Lists of edo-distinct temperaments - Revision history

Fredg999: Heading levels, misc. edits

2023-04-14T02:21:39Z

Heading levels, misc. edits

← Older revision		Revision as of 02:21, 14 April 2023
Line 1:		Line 1:
	For any [[~~Equal\|~~equal]] ~~temperament~~, there are technically an unlimited number of different [[~~Abstract_regular_temperament\|~~abstract regular temperaments]] that it "[[support]]s" in the sense of tempering out all the same commas, thus allowing music in the non-equal temperament to be faithfully and mechanically played in the equal temperament.		For any [[equal temperament]], there are technically an unlimited number of different [[abstract regular temperaments]] that it "[[support]]s" in the sense of tempering out all the same commas, thus allowing music in the non-equal temperament to be faithfully and mechanically played in the equal temperament.

	However, some of these non-equal regular temperaments become exactly the same as each other when tuned to the equal temperament. For example, in [[~~12edo\|~~12edo]], [[~~pajara\|~~pajara]] and [[~~Injera\|~~injera]] become the same, even though in anything other than 12 they are distinct temperaments.		However, some of these non-equal regular temperaments become exactly the same as each other when tuned to the equal temperament. For example, in [[12edo]], [[pajara]] and [[injera]] become the same, even though in anything other than 12 they are distinct temperaments.

	Two temperaments are called "edo-distinct" if they remain distinct even when tuned to the same equal temperament. For rank-2, it turns out that the number of edo-distinct rank-2 temperaments in N-edo is floor(N/2); that is, N/2 if N is even and (N-1)/2 if N is odd.		Two temperaments are called '''edo-distinct''' if they remain distinct even when tuned to the same equal temperament. For rank-2, it turns out that the number of edo-distinct rank-2 temperaments in N-edo is floor(N/2); that is, N/2 if N is even and (N-1)/2 if N is odd.

	~~=Rank-2 lists=~~

			== Rank-2 lists ==
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
Line 67:		Line 66:
	\|}		\|}

	==No fives==		=== No-fives ===

	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-

Fredg999: Categories

2023-04-14T02:18:10Z

BudjarnLambeth: Added to category “lists”

2023-04-14T01:53:29Z

Added to category “lists”

← Older revision		Revision as of 01:53, 14 April 2023
Line 74:		Line 74:
	\| \|		\| \|
	\|}		\|}
			[[Category:Lists]]

Cmloegcmluin: link to new page for Supports

2022-01-25T18:37:07Z

link to new page for Supports

← Older revision		Revision as of 18:37, 25 January 2022
Line 1:		Line 1:
	For any [[Equal\|equal]] temperament, there are technically an unlimited number of different [[Abstract_regular_temperament\|abstract regular temperaments]] that it "~~supports~~" in the sense of tempering out all the same commas, thus allowing music in the non-equal temperament to be faithfully and mechanically played in the equal temperament.		For any [[Equal\|equal]] temperament, there are technically an unlimited number of different [[Abstract_regular_temperament\|abstract regular temperaments]] that it "[[support]]s" in the sense of tempering out all the same commas, thus allowing music in the non-equal temperament to be faithfully and mechanically played in the equal temperament.

	However, some of these non-equal regular temperaments become exactly the same as each other when tuned to the equal temperament. For example, in [[12edo\|12edo]], [[pajara\|pajara]] and [[Injera\|injera]] become the same, even though in anything other than 12 they are distinct temperaments.		However, some of these non-equal regular temperaments become exactly the same as each other when tuned to the equal temperament. For example, in [[12edo\|12edo]], [[pajara\|pajara]] and [[Injera\|injera]] become the same, even though in anything other than 12 they are distinct temperaments.

