Luna and hemithirds: Difference between revisions
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Cmloegcmluin (talk | contribs) →Spectrum of hemithirds tunings by eigenmonzos: improve and standardize tuning spectra tables |
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{{main| Chords of hemithirds }} | {{main| Chords of hemithirds }} | ||
== | == Tuning spectrum == | ||
Gencom: [2 28/25; 196/195 352/351 385/384 625/624] | 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}}] | Gencom map: [{{val|1 4 2 2 7 0}}, {{val|0 -15 2 5 -22 23}}] | ||
{| class="wikitable center- | {| class="wikitable center-all" | ||
|- | |- | ||
! | ! [[eigenmonzo|eigenmonzo<br>(unchanged interval]]) | ||
! | ! hemithird<br>(¢) | ||
! | ! comments | ||
|- | |- | ||
| 14/13 | | 14/13 | ||
Revision as of 00:24, 30 September 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
Tuning spectrum
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 (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 |