Map of rank-2 temperaments
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author keenanpepper and made on 2011-09-04 21:34:36 UTC.
- The original revision id was 250717844.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
This is intended to be a map of all interesting linear (rank-2) temperaments that are compatible with octave equivalence. The only linear temperaments not appearing here should be ones like [[Bohlen-Pierce]] that completely lack octaves. Please make sure each fraction of a period is always the [[mediant]] of the ones directly above and below. ==One period per octave== Since this is the largest subset, it has its own page: [[Map of period-1 temperaments]]. ==Two periods per octave== ||||||||||||||||||||||||~ Generator ||~ Cents ||~ Comments || || 0\2 || || || || || || || || || || || || 0 || || || || || || || || || || || || || 1\24 || || 50.000 || [[Shrutar]] || || || || || || || || || || || || || 2\46 || 52.174 || Shrutar || || || || || || || || || || || 1\22 || || || 54.545 || Shrutar || || || || || || || || || || 1\20 || || || || || || || || || || || || || || 1\18 || || || || || || || || || || || || || || 1\16 || || || || || || || || || || || || || || 1\14 || || || || || || || || || || || || || || || || 2\26 || || || || || || 92.308 || [[Injera]] || || || || || || || || || 3\38 || || || || || 94.737 || Injera || || || || || || 1\12 || || || || || || || || 100.000 || [[Srutal]]/[[pajara]]/injera || || || || || || || || || 4\46 || || || || || 104.348 || Srutal/pajara/[[diaschismic]] || || || || || || || || 3\34 || || || || || || 105.882 || Srutal/pajara/diaschismic || || || || || || || 2\22 || || || || || || || 109.091 || Srutal/pajara || || || || || 1\10 || || || || || || || || || || || || || || || || 2\18 || || || || || || || || 133.333 || [[Octokaidecal]] || || || || 1\8 || || || || || || || || || || || || || || || || || || 4\30 || || || || || || || || || || || || || || 3\22 || || || || || || || || 163.636 || [[Hedgehog]]/[[echidna]] || || || || || || || || 8\58 || || || || || || 165.517 || Hedgehog/echidna || || || || || || || 5\36 || || || || || || || 166.667 || Hedgehog/echidna || || || || || 2\14 || || || || || || || || || || || || || 1\6 || || || || || || || || || || || || || || || || || || || 5\28 || || || || || || || || || || || || || || || || 9\50 || || || || || || || || || || || || || || || || 13\72 || || || || || 216.667 || [[Antikythera]]/[[astrology]]/[[wizard]] || || || || || || 4\22 || || || || || || || || 218.182 || Antikythera/astrology || || || || || 3\16 || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || 5\26 || || || || || || || || 230.769 || [[Lemba]] || || || || || || || 7\36 || || || || || || || 233.333 || Lemba || || || || || || || || 9\46 || || || || || || 234.783 || || || || || 2\10 || || || || || || || || || || 240.000 || [[Decimal]] || || || || || || || 7\34 || || || || || || || 247.059 || Decimal || || || || || || 5\24 || || || || || || || || 250.000 || Decimal || || || || || 3\14 || || || || || || || || || || || || || || || || 4\18 || || || || || || || || || || || || || || || || 5\22 || || || || || || || 272.727 || [[Doublewide]] || || || || || || || || || 11\48 || || || || || 275.000 || Doublewide || || || || || || || || 6\26 || || || || || || 276.923 || Doublewide || || 1\4 || || || || || || || || || || || || || || ==Three periods per octave== ==Four periods per octave== ==Five periods per octave== ==More than five periods per octave==
Original HTML content:
<html><head><title>Map of rank-2 temperaments</title></head><body>This is intended to be a map of all interesting linear (rank-2) temperaments that are compatible with octave equivalence. The only linear temperaments not appearing here should be ones like <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> that completely lack octaves.<br />
Please make sure each fraction of a period is always the <a class="wiki_link" href="/mediant">mediant</a> of the ones directly above and below.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-One period per octave"></a><!-- ws:end:WikiTextHeadingRule:0 -->One period per octave</h2>
Since this is the largest subset, it has its own page: <a class="wiki_link" href="/Map%20of%20period-1%20temperaments">Map of period-1 temperaments</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-Two periods per octave"></a><!-- ws:end:WikiTextHeadingRule:2 -->Two periods per octave</h2>
<table class="wiki_table">
<tr>
<th colspan="12">Generator<br />
</th>
<th>Cents<br />
</th>
<th>Comments<br />
</th>
</tr>
<tr>
<td>0\2<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>0<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1\24<br />
</td>
<td><br />
</td>
<td>50.000<br />
</td>
<td><a class="wiki_link" href="/Shrutar">Shrutar</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>2\46<br />
</td>
<td>52.174<br />
</td>
<td>Shrutar<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1\22<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>54.545<br />
</td>
