Well temperament: Difference between revisions
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Add (Vincenzo) Galilei's tuning |
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# seven [[3/2|pure]] fifths | # seven [[3/2|pure]] fifths | ||
* [[Werck3]] – Werckmeister temperament III | * [[Werck3|Werckmeister III]] – Werckmeister temperament III | ||
# four tempered fifths (C–G, D–A, G–D and B–F#) are tuned flat by 1/4 comma (''Werckmeister did not specify whether the syntonic or [[pythagorean comma|Pythagorean]] comma should be used, so either is acceptable'') | # four tempered fifths (C–G, D–A, G–D and B–F#) are tuned flat by 1/4 comma (''Werckmeister did not specify whether the syntonic or [[pythagorean comma|Pythagorean]] comma should be used, so either is acceptable'') | ||
# eight [[3/2|pure]] fifths | # eight [[3/2|pure]] fifths | ||
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# six tempered fifths (C–G, D–A, E–B, F–C, G–D and A–E) are flat by 1/6 Pythagorean comma | # six tempered fifths (C–G, D–A, E–B, F–C, G–D and A–E) are flat by 1/6 Pythagorean comma | ||
# six pure fifths | # six pure fifths | ||
* [[Galilei's tuning]] | |||
# eleven [[18/17]] (~99{{cent}}) semitones | |||
# one (2/1)/(18/17)<sup>11</sup> (~111.5{{cent}}) semitone (B-C) | |||
== Classification by approaches == | == Classification by approaches == | ||
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== Relation to regular temperaments == | == Relation to regular temperaments == | ||
Through the lens of regular temperament theory, a well temperament can be viewed as a result of applying an irregular [[tuning map]] to the abstract intervals of an [[equal temperament]] (i.e. a rank-1 abstract regular temperament), though tuning maps in the technical sense are defined to be regular. However, note that when nejis are considered well temperaments in this sense, the JI ratios the intervals are said to represent and the actual JI ratios of the neji tuning must be distinguished, and the JI ratios that occur in the neji should not be assumed to be consistent with the val. | Through the lens of regular temperament theory, a well temperament can be viewed as a result of applying an irregular [[tuning map]] to the abstract intervals of an [[equal temperament]] (i.e. a rank-1 abstract regular temperament), though tuning maps in the technical sense are defined to be regular. However, note that when nejis are considered well temperaments in this sense, the JI ratios the intervals are said to represent and the actual JI ratios of the neji tuning must be distinguished, and the JI ratios that occur in the neji should not be assumed to be consistent with the val. | ||
== External links == | == External links == | ||