270edo: Difference between revisions
→Regular temperament properties: local best relative accuracy in the 19-limit, actually |
OPV for these important temps: hemiennealimmal, vulture, eagle, and avicenna |
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In the [[11-limit]], it tempers out [[3025/3024]], [[5632/5625]], and [[9801/9800]], meaning it tempers out the four smallest [[superparticular]] commas in the 11-limit (2401/2400, 3025/3024, 4375/4374 and 9801/9800). In addition to these, it also tempers out both the [[nexus comma]] (1771561/1769472) and the [[quartisma]] (117440512/117406179), which, in turn means that the [[symbiotic comma]] (19712/19683) is tempered out as well. | In the [[11-limit]], it tempers out [[3025/3024]], [[5632/5625]], and [[9801/9800]], meaning it tempers out the four smallest [[superparticular]] commas in the 11-limit (2401/2400, 3025/3024, 4375/4374 and 9801/9800). In addition to these, it also tempers out both the [[nexus comma]] (1771561/1769472) and the [[quartisma]] (117440512/117406179), which, in turn means that the [[symbiotic comma]] (19712/19683) is tempered out as well. | ||
Finally, in the [[13-limit]] it is not quite as accurate but still very accurate, as it tempers out [[676/675]], [[1001/1000]], [[1716/1715]] and [[2080/2079]], making it an [[The Archipelago|archipelago]] tuning, and the [[optimal patent val]] for some of the archipelago temperaments. | Finally, in the [[13-limit]] it is not quite as accurate but still very accurate, as it tempers out [[676/675]], [[1001/1000]], [[1716/1715]] and [[2080/2079]], making it an [[The Archipelago|archipelago]] tuning, and the [[optimal patent val]] for some of the archipelago temperaments such as [[hemiennealimmal]], [[vulture]], [[eagle]], and [[avicenna (temperament)|avicenna]]. | ||
The excellent tuning accuracy does not bar it from the utility of [[essentially tempered chord]]s, including [[sinbadmic chords]] in the 13-odd-limit and [[island chords]] in the 15-odd-limit. | The excellent tuning accuracy does not bar it from the utility of [[essentially tempered chord]]s, including [[sinbadmic chords]] in the 13-odd-limit and [[island chords]] in the 15-odd-limit. | ||
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<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | <nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | ||
[[Category:Hemiennealimmal]] | |||
[[Category:Vulture]] | |||
[[Category:Eagle]] | |||
[[Category:Avicenna (temperament)]] | |||