Consonant class scale: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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).
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:hearneg|hearneg]] and made on <tt>2014-12-30 04:02:17 UTC</tt>.<br>
: The original revision id was <tt>536011466</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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.
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==  
==Rank-2 consonant class scales==
===3-limit===  
 
===={4/3, 3/2}====  
===3-limit===
* Augmented[6] (3-step intervals consist of 3 4/3's and 3 3/2's)
 
===5-limit===  
===={4/3, 3/2}====
===={6/5, 5/4}====  
<ul><li>Augmented[6] (3-step intervals consist of 3 4/3's and 3 3/2's)</li></ul>
* Meantone[7] (2-step intervals consist of 4 6/5's and 3 5/4's)
===5-limit===
* 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)
===={6/5, 5/4}====
* Srutal[10] (3-step intervals consist of 4 6/5's and 6 5/4's)
<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>Godzilla[14] (4-step intervals consist of 8 6/5's and 6 5/4's)</li><li>Helmholtz[17] (5-step intervals consist of 8 6/5's and 9 5/4's)</li><li>Superpyth[17] (5-step intervals consist of 9 6/5's and 8 5/4's)</li></ul>
* Negri[10] (3-step intervals consist of 3 6/5's and 7 5/4's)
===={6/5, 4/3}====
* Blackwood[10] (3-step intervals consist of 5 6/5's and 5 5/4's)
<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>
* Sensi[11] (3-step intervals consist of 9 6/5's and 2 5/4's)
===={5/4, 4/3}====
* Orson[13] (4-step intervals consist of 3 6/5's and 10 5/4's)
<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>
* Godzilla[14] (4-step intervals consist of 8 6/5's and 6 5/4's)
===7-limit===
* Helmholtz[17] (5-step intervals consist of 8 6/5's and 9 5/4's)
 
* Superpyth[17] (5-step intervals consist of 9 6/5's and 8 5/4's)
===={8/7, 7/6}====
===={6/5, 4/3}====  
<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><li>Hedgehog[14] (3-step intervals consist of 4 8/7's and 10 7/6's)</li><li>Porcupine[15] (3-step intervals consist of 9 8/7's and 6 7/6's)</li><li>Augene[15] (3-step intervals consist of 6 8/7's and 9 7/6's)</li><li>Meantone[19] (4-step intervals consist of 9 8/7's and 10 7/6's)</li><li>Sensi[19] (4-step intervals consist of 6 8/7's and 13 7/6's)</li></ul>
* Mavila[5] (2-step intervals consist of 1 6/5 and 4 4/3's)
===={8/7, 6/5}====
* Hanson[7] (2-step intervals consist of 6 6/5's and 1 4/3)
<ul><li>Keemun[4] (aka [[magical_seventh_chord|magical seventh chord]])</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><li>Mohajira[17] (4-step intervals consist of 6 8/7's and 11 6/5's)</li></ul>
* Srutal[8] (3-step intervals consist of 2 6/5's and 6 4/3's)
===={8/7, 5/4}====
* Doublewide[10] (3-step intervals consist of 8 6/5's and 2 4/3's)
<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><li>Magic[13] (4-step intervals consist of 1 8/7 and 12 5/4's)</li></ul>
===={5/4, 4/3}====  
===={7/6, 6/5}====
* Meantone[5] (2-step intervals consist of 1 5/4 and 4 4/3's)
<ul><li>Myna[4] (aka [[starling_tetrad|starling tetrad]])</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>Pajara[12] (3-step intervals consist of 6 7/6's and 6 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><li>Miracle[21] (5-step intervals consist of 13 7/6's and 8 6/5's)</li></ul>{7/6, 5/4}
* 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)
<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><li>Superpyth[12] (3-step intervals consist of 9 7/6's and 3 5/4's)</li></ul>{6/5, 9/7}
* 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)
<ul><li>Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)</li><li>Superpyth[12] (4-step intervals consist of 4 6/5's and 8 9/7's)</li></ul>{5/4, 7/5}
* Tetracot[13] (5-step intervals consist of 4 5/4's and 9 4/3's)
 
===7-limit===  
<ul><li>Keemun[7] (3-step intervals consist of 2 5/4's and 5 7/5's)</li></ul>
===={8/7, 7/6}====  
===={4/3, 7/5}====
* Slendric[5] (1-step intervals consist of 4 8/7's and 1 7/6)
<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><li>Miracle[11] (5-step intervals consist of 5 4/3's and 6 7/5's)</li><li>Magic[16] (7-step intervals consist of 11 4/3's and 5 7/5's)</li></ul>
* Superpyth[5] (1-step intervals consist of 3 8/7's and 2 7/6's)
===={4/3, 10/7}====
* Orwell[9] (2-step intervals consist of 1 8/7 and 8 7/6's)
<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>Superpyth[12] (5-step intervals consist of 11 4/3's and 1 10/7)</li><li>Muggles[13] (6-step intervals consist of 8 4/3's and 5 10/7's)</li><li>Rodan[21] (9-step intervals consist of 18 4/3's and 3 10/7's)</li></ul>
* Miracle[10] (2-step intervals consist of 8 8/7's and 2 7/6's)
===={7/5, 10/7}====
* Pajara[10] (2-step intervals consist of 6 8/7's and 4 7/6's)
<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><li>Meantone[12] (6-step intervals consist of 6 7/5's and 6 10/7's)</li><li>Augene[12] (6-step intervals consist of 6 7/5's and 6 10/7's)</li><li>Muggles[16] (8-step intervals consist of 8 7/5's and 8 10/7's)</li><li>Superpyth[22] (11-step intervals consist of 11 7/5's and 11 10/7's)</li></ul>
* Beatles/Maqamic/Hemif[10] (2-step intervals consist of 6 8/7's and 4 7/6's)
===9-limit===
* Hedgehog[14] (3-step intervals consist of 4 8/7's and 10 7/6's)
 
