1817edo - Revision history

FloraC: Cleanup and update

2025-03-16T13:42:35Z

Cleanup and update

← Older revision		Revision as of 13:42, 16 March 2025
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	{{ED intro}}		{{ED intro}}

	1817edo distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system. Past that, adding the mapping for [[29/16\|29]] is worth considering.		1817edo is distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system. Past that, adding the mapping for [[29/16\|29]] is worth considering.

	In the 5-limit, it is a strong tuning for [[~~tricot~~]]. It also tempers out ~~are~~ {{monzo\|128 13 -64}}, the 323 & 1171 temperament, which divides the [[3/1\|third harmonic]] into 64 equal parts, as well as {{monzo\|-89 -42 67}} and {{monzo\|-50 -71 70}}. In the 7-limit, it tempers out [[4375/4374]] (~~the~~ ragisma). In the 11-limit it tempers out 117649/117612, 2097152/2096325, and tunes rank-3 temperaments [[heimdall]] and [[bragi]]. In the 13-limit, it tempers out [[4096/4095]], [[6656/6655]], and in the 17-limit, [[12376/12375]] and [[14400/14399]].		In the 5-limit, it is a strong tuning for [[alphatricot]]. It also [[tempering out\|tempers out]] {{monzo\| 128 13 -64 }}, corresponding to the 323 & 1171 temperament, which divides the [[3/1\|third harmonic]] into 64 equal parts, as well as {{monzo\| -89 -42 67 }} and {{monzo\| -50 -71 70 }}. In the 7-limit, it tempers out [[4375/4374]] (ragisma). In the 11-limit it tempers out 117649/117612, 2097152/2096325, and tunes rank-3 temperaments [[heimdall]] and [[bragi]]. In the 13-limit, it tempers out [[4096/4095]], [[6656/6655]], and in the 17-limit, [[12376/12375]] and [[14400/14399]].

	In the 17-limit and the 2.3.5.7.11.13.17.37 subgroup (add-37 ~~17-limit~~), the patent val tunes the [[gold]] temperament which divides the octave into 79 parts, though it is worth noting that the error on the 37th harmonic is quite large.		In the 17-limit and the 2.3.5.7.11.13.17.37 subgroup (17-limit add-37), the [[patent val]] tunes the [[gold]] temperament which divides the octave into 79 parts, though it is worth noting that the error on the 37th harmonic is quite large.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1817 factors into {{~~factorization~~\|~~1817~~}}, 1817edo contains [[23edo]] and [[79edo]] as subsets.		Since 1817 factors into primes as {{nowrap\| 23 × 79 }}, 1817edo contains [[23edo]] and [[79edo]] as subsets.

ArrowHead294 at 14:08, 20 February 2025

2025-02-20T14:08:19Z

← Older revision		Revision as of 14:08, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1817~~}}		{{ED intro}}

	1817edo distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system. Past that, adding the mapping for [[29/16\|29]] is worth considering.		1817edo distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system. Past that, adding the mapping for [[29/16\|29]] is worth considering.

Francium: typo

2024-01-09T08:04:01Z

typo

← Older revision		Revision as of 08:04, 9 January 2024
Line 4:		Line 4:
	1817edo distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system. Past that, adding the mapping for [[29/16\|29]] is worth considering.		1817edo distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system. Past that, adding the mapping for [[29/16\|29]] is worth considering.

	In the 5-limit, it is a strong tuning for [[tricot]]. It also tempers out are {{monzo\|128 13 -64}}, the 323 & 1171 temperament, which divides the [[3/1\|third harmonic]] into 64 equal parts, as well as {{monzo\|-89 -42 67}} and {{monzo\|-50 -71 70}}. In the 7-limit, it tempers out [[4375/4374]] (the ragisma). In the 11-limit it tempers out 117649/117612, 2097152/2096325, and tunes rank-3 temperaments [[heimdall]] and [[~~brage~~]]. In the 13-limit, it tempers out [[4096/4095]], [[6656/6655]], and in the 17-limit, [[12376/12375]] and [[14400/14399]].		In the 5-limit, it is a strong tuning for [[tricot]]. It also tempers out are {{monzo\|128 13 -64}}, the 323 & 1171 temperament, which divides the [[3/1\|third harmonic]] into 64 equal parts, as well as {{monzo\|-89 -42 67}} and {{monzo\|-50 -71 70}}. In the 7-limit, it tempers out [[4375/4374]] (the ragisma). In the 11-limit it tempers out 117649/117612, 2097152/2096325, and tunes rank-3 temperaments [[heimdall]] and [[bragi]]. In the 13-limit, it tempers out [[4096/4095]], [[6656/6655]], and in the 17-limit, [[12376/12375]] and [[14400/14399]].

