1506edo - Revision history

ArrowHead294 at 17:07, 18 February 2025

2025-02-18T17:07:00Z

← Older revision		Revision as of 17:07, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1506~~}}		{{ED intro}}

	1506edo is a very strong 13- and 17-limit system, since it is the first past [[494edo\|494]] with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is [[consistency\|distinctly consistent]] through the [[17-odd-limit]]. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13-limit [[comma]]s is {[[4096/4095]], [[6656/6655]], [[9801/9800]], 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, [[4914/4913]], [[5832/5831]], 6656/6655, 9801/9800, [[28561/28560]], 105644/105625}.		1506edo is a very strong 13- and 17-limit system, since it is the first past [[494edo\|494]] with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is [[consistency\|distinctly consistent]] through the [[17-odd-limit]]. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13-limit [[comma]]s is {[[4096/4095]], [[6656/6655]], [[9801/9800]], 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, [[4914/4913]], [[5832/5831]], 6656/6655, 9801/9800, [[28561/28560]], 105644/105625}.

FloraC: Adopt template: Factorization; misc. cleanup

2023-10-31T09:06:24Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 09:06, 31 October 2023
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	{{EDO intro\|1506}}		{{EDO intro\|1506}}

	1506edo is a very strong 13- and 17-limit system, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is ~~distinctly~~ [[consistent]] through the 17-odd-limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit ~~commas~~ is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.		1506edo is a very strong 13- and 17-limit system, since it is the first past [[494edo\|494]] with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is [[consistency\|distinctly consistent]] through the [[17-odd-limit]]. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13-limit [[comma]]s is {[[4096/4095]], [[6656/6655]], [[9801/9800]], 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, [[4914/4913]], [[5832/5831]], 6656/6655, 9801/9800, [[28561/28560]], 105644/105625}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1506\|columns=11}}		{{Harmonics in equal\|1506\|columns=11}}

	=== ~~Divisors~~ ===		=== Subsets and supersets ===
	Since 1506 factors into ~~2 × 3 × 251~~, 1506edo has subset edos 2, 3, 6, 251, 502, and 753.		Since 1506 factors into {{factorization\|1506}}, 1506edo has subset edos 2, 3, 6, 251, 502, and 753.

BudjarnLambeth at 06:54, 9 July 2023

2023-07-09T06:54:21Z

← Older revision		Revision as of 06:54, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1506}}		{{EDO intro\|1506}}

BudjarnLambeth at 05:08, 9 July 2023

2023-07-09T05:08:11Z

← Older revision		Revision as of 05:08, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|1506}}		{{EDO intro\|1506}}

FloraC: Improve intro and +divisors

2023-01-08T04:24:57Z

Improve intro and +divisors

← Older revision		Revision as of 04:24, 8 January 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The~~ 1506 ~~division divides the octave into 1506 parts of 0.7968 [[cent]]s each. It~~ is a very strong 13- and 17-limit system, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly [[consistent]] through the 17-odd-limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.		{{EDO intro\|1506}}

			1506edo is a very strong 13- and 17-limit system, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly [[consistent]] through the 17-odd-limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1506\|columns=11}}		{{Harmonics in equal\|1506\|columns=11}}

	~~[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->~~		=== Divisors ===
			Since 1506 factors into 2 × 3 × 251, 1506edo has subset edos 2, 3, 6, 251, 502, and 753.

FloraC: +prime error table

2022-10-29T09:20:48Z

+prime error table

← Older revision		Revision as of 09:20, 29 October 2022
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	{{Infobox ET}}		{{Infobox ET}}
	The 1506 division divides the octave into 1506 parts of 0.7968 ~~cents~~ each. It is a very strong 13 and 17 limit ~~division~~, since it is the first past 494 with a lower 13-limit [[Tenney-~~Euclidean_temperament_measures~~#TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17 limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.		The 1506 division divides the octave into 1506 parts of 0.7968 [[cent]]s each. It is a very strong 13- and 17-limit system, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly [[consistent]] through the 17-odd-limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.

			=== Prime harmonics ===
			{{Harmonics in equal\|1506\|columns=11}}

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

Plumtree: Infobox ET added

2022-10-04T22:10:21Z

Infobox ET added

← Older revision		Revision as of 22:10, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	The 1506 division divides the octave into 1506 parts of 0.7968 cents each. It is a very strong 13 and 17 limit division, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17 limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.		The 1506 division divides the octave into 1506 parts of 0.7968 cents each. It is a very strong 13 and 17 limit division, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17 limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.

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

Fredg999 category edits: Categories

2022-07-04T01:16:40Z

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
Line 1:		Line 1:
	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		The 1506 division divides the octave into 1506 parts of 0.7968 cents each. It is a very strong 13 and 17 limit division, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17 limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2015-08-15 17:44:53 UTC</tt>.<br>~~
	~~: The original revision id was <tt>556740489</tt>.<br>~~
	~~: The revision comment was: <tt></tt><br>~~
	~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~
	~~<h4>Original Wikitext content:</h4>~~
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The 1506 division divides the octave into 1506 parts of 0.7968 cents each. It is a very strong 13 and 17 limit division, since it is the first past 494 with a lower 13-limit [[Tenney-~~Euclidean temperament measures~~#TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17 limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.~~</pre></div>~~
	~~<h4>Original HTML content:</h4>~~
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>1506edo</title></head><body>The 1506 division divides the octave into 1506 parts of 0.7968 cents each. It is a very strong 13 and 17 limit division, since it is the first past 494 with a lower 13-limit <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a>, and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17 limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.</body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 556740489 - Original comment:

2015-08-15T17:44:53Z

**Imported revision 556740489 - Original comment: **

New page

<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-08-15 17:44:53 UTC</tt>.<br>
: The original revision id was <tt>556740489</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The 1506 division divides the octave into 1506 parts of 0.7968 cents each. It is a very strong 13 and 17 limit division, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17 limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>1506edo</title></head><body>The 1506 division divides the octave into 1506 parts of 0.7968 cents each. It is a very strong 13 and 17 limit division, since it is the first past 494 with a lower 13-limit <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a>, and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17 limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.</body></html></pre></div>

← Older revision		Revision as of 01:16, 4 July 2022
Line 1:		Line 1:
	The 1506 division divides the octave into 1506 parts of 0.7968 cents each. It is a very strong 13 and 17 limit division, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17 limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.		The 1506 division divides the octave into 1506 parts of 0.7968 cents each. It is a very strong 13 and 17 limit division, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17 limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.

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