Ptolemy's intense diatonic: Difference between revisions

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{{interwiki

| de = Durtonleiter

| en = Ptolemy's intense diatonic

}}

[[File:zarlino2.png|400px|thumb|right|The left and right handed variations of the just diatonic scale on the [[5-limit]] [[lattice]].]]

'''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. Both versions contain a [[40/27]] wolf fifth.

~~{{Wikipedia|Ptolemy's intense diatonic scale}}~~

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]].

~~'''Ptolemy's intense diatonic''' scale is~~ a [[~~heptatonic~~]] [[~~5-limit~~]] [[JI]] [[~~scale~~]] ~~with the~~ [[~~nicetone~~]] ~~step pattern~~.

It can also be derived from tuning the tonic, dominant and subdominant chords as 5-limit just major chords ([[4:5:6]]): {{dash|FAC, CEG, GBD}}.

<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

~~! x^7-11*x^5-10*x^4+21*x^3+30*x^2+9*x~~

!

! wakalix info:

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2/1

</pre>

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

!

Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(<7 11 16|)

~~! x^7-11*x^5-10*x^4+21*x^3+30*x^2+9*x~~

7

!

Line 38:

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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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* [[Nicetone]] – regular 3L 2m 2s scale

* [[Superzarlino]]

* [[mavchrome6]], [[dimeanmav2]]

[[Category:7-tone scales]]

@@ Line 1: / Line 1: @@
-{{Main|Nicetone}}
+{{interwiki
+| de = Durtonleiter
+| en = Ptolemy's intense diatonic
+}}
+{{Wikipedia|Ptolemy's intense diatonic scale}}
+[[File:zarlino2.png|400px|thumb|right|The left and right handed variations of the just diatonic scale on the [[5-limit]] [[lattice]].]]
+'''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. Both versions contain a [[40/27]] wolf fifth.
-{{Wikipedia|Ptolemy's intense diatonic scale}}
+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]].
-'''Ptolemy's intense diatonic''' scale is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern.
+It can also be derived from tuning the tonic, dominant and subdominant chords as 5-limit just major chords ([[4:5:6]]): {{dash|FAC, CEG, GBD}}.
+{{Clear}}
 <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
-! x^7-11*x^5-10*x^4+21*x^3+30*x^2+9*x
 !
 ! wakalix info:
@@ Line 23: / Line 29: @@
 /1
 </pre>
+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
 !
 Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(&lt;7 11 16|)
-! x^7-11*x^5-10*x^4+21*x^3+30*x^2+9*x
 !
@@ Line 38: / Line 46: @@
 /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
@@ Line 66: / Line 77: @@
 * [[Nicetone]] – regular 3L 2m 2s scale
 * [[Superzarlino]]
+* [[mavchrome6]], [[dimeanmav2]]
 [[Category:7-tone scales]]