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 Kosmorsky and made on 2012-04-10 14:07:11 UTC.
- The original revision id was 319165762.
- 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 an octave 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 || || || || || || || || || || || || || || || || 2\34 || || || || 70.588 || [[Vishnu]] || || || || || || || || || || || || || 7\118 || 71.186 || [[Vishnu]] || || || || || || || || || || || || 5\84 || || || || || || || || || || || || || || 3\50 || || || || || || || || || || || || 1\16 || || || || || || || || || || || || || || || || 2\30 || || || || || || || || || || || || || || || || 3\44 || || || || || || || || || || || || || || || || 4\58 || || || 82.759 || [[Harry]] || || || || || || || || || || || || 5\72 || || 83.333 || Harry || || || || || || || 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]] || || || || || || || 3\26 || || || || || || || 138.462 || || || || || || || || || 4\34 || || || || || || 141.176 || [[Fifive]] || || || || 1\8 || || || || || || || || || || || || || || || || || || 4\30 || || || || || || || || || || || || || || 3\22 || || || || || || || || 163.636 || [[Hedgehog]]/[[echidna]] || || || || || || || || 8\58 || || || || || || 165.517 || Hedgehog/echidna || || || || || || || 5\36 || || || || || || || 166.667 || Hedgehog/echidna || || || || || 2\14 || || || || || || || || || || || || || || || || 3\20 || || || || || || || || || || || || || || || || || 7\46 || || || || || || 182.609 || [[Unidec]]/[[hendec]] || || || || || || || || || 11\72 || || || || || 183.333 || Unidec/hendec || || || || || || || 4\26 || || || || || || || || || || || 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 || [[Echidnic]] || || || || 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== ||||||||||||||||||~ Generator ||~ Cents ||~ Comments || || 0\3 || || || || || || || || || || || || || || || || || || || 1\27 || || 44.444 || [[Semiaug]] || || || || || || || || || || 2\51 || 47.059 || Semiaug || || || || || || || || 1\24 || || || 50.000 || Semiaug || || || || || || || 1\21 || || || || || || || || || || || 1\18 || || || || || || || || || || || 1\15 || || || || || || || || || || || || || || || || || 6\87 || 82.759 || [[Tritikleismic]] || || || || || || || || || 5\72 || || 83.333 || Tritikleismic || || || || || || || || 4\57 || || || || || || || || || || || 3\42 || || || || || || || || || || || 2\27 || || || || || 88.889 || [[Augmented]]/[[augene]] || || || || 1\12 || || || || || || || 100.000 || Augmented/augene/[[august]] || || || || || || 3\33 || || || || || 109.091 || Augmented/august || || || || || 2\21 || || || || || || || || || || 1\9 || || || || || || || || || || || || || || 3\24 || || || || || || 150.0 || [[Triforce]] || || || || 2\15 || || || || || || || || || || 1\6 || || || || || || || || || || || ==Four periods per octave== ||||||||||||||||||||||||||||||||||||~ Generator ||~ Cents ||~ Comments || || 0\4 || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || 1\72 || || || [[Quadritikleismic]] || || || || || || || || || || || || || || || || || || || 2\140 || || || || || || || || || || || || || || || || || || || 1\68 || || || || || || || || || || || || || || || || || || || || 1\64 || || || || || || || || || || || || || || || || || || || || 1\60 || || || || || || || || || || || || || || || || || || || || 1\56 || || || || || || || || || || || || || || || || || || || || 1\52 || || || || || || || || || || || || || || || || || || || || 1\48 || || || || || || || || || || || || || || || || || || || || 1\44 || || || || || || || || || || || || || || || || || || || || 1\40 || || || || || || || || || || || || || || || || || || || || 1\36 || || || || || || || || || || || || || || || || || || || || 1\32 || || || || || || || || || || || || || || || || || || || || 1\28 || || || || || || || || || || || || || || || || || || || || 1\24 || || || || || || || || || || || || || || || || || || || || 1\20 || || || || || || || || || || || || || || || || || || || || 1\16 || || || || || || || || || || || || || || || || || [[Diminished]] || || || 1\12 || || || || || || || || || || || || || || || || || || Diminished || || || || || || || || 6\68 || || || || || || || || || || || || || [[Bidia]] || || || || || || || 5\56 || || || || || || || || || || || || || || || || || || || || 4\44 || || || || || || || || || || || || || || || || || || || || 3\32 || || || || || || || || || || || || || || || || || || || || 2\20 || || || || || || || || || || || || || || || || || || || 1\8 || || || || || || || || || || || || || || || || || || || || ==Five periods per octave== * [[Blackwood]]/[[blacksmith]] - The prime 3, and in blacksmith also 7, is represented using [[5edo]]. The generator gets you to all intervals of 5. * Elderthing - generator of phi. Two generators up to 3, two down to 7, other intervals are more complex. One generator up and one down are ambiguous 13. ==Six periods per octave== * [[Hexe]] - The 2.5.7 subgroup is represented using [[6edo]], and the generator gets you to 4/3 and 3/2. Makes little sense not to additionally temper down to [[12edo]]. ==Seven periods per octave== * [[Whitewood]] - Analogue of blackwood. The prime 3 is represented using 7edo, the generator is used for 5. * [[Jamesbond]]/[[septimal]] - The 5-limit (and in septimal the prime 11) is represented using [[7edo]], and the generator is only used for intervals of 7. * [[Sevond]] - 10/9 is tempered to be exactly 1\7 of an octave. Therefore 3/2 is 1 generator sharp of a 7edo step and 5/4 is 2 generators sharp. * [[Absurdity]] - A complex temperament (perhaps "absurdly" so). ==Eight periods per octave== * [[Octoid]] - 16-cent generator, sub-cent accuracy. ==Nine periods per octave== * [[Ennealimmal]] - The generator is 49.02 cents, and don't forget the ".02" because it really is that accurate. ==Twelve periods per octave== See also: [[Pythagorean family]] Temperaments in this family are interesting because they can be thought of as [[12edo]] with microtonal alterations. * [[Compton]] - 3-limit as in 12edo; intervals of 5 are off by one generator. In the 7-limit (sometimes called [[waage]]), intervals of 7 are off by two generators. In the 11-limit, intervals of 11 are off by 3 generators. Thinking of [[72edo]] might make this more concrete. * [[Catler]] - 5-limit as in 12edo; intervals of 7 are off by one generator. * [[Atomic]] - Does not temper out the Pythagorean comma, so 3/2 is actually one generator sharp of its 12edo value. Extremely accurate.
