1665edo: Difference between revisions
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Cleanup; clarify the title row of the rank-2 temp table |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1665}} | {{EDO intro|1665}} | ||
==Theory== | |||
== Theory == | |||
1665edo is a very strong 5-limit (as well as 2.3.5.11 subgroup) tuning and it is consistent in the 15-odd-limit. In the 5-limit, 1665edo is a tuning for the [[gross]] temperament. | 1665edo is a very strong 5-limit (as well as 2.3.5.11 subgroup) tuning and it is consistent in the 15-odd-limit. In the 5-limit, 1665edo is a tuning for the [[gross]] temperament. | ||
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1665cc val is a tuning for the [[roentgenium]] temperament, and the patent val tunes the unnamed 111 & 1665 temperament in the 13-limit which has a comma basis {6656/6655, 123201/123200, 250047/250000, 91182091/91125000}. | 1665cc val is a tuning for the [[roentgenium]] temperament, and the patent val tunes the unnamed 111 & 1665 temperament in the 13-limit which has a comma basis {6656/6655, 123201/123200, 250047/250000, 91182091/91125000}. | ||
==Regular temperament properties== | === Prime harmonics === | ||
{{Harmonics in equal|1665}} | |||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio | ||
! Temperaments | ! Temperaments | ||
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| 127\1665 | | 127\1665 | ||
| 91.531 | | 91.531 | ||
| {{monzo|9 -32 18}} | | {{monzo| 9 -32 18 }} | ||
| [[Gross]] | | [[Gross]] | ||
|- | |- | ||
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| [[Rhodium]] | | [[Rhodium]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||