318edo - Revision history

FloraC: Cleanup

2026-03-03T10:11:45Z

Cleanup

← Older revision		Revision as of 10:11, 3 March 2026
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	318edo is [[contorted]] in both the 3-limit and the 5-limit, sharing the same mappings with [[53edo]]. Besides, it shares its representations of the 11th and 17th [[Overtone series\|harmonics]] with [[159edo]]. However, compared to 159edo, the [[patent val]]s differ on the mappings for 7, 13, and 19.		318edo is [[contorted]] in both the 3-limit and the 5-limit, sharing the same mappings with [[53edo]]. Besides, it shares its representations of the 11th and 17th [[Overtone series\|harmonics]] with [[159edo]]. However, compared to 159edo, the [[patent val]]s differ on the mappings for 7, 13, and 19.

	In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768\|schisma (32805/32768)]], the [[15625/15552\|kleisma (15625/15552)]], the [[amity comma\|amity comma (1600000/1594323)]], the [[semicomma\|semicomma (2109375/2097152)]], the [[vulture comma\|vulture comma (10485760000/10460353203)]], etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out ~~the swetisma (~~540/539), ~~the~~ [[4000/3993~~\|wizardharry (4000/3993)~~]], ~~the~~ [[9801/9800~~\|kalisma (9801/9800)~~]] and ~~the~~ [[~~nexuma\|nexus comma (~~1771561/1769472)]]. In the 13-limit, 1575/1573, 2080/2079, ~~it tempers out the~~ [[4096/4095~~\|schismina (4096/4095)~~]], and ~~the~~ [[~~cantonisma\|cantonisma (~~10985/10976)]].		In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768\|schisma (32805/32768)]], the [[15625/15552\|kleisma (15625/15552)]], the [[amity comma\|amity comma (1600000/1594323)]], the [[semicomma\|semicomma (2109375/2097152)]], the [[vulture comma\|vulture comma (10485760000/10460353203)]], etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out [[540/539]], [[4000/3993]], [[9801/9800]] and [[1771561/1769472]]. In the 13-limit, [[1575/1573]], [[2080/2079]], [[4096/4095]], and [[10985/10976]].

	At only slightly more than 3.5{{c}}, the step size of 318edo is really close to being [[unnoticeable comma\|unnoticeable]] as is the case with other mega-~~EDOs~~ in this vicinity, so the steps themselves run a pretty high risk of blending completely into one another.		At only slightly more than 3.5{{c}}, the step size of 318edo is really close to being [[unnoticeable comma\|unnoticeable]] as is the case with other mega-edos in this vicinity, so the steps themselves run a pretty high risk of blending completely into one another.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{~~harmonics~~ in equal\|318}}		{{Harmonics in equal\|318}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	318 = 2 × 3 × 53, ~~and~~ has subset edos {{EDOs\|1, 2, 3, 6, 53, 106, 159}}.		{{nowrap\| 318 = 2 × 3 × 53 }}, so 318edo has subset edos {{EDOs\| 2, 3, 6, 53, 106, 159 }}.

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	[[Category:53edo]]		[[Category:53edo]]
	[[Category:159edo]]		[[Category:159edo]]
	[[Category:Nexus]]		[[Category:Nexus]]

ArrowHead294 at 22:50, 20 February 2025

2025-02-20T22:50:00Z

← Older revision		Revision as of 22:50, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|318~~}}		{{ED intro}}

	318edo is [[contorted]] in both the 3-limit and the 5-limit, sharing the same mappings with [[53edo]]. Besides, it shares its representations of the 11th and 17th [[Overtone series\|harmonics]] with [[159edo]]. However, compared to 159edo, the [[patent val]]s differ on the mappings for 7, 13, and 19.		318edo is [[contorted]] in both the 3-limit and the 5-limit, sharing the same mappings with [[53edo]]. Besides, it shares its representations of the 11th and 17th [[Overtone series\|harmonics]] with [[159edo]]. However, compared to 159edo, the [[patent val]]s differ on the mappings for 7, 13, and 19.
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	In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768\|schisma (32805/32768)]], the [[15625/15552\|kleisma (15625/15552)]], the [[amity comma\|amity comma (1600000/1594323)]], the [[semicomma\|semicomma (2109375/2097152)]], the [[vulture comma\|vulture comma (10485760000/10460353203)]], etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out the swetisma (540/539), the [[4000/3993\|wizardharry (4000/3993)]], the [[9801/9800\|kalisma (9801/9800)]] and the [[nexuma\|nexus comma (1771561/1769472)]]. In the 13-limit, 1575/1573, 2080/2079, it tempers out the [[4096/4095\|schismina (4096/4095)]], and the [[cantonisma\|cantonisma (10985/10976)]].		In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768\|schisma (32805/32768)]], the [[15625/15552\|kleisma (15625/15552)]], the [[amity comma\|amity comma (1600000/1594323)]], the [[semicomma\|semicomma (2109375/2097152)]], the [[vulture comma\|vulture comma (10485760000/10460353203)]], etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out the swetisma (540/539), the [[4000/3993\|wizardharry (4000/3993)]], the [[9801/9800\|kalisma (9801/9800)]] and the [[nexuma\|nexus comma (1771561/1769472)]]. In the 13-limit, 1575/1573, 2080/2079, it tempers out the [[4096/4095\|schismina (4096/4095)]], and the [[cantonisma\|cantonisma (10985/10976)]].

