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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>
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| : This revision was by author [[User:hearneg|hearneg]] and made on <tt>2014-12-30 02:06:51 UTC</tt>.<br>
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| : The original revision id was <tt>536009582</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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).
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| 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. |
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| ==Rank-2 consonant class scales== | | ==Rank-2 consonant class scales== |
| ===3-limit===
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| ===={4/3, 3/2}====
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| * Augmented[6] (3-step intervals consist of 3 4/3's and 3 3/2's)
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| ===5-limit===
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| ===={6/5, 5/4}====
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| * Meantone[7] (2-step intervals consist of 4 6/5's and 3 5/4's)
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| * Porcupine[7] (2-step intervals consist of 5 6/5's and 2 5/4's)
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| * Mavila[7] (2-step intervals consist of 3 6/5's and 4 5/4's)
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| * Srutal[10] (3-step intervals consist of 4 6/5's and 6 5/4's)
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| * Negri[10] (3-step intervals consist of 3 6/5's and 7 5/4's)
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| * Blackwood[10] (3-step intervals consist of 5 6/5's and 5 5/4's)
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| * Sensi[11] (3-step intervals consist of 9 6/5's and 2 5/4's)
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| * Orson[13] (4-step intervals consist of 3 6/5's and 10 5/4's)
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| * Helmholtz[17] (5-step intervals consist of 8 6/5's and 9 5/4's)
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| ===={6/5, 4/3}====
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| * Mavila[5] (2-step intervals consist of 1 6/5 and 4 4/3's)
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| * Hanson[7] (2-step intervals consist of 6 6/5's and 1 4/3)
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| * Srutal[8] (3-step intervals consist of 2 6/5's and 6 4/3's)
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| * Doublewide[10] (3-step intervals consist of 8 6/5's and 2 4/3's)
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| ===={5/4, 4/3}====
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| * Meantone[5] (2-step intervals consist of 1 5/4 and 4 4/3's)
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| * Porcupine[8] (3-step intervals consist of 3 5/4's and 5 4/3's)
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| * Diminished[8] (3-step intervals consist of 4 5/4's and 4 4/3's)
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| * Mohajira/Maqamic[10] (4-step intervals consist of 2 5/4's and 8 4/3's)
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| * Hanson[11] (4-step intervals consist of 6 5/4's and 5 4/3's)
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| * Tetracot[13] (5-step intervals consist of 4 5/4's and 9 4/3's)
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| ===7-limit===
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| ===={8/7, 7/6}====
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| * Slendric[5] (1-step intervals consist of 4 8/7's and 1 7/6)
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| * Superpyth[5] (1-step intervals consist of 3 8/7's and 2 7/6's)
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| * Orwell[9] (2-step intervals consist of 1 8/7 and 8 7/6's)
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| * Miracle[10] (2-step intervals consist of 8 8/7's and 2 7/6's)
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| * Pajara[10] (2-step intervals consist of 6 8/7's and 4 7/6's)
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| * Beatles/Maqamic/Hemif[10] (2-step intervals consist of 6 8/7's and 4 7/6's)
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| ===={8/7, 6/5}====
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| * Keemun[4] (aka [[xenharmonic/magical seventh chord|magical seventh chord]])
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| * Gorgo[5] (1-step intervals consist of 4 8/7's and 1 6/5)
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| * Porcupine[8] (2-step intervals consist of 2 8/7's and 6 6/5's)
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| * Armodue[9] (2-step intervals consist of 4 8/7's and 5 6/5's)
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| * Negri[9] (2 step intervals consist of 7 8/7's and 2 6/5's)
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| * Astrology[10] (2-step intervals consist of 8 8/7's and 2 6/5's)
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| * Maqamic[10] (2-step intervals consist of 6 8/7's and 4 7/6's)
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| * Flattone[12] (3-step intervals consist of 3 8/7's and 9 6/5's)
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| * Magic[16] (4-step intervals consist of 4 8/7's and 12 6/5's)
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| ===={8/7, 5/4}====
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| * Hemithirds[7] (2-step intervals consist of 5 5/4's and 2 8/7's)
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| * Godzilla[9] (2-step intervals consist of 8 7/6's and 1 5/4)
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| ===={7/6, 6/5}====
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| * Myna[4] (aka [[xenharmonic/starling tetrad|starling tetrad]])
