Ptolemy's intense diatonic: Difference between revisions

(3 intermediate revisions by 3 users not shown)

Line 1:

{{interwiki

| de = Durtonleiter

| en = Ptolemy's intense diatonic

}}

'''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.

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

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

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]].

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

Line 27:

Line 30:

</pre>

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

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}}.

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>

@@ Line 1: / Line 1: @@
+{{interwiki
+| de = Durtonleiter
+| en = Ptolemy's intense diatonic
+}}
 {{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.
+[[File:zarlino2.png|400px|thumb|right|The left and right handed variations of the just diatonic scale on the [[5-limit]] [[lattice]].]]
-In [[Ben Johnston's notation]], the scale is the basic uninflected 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. 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.
-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]].
 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
@@ Line 27: / Line 30: @@
 </pre>
-The left-handed variation has 10/9 instead of 9/8 on the second degree.
+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}}.
-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>