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>genewardsmith: Imported revision 514265010 - Original comment:

2014-06-17T21:22:25Z

**Imported revision 514265010 - Original comment: **

← Older revision		Revision as of 21:22, 17 June 2014
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		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>2014-06-17 21:21:54 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2014-06-17 21:22:25 UTC</tt>.<br>
	: The original revision id was <tt>~~514264974~~</tt>.<br>		: The original revision id was <tt>514265010</tt>.<br>
	: The revision comment was: <tt></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>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 30:		Line 30:
	\|\| [[List of edo-distinct 50et rank two temperaments\|50]] \|\| \|\|		\|\| [[List of edo-distinct 50et rank two temperaments\|50]] \|\| \|\|
	\|\| [[List of edo-distinct 53et rank two temperaments\|53]] \|\| \|\|		\|\| [[List of edo-distinct 53et rank two temperaments\|53]] \|\| \|\|
	\|\| [[List of edo-distinct 58et rank two temperaments\|53]] \|\| \|\|		\|\| [[List of edo-distinct 58et rank two temperaments\|58]] \|\| \|\|
	\|\| [[List of edo-distinct 72et rank two temperaments\|72]] \|\| \|\|		\|\| [[List of edo-distinct 72et rank two temperaments\|72]] \|\| \|\|

Line 149:		Line 149:
	</tr>		</tr>
	<tr>		<tr>
	<td><a class="wiki_link" href="/List%20of%20edo-distinct%2058et%20rank%20two%20temperaments">53</a><br />		<td><a class="wiki_link" href="/List%20of%20edo-distinct%2058et%20rank%20two%20temperaments">58</a><br />
	</td>		</td>
	<td><br />		<td><br />

Wikispaces>genewardsmith: Imported revision 514264974 - Original comment:

2014-06-17T21:21:54Z

**Imported revision 514264974 - Original comment: **

← Older revision		Revision as of 21:21, 17 June 2014
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		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>2014-02-~~20 11~~:36:31 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2014-06-17 21:21:54 UTC</tt>.<br>
	: The original revision id was <tt>~~490768698~~</tt>.<br>		: The original revision id was <tt>514264974</tt>.<br>
	: The revision comment was: <tt></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>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 30:		Line 30:
	\|\| [[List of edo-distinct 50et rank two temperaments\|50]] \|\| \|\|		\|\| [[List of edo-distinct 50et rank two temperaments\|50]] \|\| \|\|
	\|\| [[List of edo-distinct 53et rank two temperaments\|53]] \|\| \|\|		\|\| [[List of edo-distinct 53et rank two temperaments\|53]] \|\| \|\|
			\|\| [[List of edo-distinct 58et rank two temperaments\|53]] \|\| \|\|
	\|\| [[List of edo-distinct 72et rank two temperaments\|72]] \|\| \|\|		\|\| [[List of edo-distinct 72et rank two temperaments\|72]] \|\| \|\|

Line 143:		Line 144:
	<tr>		<tr>
	<td><a class="wiki_link" href="/List%20of%20edo-distinct%2053et%20rank%20two%20temperaments">53</a><br />		<td><a class="wiki_link" href="/List%20of%20edo-distinct%2053et%20rank%20two%20temperaments">53</a><br />
			</td>
			<td><br />
			</td>
			</tr>
			<tr>
			<td><a class="wiki_link" href="/List%20of%20edo-distinct%2058et%20rank%20two%20temperaments">53</a><br />
	</td>		</td>
	<td><br />		<td><br />

Wikispaces>genewardsmith: Imported revision 490768698 - Original comment:

2014-02-20T11:36:31Z

**Imported revision 490768698 - Original comment: **

← Older revision		Revision as of 11:36, 20 February 2014
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		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>2014-02-11 16:30:42 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2014-02-20 11:36:31 UTC</tt>.<br>
	: The original revision id was <tt>~~488860848~~</tt>.<br>		: The original revision id was <tt>490768698</tt>.<br>
	: The revision comment was: <tt></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>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 30:		Line 30:
	\|\| [[List of edo-distinct 50et rank two temperaments\|50]] \|\| \|\|		\|\| [[List of edo-distinct 50et rank two temperaments\|50]] \|\| \|\|
	\|\| [[List of edo-distinct 53et rank two temperaments\|53]] \|\| \|\|		\|\| [[List of edo-distinct 53et rank two temperaments\|53]] \|\| \|\|
	\|\| [[List of edo-distinct 72et rank two temperaments\|72]] \|\| \|\|</pre></div>		\|\| [[List of edo-distinct 72et rank two temperaments\|72]] \|\| \|\|

