Consonant class scale

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A **consonant class scale** is a scale with a **consonant interval class**, that is, a number n such that all n-step intervals of the scale are "consonances" (of a certain odd limit).

The models for such scales are meantone[5] (in which the 2-step intervals are 5/4 and 4/3), and even better known, meantone[7] (in which the 2-step intervals are 6/5 and 5/4). Harmonizing a diatonic melody by parallel thirds is a commonly used formula that reliably produces beautiful harmony. Consonant class scales are an attempt to generalize this property of the diatonic scale.

==Rank-2 consonant class scales== 
===3-limit=== 
===={4/3, 3/2}==== 
* Augmented[6] (3-step intervals consist of 3 4/3's and 3 3/2's)
===5-limit=== 
===={6/5, 5/4}==== 
* Meantone[7] (2-step intervals consist of 4 6/5's and 3 5/4's)
* Porcupine[7] (2-step intervals consist of 5 6/5's and 2 5/4's)
* Mavila[7] (2-step intervals consist of 3 6/5's and 4 5/4's)
* Srutal[10] (3-step intervals consist of 4 6/5's and 6 5/4's)
* Negri[10] (3-step intervals consist of 3 6/5's and 7 5/4's)
* Blackwood[10] (3-step intervals consist of 5 6/5's and 5 5/4's)
* Sensi[11] (3-step intervals consist of 9 6/5's and 2 5/4's)
* Orson[13] (4-step intervals consist of 3 6/5's and 10 5/4's)
* Helmholtz[17] (5-step intervals consist of 8 6/5's and 9 5/4's)
===={6/5, 4/3}==== 
* Mavila[5] (2-step intervals consist of 1 6/5 and 4 4/3's)
* Hanson[7] (2-step intervals consist of 6 6/5's and 1 4/3)
* Srutal[8] (3-step intervals consist of 2 6/5's and 6 4/3's)
* Doublewide[10] (3-step intervals consist of 8 6/5's and 2 4/3's)
===={5/4, 4/3}==== 
* Meantone[5] (2-step intervals consist of 1 5/4 and 4 4/3's)
* Porcupine[8] (3-step intervals consist of 3 5/4's and 5 4/3's)
* Diminished[8] (3-step intervals consist of 4 5/4's and 4 4/3's)
* Mohajira/Maqamic[10] (4-step intervals consist of 2 5/4's and 8 4/3's)
* Hanson[11] (4-step intervals consist of 6 5/4's and 5 4/3's)
* Tetracot[13] (5-step intervals consist of 4 5/4's and 9 4/3's)
===7-limit=== 
===={8/7, 7/6}==== 
* Slendric[5] (1-step intervals consist of 4 8/7's and 1 7/6)
* Superpyth[5] (1-step intervals consist of 3 8/7's and 2 7/6's)
* Orwell[9] (2-step intervals consist of 1 8/7 and 8 7/6's)
* Miracle[10] (2-step intervals consist of 8 8/7's and 2 7/6's)
* Pajara[10] (2-step intervals consist of 6 8/7's and 4 7/6's)
* Beatles/Maqamic/Hemif[10] (2-step intervals consist of 6 8/7's and 4 7/6's)
===={8/7, 6/5}==== 
* Keemun[4] (aka [[xenharmonic/magical seventh chord|magical seventh chord]])
* Gorgo[5] (1-step intervals consist of 4 8/7's and 1 6/5)
* Porcupine[8] (2-step intervals consist of 2 8/7's and 6 6/5's)
* Armodue[9] (2-step intervals consist of 4 8/7's and 5 6/5's)
* Negri[9] (2 step intervals consist of 7 8/7's and 2 6/5's)
* Astrology[10] (2-step intervals consist of 8 8/7's and 2 6/5's)
* Maqamic[10] (2-step intervals consist of 6 8/7's and 4 7/6's)
