Whitewood: Difference between revisions

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| 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.

'''Whitewood''' is the [[rank-2 temperament]] tempering out [[2187/2048]], the Pythagorean chromatic semitone. As a result, the [[circle of fifths]] is the same as that of [[7edo]], 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.

The canonical [[extension]] 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]].

@@ Line 14: / Line 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.
+'''Whitewood''' is the [[rank-2 temperament]] tempering out [[2187/2048]], the Pythagorean chromatic semitone. As a result, the [[circle of fifths]] is the same as that of [[7edo]], 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.
+The canonical [[extension]] 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]].