Kirnberger I: Difference between revisions
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Kirnberger I is very similar to [[Pythagorean tuning]] but not exactly the same. In Kirnberger I, the D–A fifth is reduced by a [[syntonic comma]], making the major thirds F–A, C–E, G–B, and D–F# pure, though the fifth based on D is a ratio of [[40/27]] instead of [[3/2]]. | '''Kirnberger I''' is very similar to [[Pythagorean12|12-tone Pythagorean tuning]] but not exactly the same. In Kirnberger I, the D–A fifth is reduced by a [[syntonic comma]], making the major thirds F–A, C–E, G–B, and D–F# pure, though the fifth based on D is a ratio of [[40/27]] instead of [[3/2]]. This leaves 10 pure fifths and one that is flat by a [[schisma]], placed between C# and Ab. | ||
<pre> | |||
! kirnberger_1.scl | |||
! | |||
Kirnberger's well temperament, also called Kirnberger I. | |||
12 | |||
! | |||
135/128 | |||
9/8 | |||
32/27 | |||
5/4 | |||
4/3 | |||
45/32 | |||
3/2 | |||
128/81 | |||
5/3 | |||
16/9 | |||
15/8 | |||
2/1 | |||
</pre> | |||
Suggested keyboard mappings: | |||
* Central C | |||
[[Category:Pages with Scala files]] | |||
[[Category:12-tone scales]] | |||
[[Category:Well temperaments]] | [[Category:Well temperaments]] | ||
[[Category:Just intonation scales]] | |||
[[Category:Historical]] | [[Category:Historical]] | ||
[[Category: | [[Category:Kirnberger]] | ||
Latest revision as of 18:16, 24 June 2025
Kirnberger I is very similar to 12-tone Pythagorean tuning but not exactly the same. In Kirnberger I, the D–A fifth is reduced by a syntonic comma, making the major thirds F–A, C–E, G–B, and D–F# pure, though the fifth based on D is a ratio of 40/27 instead of 3/2. This leaves 10 pure fifths and one that is flat by a schisma, placed between C# and Ab.
! kirnberger_1.scl ! Kirnberger's well temperament, also called Kirnberger I. 12 ! 135/128 9/8 32/27 5/4 4/3 45/32 3/2 128/81 5/3 16/9 15/8 2/1
Suggested keyboard mappings:
- Central C