* Porcupine[15] (3-step intervals consist of 9 8/7's and 6 7/6's)
===={7/6, 9/7}====
* Augene[15] (3-step intervals consist of 6 8/7's and 9 7/6's)
<ul><li>Superpyth[7] (2-step intervals consist of 3 9/7's and 4 7/6's)</li></ul>
* Meantone[19] (4-step intervals consist of 9 8/7's and 10 7/6's)
===={6/5, 9/7}====
* Sensi[19] (4-step intervals consist of 6 8/7's and 13 7/6's)
<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>
===={8/7, 6/5}====  
===={5/4, 9/7}====
* Keemun[4] (aka [[xenharmonic/magical seventh chord|magical seventh chord]])
<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><li>Meantone[12] (4-step intervals consist of 8 5/4's and 4 9/7's)</li><li>Pajara[12] (4-step intervals consist of 8 5/4's and 4 9/7's)</li><li>Miracle[21] (7-step interval consists of 14 5/4's and 7 9/7's)</li></ul>
* Gorgo[5] (1-step intervals consist of 4 8/7's and 1 6/5)
===={9/7, 4/3}====
* Porcupine[8] (2-step intervals consist of 2 8/7's and 6 6/5's)
<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><li>Orwell[13] (5-step intervals consist of 7 9/7's and 6 4/3's)</li><li>Keemun[15] (6-step intervals consist of 6 9/7's and 9 4/3's)</li><li>Augene[15] (6-step intervals consist of 3 9/7's and 12 4/3's)</li><li>Mohajira[17] (7-step intervals consist of 2 9/7's and 17 4/3's)</li></ul>
* Armodue[9] (2-step intervals consist of 4 8/7's and 5 6/5's)
===={9/7, 7/5}====
* Negri[9] (2 step intervals consist of 7 8/7's and 2 6/5's)
<ul><li>Deutone[7] (3-step intervals consist of 4 7/5's and 3 9/7's)</li><li>Magic[13] (5-step intervals consist of 11 9/7's and 2 7/5's)</li></ul>
* Astrology[10] (2-step intervals consist of 8 8/7's and 2 6/5's)
===={9/7,10/7}====
* Maqamic[10] (2-step intervals consist of 6 8/7's and 4 7/6's)
<ul><li>Muggles[10] (5-step intervals consist of 8 9/7's and 2 10/7's)</li></ul>
* Flattone[12] (3-step intervals consist of 3 8/7's and 9 6/5's)
===={9/7, 3/2}====
* Magic[16] (4-step intervals consist of 4 8/7's and 12 6/5's)
<ul><li>Magic[7] (3-step intervals consist of 5 9/7's and 2 3/2's)</li></ul>
* Mohajira[17] (4-step intervals consist of 6 8/7's and 11 6/5's)
===3.5.7-subgroup===
===={8/7, 5/4}====  
 
* Hemithirds[7] (2-step intervals consist of 5 5/4's and 2 8/7's)
===={9/7, 7/5}====
* Godzilla[9] (2-step intervals consist of 8 7/6's and 1 5/4)
<ul><li>Sirius[7] (2-step intervals consist of 2 9/7's and 5 7/5's)</li></ul>
* Magic[13] (4-step intervals consist of 1 8/7 and 12 5/4's)
===={7/5, 5/3}====
===={7/6, 6/5}====  
<ul><li>Rank-2 Bohlen-Pierce[5] (2-step intervals consist of 2 7/5's and 3 5/3's)</li></ul>
* Myna[4] (aka [[xenharmonic/starling tetrad|starling tetrad]])
===={5/3, 9/5}====
* Sensi[8] (2-step intervals consist of 2 7/6's and 6 6/5's)
<ul><li>Sirius[6] (3-step intervals consist of 3 5/3's and 3 9/5's)</li></ul>
* 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)
==Rank-3 consonant class scales==
* 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)
===7-limit===
* Pajara[12] (3-step intervals consist of 6 7/6's and 6 6/5's)
 
