1395edo - Revision history

Tristanbay: typo fix

2026-03-01T07:55:20Z

typo fix

← Older revision		Revision as of 07:55, 1 March 2026
Line 2:		Line 2:
	{{ED intro}}		{{ED intro}}

	1395edo is a strong higher-limit system, being a [[zeta edo\|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo\|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]]. ~~Howewver~~, it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1\|23]] being all of 0.3 cents flat, causing [[23/19]] to become inconsistent, though it remains the only inconsistency up to the [[39-odd-limit]]. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.		1395edo is a strong higher-limit system, being a [[zeta edo\|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo\|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]]. However, it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1\|23]] being all of 0.3 cents flat, causing [[23/19]] to become inconsistent, though it remains the only inconsistency up to the [[39-odd-limit]]. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.

	Some no-23 37-limit commas it tempers out are 3367/3366, 7696/7695, 9425/9424, 11781/11780, 13300/13299, 13950/13949, 16576/16575, 20350/20349, 40300/40293, 55056/55055.		Some no-23 37-limit commas it tempers out are 3367/3366, 7696/7695, 9425/9424, 11781/11780, 13300/13299, 13950/13949, 16576/16575, 20350/20349, 40300/40293, 55056/55055.

Overthink: /* Prime harmonics */ title

2026-01-17T00:23:08Z

Prime harmonics: title

← Older revision		Revision as of 00:23, 17 January 2026
Line 8:		Line 8:
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1395\|columns=11}}		{{Harmonics in equal\|1395\|columns=11}}
	{{Harmonics in equal\|1395\|columns=11\|start=12}}		{{Harmonics in equal\|1395\|columns=11\|start=12\|title=Approximation of prime harmonics in 1395edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1395 factors into {{factorization\|1395}}, 1395edo has subset edos {{EDOs\|3, 5, 9, 15, 31, 45, 93, 155, 279, and 465}}.		Since 1395 factors into {{factorization\|1395}}, 1395edo has subset edos {{EDOs\|3, 5, 9, 15, 31, 45, 93, 155, 279, and 465}}.

Overthink: /* Prime harmonics */ reformat tables

2026-01-17T00:22:32Z

Prime harmonics: reformat tables

← Older revision		Revision as of 00:22, 17 January 2026
Line 7:		Line 7:

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1395\|columns=15}}		{{Harmonics in equal\|1395\|columns=11}}
			{{Harmonics in equal\|1395\|columns=11\|start=12}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1395 factors into {{factorization\|1395}}, 1395edo has subset edos {{EDOs\|3, 5, 9, 15, 31, 45, 93, 155, 279, and 465}}.		Since 1395 factors into {{factorization\|1395}}, 1395edo has subset edos {{EDOs\|3, 5, 9, 15, 31, 45, 93, 155, 279, and 465}}.

Overthink: expand on consistency

2026-01-16T23:43:10Z

expand on consistency

← Older revision		Revision as of 23:43, 16 January 2026
Line 2:		Line 2:
	{{ED intro}}		{{ED intro}}

	1395edo is a strong higher-limit system, being a [[zeta edo\|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo\|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], ~~though~~ it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1\|23]] being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.		1395edo is a strong higher-limit system, being a [[zeta edo\|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo\|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]]. Howewver, it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1\|23]] being all of 0.3 cents flat, causing [[23/19]] to become inconsistent, though it remains the only inconsistency up to the [[39-odd-limit]]. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.

	Some no-23 37-limit commas it tempers out are 3367/3366, 7696/7695, 9425/9424, 11781/11780, 13300/13299, 13950/13949, 16576/16575, 20350/20349, 40300/40293, 55056/55055.		Some no-23 37-limit commas it tempers out are 3367/3366, 7696/7695, 9425/9424, 11781/11780, 13300/13299, 13950/13949, 16576/16575, 20350/20349, 40300/40293, 55056/55055.

ArrowHead294 at 17:01, 18 February 2025

2025-02-18T17:01:58Z

← Older revision		Revision as of 17:01, 18 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1395~~}}		{{ED intro}}

	1395edo is a strong higher-limit system, being a [[zeta edo\|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo\|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], though it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1\|23]] being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.		1395edo is a strong higher-limit system, being a [[zeta edo\|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo\|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], though it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1\|23]] being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.

Eliora at 22:46, 4 October 2024

2024-10-04T22:46:24Z

← Older revision		Revision as of 22:46, 4 October 2024
Line 3:		Line 3:

	1395edo is a strong higher-limit system, being a [[zeta edo\|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo\|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], though it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1\|23]] being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.		1395edo is a strong higher-limit system, being a [[zeta edo\|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo\|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], though it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1\|23]] being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.

			Some no-23 37-limit commas it tempers out are 3367/3366, 7696/7695, 9425/9424, 11781/11780, 13300/13299, 13950/13949, 16576/16575, 20350/20349, 40300/40293, 55056/55055.

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

Eliora: /* Subsets and supersets */

2024-10-03T20:45:52Z

Subsets and supersets

← Older revision		Revision as of 20:45, 3 October 2024
Line 8:		Line 8:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1395 factors into {{factorization\|1395}}, 1395edo has subset edos 3, 5, 9, 15, 31, 45, 93, 155, 279, and 465.		Since 1395 factors into {{factorization\|1395}}, 1395edo has subset edos {{EDOs\|3, 5, 9, 15, 31, 45, 93, 155, 279, and 465}}.

FloraC: Adopt template: Factorization; misc. cleanup

2023-10-31T09:22:19Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 09:22, 31 October 2023
Line 2:		Line 2:
	{{EDO intro\|1395}}		{{EDO intro\|1395}}

	1395edo is a strong higher-limit system, being a [[~~The Riemann~~ zeta ~~function and tuning #Zeta EDO lists~~\|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after 311 with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], though it is only [[consistent]] through the 21-odd-limit, due to 23 being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], 4914/4913, 5929/5928, 10985/10982, 12636/12635, 14875/14872}.		1395edo is a strong higher-limit system, being a [[zeta edo\|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo\|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], though it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1\|23]] being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 8:		Line 8:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1395 factors into ~~3<sup>2</sup> × 5 × 31~~, 1395edo has subset edos 3, 5, 9, 15, 31, 45, 93, 155, 279, and 465.		Since 1395 factors into {{factorization\|1395}}, 1395edo has subset edos 3, 5, 9, 15, 31, 45, 93, 155, 279, and 465.

BudjarnLambeth at 06:53, 9 July 2023

2023-07-09T06:53:18Z

← Older revision		Revision as of 06:53, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1395}}		{{EDO intro\|1395}}

BudjarnLambeth at 05:12, 9 July 2023

2023-07-09T05:12:52Z

← Older revision		Revision as of 05:12, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|1395}}		{{EDO intro\|1395}}