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| * Sensi[8] (2-step intervals consist of 2 7/6's and 6 6/5's)
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| * Hedgehog[8] (2-step intervals consist of 4 7/6's and 4 6/5's)
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| * Superpelog[9] (2-step intervals consist of 8 7/6's and 1 6/5)
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| * Negri[9] (2 step intervals consist of 7 7/6's and 2 6/5's)
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| * Meantone[12] (3-step intervals consist of 3 7/6's and 9 6/5's)
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| * Augene[12] (3-step intervals consist of 3 7/6's and 9 6/5's)
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| * Valentine[16] (4-step intervals consist of 4 7/6's and 12 6/5's)
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| * Muggles[16] (4-step intervals consist of 4 7/6's and 12 6/5's)
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| {7/6, 5/4}
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| * Deutone[7] (2-step intervals consist of 2 7/6's and 5 5/4's)
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| * Godzilla[9] (2-step intervals consist of 8 7/6's and 1 5/4)
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| * Superpyth[12] (3-step intervals consist of 9 7/6's and 3 5/4's)
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| {6/5, 9/7}
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| * Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)
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| * Superpyth[12] (4-step intervals consist of 4 6/5's and 8 9/7's)
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| {5/4, 7/5}
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| * Keemun[7] (3-step intervals consist of 2 5/4's and 5 7/5's)
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| ===={4/3, 7/5}====
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| * Meantone[7] (3-step intervals consist of 6 4/3's and 1 7/5; both 2-step intervals are also consonant)
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| * Beatles[7] (3-step intervals consist of 5 4/3's and 2 7/5')
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| * Negri[9] (4-step intervals consist of 5 4/3's and 4 7/5's)
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| * Sensi[11] (5-step intervals consist of 4 4/3's and 7 7/5's)
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| ===={4/3, 10/7}====
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| * Garibaldi[7] (3-step intervals consist of 6 4/3's and 1 10/7)
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| * Dominant[7] (3-step intervals consist of 6 4/3's and 1 10/7)
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| * Augene[9] (4-step intervals consist of 6 4/3's and 3 10/7's)
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| * Godzilla[9] (4-step intervals consist of 7 4/3's and 2 10/7's)
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| * Rodan[21] (9-step intervals consist of 18 4/3's and 3 10/7's)
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| ===={7/5, 10/7}====
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| * Hemithirds[6] (3-step intervals consist of 3 7/5's and 3 10/7's)
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| * Miracle[10] (5-step intervals consist of 5 7/5's and 5 10/7's)
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| * Beatles[10] (5-step intervals consist of 5 7/5's and 5 10/7's)
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| * Negri[10] (5-step intervals consist of 5 7/5's and 5 10/7's)
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| * Blacksmith[10] (5-step intervals consist of 5 7/5's and 5 10/7's)
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| * Meantone[12] (6-step intervals consist of 6 7/5's and 6 10/7's)
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| ===9-limit===
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| ===={7/6, 9/7}====
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| * Superpyth[7] (2-step intervals consist of 3 9/7's and 4 7/6's)
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| ===={6/5, 9/7}====
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| * Sensamagic, Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)
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| * Hedgehog[6] (2-step intervals consist of 2 6/5's and 4 9/7's)
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| ===={5/4, 9/7}====
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| * Orwell[9] (3-step intervals consist of 6 5/4's and 3 9/7's)
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| * Negri[9] (3-step intervals consist of 6 5/4's and 3 9/7's)
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| * Meantone[12] (4-step intervals consist of 8 5/4's and 4 9/7's)
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| ===={9/7, 4/3}====
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| * Semaphore[5] (2-step intervals consist of 2 9/7's and 3 4/3's)
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| * Superpyth[5] (2-step intervals consist of 1 9/7 and 4 4/3's)
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| * Diminished[8] (3-step intervals consist of 4 9/7's and 4 4/3's)
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| * Sensi[8] (3-step intervals consist of 7 9/7's and 1 4/3)
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| * Hedgehog[8] (3-step intervals consist of 6 9/7's and 2 4/3's)
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| * Beatles/Hemif/Maqamic[10] (4-step intervals consist of 2 9/7's and 8 4/3's)
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| * Pajara[10] (4-step intervals consist of 2 9/7's and 8 4/3's)
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| * Negri[10] (4-step intervals consist of 4 9/7's and 6 4/3's)
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| ===={9/7, 7/5}====