	At only slightly more than 3.5 ~~cents~~, the step size of 318edo is really close to being [[unnoticeable comma\|unnoticeable]] as is the case with other mega-EDOs in this vicinity, so the steps themselves run a pretty high risk of blending completely into one another.		At only slightly more than 3.5{{c}}, the step size of 318edo is really close to being [[unnoticeable comma\|unnoticeable]] as is the case with other mega-EDOs in this vicinity, so the steps themselves run a pretty high risk of blending completely into one another.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{harmonics in equal\|318}}		{{harmonics in equal\|318}}

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

	318 = 2 × 3 × 53, and has subset edos {{EDOs\|1, 2, 3, 6, 53, 106, 159}}.		318 = 2 × 3 × 53, and has subset edos {{EDOs\|1, 2, 3, 6, 53, 106, 159}}.


	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Eliora: cleanup

2023-07-19T22:38:57Z

cleanup

← Older revision		Revision as of 22:38, 19 July 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''318edo''' is the '''~~318 ~~equal division of the octave''' into equal parts of 3.774 cents each.~~		{{EDO intro\|318}}

	~~At only slightly more than~~ 3.5 ~~cents~~, the ~~step size~~ of ~~318edo is really close to being~~ [[~~unnoticeable comma~~\|~~unnoticeable~~]] ~~as is the case~~ with ~~other mega-EDOs in this vicinity~~, so the ~~steps themselves run a pretty high risk of blending completely into one another~~.		318edo is [[contorted]] in both the 3-limit and the 5-limit, sharing the same mappings with [[53edo]]. Besides, it shares its representations of the 11th and 17th [[Overtone series\|harmonics]] with [[159edo]]. However, compared to 159edo, the [[patent val]]s differ on the mappings for 7, 13, and 19.

	~~== Approximation of primes ==~~		In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768\|schisma (32805/32768)]], the [[15625/15552\|kleisma (15625/15552)]], the [[amity comma\|amity comma (1600000/1594323)]], the [[semicomma\|semicomma (2109375/2097152)]], the [[vulture comma\|vulture comma (10485760000/10460353203)]], etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out the swetisma (540/539), the [[4000/3993\|wizardharry (4000/3993)]], the [[9801/9800\|kalisma (9801/9800)]] and the [[nexuma\|nexus comma (1771561/1769472)]]. In the 13-limit, 1575/1573, 2080/2079, it tempers out the [[4096/4095\|schismina (4096/4095)]], and the [[cantonisma\|cantonisma (10985/10976)]].

	~~{{Primes in edo\|318\|columns=11}}~~		At only slightly more than 3.5 cents, the step size of 318edo is really close to being [[unnoticeable comma\|unnoticeable]] as is the case with other mega-EDOs in this vicinity, so the steps themselves run a pretty high risk of blending completely into one another.
			=== Prime harmonics ===
	~~== Mappings ==~~		{{harmonics in equal\|318}}

	~~318 = 2 ×~~ 3 ~~× 53~~, ~~and~~ 318edo is [[~~contorted~~]] ~~in both~~ the 3-~~limit and the 5-limit~~, ~~sharing~~ the ~~same mappings with [[53edo]].~~

	~~Besides, it shares its representations~~ of ~~the 11th and 17th [[Overtone series\|harmonics]] with [[159edo]]. However, compared to 159edo, the [[patent val]]s differ on the mappings for 7, 13, and 19~~.

	== ~~Commas~~ ==

	~~In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768~~\|schisma (32805/32768)]], the [[15625/15552\|kleisma (15625/15552)]], the [[amity comma\|amity comma (1600000/1594323)]], the [[semicomma\|semicomma (2109375/2097152)]], the [[vulture comma\|vulture comma (10485760000/10460353203)]], etc.