* Valentine[16] (4-step intervals consist of 4 7/6's and 12 6/5's)
===={8/7, 6/5, 5/4}====
* Muggles[16] (4-step intervals consist of 4 7/6's and 12 6/5's)
<ul><li>Marvel, [[marvel11max7a|marvel11max7a]] and marvel11max7b, 7 notes (2-step intervals consist of 1 8/7, 2 6/5's, and 4 5/4's)</li></ul>
* Miracle[21] (5-step intervals consist of 13 7/6's and 8 6/5's)
===={7/6, 6/5, 5/4}====
{7/6, 5/4}
<ul><li>Hewuermity or [[zeus7|Zeus]], [[zeus7tri|zeus7tri]], 7 notes (2-step intervals consist of 2 7/6's, 1 6/5, and 4 5/4's)</li></ul>
* Deutone[7] (2-step intervals consist of 2 7/6's and 5 5/4's)
===={5/4, 4/3, 7/5}====
* Godzilla[9] (2-step intervals consist of 8 7/6's and 1 5/4)
<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>
* Superpyth[12] (3-step intervals consist of 9 7/6's and 3 5/4's)
===={7/6, 6/5, 5/4}====
{6/5, 9/7}
* Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)
* Superpyth[12] (4-step intervals consist of 4 6/5's and 8 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)
* Miracle[11] (5-step intervals consist of 5 4/3's and 6 7/5's)
* Magic[16] (7-step intervals consist of 11 4/3's and 5 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)
* Superpyth[12] (5-step intervals consist of 11 4/3's and 1 10/7)
* Muggles[13] (6-step intervals consist of 8 4/3's and 5 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)
* Meantone[12] (6-step intervals consist of 6 7/5's and 6 10/7's)
* Augene[12] (6-step intervals consist of 6 7/5's and 6 10/7's)
* Muggles[16] (8-step intervals consist of 8 7/5's and 8 10/7's)
* Superpyth[22] (11-step intervals consist of 11 7/5's and 11 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)
* Meantone[12] (4-step intervals consist of 8 5/4's and 4 9/7's)
* Pajara[12] (4-step intervals consist of 8 5/4's and 4 9/7's)
* Miracle[21] (7-step interval consists of 14 5/4's and 7 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)
* Orwell[13] (5-step intervals consist of 7 9/7's and 6 4/3's)
* Keemun[15] (6-step intervals consist of 6 9/7's and 9 4/3's)
* Augene[15] (6-step intervals consist of 3 9/7's and 12 4/3's)
* Mohajira[17] (7-step intervals consist of 2 9/7's and 17 4/3's)
===={9/7, 7/5}====  
* Deutone[7] (3-step intervals consist of 4 7/5's and 3 9/7's)
* Magic[13] (5-step intervals consist of 11 9/7's and 2 7/5'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
Portent; 4 5/4's 4 6/5's and 3 7/6's in the third class


=Links=  
=Links=
http://tech.groups.yahoo.com/group/tuning-math/message/6056
[http://tech.groups.yahoo.com/group/tuning-math/message/6056 http://tech.groups.yahoo.com/group/tuning-math/message/6056]
http://tech.groups.yahoo.com/group/tuning-math/message/6060
 
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http://tech.groups.yahoo.com/group/tuning-math/message/6065
[http://tech.groups.yahoo.com/group/tuning-math/message/6062 http://tech.groups.yahoo.com/group/tuning-math/message/6062]
http://tech.groups.yahoo.com/group/tuning-math/message/6067
 
http://tech.groups.yahoo.com/group/tuning-math/message/6068
[http://tech.groups.yahoo.com/group/tuning-math/message/6064 http://tech.groups.yahoo.com/group/tuning-math/message/6064]
http://tech.groups.yahoo.com/group/tuning-math/message/6075
 
http://tech.groups.yahoo.com/group/tuning-math/message/6082
[http://tech.groups.yahoo.com/group/tuning-math/message/6065 http://tech.groups.yahoo.com/group/tuning-math/message/6065]
http://tech.groups.yahoo.com/group/tuning-math/message/6086
 
http://tech.groups.yahoo.com/group/tuning-math/message/6088
[http://tech.groups.yahoo.com/group/tuning-math/message/6067 http://tech.groups.yahoo.com/group/tuning-math/message/6067]
http://tech.groups.yahoo.com/group/tuning-math/message/6089
 
http://tech.groups.yahoo.com/group/tuning-math/message/6090
[http://tech.groups.yahoo.com/group/tuning-math/message/6068 http://tech.groups.yahoo.com/group/tuning-math/message/6068]
http://tech.groups.yahoo.com/group/tuning-math/message/6092
 
http://tech.groups.yahoo.com/group/tuning-math/message/6094
[http://tech.groups.yahoo.com/group/tuning-math/message/6075 http://tech.groups.yahoo.com/group/tuning-math/message/6075]
http://tech.groups.yahoo.com/group/tuning-math/message/6097
 
http://tech.groups.yahoo.com/group/tuning-math/message/6100
[http://tech.groups.yahoo.com/group/tuning-math/message/6082 http://tech.groups.yahoo.com/group/tuning-math/message/6082]
http://tech.groups.yahoo.com/group/tuning-math/message/6102
 
http://tech.groups.yahoo.com/group/tuning-math/message/6103
[http://tech.groups.yahoo.com/group/tuning-math/message/6086 http://tech.groups.yahoo.com/group/tuning-math/message/6086]
http://tech.groups.yahoo.com/group/tuning-math/message/6104
 
http://tech.groups.yahoo.com/group/tuning-math/message/6169
[http://tech.groups.yahoo.com/group/tuning-math/message/6088 http://tech.groups.yahoo.com/group/tuning-math/message/6088]
http://tech.groups.yahoo.com/group/tuning-math/message/15082
 
http://tech.groups.yahoo.com/group/tuning-math/message/15102
[http://tech.groups.yahoo.com/group/tuning-math/message/6089 http://tech.groups.yahoo.com/group/tuning-math/message/6089]
http://tech.groups.yahoo.com/group/tuning-math/message/15103
 