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| * Deutone[7] (3-step intervals consist of 4 7/5's and 3 9/7's)
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| ===={9/7,10/7}====
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| * Muggles[10] (5-step intervals consist of 8 9/7's and 2 10/7's)
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| ===={9/7, 3/2}====
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| * Magic[7] (3-step intervals consist of 5 9/7's and 2 3/2's)
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| ===3.5.7-subgroup===
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| ===={9/7, 7/5}====
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| * Sirius[7] (2-step intervals consist of 2 9/7's and 5 7/5's)
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| ===={7/5, 5/3}====
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| * Rank-2 Bohlen-Pierce[5] (2-step intervals consist of 2 7/5's and 3 5/3's)
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| ===={5/3, 9/5}====
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| * Sirius[6] (3-step intervals consist of 3 5/3's and 3 9/5's)
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| ==== ====
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| ==Rank-3 consonant class scales==
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| ===7-limit===
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| ===={8/7, 6/5, 5/4}====
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| * Marvel, [[marvel11max7a]] and marvel11max7b, 7 notes (2-step intervals consist of 1 8/7, 2 6/5's, and 4 5/4's)
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| ===={7/6, 6/5, 5/4}====
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| * 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)
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| ===={5/4, 4/3, 7/5}====
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| * Breed or Jove, 7 notes (3-step intervals consist of 2 5/4's, 1 4/3, and 4 7/5's)
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| ===={7/6, 6/5, 5/4}====
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| Portent; 4 5/4's 4 6/5's and 3 7/6's in the third class
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| =Links= | | ===3-limit=== |
| http://tech.groups.yahoo.com/group/tuning-math/message/6056
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| http://tech.groups.yahoo.com/group/tuning-math/message/6060
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| http://tech.groups.yahoo.com/group/tuning-math/message/6062
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| http://tech.groups.yahoo.com/group/tuning-math/message/6064
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| http://tech.groups.yahoo.com/group/tuning-math/message/6065
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| http://tech.groups.yahoo.com/group/tuning-math/message/6067
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| http://tech.groups.yahoo.com/group/tuning-math/message/6068
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| http://tech.groups.yahoo.com/group/tuning-math/message/6075
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| http://tech.groups.yahoo.com/group/tuning-math/message/6082
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| http://tech.groups.yahoo.com/group/tuning-math/message/6086
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| http://tech.groups.yahoo.com/group/tuning-math/message/6088
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| http://tech.groups.yahoo.com/group/tuning-math/message/6089
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| http://tech.groups.yahoo.com/group/tuning-math/message/6090
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| http://tech.groups.yahoo.com/group/tuning-math/message/6092
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| http://tech.groups.yahoo.com/group/tuning-math/message/6094
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| http://tech.groups.yahoo.com/group/tuning-math/message/6097
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| http://tech.groups.yahoo.com/group/tuning-math/message/6100
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| http://tech.groups.yahoo.com/group/tuning-math/message/6102
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| http://tech.groups.yahoo.com/group/tuning-math/message/6103
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| http://tech.groups.yahoo.com/group/tuning-math/message/6104
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| http://tech.groups.yahoo.com/group/tuning-math/message/6169
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| http://tech.groups.yahoo.com/group/tuning-math/message/15082
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| http://tech.groups.yahoo.com/group/tuning-math/message/15102
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| http://tech.groups.yahoo.com/group/tuning-math/message/15103
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| http://tech.groups.yahoo.com/group/tuning-math/message/15123
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| http://tech.groups.yahoo.com/group/tuning-math/message/15483
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| http://tech.groups.yahoo.com/group/tuning-math/message/15501
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| http://tech.groups.yahoo.com/group/tuning-math/message/19390
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| http://tech.groups.yahoo.com/group/tuning-math/message/19410
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| http://launch.groups.yahoo.com/group/tuning/message/41360</pre></div>
| | ===={4/3, 3/2}==== |
| <h4>Original HTML content:</h4>
| | <ul><li>Augmented[6] (3-step intervals consist of 3 4/3's and 3 3/2's)</li></ul> |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em
| | ===5-limit=== |
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| | ===={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 |