* Flattone[12] (3-step intervals consist of 3 8/7's and 9 6/5's)
* Magic[16] (4-step intervals consist of 4 8/7's and 12 6/5's)
===={8/7, 5/4}==== 
* Hemithirds[7] (2-step intervals consist of 5 5/4's and 2 8/7's)
* Godzilla[9] (2-step intervals consist of 8 7/6's and 1 5/4)
===={7/6, 6/5}==== 
* Myna[4] (aka [[xenharmonic/starling tetrad|starling tetrad]])
* Sensi[8] (2-step intervals consist of 2 7/6's and 6 6/5's)
* Hedgehog[8] (2-step intervals consist of 4 7/6's and 4 6/5's)
* Superpelog[9] (2-step intervals consist of 8 7/6's and 1 6/5)
* Negri[9] (2 step intervals consist of 7 7/6's and 2 6/5's)
* Meantone[12] (3-step intervals consist of 3 7/6's and 9 6/5's)
* Augene[12] (3-step intervals consist of 3 7/6's and 9 6/5's)
* Valentine[16] (4-step intervals consist of 4 7/6's and 12 6/5's)
* Muggles[16] (4-step intervals consist of 4 7/6's and 12 6/5's)
{7/6, 5/4}
* Deutone[7] (2-step intervals consist of 2 7/6's and 5 5/4's)
* Godzilla[9] (2-step intervals consist of 8 7/6's and 1 5/4)
{6/5, 9/7}
* Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)
{5/4, 7/5}
* Keemun[7] (3-step intervals consist of 2 5/4's and 5 7/5's)
===={4/3, 7/5}==== 
* Meantone[7] (3-step intervals consist of 6 4/3's and 1 7/5; both 2-step intervals are also consonant)
* Beatles[7] (3-step intervals consist of 5 4/3's and 2 7/5')
* Negri[9] (4-step intervals consist of 5 4/3's and 4 7/5's)
* Sensi[11] (5-step intervals consist of 4 4/3's and 7 7/5's)
===={4/3, 10/7}==== 
* Garibaldi[7] (3-step intervals consist of 6 4/3's and 1 10/7)
* Dominant[7] (3-step intervals consist of 6 4/3's and 1 10/7)
* Augene[9] (4-step intervals consist of 6 4/3's and 3 10/7's)
* Godzilla[9] (4-step intervals consist of 7 4/3's and 2 10/7's)
* Rodan[21] (9-step intervals consist of 18 4/3's and 3 10/7's)
===={7/5, 10/7}==== 
* Hemithirds[6] (3-step intervals consist of 3 7/5's and 3 10/7's)
* Miracle[10] (5-step intervals consist of 5 7/5's and 5 10/7's)
* Beatles[10] (5-step intervals consist of 5 7/5's and 5 10/7's)
* Negri[10] (5-step intervals consist of 5 7/5's and 5 10/7's)
* Blacksmith[10] (5-step intervals consist of 5 7/5's and 5 10/7's)
===9-limit=== 
===={7/6, 9/7}==== 
* Superpyth[7] (2-step intervals consist of 3 9/7's and 4 7/6's)
===={6/5, 9/7}==== 
* Sensamagic, Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)
* Hedgehog[6] (2-step intervals consist of 2 6/5's and 4 9/7's)
===={5/4, 9/7}==== 
* Orwell[9] (3-step intervals consist of 6 5/4's and 3 9/7's)
* Negri[9] (3-step intervals consist of 6 5/4's and 3 9/7's)
===={9/7, 4/3}==== 
* Semaphore[5] (2-step intervals consist of 2 9/7's and 3 4/3's)
* Superpyth[5] (2-step intervals consist of 1 9/7 and 4 4/3's)
* Diminished[8] (3-step intervals consist of 4 9/7's and 4 4/3's)
* Sensi[8] (3-step intervals consist of 7 9/7's and 1 4/3)
* Hedgehog[8] (3-step intervals consist of 6 9/7's and 2 4/3's)
* Beatles/Hemif/Maqamic[10] (4-step intervals consist of 2 9/7's and 8 4/3's)
* Pajara[10] (4-step intervals consist of 2 9/7's and 8 4/3's)
