Luna and hemithirds: Difference between revisions
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'''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). | '''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. | See [[Hemimean clan #Hemithirds]] or [[Luna family #Hemithirds]] for more information. | ||
| Line 16: | Line 16: | ||
! Hemithird | ! Hemithird | ||
! Comments | ! Comments | ||
|- | |||
| 14/13 | |||
| 192.872 | |||
| | |||
|- | |- | ||
| 12/11 | | 12/11 | ||
| 192.948 | | 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 | |||
| | | | ||
|- | |- | ||
| Line 27: | Line 55: | ||
| 11/10 | | 11/10 | ||
| 193.125 | | 193.125 | ||
| | |||
|- | |||
| 18/13 | |||
| 193.144 | |||
| | | | ||
|- | |- | ||
| Line 43: | Line 75: | ||
| 4/3 | | 4/3 | ||
| 193.203 | | 193.203 | ||
| | |||
|- | |||
| 16/15 | |||
| 193.210 | |||
| | | | ||
|- | |- | ||
| Line 56: | Line 92: | ||
| 193.344 | | 193.344 | ||
| 7-odd-limit minimax | | 7-odd-limit minimax | ||
|- | |||
| 15/14 | |||
| 193.364 | |||
| | |||
|- | |- | ||
| 11/9 | | 11/9 | ||
Revision as of 23:07, 2 July 2021
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
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 |
|---|---|---|
| 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 |