Hemithirds

The hemithirds temperament has a half of major third interval of 5/4 as a generator (hemithird, ~28/25, around 193.2 cents). Aside from two generator represents ~5/4, five generator gives ~7/4 and fifteen gives ~16/3 (tempering out 1029/1024 and 3136/3125 in the 7-limit).

See Hemimean clan #Hemithirds or Luna family #Hemithirds for more information.

Chords

Main article: Chords of hemithirds

Tuning spectrum

Gencom: [2 28/25; 196/195 352/351 385/384 625/624]

Gencom mapping: [⟨1 4 2 2 7 0], ⟨0 -15 2 5 -22 23]]

Eigenmonzo (Unchanged-interval)	Generator (¢)	Comments
14/13	192.872
12/11	192.948
15/11	192.995
13/10	193.058
16/13	193.066
13/11	193.094
15/13	193.118
13/12	193.120
11/8	193.122
11/10	193.125
18/13	193.144
5/4	193.157
6/5	193.198	5-odd-limit minimax
10/9	193.200
4/3	193.203
16/15	193.210
14/11	193.241	11-odd-limit minimax
9/7	193.283	9-odd-limit minimax
7/6	193.344	7-odd-limit minimax
15/14	193.364
11/9	193.426
8/7	193.765
7/5	194.171