http://tech.groups.yahoo.com/group/tuning-math/message/15123
[http://tech.groups.yahoo.com/group/tuning-math/message/6090 http://tech.groups.yahoo.com/group/tuning-math/message/6090]
http://tech.groups.yahoo.com/group/tuning-math/message/15483
 
http://tech.groups.yahoo.com/group/tuning-math/message/15501
[http://tech.groups.yahoo.com/group/tuning-math/message/6092 http://tech.groups.yahoo.com/group/tuning-math/message/6092]
http://tech.groups.yahoo.com/group/tuning-math/message/19390
 
http://tech.groups.yahoo.com/group/tuning-math/message/19410
[http://tech.groups.yahoo.com/group/tuning-math/message/6094 http://tech.groups.yahoo.com/group/tuning-math/message/6094]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/6097 http://tech.groups.yahoo.com/group/tuning-math/message/6097]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/6100 http://tech.groups.yahoo.com/group/tuning-math/message/6100]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/6102 http://tech.groups.yahoo.com/group/tuning-math/message/6102]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/6103 http://tech.groups.yahoo.com/group/tuning-math/message/6103]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/6104 http://tech.groups.yahoo.com/group/tuning-math/message/6104]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/6169 http://tech.groups.yahoo.com/group/tuning-math/message/6169]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/15082 http://tech.groups.yahoo.com/group/tuning-math/message/15082]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/15102 http://tech.groups.yahoo.com/group/tuning-math/message/15102]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/15103 http://tech.groups.yahoo.com/group/tuning-math/message/15103]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/15123 http://tech.groups.yahoo.com/group/tuning-math/message/15123]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/15483 http://tech.groups.yahoo.com/group/tuning-math/message/15483]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/15501 http://tech.groups.yahoo.com/group/tuning-math/message/15501]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/19390 http://tech.groups.yahoo.com/group/tuning-math/message/19390]
 
[http://tech.groups.yahoo.com/group/tuning-math/message/19410 http://tech.groups.yahoo.com/group/tuning-math/message/19410]