			==No fives==
			\|\| [[List of edo-distinct 17et no-fives rank two temperaments\|17]] \|\| \|\|</pre></div>
	<h4>Original HTML content:</h4>		<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>Lists of edo-distinct temperaments</title></head><body>For any <a class="wiki_link" href="/equal">equal</a> temperament, there are technically an unlimited number of different <a class="wiki_link" href="/abstract%20regular%20temperament">abstract regular temperaments</a> that it &quot;supports&quot; in the sense of tempering out all the same commas, thus allowing music in the non-equal temperament to be faithfully and mechanically played in the equal temperament.<br />		<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>Lists of edo-distinct temperaments</title></head><body>For any <a class="wiki_link" href="/equal">equal</a> temperament, there are technically an unlimited number of different <a class="wiki_link" href="/abstract%20regular%20temperament">abstract regular temperaments</a> that it &quot;supports&quot; in the sense of tempering out all the same commas, thus allowing music in the non-equal temperament to be faithfully and mechanically played in the equal temperament.<br />
Line 146:		Line 149:
	<tr>		<tr>
	<td><a class="wiki_link" href="/List%20of%20edo-distinct%2072et%20rank%20two%20temperaments">72</a><br />		<td><a class="wiki_link" href="/List%20of%20edo-distinct%2072et%20rank%20two%20temperaments">72</a><br />
			</td>
			<td><br />
			</td>
			</tr>
			</table>

			<br />
			<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Rank-2 lists-No fives"></a><!-- ws:end:WikiTextHeadingRule:2 -->No fives</h2>


			<table class="wiki_table">
			<tr>
			<td><a class="wiki_link" href="/List%20of%20edo-distinct%2017et%20no-fives%20rank%20two%20temperaments">17</a><br />
	</td>		</td>
	<td><br />		<td><br />

Wikispaces>genewardsmith: Imported revision 488860848 - Original comment:

2014-02-11T16:30:42Z

**Imported revision 488860848 - Original comment: **

← Older revision		Revision as of 16:30, 11 February 2014
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		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>2014-02-~~09 12~~:33:58 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2014-02-11 16:30:42 UTC</tt>.<br>
	: The original revision id was <tt>~~488278318~~</tt>.<br>		: The original revision id was <tt>488860848</tt>.<br>
	: The revision comment was: <tt></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>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 29:		Line 29:
	\|\| [[List of edo-distinct 46et rank two temperaments\|46]] \|\| \|\|		\|\| [[List of edo-distinct 46et rank two temperaments\|46]] \|\| \|\|
	\|\| [[List of edo-distinct 50et rank two temperaments\|50]] \|\| \|\|		\|\| [[List of edo-distinct 50et rank two temperaments\|50]] \|\| \|\|
	\|\| [[List of edo-distinct 53et rank two temperaments\|53]] \|\| \|\|</pre></div>		\|\| [[List of edo-distinct 53et rank two temperaments\|53]] \|\| \|\|
			\|\| [[List of edo-distinct 72et rank two temperaments\|72]] \|\| \|\|</pre></div>
	<h4>Original HTML content:</h4>		<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>Lists of edo-distinct temperaments</title></head><body>For any <a class="wiki_link" href="/equal">equal</a> temperament, there are technically an unlimited number of different <a class="wiki_link" href="/abstract%20regular%20temperament">abstract regular temperaments</a> that it &quot;supports&quot; in the sense of tempering out all the same commas, thus allowing music in the non-equal temperament to be faithfully and mechanically played in the equal temperament.<br />		<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>Lists of edo-distinct temperaments</title></head><body>For any <a class="wiki_link" href="/equal">equal</a> temperament, there are technically an unlimited number of different <a class="wiki_link" href="/abstract%20regular%20temperament">abstract regular temperaments</a> that it &quot;supports&quot; in the sense of tempering out all the same commas, thus allowing music in the non-equal temperament to be faithfully and mechanically played in the equal temperament.<br />
Line 139:		Line 140:
	<tr>		<tr>
	<td><a class="wiki_link" href="/List%20of%20edo-distinct%2053et%20rank%20two%20temperaments">53</a><br />		<td><a class="wiki_link" href="/List%20of%20edo-distinct%2053et%20rank%20two%20temperaments">53</a><br />
			</td>
			<td><br />
			</td>
			</tr>
			<tr>
			<td><a class="wiki_link" href="/List%20of%20edo-distinct%2072et%20rank%20two%20temperaments">72</a><br />
	</td>		</td>
	<td><br />		<td><br />

Wikispaces>genewardsmith: Imported revision 488278318 - Original comment:

2014-02-09T12:33:58Z

**Imported revision 488278318 - Original comment: **