	~~In the 7-limit it tempers out the stearnsma (118098/117649)~~ and ~~589824/588245.~~		=== Subsets and supersets ===

	~~In the 11-limit it tempers out the swetisma (540/539)~~, ~~the [[4000/3993~~\|~~wizardharry (4000/3993)]]~~, ~~the [[9801/9800\|kalisma (9801/9800)]] and the [[nexuma\|nexus comma (1771561/1769472)]]~~.		318 = 2 × 3 × 53, and has subset edos {{EDOs\|1, 2, 3, 6, 53, 106, 159}}.

	~~In the 13-limit, 1575/1573, 2080/2079, the [[4096/4095\|schismina (4096/4095)]], and the [[cantonisma\|cantonisma (10985/10976)]] have been found to be tempered out by this EDO.~~

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

BudjarnLambeth: Removed novelty tag for now. We can add it back later, but I think we should start with the biggest edos: 6000000, 4191814, 2901533… and work our way down. We should add the tag to bigger ones first.

2023-07-09T02:02:50Z

Removed novelty tag for now. We can add it back later, but I think we should start with the biggest edos: 6000000, 4191814, 2901533… and work our way down. We should add the tag to bigger ones first.

← Older revision		Revision as of 02:02, 9 July 2023
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	~~{{Novelty}}~~
	{{Infobox ET}}		{{Infobox ET}}
	'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.		'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.

Fredg999: Categories

2023-07-08T15:13:10Z

Fredg999: Marked as novelty

2023-07-08T15:13:05Z

Marked as novelty

← Older revision		Revision as of 15:13, 8 July 2023
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			{{Novelty}}
	{{Infobox ET}}		{{Infobox ET}}
	'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.		'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.

BudjarnLambeth at 02:31, 7 July 2023

2023-07-07T02:31:19Z

← Older revision		Revision as of 02:31, 7 July 2023
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	== Mappings ==		== Mappings ==

	318 = 2 × 3 × 53, and 318edo is [[contorted]] in both the 3-limit and the 5-limit, sharing the same mappings with [[53edo]]. Besides, it shares its representations of the 11th and 17th [[Overtone series\|harmonics]] with [[159edo]]. However, compared to 159edo, the [[patent val]]s differ on the mappings for 7, 13, and 19.		318 = 2 × 3 × 53, and 318edo is [[contorted]] in both the 3-limit and the 5-limit, sharing the same mappings with [[53edo]].

			Besides, it shares its representations of the 11th and 17th [[Overtone series\|harmonics]] with [[159edo]]. However, compared to 159edo, the [[patent val]]s differ on the mappings for 7, 13, and 19.

	== Commas ==		== Commas ==

	In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768\|schisma (32805/32768)]], the [[15625/15552\|kleisma (15625/15552)]], the [[amity comma\|amity comma (1600000/1594323)]], the [[semicomma\|semicomma (2109375/2097152)]], the [[vulture comma\|vulture comma (10485760000/10460353203)]], etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out the swetisma (540/539), the [[4000/3993\|wizardharry (4000/3993)]], the [[9801/9800\|kalisma (9801/9800)]] and the [[nexuma\|nexus comma (1771561/1769472)]]. In the 13-limit, 1575/1573, 2080/2079, the [[4096/4095\|schismina (4096/4095)]], and the [[cantonisma\|cantonisma (10985/10976)]] have been found to be tempered out by this EDO.		In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768\|schisma (32805/32768)]], the [[15625/15552\|kleisma (15625/15552)]], the [[amity comma\|amity comma (1600000/1594323)]], the [[semicomma\|semicomma (2109375/2097152)]], the [[vulture comma\|vulture comma (10485760000/10460353203)]], etc.

			In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245.

			In the 11-limit it tempers out the swetisma (540/539), the [[4000/3993\|wizardharry (4000/3993)]], the [[9801/9800\|kalisma (9801/9800)]] and the [[nexuma\|nexus comma (1771561/1769472)]].

			In the 13-limit, 1575/1573, 2080/2079, the [[4096/4095\|schismina (4096/4095)]], and the [[cantonisma\|cantonisma (10985/10976)]] have been found to be tempered out by this EDO.

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

BudjarnLambeth: Improved readability slightly

2023-07-07T02:30:06Z

Improved readability slightly

← Older revision		Revision as of 02:30, 7 July 2023
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	'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.		'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.

	== ~~Theory~~ ==		At only slightly more than 3.5 cents, the step size of 318edo is really close to being [[unnoticeable comma\|unnoticeable]] as is the case with other mega-EDOs in this vicinity, so the steps themselves run a pretty high risk of blending completely into one another.