http://launch.groups.yahoo.com/group/tuning/message/41360</pre></div>
[http://launch.groups.yahoo.com/group/tuning/message/41360 http://launch.groups.yahoo.com/group/tuning/message/41360]
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Consonant class scale&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;strong&gt;consonant class scale&lt;/strong&gt; is a scale with a &lt;strong&gt;consonant interval class&lt;/strong&gt;, that is, a number n such that all n-step intervals of the scale are &amp;quot;consonances&amp;quot; (of a certain odd limit).&lt;br /&gt;
&lt;br /&gt;
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.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Rank-2 consonant class scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Rank-2 consonant class scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Rank-2 consonant class scales-3-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;3-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc2"&gt;&lt;a name="x-Rank-2 consonant class scales-3-limit-{4/3, 3/2}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;{4/3, 3/2}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Augmented[6] (3-step intervals consist of 3 4/3's and 3 3/2's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Rank-2 consonant class scales-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;5-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc4"&gt;&lt;a name="x-Rank-2 consonant class scales-5-limit-{6/5, 5/4}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;{6/5, 5/4}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Meantone[7] (2-step intervals consist of 4 6/5's and 3 5/4's)&lt;/li&gt;&lt;li&gt;Porcupine[7] (2-step intervals consist of 5 6/5's and 2 5/4's)&lt;/li&gt;&lt;li&gt;Mavila[7] (2-step intervals consist of 3 6/5's and 4 5/4's)&lt;/li&gt;&lt;li&gt;Srutal[10] (3-step intervals consist of 4 6/5's and 6 5/4's)&lt;/li&gt;&lt;li&gt;Negri[10] (3-step intervals consist of 3 6/5's and 7 5/4's)&lt;/li&gt;&lt;li&gt;Blackwood[10] (3-step intervals consist of 5 6/5's and 5 5/4's)&lt;/li&gt;&lt;li&gt;Sensi[11] (3-step intervals consist of 9 6/5's and 2 5/4's)&lt;/li&gt;&lt;li&gt;Orson[13] (4-step intervals consist of 3 6/5's and 10 5/4's)&lt;/li&gt;&lt;li&gt;Godzilla[14] (4-step intervals consist of 8 6/5's and 6 5/4's)&lt;/li&gt;&lt;li&gt;Helmholtz[17] (5-step intervals consist of 8 6/5's and 9 5/4's)&lt;/li&gt;&lt;li&gt;Superpyth[17] (5-step intervals consist of 9 6/5's and 8 5/4's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc5"&gt;&lt;a name="x-Rank-2 consonant class scales-5-limit-{6/5, 4/3}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;{6/5, 4/3}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Mavila[5] (2-step intervals consist of 1 6/5 and 4 4/3's)&lt;/li&gt;&lt;li&gt;Hanson[7] (2-step intervals consist of 6 6/5's and 1 4/3)&lt;/li&gt;&lt;li&gt;Srutal[8] (3-step intervals consist of 2 6/5's and 6 4/3's)&lt;/li&gt;&lt;li&gt;Doublewide[10] (3-step intervals consist of 8 6/5's and 2 4/3's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc6"&gt;&lt;a name="x-Rank-2 consonant class scales-5-limit-{5/4, 4/3}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;{5/4, 4/3}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Meantone[5] (2-step intervals consist of 1 5/4 and 4 4/3's)&lt;/li&gt;&lt;li&gt;Porcupine[8] (3-step intervals consist of 3 5/4's and 5 4/3's)&lt;/li&gt;&lt;li&gt;Diminished[8] (3-step intervals consist of 4 5/4's and 4 4/3's)&lt;/li&gt;&lt;li&gt;Mohajira/Maqamic[10] (4-step intervals consist of 2 5/4's and 8 4/3's)&lt;/li&gt;&lt;li&gt;Hanson[11] (4-step intervals consist of 6 5/4's and 5 4/3's)&lt;/li&gt;&lt;li&gt;Tetracot[13] (5-step intervals consist of 4 5/4's and 9 4/3's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Rank-2 consonant class scales-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;7-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc8"&gt;&lt;a name="x-Rank-2 consonant class scales-7-limit-{8/7, 7/6}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;{8/7, 7/6}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Slendric[5] (1-step intervals consist of 4 8/7's and 1 7/6)&lt;/li&gt;&lt;li&gt;Superpyth[5] (1-step intervals consist of 3 8/7's and 2 7/6's)&lt;/li&gt;&lt;li&gt;Orwell[9] (2-step intervals consist of 1 8/7 and 8 7/6's)&lt;/li&gt;&lt;li&gt;Miracle[10] (2-step intervals consist of 8 8/7's and 2 7/6's)&lt;/li&gt;&lt;li&gt;Pajara[10] (2-step intervals consist of 6 8/7's and 4 7/6's)&lt;/li&gt;&lt;li&gt;Beatles/Maqamic/Hemif[10] (2-step intervals consist of 6 8/7's and 4 7/6's)&lt;/li&gt;&lt;li&gt;Hedgehog[14] (3-step intervals consist of 4 8/7's and 10 7/6's)&lt;/li&gt;&lt;li&gt;Porcupine[15] (3-step intervals consist of 9 8/7's and 6 7/6's)&lt;/li&gt;&lt;li&gt;Augene[15] (3-step intervals consist of 6 8/7's and 9 7/6's)&lt;/li&gt;&lt;li&gt;Meantone[19] (4-step intervals consist of 9 8/7's and 10 7/6's)&lt;/li&gt;&lt;li&gt;Sensi[19] (4-step intervals consist of 6 8/7's and 13 7/6's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc9"&gt;&lt;a name="x-Rank-2 consonant class scales-7-limit-{8/7, 6/5}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;{8/7, 6/5}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Keemun[4] (aka &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/magical%20seventh%20chord"&gt;magical seventh chord&lt;/a&gt;)&lt;/li&gt;&lt;li&gt;Gorgo[5] (1-step intervals consist of 4 8/7's and 1 6/5)&lt;/li&gt;&lt;li&gt;Porcupine[8] (2-step intervals consist of 2 8/7's and 6 6/5's)&lt;/li&gt;&lt;li&gt;Armodue[9] (2-step intervals consist of 4 8/7's and 5 6/5's)&lt;/li&gt;&lt;li&gt;Negri[9] (2 step intervals consist of 7 8/7's and 2 6/5's)&lt;/li&gt;&lt;li&gt;Astrology[10] (2-step intervals consist of 8 8/7's and 2 6/5's)&lt;/li&gt;&lt;li&gt;Maqamic[10] (2-step intervals consist of 6 8/7's and 4 7/6's)&lt;/li&gt;&lt;li&gt;Flattone[12] (3-step intervals