107edo - Revision history

BudjarnLambeth: /* Octave stretch */ typo

2025-09-27T08:57:45Z

Octave stretch: typo

← Older revision		Revision as of 08:57, 27 September 2025
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	107edo’s approximations of 3/1, 5/1, 7/1, 13/1, 17/1 and 19/1 are all improved by [[AS\|1ed175/174]], a [[Octave stretch\|stretched-octave]] version of 107edo. The trade-off is a slightly worse 2/1 and 11/1.		107edo’s approximations of 3/1, 5/1, 7/1, 13/1, 17/1 and 19/1 are all improved by [[AS\|1ed175/174]], a [[Octave stretch\|stretched-octave]] version of 107edo. The trade-off is a slightly worse 2/1 and 11/1.

	There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used to improve some harmonics at the expense of others: 622zpi, 623zpi, 624zpi, 625zpi, ~~626zpu~~, 627zpi, 628zpi and 629zpi.		There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used to improve some harmonics at the expense of others: 622zpi, 623zpi, 624zpi, 625zpi, 626zpi, 627zpi, 628zpi and 629zpi.

	The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)\|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.		The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)\|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.

BudjarnLambeth: /* Octave stretch */ replace my esoteric APS with 1ed175/174

2025-09-17T10:59:58Z

Octave stretch: replace my esoteric APS with 1ed175/174

← Older revision		Revision as of 10:59, 17 September 2025
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	=== Octave stretch ===		=== Octave stretch ===
	107edo’s approximations of 3/1, 5/1, 7/1, 13/1, 17/1 and 19/1 are all improved by [[~~Gallery of arithmetic pitch sequences#APS of tinas~~\|~~APS70tina~~]], a [[Octave stretch\|stretched-octave]] version of 107edo. The trade-off is a slightly worse 2/1 and 11/1.		107edo’s approximations of 3/1, 5/1, 7/1, 13/1, 17/1 and 19/1 are all improved by [[AS\|1ed175/174]], a [[Octave stretch\|stretched-octave]] version of 107edo. The trade-off is a slightly worse 2/1 and 11/1.

	There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used to improve some harmonics at the expense of others: 622zpi, 623zpi, 624zpi, 625zpi, 626zpu, 627zpi, 628zpi and 629zpi.		There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used to improve some harmonics at the expense of others: 622zpi, 623zpi, 624zpi, 625zpi, 626zpu, 627zpi, 628zpi and 629zpi.

BudjarnLambeth: /* Octave stretch */

2025-09-17T10:53:38Z

Octave stretch

← Older revision		Revision as of 10:53, 17 September 2025
Line 19:		Line 19:
	107edo’s approximations of 3/1, 5/1, 7/1, 13/1, 17/1 and 19/1 are all improved by [[Gallery of arithmetic pitch sequences#APS of tinas\|APS70tina]], a [[Octave stretch\|stretched-octave]] version of 107edo. The trade-off is a slightly worse 2/1 and 11/1.		107edo’s approximations of 3/1, 5/1, 7/1, 13/1, 17/1 and 19/1 are all improved by [[Gallery of arithmetic pitch sequences#APS of tinas\|APS70tina]], a [[Octave stretch\|stretched-octave]] version of 107edo. The trade-off is a slightly worse 2/1 and 11/1.

	There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used ~~for this same purpose~~: 622zpi, 623zpi, 624zpi, 625zpi, 626zpu, 627zpi, 628zpi and 629zpi.		There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used to improve some harmonics at the expense of others: 622zpi, 623zpi, 624zpi, 625zpi, 626zpu, 627zpi, 628zpi and 629zpi.

	The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)\|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.		The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)\|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.

ArrowHead294 at 16:36, 20 February 2025

2025-02-20T16:36:12Z

← Older revision		Revision as of 16:36, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|107~~}}		{{ED intro}}

	== Theory ==		== Theory ==

BudjarnLambeth: Add section on octave stretch

2024-12-13T07:33:49Z

Add section on octave stretch

← Older revision		Revision as of 07:33, 13 December 2024
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|107}}		{{Harmonics in equal\|107}}

			=== Octave stretch ===
			107edo’s approximations of 3/1, 5/1, 7/1, 13/1, 17/1 and 19/1 are all improved by [[Gallery of arithmetic pitch sequences#APS of tinas\|APS70tina]], a [[Octave stretch\|stretched-octave]] version of 107edo. The trade-off is a slightly worse 2/1 and 11/1.

