Whitewood: Difference between revisions
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{{Infobox regtemp | |||
| Title = | |||
| Subgroups = 2.3.5, 2.3.5.7 | |||
| Comma basis = [[2187/2048]] (2.3.5);<br> [[36/35]], [[2187/2048]] (2.3.5.7) | |||
| Edo join 1 = 7 | Edo join 2 = 14 | |||
| Mapping = 7; 0 1 -1 | |||
| Generators = 5/4 | |||
| Generators tuning = 392.7 | |||
| Optimization method = CWE | |||
| MOS scales = [[7L 7s]], [[7L 14s]], ... | |||
| Pergen = (P8/7, ^1) | |||
| Color name = Lawati | |||
| Odd limit 1 = 5 | Mistuning 1 = 16.2 | Complexity 1 = 14 | |||
| Odd limit 2 = 9 | Mistuning 2 = 40.6 | Complexity 2 = 21 | |||
}} | |||
'''Whitewood''' is the [[rank-2 temperament]] tempering out [[2187/2048]], the Pythagorean chromatic semitone. As a result, the [[circle of fifths]] closes after seven steps, and every interval on the chain of fifths is [[neutral (interval quality)|neutral]] in quality. The whitewood temperament adds prime [[5/1|5]] as an independent [[generator]], adding major and minor intervals on either side of the neutral ones. | |||
The canonical extenison to prime [[7/1|7]] adds [[36/35]] to the commas, thus equating [[5-limit]] major and minor intervals with [[7-limit]] subminor and supermajor ones. It finds [[7/4]] at the minor seventh, [[7/6]] at the minor third, and [[9/7]] at the major third. | |||
For technical data, see [[Whitewood family #Whitewood]]. | |||
== Intervals == | |||
<!--{| class="wikitable" | |||
|- | |||
! Gen | |||
! Period→ | |||
! 0 | |||
! 1 | |||
! 2 | |||
! 3 | |||
! 4 | |||
! 5 | |||
! 6 | |||
|- | |||
! rowspan=2 | +1 | |||
! Cents* | |||
| 49.9 | |||
| 221.3 | |||
| 392.7 | |||
| 564.2 | |||
| 735.6 | |||
| 907.0 | |||
| 1078.5 | |||
|- | |||
! Approx. Ratios | |||
| 135/128 | |||
| 10/9, 8/7--> | |||
{{Todo|complete section|inline=1}} | |||
== Tunings == | |||
{{Todo|complete section|inline=1}} | |||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Whitewood family]] | [[Category:Whitewood family]] | ||
[[Category:Mint temperaments]] | [[Category:Mint temperaments]] | ||