Mediant (tonality)
This page is about the way of dividing fifths into "thirds". For the use of "mediant" in the context of general mathematics and just intonation, see Mediant (just intonation).
"Mediant" is a term devised by Vector to refer to an interval as 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 10%, and for the septimal thirds it's about 24%.
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% |
Vector's nomenclature for mediants
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/interseptimals | |
| 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% | - | |||
Diatonic and antidiatonic fifths can also be categorized by the contrastiveness of the mediants they generate:
| Third type | Category | Tuning range | EDO |
| Interseptimal | Inframedio | 654.6-661.4 | 11edo |
| Septimal | Avila | 661.4-665.3 | 29edo |
| Neogothic | Pelogic | 665.3-669.3 | 9edo |
| Pythagorean | Mediocratic | 669.3-673.3 | 25edo |
| Classical | Mavila | 673.3-678.7 | 16edo |
| Intraclassical | Sharpmavila | 678.8-682.9 | 30edo |
| Neutral | Neutral | 682.9-688.5 | 7edo |
| Intraclassical | Flattone | 688.5-692.8 | 26edo |
| Classical | Meantone | 692.8-698.5 | 19edo |
| Pythagorean | Pythagorean | 698.5-702.9 | 12edo |
| Neogothic | Neogothic | 702.9-707.3 | 17edo |
| Septimal | Archy | 707.4-711.9 | 22edo |
| Interseptimal | Ultrapyth | 711.9-720 | 5edo |