Latitude

The spectrum of mediants

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%