User:VectorGraphics/Latitude

The spectrum of mediants

"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 0.1, and for the septimal thirds it's about 0.24.

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