<td>Shrutar<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1\20<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1\18<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1\16<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1\14<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>2\26<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>92.308<br />
</td>
<td><a class="wiki_link" href="/Injera">Injera</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>3\38<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>94.737<br />
</td>
<td>Injera<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1\12<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>100.000<br />
</td>
<td><a class="wiki_link" href="/Srutal">Srutal</a>/<a class="wiki_link" href="/pajara">pajara</a>/injera<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>4\46<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>104.348<br />
</td>
<td>Srutal/pajara/<a class="wiki_link" href="/diaschismic">diaschismic</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>3\34<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>105.882<br />
</td>
<td>Srutal/pajara/diaschismic<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>2\22<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>109.091<br />
</td>
<td>Srutal/pajara<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1\10<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>2\18<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>133.333<br />
</td>
<td><a class="wiki_link" href="/Octokaidecal">Octokaidecal</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>1\8<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>4\30<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>3\22<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>163.636<br />
</td>
<td><a class="wiki_link" href="/Hedgehog">Hedgehog</a>/<a class="wiki_link" href="/echidna">echidna</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>8\58<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>165.517<br />
</td>
<td>Hedgehog/echidna<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\36<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>166.667<br />
</td>
<td>Hedgehog/echidna<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>2\14<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>1\6<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\28<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>9\50<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>13\72<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>216.667<br />
</td>
<td><a class="wiki_link" href="/Antikythera">Antikythera</a>/<a class="wiki_link" href="/astrology">astrology</a>/<a class="wiki_link" href="/wizard">wizard</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>4\22<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>218.182<br />
</td>
<td>Antikythera/astrology<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>3\16<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\26<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>230.769<br />
</td>
<td><a class="wiki_link" href="/Lemba">Lemba</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>7\36<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>233.333<br />
</td>
<td>Lemba<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>9\46<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>234.783<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>2\10<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>240.000<br />
</td>
<td><a class="wiki_link" href="/Decimal">Decimal</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>7\34<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>247.059<br />
</td>
<td>Decimal<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\24<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>250.000<br />
</td>
<td>Decimal<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>3\14<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>4\18<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\22<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>272.727<br />
</td>
<td><a class="wiki_link" href="/Doublewide">Doublewide</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>11\48<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>275.000<br />
</td>
<td>Doublewide<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>6\26<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>276.923<br />
</td>
<td>Doublewide<br />
</td>
</tr>
<tr>
<td>1\4<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x-Three periods per octave"></a><!-- ws:end:WikiTextHeadingRule:4 -->Three periods per octave</h2>
<!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x-Four periods per octave"></a><!-- ws:end:WikiTextHeadingRule:6 -->Four periods per octave</h2>
<!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="x-Five periods per octave"></a><!-- ws:end:WikiTextHeadingRule:8 -->Five periods per octave</h2>
<!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x-More than five periods per octave"></a><!-- ws:end:WikiTextHeadingRule:10 -->More than five periods per octave</h2>
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