Tsal Music

The predominant musical system of Tsal is a system of 31-tone equal temperament.

Harmony

The motivating factor behind 31-EDO becoming the dominant tuning system of Tsalian music is its strong approximations of the 5th and 7th harmonics and their corresponding limit intervals, which have long been regarded in the Tsalian theory as consonances.

Naming

In Tsalian theory, just intervals are named after gemstones in a practice dating to ancient times. Pairs of inversions are "greater" and "lesser" variants of the same stone, though the simpler ration in each pair is considered the primary inversion and is often referred to using the gem alone.

Common 7-Limit Just Intervals
Ratio	Interval Name			31-EDO Approximation
	Tsal "Gemstone Notation"		English	Tsal	English	EDOstep
2:1	Diamond		Octave		C	0
3:2	Ruby		Perfect fifth		G	18
4:3	Lesser Ruby		Perfect fourth		F	13
5:4	Sapphire		Major third		E	10
8:5	Greater Sapphire		Minor sixth		A	21
5:3	Amethyst		Major sixth		A	23
6:5	Lesser Amethyst		Minor third		E	8
7:4	Emerald		Septimal minor seventh		A	25
8:7	Lesser Emerald		Septimal whole tone		D	6
7:5	Qomuk		Lesser septimal tritone, Augmented fourth		F	15
10:7	Greater Qomuk		Greater septimal tritone, Diminished fifth		G	16

Some intervals beyond the 7-limit also have gemstone names, but these intervals are less likely to be considered consonant.

Rarer Just Intervals
Ratio	Interval Name			31-EDO Approximation
	Tsal "Gemstone Notation"		English	Tsal	English	EDOstep
11:8	Topaz		Undecimal superfourth		F	14
16:11	Greater Topaz		Undecimal subfifth		G	17

Rhythm

Tsalian music commonly employs irregular rhythms. One common pattern in use is the "frog rhythm", a four beat cycle in which the first and third beats are longer. This corresponds to a 10/8 (3+2+3+2) time signature in Western Terran music theory.