Hemithirds

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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
)
hemithird
(¢)
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