Fokker block: Difference between revisions

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== Examples ==

=== Ptolemy's intense diatonic ===

[[File:Fokker_block_zarlino.png|400px|thumb|Fokker block corresponding to the just diatonic scale. The gray grid is the interval lattice, and the black lines show the sublattice generated by the chromas. The fundamental domain is colored in blue.]]Let's take [[5-limit]] just ~~intation~~, and pick the [[25/24|just chromatic semitone]] (25/24) and the [[syntonic comma]] (81/80) as our chromas.

[[File:Fokker_block_zarlino.png|400px|thumb|Fokker block corresponding to the just diatonic scale. The gray grid is the interval lattice, and the black lines show the sublattice generated by the chromas. The fundamental domain is colored in blue.]]Let's take [[5-limit]] just intonation, and pick the [[25/24|just chromatic semitone]] (25/24) and the [[syntonic comma]] (81/80) as our chromas.

The octave equivalent lattice is generated by fifths and just major thirds.

Since <math>25/24 = 2^{-3} \cdot 3^{-1} \cdot 5^2</math>, it has coordinates <math>(-1, 2)</math> in the octave-equivalent lattice.

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* Tempering out the chromatic semitone gives the [[mosh]] LsLsLss (a 7-note neutral scale), in [[dicot]].

If we temper out both 25/24 and 81/80, we get [[7edo|7 equal temperament]], which we can interpret as an equalized diatonic scale.

This scale is a Fokker block in multiple ways: it is also possible to arrive at the same set of notes using [[135/128]] together with either 81/80 or 25/24 as the chromas.

=== Duodene and 12 equal temperament ===

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 == Examples ==
 === Ptolemy's intense diatonic ===
-[[File:Fokker_block_zarlino.png|400px|thumb|Fokker block corresponding to the just diatonic scale. The gray grid is the interval lattice, and the black lines show the sublattice generated by the chromas. The fundamental domain is colored in blue.]]Let's take [[5-limit]] just intation, and pick the [[25/24|just chromatic semitone]] (25/24) and the [[syntonic comma]] (81/80) as our chromas.
+[[File:Fokker_block_zarlino.png|400px|thumb|Fokker block corresponding to the just diatonic scale. The gray grid is the interval lattice, and the black lines show the sublattice generated by the chromas. The fundamental domain is colored in blue.]]Let's take [[5-limit]] just intonation, and pick the [[25/24|just chromatic semitone]] (25/24) and the [[syntonic comma]] (81/80) as our chromas.
 The octave equivalent lattice is generated by fifths and just major thirds.
 Since <math>25/24 = 2^{-3} \cdot 3^{-1} \cdot 5^2</math>, it has coordinates <math>(-1, 2)</math> in the octave-equivalent lattice.
@@ Line 31: / Line 31: @@
 * Tempering out the chromatic semitone gives the [[mosh]] LsLsLss (a 7-note neutral scale), in [[dicot]].
 If we temper out both 25/24 and 81/80, we get [[7edo|7 equal temperament]], which we can interpret as an equalized diatonic scale.
 This scale is a Fokker block in multiple ways: it is also possible to arrive at the same set of notes using [[135/128]] together with either 81/80 or 25/24 as the chromas.
 === Duodene and 12 equal temperament ===