	In the 17-limit and the 2.3.5.7.11.13.17.37 subgroup (add-37 17-limit), the patent val tunes the [[gold]] temperament which divides the octave into 79 parts, though it is worth noting that the error on the 37th harmonic is quite large.		In the 17-limit and the 2.3.5.7.11.13.17.37 subgroup (add-37 17-limit), the patent val tunes the [[gold]] temperament which divides the octave into 79 parts, though it is worth noting that the error on the 37th harmonic is quite large.

Eliora at 16:46, 7 December 2023

2023-12-07T16:46:34Z

← Older revision		Revision as of 16:46, 7 December 2023
Line 2:		Line 2:
	{{EDO intro\|1817}}		{{EDO intro\|1817}}

	1817edo distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system.		1817edo distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system. Past that, adding the mapping for [[29/16\|29]] is worth considering.

			In the 5-limit, it is a strong tuning for [[tricot]]. It also tempers out are {{monzo\|128 13 -64}}, the 323 & 1171 temperament, which divides the [[3/1\|third harmonic]] into 64 equal parts, as well as {{monzo\|-89 -42 67}} and {{monzo\|-50 -71 70}}. In the 7-limit, it tempers out [[4375/4374]] (the ragisma). In the 11-limit it tempers out 117649/117612, 2097152/2096325, and tunes rank-3 temperaments [[heimdall]] and [[brage]]. In the 13-limit, it tempers out [[4096/4095]], [[6656/6655]], and in the 17-limit, [[12376/12375]] and [[14400/14399]].

			In the 17-limit and the 2.3.5.7.11.13.17.37 subgroup (add-37 17-limit), the patent val tunes the [[gold]] temperament which divides the octave into 79 parts, though it is worth noting that the error on the 37th harmonic is quite large.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: +subsets and supersets

2023-10-30T12:33:32Z

+subsets and supersets

← Older revision		Revision as of 12:33, 30 October 2023
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	{{EDO intro\|1817}}		{{EDO intro\|1817}}

	1817edo distinctly [[consistent]] in the 17-odd-limit, and a fairly strong 17-limit system.		1817edo distinctly [[consistent]] in the [[17-odd-limit]], and a fairly strong 17-limit system.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1817}}		{{Harmonics in equal\|1817}}

			=== Subsets and supersets ===
			Since 1817 factors into {{factorization\|1817}}, 1817edo contains [[23edo]] and [[79edo]] as subsets.

FloraC: Adopt template: EDO intro; cleanup

2023-10-15T14:17:45Z

Adopt template: EDO intro; cleanup

← Older revision		Revision as of 14:17, 15 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''~~1817 ~~division''' is~~ distinctly consistent in the 17-limit, and a fairly strong 17-limit system.		{{EDO intro\|1817}}

			1817edo distinctly [[consistent]] in the 17-odd-limit, and a fairly strong 17-limit system.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{~~harmonics~~ in equal\|1817}}		{{Harmonics in equal\|1817}}
	~~[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->~~

BudjarnLambeth at 06:57, 9 July 2023

2023-07-09T06:57:55Z

← Older revision		Revision as of 06:57, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	The '''1817 division''' is distinctly consistent in the 17-limit, and a fairly strong 17-limit system.		The '''1817 division''' is distinctly consistent in the 17-limit, and a fairly strong 17-limit system.
	=== Prime harmonics ===		=== Prime harmonics ===
	{{harmonics in equal\|1817}}		{{harmonics in equal\|1817}}
	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->

BudjarnLambeth at 04:51, 9 July 2023

2023-07-09T04:51:23Z

← Older revision		Revision as of 04:51, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	The '''1817 division''' is distinctly consistent in the 17-limit, and a fairly strong 17-limit system.		The '''1817 division''' is distinctly consistent in the 17-limit, and a fairly strong 17-limit system.
	=== Prime harmonics ===		=== Prime harmonics ===
	{{harmonics in equal\|1817}}		{{harmonics in equal\|1817}}
	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->

Eliora at 18:49, 14 May 2023

2023-05-14T18:49:30Z

← Older revision		Revision as of 18:49, 14 May 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	The '''1817 division''' is distinctly consistent in the 17-limit, and a fairly strong 17-limit system.		The '''1817 division''' is distinctly consistent in the 17-limit, and a fairly strong 17-limit system.
			=== Prime harmonics ===
			{{harmonics in equal\|1817}}
	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->

Plumtree: Infobox ET added

2022-10-04T22:12:20Z

Infobox ET added

← Older revision		Revision as of 22:12, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	The '''1817 division''' is distinctly consistent in the 17-limit, and a fairly strong 17-limit system.		The '''1817 division''' is distinctly consistent in the 17-limit, and a fairly strong 17-limit system.

	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->