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). | |||
See [[Hemimean clan #Hemithirds]] or [[Luna family #Hemithirds]] for more information. | See [[Hemimean clan #Hemithirds]] or [[Luna family #Hemithirds]] for more information. | ||
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== Spectrum of hemithirds tunings by eigenmonzos == | == Spectrum of hemithirds tunings by eigenmonzos == | ||
Gencom: [2 28/25; 196/195 352/351 385/384 625/624] | |||
Gencom map: [{{val|1 4 2 2 7 0}}, {{val|0 -15 2 5 -22 23}}] | |||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
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[[Category:Hemimean clan]] | [[Category:Hemimean clan]] | ||
[[Category:Gamelismic]] | [[Category:Gamelismic]] | ||
Revision as of 22:47, 2 July 2021
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 |