Luna and hemithirds
Hemithirds temperament has a half of major third interval of 5/4 as a generator (~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
Spectrum of hemithirds tunings by eigenmonzos
Gencom: [2 28/25; 196/195 352/351 385/384 625/624]
Gencom map: [⟨1 4 2 2 7 0], ⟨0 -15 2 5 -22 23]]
| Eigenmonzo | Hemithird | Comments |
|---|---|---|
| 12/11 | 192.948 | |
| 11/8 | 193.122 | |
| 11/10 | 193.125 | |
| 5/4 | 193.157 | |
| 6/5 | 193.198 | 5-odd-limit minimax |
| 10/9 | 193.200 | |
| 4/3 | 193.203 | |
| 14/11 | 193.241 | 11-odd-limit minimax |
| 9/7 | 193.283 | 9-odd-limit minimax |
| 7/6 | 193.344 | 7-odd-limit minimax |
| 11/9 | 193.426 | |
| 8/7 | 193.765 | |
| 7/5 | 194.171 |