Fokker block: Difference between revisions

Line 38:

== Examples ==

=== Ptolemy's intense diatonic ===

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.

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

[[File:Fokker_block_zarlino.png|400px|thumb|none|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.]]

The corresponding Fokker block will be the [[Ptolemy's intense diatonic]], also known as Zarlino, specifically the lydian mode.

Tempering out either of the two chromas gives a MOS scale related to the temperament.

* Tempering out the syntonic comma gives the [[diatonic scale]] LLLsLLs, in [[meantone]].

* 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 ===

Let's ~~take [[5-limit]] just intation, and pick~~ the [[128/125|diesis]] (128/125) and the [[syntonic comma]] (81/80) as our chromas.

Let's now use the [[128/125|diesis]] (128/125) and the [[syntonic comma]] (81/80) as our chromas, in 5-limit JI as above.

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

The diesis is the difference between an octave and three major thirds, so it has coordinates <math>(0, -3)</math>.

The syntonic comma is reached by stacking 4 fifths and going down a major third, so it has coordinates <math>(4, -1)</math>

@@ Line 38: / Line 38: @@
 == Examples ==
+=== Ptolemy's intense diatonic ===
+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.
+The octave equivalent lattice is generated by fifths and just major thirds.
+[[File:Fokker_block_zarlino.png|400px|thumb|none|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.]]
+The corresponding Fokker block will be the [[Ptolemy's intense diatonic]], also known as Zarlino, specifically the lydian mode.
+Tempering out either of the two chromas gives a MOS scale related to the temperament.
+* Tempering out the syntonic comma gives the [[diatonic scale]] LLLsLLs, in [[meantone]].
+* 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 ===
-Let's take [[5-limit]] just intation, and pick the [[128/125|diesis]] (128/125) and the [[syntonic comma]] (81/80) as our chromas.
+Let's now use the [[128/125|diesis]] (128/125) and the [[syntonic comma]] (81/80) as our chromas, in 5-limit JI as above.
-The octave equivalent lattice is generated by fifths and just major thirds.
 The diesis is the difference between an octave and three major thirds, so it has coordinates <math>(0, -3)</math>.
 The syntonic comma is reached by stacking 4 fifths and going down a major third, so it has coordinates <math>(4, -1)</math>