* Negri[10] (4-step intervals consist of 4 9/7's and 6 4/3's)
===={9/7, 7/5}==== 
* Deutone[7] (3-step intervals consist of 4 7/5's and 3 9/7's)
===={9/7,10/7}==== 
* Muggles[10] (5-step intervals consist of 8 9/7's and 2 10/7's)
===={9/7, 3/2}==== 
* Magic[7] (3-step intervals consist of 5 9/7's and 2 3/2's)
===3.5.7-subgroup=== 
===={9/7, 7/5}==== 
* Sirius[7] (2-step intervals consist of 2 9/7's and 5 7/5's)
===={7/5, 5/3}==== 
* Rank-2 Bohlen-Pierce[5] (2-step intervals consist of 2 7/5's and 3 5/3's)
===={5/3, 9/5}==== 
* Sirius[6] (3-step intervals consist of 3 5/3's and 3 9/5's)
==== ==== 
==Rank-3 consonant class scales== 
===7-limit=== 
===={8/7, 6/5, 5/4}==== 
* Marvel, [[marvel11max7a]] and marvel11max7b, 7 notes (2-step intervals consist of 1 8/7, 2 6/5's, and 4 5/4's)
===={7/6, 6/5, 5/4}==== 
* Hewuermity or [[xenharmonic/zeus7|Zeus]], [[zeus7tri]], 7 notes (2-step intervals consist of 2 7/6's, 1 6/5, and 4 5/4's)
===={5/4, 4/3, 7/5}==== 
* Breed or Jove, 7 notes (3-step intervals consist of 2 5/4's, 1 4/3, and 4 7/5's)
===={7/6, 6/5, 5/4}==== 
Portent; 4 5/4's 4 6/5's and 3 7/6's in the third class

=Links= 
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Original HTML content:

<html><head><title>Consonant class scale</title></head><body>A <strong>consonant class scale</strong> is a scale with a <strong>consonant interval class</strong>, that is, a number n such that all n-step intervals of the scale are &quot;consonances&quot; (of a certain odd limit).<br />
<br />
The models for such scales are meantone[5] (in which the 2-step intervals are 5/4 and 4/3), and even better known, meantone[7] (in which the 2-step intervals are 6/5 and 5/4). Harmonizing a diatonic melody by parallel thirds is a commonly used formula that reliably produces beautiful harmony. Consonant class scales are an attempt to generalize this property of the diatonic scale.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Rank-2 consonant class scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->Rank-2 consonant class scales</h2>
 <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Rank-2 consonant class scales-3-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->3-limit</h3>
 <!-- ws:start:WikiTextHeadingRule:4:&lt;h4&gt; --><h4 id="toc2"><a name="x-Rank-2 consonant class scales-3-limit-{4/3, 3/2}"></a><!-- ws:end:WikiTextHeadingRule:4 -->{4/3, 3/2}</h4>
 <ul><li>Augmented[6] (3-step intervals consist of 3 4/3's and 3 3/2's)</li></ul><!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Rank-2 consonant class scales-5-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->5-limit</h3>
 <!-- ws:start:WikiTextHeadingRule:8:&lt;h4&gt; --><h4 id="toc4"><a name="x-Rank-2 consonant class scales-5-limit-{6/5, 5/4}"></a><!-- ws:end:WikiTextHeadingRule:8 -->{6/5, 5/4}</h4>