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 an octave 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><br />
</td>
<td><br />
</td>
<td>2\34<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>70.588<br />
</td>
<td><a class="wiki_link" href="/Vishnu">Vishnu</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>7\118<br />
</td>
<td>71.186<br />
</td>
<td><a class="wiki_link" href="/Vishnu">Vishnu</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>5\84<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>3\50<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><br />
</td>
<td><br />
</td>
<td>2\30<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>
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</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>3\44<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>4\58<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>82.759<br />
</td>
<td><a class="wiki_link" href="/Harry">Harry</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>5\72<br />
</td>
<td><br />
</td>
<td>83.333<br />
</td>
<td>Harry<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><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>3\26<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>138.462<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>4\34<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>141.176<br />
</td>
<td><a class="wiki_link" href="/Fifive">Fifive</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><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>3\20<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>7\46<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>182.609<br />
</td>
<td><a class="wiki_link" href="/Unidec">Unidec</a>/<a class="wiki_link" href="/hendec">hendec</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\72<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>183.333<br />
</td>
<td>Unidec/hendec<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>4\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><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><a class="wiki_link" href="/Echidnic">Echidnic</a><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>
<table class="wiki_table">
<tr>
<th colspan="9">Generator<br />
</th>
<th>Cents<br />
</th>
<th>Comments<br />
</th>
</tr>
<tr>
<td>0\3<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>1\27<br />
</td>
<td><br />
</td>
<td>44.444<br />
</td>
<td><a class="wiki_link" href="/Semiaug">Semiaug</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>2\51<br />
</td>
<td>47.059<br />
</td>
<td>Semiaug<br />
</td>
</tr>
<tr>
<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><br />
</td>
<td>50.000<br />
</td>
<td>Semiaug<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1\21<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>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>1\15<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>6\87<br />
</td>
<td>82.759<br />
</td>
<td><a class="wiki_link" href="/Tritikleismic">Tritikleismic</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>5\72<br />
</td>
<td><br />
</td>
<td>83.333<br />
</td>
<td>Tritikleismic<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>4\57<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>3\42<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\27<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>88.889<br />
</td>
<td><a class="wiki_link" href="/Augmented">Augmented</a>/<a class="wiki_link" href="/augene">augene</a><br />
</td>
</tr>
<tr>
<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>100.000<br />
</td>
<td>Augmented/augene/<a class="wiki_link" href="/august">august</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>3\33<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>109.091<br />
</td>
<td>Augmented/august<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>2\21<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\9<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>3\24<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>150.0<br />
</td>
<td><a class="wiki_link" href="/Triforce">Triforce</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>2\15<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>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>
</tr>
</table>
<!-- 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>
<table class="wiki_table">
<tr>
<th colspan="18">Generator<br />
</th>
<th>Cents<br />
</th>
<th>Comments<br />
</th>
</tr>
<tr>
<td>0\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>
<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>
<td><br />
</td>
<td><br />
</td>
<td>1\72<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/Quadritikleismic">Quadritikleismic</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><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>2\140<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>
