5809edo - Revision history

FloraC: Expand the harmonics table a little

2025-10-02T16:08:02Z

Expand the harmonics table a little

← Older revision		Revision as of 16:08, 2 October 2025
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|5809\|columns=9}}		{{Harmonics in equal\|5809\|columns=11}}
	{{Harmonics in equal\|5809\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 5809edo (continued)}}		{{Harmonics in equal\|5809\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 5809edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 5809 factors into primes as {{nowrap\| 37 × 157 }}, 5809edo contains [[37edo]] and [[157edo]] as subsets.		Since 5809 factors into primes as {{nowrap\| 37 × 157 }}, 5809edo contains [[37edo]] and [[157edo]] as subsets.

FloraC: Extend the harmonics table to the 61-limit

2025-03-07T08:35:38Z

Extend the harmonics table to the 61-limit

← Older revision		Revision as of 08:35, 7 March 2025
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	5809edo is a fairly strong [[19-limit]] system, [[consistent]] to the [[21-odd-limit]]. Moreover, it is a strong no-23 [[43-limit]] system, consistent to the no-23 45-odd-limit. Its full 43-limit interpretation using the [[patent val]] is also obvious, as [[23/22]], [[23/13]], [[37/23]] and their [[octave complement]]s exhaust the inconsistently mapped intervals in the full 45-odd-limit.		5809edo is a fairly strong [[19-limit]] system, [[consistent]] to the [[21-odd-limit]]. Moreover, it is a strong no-23 [[43-limit]] system, consistent to the no-23 45-odd-limit. Its full 43-limit interpretation using the [[patent val]] is also obvious, as [[23/22]], [[23/13]], [[37/23]] and their [[octave complement]]s exhaust the inconsistently mapped intervals in the full 45-odd-limit.

	We may note that it is an [[egads]] and [[euzenius]] system, [[support]]ing [[hemiegads]]. Some simpler ~~commas~~ it [[tempering out\|tempers out]] in the higher limits include [[123201/123200]] in the 13-limit; [[14400/14399]], [[194481/194480]], and [[336141/336140]] in the 17-limit; 10830/10829, 23409/23408, 28900/28899, 43681/43680, and 89376/89375 in the 19-limit; 7866/7865, 8625/8624, 21505/21054, and [[25921/25920]] in the 23-limit.		We may note that it is an [[egads]] and [[euzenius]] system, [[support]]ing [[hemiegads]]. Some simpler [[comma]]s it [[tempering out\|tempers out]] in the higher limits include [[123201/123200]] in the [[13-limit]]; [[14400/14399]], [[194481/194480]], and [[336141/336140]] in the [[17-limit]]; 10830/10829, 23409/23408, 28900/28899, 43681/43680, and 89376/89375 in the 19-limit; 7866/7865, 8625/8624, 21505/21054, and [[25921/25920]] in the [[23-limit]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|5809\|columns=15}}		{{Harmonics in equal\|5809\|columns=9}}
			{{Harmonics in equal\|5809\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 5809edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 5809 factors into primes as 37 × 157, 5809edo contains [[37edo]] and [[157edo]] as subsets.		Since 5809 factors into primes as {{nowrap\| 37 × 157 }}, 5809edo contains [[37edo]] and [[157edo]] as subsets.

FloraC: A little expansion

2025-02-21T12:06:21Z

A little expansion

← Older revision		Revision as of 12:06, 21 February 2025
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	{{ED intro}}		{{ED intro}}

	5809edo is a fairly strong [[19-limit]] system, [[consistent]] to the [[21-odd-limit]], ~~though its~~ full 43-limit interpretation using the [[patent val]] is obvious.		5809edo is a fairly strong [[19-limit]] system, [[consistent]] to the [[21-odd-limit]]. Moreover, it is a strong no-23 [[43-limit]] system, consistent to the no-23 45-odd-limit. Its full 43-limit interpretation using the [[patent val]] is also obvious, as [[23/22]], [[23/13]], [[37/23]] and their [[octave complement]]s exhaust the inconsistently mapped intervals in the full 45-odd-limit.

	We may note that it is an [[egads]] and [[euzenius]] system, [[support]]ing [[hemiegads]]. Some simpler commas it [[tempering out\|tempers out]] in the higher limits include [[123201/123200]] in the 13-limit; [[14400/14399]], [[194481/194480]], and [[336141/336140]] in the 17-limit; 10830/10829, 23409/23408, 28900/28899, 43681/43680, and 89376/89375 in the 19-limit; 7866/7865, 8625/8624, 21505/21054, and [[25921/25920]] in the 23-limit.		We may note that it is an [[egads]] and [[euzenius]] system, [[support]]ing [[hemiegads]]. Some simpler commas it [[tempering out\|tempers out]] in the higher limits include [[123201/123200]] in the 13-limit; [[14400/14399]], [[194481/194480]], and [[336141/336140]] in the 17-limit; 10830/10829, 23409/23408, 28900/28899, 43681/43680, and 89376/89375 in the 19-limit; 7866/7865, 8625/8624, 21505/21054, and [[25921/25920]] in the 23-limit.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 5809 factors into 37 × 157, 5809edo contains [[37edo]] and [[157edo]] as subsets.		Since 5809 factors into primes as 37 × 157, 5809edo contains [[37edo]] and [[157edo]] as subsets.

Francium: changed EDO intro to ED intro

2025-02-21T05:41:15Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:41, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	5809edo is a fairly strong [[19-limit]] system, [[consistent]] to the [[21-odd-limit]], though its full 43-limit interpretation using the [[patent val]] is obvious.		5809edo is a fairly strong [[19-limit]] system, [[consistent]] to the [[21-odd-limit]], though its full 43-limit interpretation using the [[patent val]] is obvious.

FloraC: Created page with "{{Infobox ET}} {{EDO intro}} 5809edo is a fairly strong 19-limit system, consistent to the 21-odd-limit, though its full 43-limit interpretation using the paten..."

2025-01-12T12:12:23Z

Created page with "{{Infobox ET}} {{EDO intro}} 5809edo is a fairly strong 19-limit system, consistent to the 21-odd-limit, though its full 43-limit interpretation using the paten..."

New page

{{Infobox ET}}
{{EDO intro}}

5809edo is a fairly strong [[19-limit]] system, [[consistent]] to the [[21-odd-limit]], though its full 43-limit interpretation using the [[patent val]] is obvious.

We may note that it is an [[egads]] and [[euzenius]] system, [[support]]ing [[hemiegads]]. Some simpler commas it [[tempering out|tempers out]] in the higher limits include [[123201/123200]] in the 13-limit; [[14400/14399]], [[194481/194480]], and [[336141/336140]] in the 17-limit; 10830/10829, 23409/23408, 28900/28899, 43681/43680, and 89376/89375 in the 19-limit; 7866/7865, 8625/8624, 21505/21054, and [[25921/25920]] in the 23-limit.

=== Prime harmonics ===
{{Harmonics in equal|5809|columns=15}}

=== Subsets and supersets ===
Since 5809 factors into 37 × 157, 5809edo contains [[37edo]] and [[157edo]] as subsets.