consist of 3 8/7's and 9 6/5's)&lt;/li&gt;&lt;li&gt;Magic[16] (4-step intervals consist of 4 8/7's and 12 6/5's)&lt;/li&gt;&lt;li&gt;Mohajira[17] (4-step intervals consist of 6 8/7's and 11 6/5's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc10"&gt;&lt;a name="x-Rank-2 consonant class scales-7-limit-{8/7, 5/4}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;{8/7, 5/4}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Hemithirds[7] (2-step intervals consist of 5 5/4's and 2 8/7's)&lt;/li&gt;&lt;li&gt;Godzilla[9] (2-step intervals consist of 8 7/6's and 1 5/4)&lt;/li&gt;&lt;li&gt;Magic[13] (4-step intervals consist of 1 8/7 and 12 5/4's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc11"&gt;&lt;a name="x-Rank-2 consonant class scales-7-limit-{7/6, 6/5}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;{7/6, 6/5}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Myna[4] (aka &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/starling%20tetrad"&gt;starling tetrad&lt;/a&gt;)&lt;/li&gt;&lt;li&gt;Sensi[8] (2-step intervals consist of 2 7/6's and 6 6/5's)&lt;/li&gt;&lt;li&gt;Hedgehog[8] (2-step intervals consist of 4 7/6's and 4 6/5's)&lt;/li&gt;&lt;li&gt;Superpelog[9] (2-step intervals consist of 8 7/6's and 1 6/5)&lt;/li&gt;&lt;li&gt;Negri[9] (2 step intervals consist of 7 7/6's and 2 6/5's)&lt;/li&gt;&lt;li&gt;Meantone[12] (3-step intervals consist of 3 7/6's and 9 6/5's)&lt;/li&gt;&lt;li&gt;Augene[12] (3-step intervals consist of 3 7/6's and 9 6/5's)&lt;/li&gt;&lt;li&gt;Pajara[12] (3-step intervals consist of 6 7/6's and 6 6/5's)&lt;/li&gt;&lt;li&gt;Valentine[16] (4-step intervals consist of 4 7/6's and 12 6/5's)&lt;/li&gt;&lt;li&gt;Muggles[16] (4-step intervals consist of 4 7/6's and 12 6/5's)&lt;/li&gt;&lt;li&gt;Miracle[21] (5-step intervals consist of 13 7/6's and 8 6/5's)&lt;/li&gt;&lt;/ul&gt;{7/6, 5/4}&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;Deutone[7] (2-step intervals consist of 2 7/6's and 5 5/4's)&lt;/li&gt;&lt;li&gt;Godzilla[9] (2-step intervals consist of 8 7/6's and 1 5/4)&lt;/li&gt;&lt;li&gt;Superpyth[12] (3-step intervals consist of 9 7/6's and 3 5/4's)&lt;/li&gt;&lt;/ul&gt;{6/5, 9/7}&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)&lt;/li&gt;&lt;li&gt;Superpyth[12] (4-step intervals consist of 4 6/5's and 8 9/7's)&lt;/li&gt;&lt;/ul&gt;{5/4, 7/5}&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;Keemun[7] (3-step intervals consist of 2 5/4's and 5 7/5's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc12"&gt;&lt;a name="x-Rank-2 consonant class scales-7-limit-{4/3, 7/5}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;{4/3, 7/5}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Meantone[7] (3-step intervals consist of 6 4/3's and 1 7/5; both 2-step intervals are also consonant)&lt;/li&gt;&lt;li&gt;Beatles[7] (3-step intervals consist of 5 4/3's and 2 7/5')&lt;/li&gt;&lt;li&gt;Negri[9] (4-step intervals consist of 5 4/3's and 4 7/5's)&lt;/li&gt;&lt;li&gt;Sensi[11] (5-step intervals consist of 4 4/3's and 7 7/5's)&lt;/li&gt;&lt;li&gt;Miracle[11] (5-step intervals consist of 5 4/3's and 6 7/5's)&lt;/li&gt;&lt;li&gt;Magic[16] (7-step intervals consist of 11 4/3's and 5 7/5's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc13"&gt;&lt;a name="x-Rank-2 consonant class scales-7-limit-{4/3, 10/7}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;{4/3, 10/7}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Garibaldi[7] (3-step intervals consist of 6 4/3's and 1 10/7)&lt;/li&gt;&lt;li&gt;Dominant[7] (3-step intervals consist of 6 4/3's and 1 10/7)&lt;/li&gt;&lt;li&gt;Augene[9] (4-step intervals consist of 6 4/3's and 3 10/7's)&lt;/li&gt;&lt;li&gt;Godzilla[9] (4-step intervals consist of 7 4/3's and 2 10/7's)&lt;/li&gt;&lt;li&gt;Superpyth[12] (5-step intervals consist of 11 4/3's and 1 10/7)&lt;/li&gt;&lt;li&gt;Muggles[13] (6-step intervals consist of 8 4/3's and 5 10/7's)&lt;/li&gt;&lt;li&gt;Rodan[21] (9-step intervals consist of 18 4/3's and 3 10/7's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc14"&gt;&lt;a name="x-Rank-2 consonant class scales-7-limit-{7/5, 10/7}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;{7/5, 10/7}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Hemithirds[6] (3-step intervals consist of 3 7/5's and 3 10/7's)&lt;/li&gt;&lt;li&gt;Miracle[10] (5-step intervals consist of 5 7/5's and 5 10/7's)&lt;/li&gt;&lt;li&gt;Beatles[10] (5-step intervals consist of 5 7/5's and 5 10/7's)&lt;/li&gt;&lt;li&gt;Negri[10] (5-step intervals consist of 5 7/5's and 5 10/7's)&lt;/li&gt;&lt;li&gt;Blacksmith[10] (5-step intervals consist of 5 7/5's and 5 10/7's)&lt;/li&gt;&lt;li&gt;Meantone[12] (6-step intervals consist of 6 7/5's and 6 10/7's)&lt;/li&gt;&lt;li&gt;Augene[12] (6-step intervals consist of 6 7/5's and 6 10/7's)&lt;/li&gt;&lt;li&gt;Muggles[16] (8-step intervals consist of 8 7/5's and 8 10/7's)&lt;/li&gt;&lt;li&gt;Superpyth[22] (11-step intervals consist of 11 7/5's and 11 10/7's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="x-Rank-2 consonant class scales-9-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;9-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc16"&gt;&lt;a name="x-Rank-2 consonant class scales-9-limit-{7/6, 9/7}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;{7/6, 9/7}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Superpyth[7] (2-step intervals consist of 3 9/7's and 4 7/6's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc17"&gt;&lt;a name="x-Rank-2 consonant class scales-9-limit-{6/5, 9/7}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;{6/5, 9/7}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Sensamagic, Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)&lt;/li&gt;&lt;li&gt;Hedgehog[6] (2-step intervals consist of 2 6/5's and 4 9/7's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc18"&gt;&lt;a name="x-Rank-2 consonant class scales-9-limit-{5/4, 