Hemipyth: Difference between revisions
→Temperament interpretations: Make excuses for why harry is there. |
→Temperament interpretations: Add baldur, flip harry's period, add note about rank. |
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| Line 158: | Line 158: | ||
|+ Higher-prime interpretations of hemipyth intervals | |+ Higher-prime interpretations of hemipyth intervals | ||
|- | |- | ||
! Temperament !! ~√2 !! ~√(3/2) !! ~√(4/3) !! contorted | ! Temperament !! ~√2 !! ~√(3/2) !! ~√(4/3) !! contorted !! rank-2 | ||
|- | |- | ||
| [[decimal]] || ~7/5 || ~5/4 || ~7/6 || no | | [[decimal]] || ~7/5 || ~5/4 || ~7/6 || no || yes | ||
|- | |- | ||
| [[sruti]] || ~45/32 || ~175/144 || ~81/70 || no | | [[sruti]] || ~45/32 || ~175/144 || ~81/70 || no || yes | ||
|- | |- | ||
| [[harry]] || ~ | | [[harry]] || ~17/12 || ~11/9 || ~15/13 || yes || yes | ||
|- | |- | ||
| [[greenland]] || ~99/70 || ~49/40 || ~15/13 || no | | [[baldur]] || ~99/70 || ~49/40 || ~231/200 || no || no | ||
|- | |||
| [[greenland]] || ~99/70 || ~49/40 || ~15/13 || no || no | |||
|} | |} | ||
Above contorted tunings don't have a ~√2 period with a ~√3 generator, but introduce further splits. | Above contorted tunings don't have a ~√2 period with a ~√3 generator, but introduce further splits. Higher than rank-2 temperaments introduce further structure that goes beyond basic hemipyth. | ||