 <ul><li>Meantone[7] (2-step intervals consist of 4 6/5's and 3 5/4's)</li><li>Porcupine[7] (2-step intervals consist of 5 6/5's and 2 5/4's)</li><li>Mavila[7] (2-step intervals consist of 3 6/5's and 4 5/4's)</li><li>Srutal[10] (3-step intervals consist of 4 6/5's and 6 5/4's)</li><li>Negri[10] (3-step intervals consist of 3 6/5's and 7 5/4's)</li><li>Blackwood[10] (3-step intervals consist of 5 6/5's and 5 5/4's)</li><li>Sensi[11] (3-step intervals consist of 9 6/5's and 2 5/4's)</li><li>Orson[13] (4-step intervals consist of 3 6/5's and 10 5/4's)</li><li>Helmholtz[17] (5-step intervals consist of 8 6/5's and 9 5/4's)</li></ul><!-- ws:start:WikiTextHeadingRule:10:&lt;h4&gt; --><h4 id="toc5"><a name="x-Rank-2 consonant class scales-5-limit-{6/5, 4/3}"></a><!-- ws:end:WikiTextHeadingRule:10 -->{6/5, 4/3}</h4>
 <ul><li>Mavila[5] (2-step intervals consist of 1 6/5 and 4 4/3's)</li><li>Hanson[7] (2-step intervals consist of 6 6/5's and 1 4/3)</li><li>Srutal[8] (3-step intervals consist of 2 6/5's and 6 4/3's)</li><li>Doublewide[10] (3-step intervals consist of 8 6/5's and 2 4/3's)</li></ul><!-- ws:start:WikiTextHeadingRule:12:&lt;h4&gt; --><h4 id="toc6"><a name="x-Rank-2 consonant class scales-5-limit-{5/4, 4/3}"></a><!-- ws:end:WikiTextHeadingRule:12 -->{5/4, 4/3}</h4>
 <ul><li>Meantone[5] (2-step intervals consist of 1 5/4 and 4 4/3's)</li><li>Porcupine[8] (3-step intervals consist of 3 5/4's and 5 4/3's)</li><li>Diminished[8] (3-step intervals consist of 4 5/4's and 4 4/3's)</li><li>Mohajira/Maqamic[10] (4-step intervals consist of 2 5/4's and 8 4/3's)</li><li>Hanson[11] (4-step intervals consist of 6 5/4's and 5 4/3's)</li><li>Tetracot[13] (5-step intervals consist of 4 5/4's and 9 4/3's)</li></ul><!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="x-Rank-2 consonant class scales-7-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->7-limit</h3>
 <!-- ws:start:WikiTextHeadingRule:16:&lt;h4&gt; --><h4 id="toc8"><a name="x-Rank-2 consonant class scales-7-limit-{8/7, 7/6}"></a><!-- ws:end:WikiTextHeadingRule:16 -->{8/7, 7/6}</h4>
 <ul><li>Slendric[5] (1-step intervals consist of 4 8/7's and 1 7/6)</li><li>Superpyth[5] (1-step intervals consist of 3 8/7's and 2 7/6's)</li><li>Orwell[9] (2-step intervals consist of 1 8/7 and 8 7/6's)</li><li>Miracle[10] (2-step intervals consist of 8 8/7's and 2 7/6's)</li><li>Pajara[10] (2-step intervals consist of 6 8/7's and 4 7/6's)</li><li>Beatles/Maqamic/Hemif[10] (2-step intervals consist of 6 8/7's and 4 7/6's)</li></ul><!-- ws:start:WikiTextHeadingRule:18:&lt;h4&gt; --><h4 id="toc9"><a name="x-Rank-2 consonant class scales-7-limit-{8/7, 6/5}"></a><!-- ws:end:WikiTextHeadingRule:18 -->{8/7, 6/5}</h4>
