Peppermint-24: Difference between revisions

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An interesting feature of tuning systems, as implemented on keyboards (conventional or alternative), is the [[keyboard_mappings|mapping]] of pure or tempered ratios to positions on the keyboard layout.

Here I shall explore the mapping of approximate ratios, and especially of superparticular and other ratios within [~~http~~://en.wikipedia.org/wiki/Harry_Partch Harry Partch's] larger 17-limit set, in the tuning system and keyboard arrangement I call Peppermint 24.

Here I shall explore the mapping of approximate ratios, and especially of superparticular and other ratios within [https://en.wikipedia.org/wiki/Harry_Partch Harry Partch's] larger 17-limit set, in the tuning system and keyboard arrangement I call Peppermint 24.

Peppermint 24 takes as its basis a [[Regular_Temperaments|regular temperament]] mentioned in [[Erv_Wilson|Ervin Wilson]]'s Scale Tree and described on the Tuning List by [[Keenan_Pepper|Keenan Pepper]], with a fifth of about 704.096 cents, and a precise ratio of [~~http~~://en.wikipedia.org/wiki/Golden_ratio Phi], the Golden Section (~1.618) between the larger chromatic semitone (e.g. C-C#) at about 128.669 cents and the smaller diatonic semitone (e.g. C#-D) at about 79.522 cents.

Peppermint 24 takes as its basis a [[Regular_Temperaments|regular temperament]] mentioned in [[Erv_Wilson|Ervin Wilson]]'s Scale Tree and described on the Tuning List by [[Keenan_Pepper|Keenan Pepper]], with a fifth of about 704.096 cents, and a precise ratio of [https://en.wikipedia.org/wiki/Golden_ratio Phi], the Golden Section (~1.618) between the larger chromatic semitone (e.g. C-C#) at about 128.669 cents and the smaller diatonic semitone (e.g. C#-D) at about 79.522 cents.

In Peppermint 24, two regular 12-note chains of this temperament are placed at a distance of approximately 58.680 cents, so as to yield some pure ratios of 6:7 (~266.871 cents).

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33:56 (915.55) -- Usual major sixth (e.g. G4-E5, 912.29, -3.27)

[[Category:24-tone scales]]

[[Category:Todo:cleanup]]

[[Category:Todo:clarify]]

@@ Line 6: / Line 6: @@
 An interesting feature of tuning systems, as implemented on keyboards (conventional or alternative), is the [[keyboard_mappings|mapping]] of pure or tempered ratios to positions on the keyboard layout.
-Here I shall explore the mapping of approximate ratios, and especially of superparticular and other ratios within [http://en.wikipedia.org/wiki/Harry_Partch Harry Partch's] larger 17-limit set, in the tuning system and keyboard arrangement I call Peppermint 24.
+Here I shall explore the mapping of approximate ratios, and especially of superparticular and other ratios within [https://en.wikipedia.org/wiki/Harry_Partch Harry Partch's] larger 17-limit set, in the tuning system and keyboard arrangement I call Peppermint 24.
-Peppermint 24 takes as its basis a [[Regular_Temperaments|regular temperament]] mentioned in [[Erv_Wilson|Ervin Wilson]]'s Scale Tree and described on the Tuning List by [[Keenan_Pepper|Keenan Pepper]], with a fifth of about 704.096 cents, and a precise ratio of [http://en.wikipedia.org/wiki/Golden_ratio Phi], the Golden Section (~1.618) between the larger chromatic semitone (e.g. C-C#) at about 128.669 cents and the smaller diatonic semitone (e.g. C#-D) at about 79.522 cents.
+Peppermint 24 takes as its basis a [[Regular_Temperaments|regular temperament]] mentioned in [[Erv_Wilson|Ervin Wilson]]'s Scale Tree and described on the Tuning List by [[Keenan_Pepper|Keenan Pepper]], with a fifth of about 704.096 cents, and a precise ratio of [https://en.wikipedia.org/wiki/Golden_ratio Phi], the Golden Section (~1.618) between the larger chromatic semitone (e.g. C-C#) at about 128.669 cents and the smaller diatonic semitone (e.g. C#-D) at about 79.522 cents.
 In Peppermint 24, two regular 12-note chains of this temperament are placed at a distance of approximately 58.680 cents, so as to yield some pure ratios of 6:7 (~266.871 cents).
@@ Line 146: / Line 146: @@
 :56 (915.55) -- Usual major sixth (e.g. G4-E5, 912.29, -3.27)
+[[Category:24-tone scales]]
+[[Category:Todo:cleanup]]
+[[Category:Todo:clarify]]