<td><br />
</td>
<td>1\68<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>
<td>1\64<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>1\60<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>1\56<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>1\52<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>1\48<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>1\44<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>1\40<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><br />
</td>
<td><br />
</td>
<td>1\36<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><br />
</td>
<td>1\32<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><br />
</td>
<td>1\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>
<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>1\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><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>1\20<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>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<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>
<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><a class="wiki_link" href="/Diminished">Diminished</a><br />
</td>
</tr>
<tr>
<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><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>Diminished<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>6\68<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><a class="wiki_link" href="/Bidia">Bidia</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\56<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>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>4\44<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>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>3\32<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>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>2\20<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>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<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>
<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:8:<h2> --><h2 id="toc4"><a name="x-Five periods per octave"></a><!-- ws:end:WikiTextHeadingRule:8 -->Five periods per octave</h2>
<ul><li><a class="wiki_link" href="/Blackwood">Blackwood</a>/<a class="wiki_link" href="/blacksmith">blacksmith</a> - The prime 3, and in blacksmith also 7, is represented using <a class="wiki_link" href="/5edo">5edo</a>. The generator gets you to all intervals of 5.</li><li>Elderthing - generator of phi. Two generators up to 3, two down to 7, other intervals are more complex. One generator up and one down are ambiguous 13.</li></ul><!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x-Six periods per octave"></a><!-- ws:end:WikiTextHeadingRule:10 -->Six periods per octave</h2>
<ul><li><a class="wiki_link" href="/Hexe">Hexe</a> - The 2.5.7 subgroup is represented using <a class="wiki_link" href="/6edo">6edo</a>, and the generator gets you to 4/3 and 3/2. Makes little sense not to additionally temper down to <a class="wiki_link" href="/12edo">12edo</a>.</li></ul><!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="x-Seven periods per octave"></a><!-- ws:end:WikiTextHeadingRule:12 -->Seven periods per octave</h2>
<ul><li><a class="wiki_link" href="/Whitewood">Whitewood</a> - Analogue of blackwood. The prime 3 is represented using 7edo, the generator is used for 5.</li><li><a class="wiki_link" href="/Jamesbond">Jamesbond</a>/<a class="wiki_link" href="/septimal">septimal</a> - The 5-limit (and in septimal the prime 11) is represented using <a class="wiki_link" href="/7edo">7edo</a>, and the generator is only used for intervals of 7.</li><li><a class="wiki_link" href="/Sevond">Sevond</a> - 10/9 is tempered to be exactly 1\7 of an octave. Therefore 3/2 is 1 generator sharp of a 7edo step and 5/4 is 2 generators sharp.</li><li><a class="wiki_link" href="/Absurdity">Absurdity</a> - A complex temperament (perhaps "absurdly" so).</li></ul><!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="x-Eight periods per octave"></a><!-- ws:end:WikiTextHeadingRule:14 -->Eight periods per octave</h2>
<ul><li><a class="wiki_link" href="/Octoid">Octoid</a> - 16-cent generator, sub-cent accuracy.</li></ul><!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="x-Nine periods per octave"></a><!-- ws:end:WikiTextHeadingRule:16 -->Nine periods per octave</h2>
<ul><li><a class="wiki_link" href="/Ennealimmal">Ennealimmal</a> - The generator is 49.02 cents, and don't forget the ".02" because it really is that accurate.</li></ul><!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="x-Twelve periods per octave"></a><!-- ws:end:WikiTextHeadingRule:18 -->Twelve periods per octave</h2>
See also: <a class="wiki_link" href="/Pythagorean%20family">Pythagorean family</a><br />
Temperaments in this family are interesting because they can be thought of as <a class="wiki_link" href="/12edo">12edo</a> with microtonal alterations.<br />
<ul><li><a class="wiki_link" href="/Compton">Compton</a> - 3-limit as in 12edo; intervals of 5 are off by one generator. In the 7-limit (sometimes called <a class="wiki_link" href="/waage">waage</a>), intervals of 7 are off by two generators. In the 11-limit, intervals of 11 are off by 3 generators. Thinking of <a class="wiki_link" href="/72edo">72edo</a> might make this more concrete.</li><li><a class="wiki_link" href="/Catler">Catler</a> - 5-limit as in 12edo; intervals of 7 are off by one generator.</li><li><a class="wiki_link" href="/Atomic">Atomic</a> - Does not temper out the Pythagorean comma, so 3/2 is actually one generator sharp of its 12edo value. Extremely accurate.</li></ul></body></html>