 <ul><li>Keemun[4] (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magical%20seventh%20chord">magical seventh chord</a>)</li><li>Gorgo[5] (1-step intervals consist of 4 8/7's and 1 6/5)</li><li>Porcupine[8] (2-step intervals consist of 2 8/7's and 6 6/5's)</li><li>Armodue[9] (2-step intervals consist of 4 8/7's and 5 6/5's)</li><li>Negri[9] (2 step intervals consist of 7 8/7's and 2 6/5's)</li><li>Astrology[10] (2-step intervals consist of 8 8/7's and 2 6/5's)</li><li>Maqamic[10] (2-step intervals consist of 6 8/7's and 4 7/6's)</li><li>Flattone[12] (3-step intervals consist of 3 8/7's and 9 6/5's)</li><li>Magic[16] (4-step intervals consist of 4 8/7's and 12 6/5's)</li></ul><!-- ws:start:WikiTextHeadingRule:20:&lt;h4&gt; --><h4 id="toc10"><a name="x-Rank-2 consonant class scales-7-limit-{8/7, 5/4}"></a><!-- ws:end:WikiTextHeadingRule:20 -->{8/7, 5/4}</h4>
 <ul><li>Hemithirds[7] (2-step intervals consist of 5 5/4's and 2 8/7's)</li><li>Godzilla[9] (2-step intervals consist of 8 7/6's and 1 5/4)</li></ul><!-- ws:start:WikiTextHeadingRule:22:&lt;h4&gt; --><h4 id="toc11"><a name="x-Rank-2 consonant class scales-7-limit-{7/6, 6/5}"></a><!-- ws:end:WikiTextHeadingRule:22 -->{7/6, 6/5}</h4>
 <ul><li>Myna[4] (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/starling%20tetrad">starling tetrad</a>)</li><li>Sensi[8] (2-step intervals consist of 2 7/6's and 6 6/5's)</li><li>Hedgehog[8] (2-step intervals consist of 4 7/6's and 4 6/5's)</li><li>Superpelog[9] (2-step intervals consist of 8 7/6's and 1 6/5)</li><li>Negri[9] (2 step intervals consist of 7 7/6's and 2 6/5's)</li><li>Meantone[12] (3-step intervals consist of 3 7/6's and 9 6/5's)</li><li>Augene[12] (3-step intervals consist of 3 7/6's and 9 6/5's)</li><li>Valentine[16] (4-step intervals consist of 4 7/6's and 12 6/5's)</li><li>Muggles[16] (4-step intervals consist of 4 7/6's and 12 6/5's)</li></ul>{7/6, 5/4}<br />
<ul><li>Deutone[7] (2-step intervals consist of 2 7/6's and 5 5/4's)</li><li>Godzilla[9] (2-step intervals consist of 8 7/6's and 1 5/4)</li></ul>{6/5, 9/7}<br />
<ul><li>Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)</li></ul>{5/4, 7/5}<br />
<ul><li>Keemun[7] (3-step intervals consist of 2 5/4's and 5 7/5's)</li></ul><!-- ws:start:WikiTextHeadingRule:24:&lt;h4&gt; --><h4 id="toc12"><a name="x-Rank-2 consonant class scales-7-limit-{4/3, 7/5}"></a><!-- ws:end:WikiTextHeadingRule:24 -->{4/3, 7/5}</h4>
 <ul><li>Meantone[7] (3-step intervals consist of 6 4/3's and 1 7/5; both 2-step intervals are also consonant)</li><li>Beatles[7] (3-step intervals consist of 5 4/3's and 2 7/5')</li><li>Negri[9] (4-step intervals consist of 5 4/3's and 4 7/5's)</li><li>Sensi[11] (5-step intervals consist of 4 4/3's and 7 7/5's)</li></ul><!-- ws:start:WikiTextHeadingRule:26:&lt;h4&gt; --><h4 id="toc13"><a name="x-Rank-2 consonant class scales-7-limit-{4/3, 10/7}"></a><!-- ws:end:WikiTextHeadingRule:26 -->{4/3, 10/7}</h4>
 <ul><li>Garibaldi[7] (3-step intervals consist of 6 4/3's and 1 10/7)</li><li>Dominant[7] (3-step intervals consist of 6 4/3's and 1 10/7)</li><li>Augene[9] (4-step intervals consist of 6 4/3's and 3 10/7's)</li><li>Godzilla[9] (4-step intervals consist of 7 4/3's and 2 10/7's)</li><li>Rodan[21] (9-step intervals consist of 18 4/3's and 3 10/7's)</li></ul><!-- ws:start:WikiTextHeadingRule:28:&lt;h4&gt; --><h4 id="toc14"><a name="x-Rank-2 consonant class scales-7-limit-{7/5, 10/7}"></a><!-- ws:end:WikiTextHeadingRule:28 -->{7/5, 10/7}</h4>