9/7}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;{5/4, 9/7}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Orwell[9] (3-step intervals consist of 6 5/4's and 3 9/7's)&lt;/li&gt;&lt;li&gt;Negri[9] (3-step intervals consist of 6 5/4's and 3 9/7's)&lt;/li&gt;&lt;li&gt;Meantone[12] (4-step intervals consist of 8 5/4's and 4 9/7's)&lt;/li&gt;&lt;li&gt;Pajara[12] (4-step intervals consist of 8 5/4's and 4 9/7's)&lt;/li&gt;&lt;li&gt;Miracle[21] (7-step interval consists of 14 5/4's and 7 9/7's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc19"&gt;&lt;a name="x-Rank-2 consonant class scales-9-limit-{9/7, 4/3}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;{9/7, 4/3}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Semaphore[5] (2-step intervals consist of 2 9/7's and 3 4/3's)&lt;/li&gt;&lt;li&gt;Superpyth[5] (2-step intervals consist of 1 9/7 and 4 4/3's)&lt;/li&gt;&lt;li&gt;Diminished[8] (3-step intervals consist of 4 9/7's and 4 4/3's)&lt;/li&gt;&lt;li&gt;Sensi[8] (3-step intervals consist of 7 9/7's and 1 4/3)&lt;/li&gt;&lt;li&gt;Hedgehog[8] (3-step intervals consist of 6 9/7's and 2 4/3's)&lt;/li&gt;&lt;li&gt;Beatles/Hemif/Maqamic[10] (4-step intervals consist of 2 9/7's and 8 4/3's)&lt;/li&gt;&lt;li&gt;Pajara[10] (4-step intervals consist of 2 9/7's and 8 4/3's)&lt;/li&gt;&lt;li&gt;Negri[10] (4-step intervals consist of 4 9/7's and 6 4/3's)&lt;/li&gt;&lt;li&gt;Orwell[13] (5-step intervals consist of 7 9/7's and 6 4/3's)&lt;/li&gt;&lt;li&gt;Keemun[15] (6-step intervals consist of 6 9/7's and 9 4/3's)&lt;/li&gt;&lt;li&gt;Augene[15] (6-step intervals consist of 3 9/7's and 12 4/3's)&lt;/li&gt;&lt;li&gt;Mohajira[17] (7-step intervals consist of 2 9/7's and 17 4/3's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc20"&gt;&lt;a name="x-Rank-2 consonant class scales-9-limit-{9/7, 7/5}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;{9/7, 7/5}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Deutone[7] (3-step intervals consist of 4 7/5's and 3 9/7's)&lt;/li&gt;&lt;li&gt;Magic[13] (5-step intervals consist of 11 9/7's and 2 7/5's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc21"&gt;&lt;a name="x-Rank-2 consonant class scales-9-limit-{9/7,10/7}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;{9/7,10/7}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Muggles[10] (5-step intervals consist of 8 9/7's and 2 10/7's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc22"&gt;&lt;a name="x-Rank-2 consonant class scales-9-limit-{9/7, 3/2}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;{9/7, 3/2}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Magic[7] (3-step intervals consist of 5 9/7's and 2 3/2's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc23"&gt;&lt;a name="x-Rank-2 consonant class scales-3.5.7-subgroup"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;3.5.7-subgroup&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc24"&gt;&lt;a name="x-Rank-2 consonant class scales-3.5.7-subgroup-{9/7, 7/5}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;{9/7, 7/5}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Sirius[7] (2-step intervals consist of 2 9/7's and 5 7/5's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc25"&gt;&lt;a name="x-Rank-2 consonant class scales-3.5.7-subgroup-{7/5, 5/3}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;{7/5, 5/3}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Rank-2 Bohlen-Pierce[5] (2-step intervals consist of 2 7/5's and 3 5/3's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc26"&gt;&lt;a name="x-Rank-2 consonant class scales-3.5.7-subgroup-{5/3, 9/5}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;{5/3, 9/5}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Sirius[6] (3-step intervals consist of 3 5/3's and 3 9/5's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc27"&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt; &lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="x-Rank-3 consonant class scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Rank-3 consonant class scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc29"&gt;&lt;a name="x-Rank-3 consonant class scales-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;7-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc30"&gt;&lt;a name="x-Rank-3 consonant class scales-7-limit-{8/7, 6/5, 5/4}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;{8/7, 6/5, 5/4}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Marvel, &lt;a class="wiki_link" href="/marvel11max7a"&gt;marvel11max7a&lt;/a&gt; and marvel11max7b, 7 notes (2-step intervals consist of 1 8/7, 2 6/5's, and 4 5/4's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc31"&gt;&lt;a name="x-Rank-3 consonant class scales-7-limit-{7/6, 6/5, 5/4}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;{7/6, 6/5, 5/4}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Hewuermity or &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/zeus7"&gt;Zeus&lt;/a&gt;, &lt;a class="wiki_link" href="/zeus7tri"&gt;zeus7tri&lt;/a&gt;, 7 notes (2-step intervals consist of 2 7/6's, 1 6/5, and 4 5/4's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc32"&gt;&lt;a name="x-Rank-3 consonant class scales-7-limit-{5/4, 4/3, 7/5}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;{5/4, 4/3, 7/5}&lt;/h4&gt;
&lt;ul&gt;&lt;li&gt;Breed or Jove, 7 notes (3-step intervals consist of 2 5/4's, 1 4/3, and 4 7/5's)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc33"&gt;&lt;a name="x-Rank-3 consonant class scales-7-limit-{7/6, 6/5, 5/4}"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;{7/6, 6/5, 5/4}&lt;/h4&gt;
Portent; 4 5/4's 4 6/5's and 3 7/6's in the third class&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc34"&gt;&lt;a name="Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;Links&lt;/h1&gt;
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Revision as of 00:00, 17 July 2018