			== Approximation of primes ==

	{{Primes in edo\|318\|columns=11}}		{{Primes in edo\|318\|columns=11}}

	At only slightly more than 3.5 cents, the step size of 318edo is really close to being [[unnoticeable comma\|unnoticeable]] as is the case with other Mega-EDOs in this vicinity, so the steps themselves run a pretty high risk of blending completely into one another.		== Mappings ==

	=== Mappings ===

	318 = 2 × 3 × 53, and 318edo is [[contorted]] in both the 3-limit and the 5-limit, sharing the same mappings with [[53edo]]. Besides, it shares its representations of the 11th and 17th [[Overtone series\|harmonics]] with [[159edo]]. However, compared to 159edo, the [[patent val]]s differ on the mappings for 7, 13, and 19.		318 = 2 × 3 × 53, and 318edo is [[contorted]] in both the 3-limit and the 5-limit, sharing the same mappings with [[53edo]]. Besides, it shares its representations of the 11th and 17th [[Overtone series\|harmonics]] with [[159edo]]. However, compared to 159edo, the [[patent val]]s differ on the mappings for 7, 13, and 19.

	=== Commas ===		== Commas ==

	In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768\|schisma (32805/32768)]], the [[15625/15552\|kleisma (15625/15552)]], the [[amity comma\|amity comma (1600000/1594323)]], the [[semicomma\|semicomma (2109375/2097152)]], the [[vulture comma\|vulture comma (10485760000/10460353203)]], etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out the swetisma (540/539), the [[4000/3993\|wizardharry (4000/3993)]], the [[9801/9800\|kalisma (9801/9800)]] and the [[nexuma\|nexus comma (1771561/1769472)]]. In the 13-limit, 1575/1573, 2080/2079, the [[4096/4095\|schismina (4096/4095)]], and the [[cantonisma\|cantonisma (10985/10976)]] have been found to be tempered out by this EDO.		In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768\|schisma (32805/32768)]], the [[15625/15552\|kleisma (15625/15552)]], the [[amity comma\|amity comma (1600000/1594323)]], the [[semicomma\|semicomma (2109375/2097152)]], the [[vulture comma\|vulture comma (10485760000/10460353203)]], etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out the swetisma (540/539), the [[4000/3993\|wizardharry (4000/3993)]], the [[9801/9800\|kalisma (9801/9800)]] and the [[nexuma\|nexus comma (1771561/1769472)]]. In the 13-limit, 1575/1573, 2080/2079, the [[4096/4095\|schismina (4096/4095)]], and the [[cantonisma\|cantonisma (10985/10976)]] have been found to be tempered out by this EDO.

Plumtree: Infobox ET added

2022-10-04T21:49:43Z

Infobox ET added

← Older revision		Revision as of 21:49, 4 October 2022
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			{{Infobox ET}}
	'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.		'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.

Fredg999 category edits: Sort key

2022-07-03T19:18:24Z

Sort key

← Older revision		Revision as of 19:18, 3 July 2022
Line 15:		Line 15:
	In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768\|schisma (32805/32768)]], the [[15625/15552\|kleisma (15625/15552)]], the [[amity comma\|amity comma (1600000/1594323)]], the [[semicomma\|semicomma (2109375/2097152)]], the [[vulture comma\|vulture comma (10485760000/10460353203)]], etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out the swetisma (540/539), the [[4000/3993\|wizardharry (4000/3993)]], the [[9801/9800\|kalisma (9801/9800)]] and the [[nexuma\|nexus comma (1771561/1769472)]]. In the 13-limit, 1575/1573, 2080/2079, the [[4096/4095\|schismina (4096/4095)]], and the [[cantonisma\|cantonisma (10985/10976)]] have been found to be tempered out by this EDO.		In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768\|schisma (32805/32768)]], the [[15625/15552\|kleisma (15625/15552)]], the [[amity comma\|amity comma (1600000/1594323)]], the [[semicomma\|semicomma (2109375/2097152)]], the [[vulture comma\|vulture comma (10485760000/10460353203)]], etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out the swetisma (540/539), the [[4000/3993\|wizardharry (4000/3993)]], the [[9801/9800\|kalisma (9801/9800)]] and the [[nexuma\|nexus comma (1771561/1769472)]]. In the 13-limit, 1575/1573, 2080/2079, the [[4096/4095\|schismina (4096/4095)]], and the [[cantonisma\|cantonisma (10985/10976)]] have been found to be tempered out by this EDO.

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:53edo]]		[[Category:53edo]]
	[[Category:159edo]]		[[Category:159edo]]

← Older revision		Revision as of 15:13, 8 July 2023
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	[[Category:159edo]]		[[Category:159edo]]
	[[Category:Nexus]]		[[Category:Nexus]]

	~~{{todo\|improve readability}}~~