Ptolemy's intense diatonic: Difference between revisions

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'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern. ~~It is also the basis of~~ [[Ben Johnston's notation]].

'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern.

In [[Ben Johnston's notation]], the scale is the basic uninflected diatonic scale.

It is a [[chiral scale]], meaning it comes in two variations, which are called right and left-handed.

It can be constructed as a [[Fokker block]] in multiple ways, making it a [[wakalix]]. Another derivation is through a [[tetrachord]] consisting of [[16/15]], [[9/8]] and [[10/9]].

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<pre>

! zarlino-RH~~.scl AKA dimeanmav1~~.scl

! zarlino-RH.scl

Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(<7 11 16|), or Dicot-meantone-mavila wakalix 1

!

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</pre>

The left-handed variation has 10/9 instead of 9/8 on the second degree. It is most commonly encountered in the 6th mode (with 5/3 as the root) which gives the usual 5-limit minor diatonic: {{dash|1/1, 9/8, 6/5, 4/3, 3/2, 8/5, 9/5, 2/1}}.

The left-handed variation has 10/9 instead of 9/8 on the second degree.

It can be obtained from the right-handed version by reversing its steps.

It is most commonly encountered in the 6th mode (with 5/3 as the root) which gives the usual 5-limit minor diatonic: {{dash|1/1, 9/8, 6/5, 4/3, 3/2, 8/5, 9/5, 2/1}}.

<pre>

! zarlino-LH.scl

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2/1

</pre>

== Fokker blocks ==

The scale can be found in three different [[Fokker block]]s, using the chromas [[25/24]], [[81/80]] and [[135/128]].

; Fokker block 1

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 {{Wikipedia|Ptolemy's intense diatonic scale}}
-'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern. It is also the basis of [[Ben Johnston's notation]].
+'''Ptolemy's intense diatonic''' scale (also known as '''Zarlino''', or simply the '''just diatonic scale''') is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern.
+In [[Ben Johnston's notation]], the scale is the basic uninflected diatonic scale.
+It is a [[chiral scale]], meaning it comes in two variations, which are called right and left-handed.
 It can be constructed as a [[Fokker block]] in multiple ways, making it a [[wakalix]]. Another derivation is through a [[tetrachord]] consisting of [[16/15]], [[9/8]] and [[10/9]].
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 <pre>
-! zarlino-RH.scl AKA dimeanmav1.scl
+! zarlino-RH.scl
 Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(&lt;7 11 16|), or Dicot-meantone-mavila wakalix 1
 !
@@ Line 25: / Line 27: @@
 </pre>
-The left-handed variation has 10/9 instead of 9/8 on the second degree. It is most commonly encountered in the 6th mode (with 5/3 as the root) which gives the usual 5-limit minor diatonic: {{dash|1/1, 9/8, 6/5, 4/3, 3/2, 8/5, 9/5, 2/1}}.
+The left-handed variation has 10/9 instead of 9/8 on the second degree.
+It can be obtained from the right-handed version by reversing its steps.
+It is most commonly encountered in the 6th mode (with 5/3 as the root) which gives the usual 5-limit minor diatonic: {{dash|1/1, 9/8, 6/5, 4/3, 3/2, 8/5, 9/5, 2/1}}.
 <pre>
 ! zarlino-LH.scl
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 /1
 </pre>
+== Fokker blocks ==
+The scale can be found in three different [[Fokker block]]s, using the chromas [[25/24]], [[81/80]] and [[135/128]].
 ; Fokker block 1