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)
  • Godzilla[14] (4-step intervals consist of 8 6/5's and 6 5/4's)
  • Helmholtz[17] (5-step intervals consist of 8 6/5's and 9 5/4's)
  • Superpyth[17] (5-step intervals consist of 9 6/5's and 8 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)
  • Hedgehog[14] (3-step intervals consist of 4 8/7's and 10 7/6's)
  • Porcupine[15] (3-step intervals consist of 9 8/7's and 6 7/6's)
  • Augene[15] (3-step intervals consist of 6 8/7's and 9 7/6's)
  • Meantone[19] (4-step intervals consist of 9 8/7's and 10 7/6's)
  • Sensi[19] (4-step intervals consist of 6 8/7's and 13 7/6's)

{8/7, 6/5}

  • Keemun[4] (aka 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)
  • Mohajira[17] (4-step intervals consist of 6 8/7's and 11 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)
  • Magic[13] (4-step intervals consist of 1 8/7 and 12 5/4's)

{7/6, 6/5}

  • Myna[4] (aka 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)
  • Pajara[12] (3-step intervals consist of 6 7/6's and 6 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)
  • Miracle[21] (5-step intervals consist of 13 7/6's and 8 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)
  • Superpyth[12] (3-step intervals consist of 9 7/6's and 3 5/4's)

{6/5, 9/7}

  • Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)
  • Superpyth[12] (4-step intervals consist of 4 6/5's and 8 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)
  • Miracle[11] (5-step intervals consist of 5 4/3's and 6 7/5's)
  • Magic[16] (7-step intervals consist of 11 4/3's and 5 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)
  • Superpyth[12] (5-step intervals consist of 11 4/3's and 1 10/7)
  • Muggles[13] (6-step intervals consist of 8 4/3's and 5 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)
  • Meantone[12] (6-step intervals consist of 6 7/5's and 6 10/7's)
  • Augene[12] (6-step intervals consist of 6 7/5's and 6 10/7's)
  • Muggles[16] (8-step intervals consist of 8 7/5's and 8 10/7's)
  • Superpyth[22] (11-step intervals consist of 11 7/5's and 11 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)
  • Meantone[12] (4-step intervals consist of 8 5/4's and 4 9/7's)
  • Pajara[12] (4-step intervals consist of 8 5/4's and 4 9/7's)
  • Miracle[21] (7-step interval consists of 14 5/4's and 7 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)
  • Orwell[13] (5-step intervals consist of 7 9/7's and 6 4/3's)
  • Keemun[15] (6-step intervals consist of 6 9/7's and 9 4/3's)
  • Augene[15] (6-step intervals consist of 3 9/7's and 12 4/3's)
  • Mohajira[17] (7-step intervals consist of 2 9/7's and 17 4/3's)

{9/7, 7/5}

  • Deutone[7] (3-step intervals consist of 4 7/5's and 3 9/7's)
  • Magic[13] (5-step intervals consist of 11 9/7's and 2 7/5'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 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

http://tech.groups.yahoo.com/group/tuning-math/message/6056

http://tech.groups.yahoo.com/group/tuning-math/message/6060

http://tech.groups.yahoo.com/group/tuning-math/message/6062

http://tech.groups.yahoo.com/group/tuning-math/message/6064

http://tech.groups.yahoo.com/group/tuning-math/message/6065

http://tech.groups.yahoo.com/group/tuning-math/message/6067

http://tech.groups.yahoo.com/group/tuning-math/message/6068

http://tech.groups.yahoo.com/group/tuning-math/message/6075

http://tech.groups.yahoo.com/group/tuning-math/message/6082

http://tech.groups.yahoo.com/group/tuning-math/message/6086

http://tech.groups.yahoo.com/group/tuning-math/message/6088

http://tech.groups.yahoo.com/group/tuning-math/message/6089

http://tech.groups.yahoo.com/group/tuning-math/message/6090

http://tech.groups.yahoo.com/group/tuning-math/message/6092

http://tech.groups.yahoo.com/group/tuning-math/message/6094

http://tech.groups.yahoo.com/group/tuning-math/message/6097

http://tech.groups.yahoo.com/group/tuning-math/message/6100

http://tech.groups.yahoo.com/group/tuning-math/message/6102

http://tech.groups.yahoo.com/group/tuning-math/message/6103

http://tech.groups.yahoo.com/group/tuning-math/message/6104

http://tech.groups.yahoo.com/group/tuning-math/message/6169

http://tech.groups.yahoo.com/group/tuning-math/message/15082

http://tech.groups.yahoo.com/group/tuning-math/message/15102

http://tech.groups.yahoo.com/group/tuning-math/message/15103

http://tech.groups.yahoo.com/group/tuning-math/message/15123

http://tech.groups.yahoo.com/group/tuning-math/message/15483

http://tech.groups.yahoo.com/group/tuning-math/message/15501

http://tech.groups.yahoo.com/group/tuning-math/message/19390

http://tech.groups.yahoo.com/group/tuning-math/message/19410

http://launch.groups.yahoo.com/group/tuning/message/41360

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