:
	\|12		\|12
	\|871.2		\|871.2
	\|~~18/11,~~ 5/3		\|5/3
	\|-		\|-
	\|13		\|13
	\|43.8		\|43.8
	\|~~33/32,~~ 40/39~~, 45/44~~		\|40/39
	\|}		\|}
	<nowiki/>* In 5-limit CTE tuning		<nowiki/>* In 5-limit CTE tuning

Fitzgerald Lee at 05:36, 8 November 2025

2025-11-08T05:36:40Z

← Older revision		Revision as of 05:36, 8 November 2025
Line 43:		Line 43:
	\|7		\|7
	\|208.2		\|208.2
	\|~~'''9~~/~~8'''~~		\|44/39, 25/22
	\|-		\|-
	\|8		\|8

Fitzgerald Lee at 05:08, 8 November 2025

2025-11-08T05:08:31Z

← Older revision		Revision as of 05:08, 8 November 2025
Line 1:		Line 1:
	'''Submerged''' (16 & 29) is a temperament [[~~generator~~\|generated]] by a ~373¢ [[5/4]], tempering out the [[submerged comma]] in the [[5-limit]]. Its major third is slightly flat of [[magic]]'s major third, which itself is slightly flat of a just 5/4, making submerged's generator arguably a [[Submajor_and_supraminor\|submajor]] third. The comma's [[monzo]] is {{monzo\|-27 1 11}}, which implies that 11 5/4s stack to make a [[4/3]], thus making its [[ploidacot]] omega-hendecacot.		'''Submerged''' (16 & 29) is a temperament [[Periods and generators\|generated]] by a ~373¢ [[5/4]], tempering out the [[submerged comma]] in the [[5-limit]]. Its major third is slightly flat of [[magic]]'s major third, which itself is slightly flat of a just 5/4, making submerged's generator arguably a [[Submajor_and_supraminor\|submajor]] third. The comma's [[monzo]] is {{monzo\|-27 1 11}}, which implies that 11 5/4s stack to make a [[4/3]], thus making its [[ploidacot]] omega-hendecacot.

	For limits higher than 5, 9 5/4s stack to reach [[7/4]], and it tempers out [[525/512]] and [[3125/3087]] in the [[7-limit]], and in the [[11-limit]], [[441/440]] and [[121/120]]. In the [[13-limit]], in addition to tempering out [[105/104]], if we look at a submerged third, it sits in between [[16/13]] and [[5/4]], and a very logical thing to do is to temper out the difference between these two intervals, thus also tempering out [[65/64]].		For limits higher than 5, 9 5/4s stack to reach [[7/4]], and it tempers out [[525/512]] and [[3125/3087]] in the [[7-limit]], and in the [[11-limit]], [[441/440]] and [[121/120]]. In the [[13-limit]], in addition to tempering out [[105/104]], if we look at a submerged third, it sits in between [[16/13]] and [[5/4]], and a very logical thing to do is to temper out the difference between these two intervals, thus also tempering out [[65/64]].