			There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used for this same purpose: 622zpi, 623zpi, 624zpi, 625zpi, 626zpu, 627zpi, 628zpi and 629zpi.

			The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)\|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.

	=== Subsets and supersets ===		=== Subsets and supersets ===

FloraC: /* Subsets and supersets */

2024-06-27T09:56:20Z

Subsets and supersets

← Older revision		Revision as of 09:56, 27 June 2024
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	107edo is the 28th [[prime edo]]. [[214edo]], which doubles it, provides correction for the approximation to harmonics 3, 5, and 7.		107edo is the 28th [[prime edo]], following [[103edo]] and before [[109edo]]. [[214edo]], which doubles it, provides correction for the approximation to harmonics 3, 5, and 7.

	== Intervals ==		== Intervals ==

FloraC: Note the two possible subgroups

2024-06-08T08:53:19Z

Note the two possible subgroups

← Older revision		Revision as of 08:53, 8 June 2024
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	== Theory ==		== Theory ==
	107edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, ~~with four~~ [[~~mapping~~]]s ~~possible for~~ the 7-limit: {{val\| 107 170 248 300 }} ([[patent val]]), {{val\| 107 '''169''' 248 300 }} (107b), {{val\| 107 170 '''249''' 300 }} (107c), and {{val\| 107 170 '''249''' '''301''' }} (107cd).		107edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, and [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] are about halfway between its steps. Either the 2.9.5.7 or 2.9.15.21 [[subgroup]] can be used. For the full 7-limit, it has four possible [[mapping]]s: {{val\| 107 170 248 300 }} ([[patent val]]), {{val\| 107 '''169''' 248 300 }} (107b), {{val\| 107 170 '''249''' 300 }} (107c), and {{val\| 107 170 '''249''' '''301''' }} (107cd).

	Using the patent val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo\| 28 -22 3 }} in the 5-limit; [[1029/1024]], [[2240/2187]], and [[3125/3087]] in the 7-limit; [[100/99]], 1232/1215, and 1331/1323 in the 11-limit.		Using the patent val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo\| 28 -22 3 }} in the 5-limit; [[1029/1024]], [[2240/2187]], and [[3125/3087]] in the 7-limit; [[100/99]], 1232/1215, and 1331/1323 in the 11-limit.

FloraC: Group the vals by similarity; note a notable superset; misc. cleanup

2024-06-08T08:46:26Z

Group the vals by similarity; note a notable superset; misc. cleanup

← Older revision		Revision as of 08:46, 8 June 2024
Line 5:		Line 5:
	107edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with four [[mapping]]s possible for the 7-limit: {{val\| 107 170 248 300 }} ([[patent val]]), {{val\| 107 '''169''' 248 300 }} (107b), {{val\| 107 170 '''249''' 300 }} (107c), and {{val\| 107 170 '''249''' '''301''' }} (107cd).		107edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with four [[mapping]]s possible for the 7-limit: {{val\| 107 170 248 300 }} ([[patent val]]), {{val\| 107 '''169''' 248 300 }} (107b), {{val\| 107 170 '''249''' 300 }} (107c), and {{val\| 107 170 '''249''' '''301''' }} (107cd).

	Using the patent val, it tempers out [[3125/3072]] (magic comma) and ~~33554432000/31381059609~~ in the 5-limit; [[1029/1024]], 2240/2187, and 3125/3087 in the 7-limit; [[100/99]], 1232/1215, and 1331/1323 in the 11-limit.		Using the patent val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo\| 28 -22 3 }} in the 5-limit; [[1029/1024]], [[2240/2187]], and [[3125/3087]] in the 7-limit; [[100/99]], 1232/1215, and 1331/1323 in the 11-limit.

	Using the ~~107b~~ val, it tempers out [[81/~~80]] (syntonic comma) and {{monzo\| -61 -1 27 }}; in the 5-limit; [[2401/2400~~]], [[~~2430~~/~~2401~~]], and ~~234375~~/~~229376~~ in the 7-limit; [[~~385~~/~~384~~]], ~~1350~~/~~1331~~, 1375/1372, and ~~1944~~/~~1925~~ in the 11-limit.		Using the 107cd val, it tempers out [[1728/1715]], [[4000/3969]], and 28672/28125 in the 7-limit; [[121/120]], [[896/891]], [[1375/1372]], and 3168/3125 in the 11-limit.