 <ul><li>Hemithirds[6] (3-step intervals consist of 3 7/5's and 3 10/7's)</li><li>Miracle[10] (5-step intervals consist of 5 7/5's and 5 10/7's)</li><li>Beatles[10] (5-step intervals consist of 5 7/5's and 5 10/7's)</li><li>Negri[10] (5-step intervals consist of 5 7/5's and 5 10/7's)</li><li>Blacksmith[10] (5-step intervals consist of 5 7/5's and 5 10/7's)</li></ul><!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="x-Rank-2 consonant class scales-9-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->9-limit</h3>
 <!-- ws:start:WikiTextHeadingRule:32:&lt;h4&gt; --><h4 id="toc16"><a name="x-Rank-2 consonant class scales-9-limit-{7/6, 9/7}"></a><!-- ws:end:WikiTextHeadingRule:32 -->{7/6, 9/7}</h4>
 <ul><li>Superpyth[7] (2-step intervals consist of 3 9/7's and 4 7/6's)</li></ul><!-- ws:start:WikiTextHeadingRule:34:&lt;h4&gt; --><h4 id="toc17"><a name="x-Rank-2 consonant class scales-9-limit-{6/5, 9/7}"></a><!-- ws:end:WikiTextHeadingRule:34 -->{6/5, 9/7}</h4>
 <ul><li>Sensamagic, Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)</li><li>Hedgehog[6] (2-step intervals consist of 2 6/5's and 4 9/7's)</li></ul><!-- ws:start:WikiTextHeadingRule:36:&lt;h4&gt; --><h4 id="toc18"><a name="x-Rank-2 consonant class scales-9-limit-{5/4, 9/7}"></a><!-- ws:end:WikiTextHeadingRule:36 -->{5/4, 9/7}</h4>
 <ul><li>Orwell[9] (3-step intervals consist of 6 5/4's and 3 9/7's)</li><li>Negri[9] (3-step intervals consist of 6 5/4's and 3 9/7's)</li></ul><!-- ws:start:WikiTextHeadingRule:38:&lt;h4&gt; --><h4 id="toc19"><a name="x-Rank-2 consonant class scales-9-limit-{9/7, 4/3}"></a><!-- ws:end:WikiTextHeadingRule:38 -->{9/7, 4/3}</h4>
 <ul><li>Semaphore[5] (2-step intervals consist of 2 9/7's and 3 4/3's)</li><li>Superpyth[5] (2-step intervals consist of 1 9/7 and 4 4/3's)</li><li>Diminished[8] (3-step intervals consist of 4 9/7's and 4 4/3's)</li><li>Sensi[8] (3-step intervals consist of 7 9/7's and 1 4/3)</li><li>Hedgehog[8] (3-step intervals consist of 6 9/7's and 2 4/3's)</li><li>Beatles/Hemif/Maqamic[10] (4-step intervals consist of 2 9/7's and 8 4/3's)</li><li>Pajara[10] (4-step intervals consist of 2 9/7's and 8 4/3's)</li><li>Negri[10] (4-step intervals consist of 4 9/7's and 6 4/3's)</li></ul><!-- ws:start:WikiTextHeadingRule:40:&lt;h4&gt; --><h4 id="toc20"><a name="x-Rank-2 consonant class scales-9-limit-{9/7, 7/5}"></a><!-- ws:end:WikiTextHeadingRule:40 -->{9/7, 7/5}</h4>
 <ul><li>Deutone[7] (3-step intervals consist of 4 7/5's and 3 9/7's)</li></ul><!-- ws:start:WikiTextHeadingRule:42:&lt;h4&gt; --><h4 id="toc21"><a name="x-Rank-2 consonant class scales-9-limit-{9/7,10/7}"></a><!-- ws:end:WikiTextHeadingRule:42 -->{9/7,10/7}</h4>
 <ul><li>Muggles[10] (5-step intervals consist of 8 9/7's and 2 10/7's)</li></ul><!-- ws:start:WikiTextHeadingRule:44:&lt;h4&gt; --><h4 id="toc22"><a name="x-Rank-2 consonant class scales-9-limit-{9/7, 3/2}"></a><!-- ws:end:WikiTextHeadingRule:44 -->{9/7, 3/2}</h4>
