Well temperament: Difference between revisions
Add (Vincenzo) Galilei's tuning |
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One of the advantages of these tunings is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly. | One of the advantages of these tunings is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly. | ||
Despite their sharing the word "temperament" in their names, well temperaments and the modern notion of [[regular temperament]]s are two different concepts, | Despite their sharing the word "temperament" in their names, well temperaments and the modern notion of [[regular temperament]]s are two different concepts. In fact, a well temperament is an ''ir''regular temperament. But sometimes one can guide construction of the other. | ||
== Historical well temperaments == | == Historical well temperaments == | ||
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* [[Kirnberger I]] – Kirnberger temperament I | * [[Kirnberger I]] – Kirnberger temperament I | ||
# one tempered fifth (D–A) is flat by 1 [[syntonic comma]] | # one tempered fifth (D–A) is flat by 1 [[syntonic comma]] | ||
# | # one tempered fifth (C#-Ab) is flat by 1 [[schisma]] | ||
# ten [[3/2|pure]] fifths | |||
* [[Kirnberger II]] – Kirnberger temperament II | * [[Kirnberger II]] – Kirnberger temperament II | ||
# two tempered fifths (D–A and A–E) are flat by 1/2 syntonic comma (→ [[1/2-comma meantone]]) | # two tempered fifths (D–A and A–E) are flat by 1/2 syntonic comma (→ [[1/2-comma meantone]]) | ||
# | # one tempered fifth (C#-Ab) is flat by 1 [[schisma]] | ||
# nine [[3/2|pure]] fifths | |||
* [[Kirnberger III]] – Kirnberger temperament III | * [[Kirnberger III]] – Kirnberger temperament III | ||
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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 == | ||
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[[Category:Well temperament| ]] <!-- main article --> | [[Category:Well temperament| ]] <!-- main article --> | ||
[[Category:Historical]] | [[Category:Historical]][[Category:Regular temperament theory]] | ||