Latitude
A mediant is an interval defined by being a specified portion of a fifth, and that can be used in a chord with that fifth to produce a certain quality. A mediant always has a fifth complement, and the portion of the fifth that they differ by is the contrastiveness of that pair of mediants. For example, the contrastiveness of the classical major and minor thirds is 0.1, and for the septimal thirds it's about 0.24.
Mediant names can be assigned based on contrastiveness, as follows:
| Contrastiveness | Major name | Minor name | General name | Type |
|---|---|---|---|---|
| 0% to 2.9% | (Tendo)-neutral third | (Arto)-neutral third | Neutral thirds | Third |
| 2.9% to 7.1% | Submajor third | Supraminor third | Intraclassical thirds | |
| 7.1% to 12.9% | Classical major third | Classical minor third | Classical thirds | |
| 12.9% to 17.1% | Pythagorean major third | Pythagorean minor third | Pythagorean thirds | |
| 17.1% to 21.4% | Neogothic major third | Neogothic minor third | Neogothic thirds | |
| 21.4% to 25.7% | Septimal major third, supermajor third | Septimal minor third, subminor third | Septimal thirds | |
| 25.7% to 30% | Tendo third, ultramajor third | Arto third, inframinor third | Tridecimal thirds | |
| 30% to 35.7% | Major paraslendric | Minor paraslendric | Paraslendrics | Second/fourth |
| 35.7% to 40% | Supraslendric | Subslendric | Extraslendrics | |
| 40% to 44.3% | Major suspended | Minor suspended | Suspendeds | |
| 44.3% to 47.1% | Suprasuspended | Subsuspended | Extrasuspendeds | |
| 47.1% to 52.9% | Major paratetracot | Minor paratetracot | Paratetracots | |
| >52.9% | - | |||
Pairs of mediants with higher contrastiveness than 50% tend to sound more dissonant against the fifth or root than lower-contrastiveness mediants, and extremely low-contrastiveness mediants may not sound distinct from each other. Higher contrastiveness enables "cross-tonality", where both mediants in the pair can be played at once in the same chord, as in suspended or arto/tendo chords.
Here is a table of the contrastiveness of mediants up to 50% in various EDOs:
| Fifth size in edosteps | Edos | Contrastiveness of mediant pairs |
|---|---|---|
| 3 | 5 | 33.3% |
| 4 | 7 | 0%, 50% |
| 5 | 9 | 20% |
| 6 | 10 | 0%, 33.3% |
| 7 | 12 | 14.3%, 42.9% |
| 8 | 13, 14 | 0%, 25%, 50% |
| 9 | 15, 16 | 11.1%, 33.3% |
| 10 | 17, 18 | 0%, 20%, 40% |
| 11 | 18, 19 | 9.1%, 27.3%, 45.5% |
| 12 | 20, 21 | 0.0%, 16.7%, 33.3%, 50% |
| 13 | 22, 23 | 7.7%, 23.1%, 38.5% |
| 14 | 23, 24, 25 | 0%, 14.3%, 28.6%, 42.9% |
| 15 | 25, 26, 27 | 6.7%, 20%, 33.3%, 46.7% |
| 16 | 26, 27, 28 | 0%, 12.5%, 25%, 37.5%, 50% |
| 17 | 28, 29, 30 | 5.9%, 17.6%, 29.4%, 41.2% |
| 18 | 30, 31, 32 | 11.1%, 22.2%, 33.3%, 44.4% |
| 19 | 31, 32, 33, 34 | 5.3%, 15.8%, 26.3%, 36.8%, 47.4% |
| 20 | 33, 34, 35, 36 | 0%, 10%, 20%, 30%, 40%, 50% |
| 21 | 35, 36, 37, 38 | 4.8%, 14.3%, 23.8%, 33.3%, 42.9% |
| 22 | 36, 37, 38, 39 | 9.1%, 18.2%, 27.3%, 36.4%, 45.5% |
| 23 | 38, 39, 40, 41 | 4.3%, 13%, 21.7%, 30.4%, 39.1%, 47.8% |
| 24 | 39, 40, 41, 42, 43 | 0.0%, 8.3%, 16.7%, 25%, 33.3%, 41.7%, 50% |
| 25 | 41, 42, 43, 44, 45 | 4%, 12%, 20%, 28%, 36%, 44% |
| 26 | 43, 44, 45, 46, 47 | 7.7%, 15.4%, 23.1%, 30.8%, 38.5%, 46.2% |
| 27 | 44, 45, 46, 47, 48 | 3.7%, 11.1%, 18.5%, 25.9%, 33.3%, 40.7%, 48.1% |
| 28 | 46, 47, 48, 49, 50 | 0%, 7.1%, 14.3%, 21.4%, 28.6%, 35.7%, 42.9% |
| 29 | 48, 49, 50, 51, 52 | 3.4%, 10.3%, 17.2%, 24.1%, 31.0%, 37.9%, 44.8% |
| 30 | 49, 50, 51, 52, 53, 54 | 6.7%, 13.3%, 20%, 26.7%, 33.3%, 40% 46.7% |
| 31 | 51, 52, 53, 54, 55, 56 | 3.2%, 9.7%, 16.1%, 22.6%, 29.0%, 35.5%, 41.9%, 48.4% |