	Using the 107c val, it tempers out 1638400/1594323 (immunity comma) and 1990656/1953125 (valentine comma) in the 5-limit; [[126/125]], [[1029/1024]], and 307328/295245 in the 7-limit; [[121/120]], [[176/175]], [[441/440]], and 184877/177147 in the 11-limit.		Using the 107c val, it tempers out 1638400/1594323 ([[immunity comma]]) and 1990656/1953125 ([[valentine comma]]) in the 5-limit; [[126/125]], 1029/1024, and 307328/295245 in the 7-limit; 121/120, [[176/175]], [[441/440]], and 184877/177147 in the 11-limit.

	Using the ~~107cd~~ val, it tempers out [[~~1728~~/~~1715~~]], ~~4000~~/~~3969~~, and ~~28672~~/~~28125~~ in the 7-limit; ~~121/120,~~ [[~~896~~/~~891~~]], 1375/1372, and ~~3168~~/~~3125~~ in the 11-limit.		Using the 107b val, it tempers out 81/80 ([[syntonic comma]]) and {{monzo\| -61 -1 27 }}; in the 5-limit; [[2401/2400]], [[2430/2401]], and 234375/229376 in the 7-limit; [[385/384]], 1350/1331, 1375/1372, and 1944/1925 in the 11-limit.

	~~=== Subsets and supersets ===~~
	~~107edo is the 28th [[prime edo]]~~.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|107}}		{{Harmonics in equal\|107}}

			=== Subsets and supersets ===
			107edo is the 28th [[prime edo]]. [[214edo]], which doubles it, provides correction for the approximation to harmonics 3, 5, and 7.

	== Intervals ==		== Intervals ==
Line 35:		Line 35:
	\| 2.9		\| 2.9
	\| {{monzo\| 339 -107 }}		\| {{monzo\| 339 -107 }}
	\| {{~~val~~\| 107 339 }}		\| {{mapping\| 107 339 }}
	\| +0.322		\| +0.322
	\| 0.322		\| 0.322
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	\| 2.9.5		\| 2.9.5
	\| 9765625/9565938, {{monzo\| -34 10 1 }}		\| 9765625/9565938, {{monzo\| -34 10 1 }}
	\| {{~~val~~\| 107 339 248 }}		\| {{mapping\| 107 339 248 }}
	\| +0.933		\| +0.933
	\| 0.904		\| 0.904
Line 49:		Line 49:
	\| 2.9.5.7		\| 2.9.5.7
	\| 225/224, 84035/82944, {{monzo\| 14 -6 7 -4 }}		\| 225/224, 84035/82944, {{monzo\| 14 -6 7 -4 }}
	\| {{~~val~~\| 107 339 248 300 }}		\| {{mapping\| 107 339 248 300 }}
	\| +1.087		\| +1.087
	\| 0.827		\| 0.827
Line 56:		Line 56:
	\| 2.9.5.7.11		\| 2.9.5.7.11
	\| 225/224, 441/440, 26411/26244, 161280/161051		\| 225/224, 441/440, 26411/26244, 161280/161051
	\| {{~~val~~\| 107 339 248 300 370 }}		\| {{mapping\| 107 339 248 300 370 }}
	\| +0.973		\| +0.973
	\| 0.774		\| 0.774
Line 63:		Line 63:
	\| 2.9.5.7.11.13		\| 2.9.5.7.11.13
	\| 225/224, 325/324, 441/440, 847/845, 24500/24167		\| 225/224, 325/324, 441/440, 847/845, 24500/24167
	\| {{~~val~~\| 107 339 248 300 370 396 }}		\| {{mapping\| 107 339 248 300 370 396 }}
	\| +0.783		\| +0.783
	\| 0.823		\| 0.823
Line 70:		Line 70:
	\| 2.9.5.7.11.13.17		\| 2.9.5.7.11.13.17
	\| 170/169, 225/224, 325/324, 441/440, 847/845, 2000/1989		\| 170/169, 225/224, 325/324, 441/440, 847/845, 2000/1989
	\| {{~~val~~\| 107 339 248 300 370 396 437 }}		\| {{mapping\| 107 339 248 300 370 396 437 }}
	\| +0.812		\| +0.812
	\| 0.765		\| 0.765
	\| 6.82		\| 6.82
	\|}		\|}

BudjarnLambeth: Added interval table

2024-01-21T06:23:23Z

Added interval table

← Older revision		Revision as of 06:23, 21 January 2024
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|107}}		{{Harmonics in equal\|107}}

			== Intervals ==
			{{Interval table}}

	== Regular temperament properties ==		== Regular temperament properties ==

Eliora: /* Scales */

2023-05-30T21:13:49Z

Scales

Show changes