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consonant class scaleis a scale with aconsonant 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}

## 5-limit

## {6/5, 5/4}

## {6/5, 4/3}

## {5/4, 4/3}

## 7-limit

## {8/7, 7/6}

## {8/7, 6/5}

## {8/7, 5/4}

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

## {4/3, 10/7}

## {7/5, 10/7}

## 9-limit

## {7/6, 9/7}

## {6/5, 9/7}

## {5/4, 9/7}

## {9/7, 4/3}

## {9/7, 7/5}

## {9/7,10/7}

## {9/7, 3/2}

## 3.5.7-subgroup

## {9/7, 7/5}

## {7/5, 5/3}

## {5/3, 9/5}

## Rank-3 consonant class scales

## 7-limit

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

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

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

## {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/6056http://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