 <ul><li>Magic[7] (3-step intervals consist of 5 9/7's and 2 3/2's)</li></ul><!-- ws:start:WikiTextHeadingRule:46:&lt;h3&gt; --><h3 id="toc23"><a name="x-Rank-2 consonant class scales-3.5.7-subgroup"></a><!-- ws:end:WikiTextHeadingRule:46 -->3.5.7-subgroup</h3>
 <!-- ws:start:WikiTextHeadingRule:48:&lt;h4&gt; --><h4 id="toc24"><a name="x-Rank-2 consonant class scales-3.5.7-subgroup-{9/7, 7/5}"></a><!-- ws:end:WikiTextHeadingRule:48 -->{9/7, 7/5}</h4>
 <ul><li>Sirius[7] (2-step intervals consist of 2 9/7's and 5 7/5's)</li></ul><!-- ws:start:WikiTextHeadingRule:50:&lt;h4&gt; --><h4 id="toc25"><a name="x-Rank-2 consonant class scales-3.5.7-subgroup-{7/5, 5/3}"></a><!-- ws:end:WikiTextHeadingRule:50 -->{7/5, 5/3}</h4>
 <ul><li>Rank-2 Bohlen-Pierce[5] (2-step intervals consist of 2 7/5's and 3 5/3's)</li></ul><!-- ws:start:WikiTextHeadingRule:52:&lt;h4&gt; --><h4 id="toc26"><a name="x-Rank-2 consonant class scales-3.5.7-subgroup-{5/3, 9/5}"></a><!-- ws:end:WikiTextHeadingRule:52 -->{5/3, 9/5}</h4>
 <ul><li>Sirius[6] (3-step intervals consist of 3 5/3's and 3 9/5's)</li></ul><!-- ws:start:WikiTextHeadingRule:54:&lt;h4&gt; --><h4 id="toc27"><!-- ws:end:WikiTextHeadingRule:54 --> </h4>
 <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="x-Rank-3 consonant class scales"></a><!-- ws:end:WikiTextHeadingRule:56 -->Rank-3 consonant class scales</h2>
 <!-- ws:start:WikiTextHeadingRule:58:&lt;h3&gt; --><h3 id="toc29"><a name="x-Rank-3 consonant class scales-7-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->7-limit</h3>
 <!-- ws:start:WikiTextHeadingRule:60:&lt;h4&gt; --><h4 id="toc30"><a name="x-Rank-3 consonant class scales-7-limit-{8/7, 6/5, 5/4}"></a><!-- ws:end:WikiTextHeadingRule:60 -->{8/7, 6/5, 5/4}</h4>
 <ul><li>Marvel, <a class="wiki_link" href="/marvel11max7a">marvel11max7a</a> and marvel11max7b, 7 notes (2-step intervals consist of 1 8/7, 2 6/5's, and 4 5/4's)</li></ul><!-- ws:start:WikiTextHeadingRule:62:&lt;h4&gt; --><h4 id="toc31"><a name="x-Rank-3 consonant class scales-7-limit-{7/6, 6/5, 5/4}"></a><!-- ws:end:WikiTextHeadingRule:62 -->{7/6, 6/5, 5/4}</h4>
 <ul><li>Hewuermity or <a class="wiki_link" href="http://xenharmonic.wikispaces.com/zeus7">Zeus</a>, <a class="wiki_link" href="/zeus7tri">zeus7tri</a>, 7 notes (2-step intervals consist of 2 7/6's, 1 6/5, and 4 5/4's)</li></ul><!-- ws:start:WikiTextHeadingRule:64:&lt;h4&gt; --><h4 id="toc32"><a name="x-Rank-3 consonant class scales-7-limit-{5/4, 4/3, 7/5}"></a><!-- ws:end:WikiTextHeadingRule:64 -->{5/4, 4/3, 7/5}</h4>
 <ul><li>Breed or Jove, 7 notes (3-step intervals consist of 2 5/4's, 1 4/3, and 4 7/5's)</li></ul><!-- ws:start:WikiTextHeadingRule:66:&lt;h4&gt; --><h4 id="toc33"><a name="x-Rank-3 consonant class scales-7-limit-{7/6, 6/5, 5/4}"></a><!-- ws:end:WikiTextHeadingRule:66 -->{7/6, 6/5, 5/4}</h4>
 Portent; 4 5/4's 4 6/5's and 3 7/6's in the third class<br />
<br />
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