Consonant class scale: Difference between revisions

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).

==Rank-2 consonant class scales==

===3-limit===

===={4/3, 3/2}====

<ul><li>Augmented[6] (3-step intervals consist of 3 4/3's and 3 3/2's)</li></ul>

===5-limit===

 

===={6/5, 5/4}====

<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>

===={6/5, 4/3}====

<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>

===={5/4, 4/3}====

<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/Neutrominant[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>

===7-limit===

 

===={8/7, 7/6}====

<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/Neutrominant/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>

===={8/7, 6/5}====

<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>Neutrominant[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>

===={8/7, 5/4}====

<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>

===={7/6, 6/5}====

<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} ====

<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>

 

<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>

 

<ul><li>Keemun[7] (3-step intervals consist of 2 5/4's and 5 7/5's)</li></ul>

===={4/3, 7/5}====

<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>

<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>

<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>

===9-limit===

 

===={7/6, 9/7}====

<ul><li>Superpyth[7] (2-step intervals consist of 3 9/7's and 4 7/6's)</li></ul>

===={6/5, 9/7}====

<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>

===={5/4, 9/7}====

<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>

===={9/7, 4/3}====

<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/Neutrominant[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>

===={9/7, 7/5}====

<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>

===={9/7,10/7}====

<ul><li>Muggles[10] (5-step intervals consist of 8 9/7's and 2 10/7's)</li></ul>

===={9/7, 3/2}====

<ul><li>Magic[7] (3-step intervals consist of 5 9/7's and 2 3/2's)</li></ul>

 

=== 11-limit ===

 

==== {12/11, 9/8} ====

 

* Mohajira[7] (1-step intervals consist of 4 12/11's and 3 9/8s)

 

==== {6/5, 11/9} ====

 

* Mohajira[7] (2-step intervals consist of 1 6/5 and 6 11/9's)

 

==== {4/3, 11/8} ====

 

* Mohajira[7] (3-step intervals consist of 5 4/3's and 2 11/8's)

* Orwell[9] (4-step intervals consist of 2 4/3's and 7 11/8's)

 

=== 13-limit ===

 

==== {13/11, 13/10} ====

 

* Shoe[6] (2-step intervals consist of  2 13/11's and 4 13/10's)

 

===3.5.7-subgroup===

 

===={9/7, 7/5}====

<ul><li>Sirius[7] (2-step intervals consist of 2 9/7's and 5 7/5's)</li></ul>

===={7/5, 5/3}====

<ul><li>Rank-2 Bohlen-Pierce[5] (2-step intervals consist of 2 7/5's and 3 5/3's)</li></ul>

===={5/3, 9/5}====

<ul><li>Sirius[6] (3-step intervals consist of 3 5/3's and 3 9/5's)</li></ul>

 

==Rank-3 consonant class scales==

 

===7-limit===

 

===={8/7, 6/5, 5/4}====

<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>

===={7/6, 6/5, 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>

===={5/4, 4/3, 7/5}====

<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>

===={7/6, 6/5, 5/4}====

* Portent; 4 5/4's 4 6/5's and 3 7/6's in the third class

 

 

=== 5-limit ===

 

==== {6/5, 5/4, 4/3} ====

* 1-3-5-11 hexany, 6 notes (2-step intervals consist of 2 6/5's, 2 5/4's, and 2 4/3's)

 

* http://tech.groups.yahoo.com/group/tuning-math/message/6056{{dead link}}

* 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

 

[[Category:Scale]]