Ptolemy's intense diatonic: Difference between revisions

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 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}}
+== Modes ==
+[[File:heji_just_major.png|400px|thumb|right|Right-handed just major scale on C, in [[HEJI]] notation.]]
+The major mode of the right-handed version gives the usual 5-limit major diatonic: {{dash|1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2/1}}.
+{| class="wikitable left-1" style="text-align:center"
+|+ Modes of Zarlino (right-handed)
+|-
+! Mode name
+! colspan=7 | Intervals
+|-
+| Lydian || 9/8 || 5/4 || 45/32 || 3/2 || 27/16 || 15/8 || 2/1
+|-
+| Ionian (major) || 9/8 || 5/4 || 4/3 || 3/2 || 5/3 || 15/8 || 2/1
+|-
+| Mixolydian || 10/9 || 5/4 || 4/3 || 3/2 || 5/3 || 16/9 || 2/1
+|-
+| Dorian || 10/9 || 32/27 || 4/3 || 40/27 || 5/3 || 16/9 || 2/1
+|-
+| Aeolian (minor) || 9/8 || 6/5 || 27/20 || 3/2 || 8/5 || 9/5 || 2/1
+|-
+| Phrygian || 16/15 || 6/5 || 4/3 || 3/2 || 8/5 || 9/5 || 2/1
+|-
+| Locrian || 16/15 || 6/5 || 4/3 || 64/45 || 8/5 || 16/9 || 2/1
+|}
+[[File:heji_just_minor.png|400px|thumb|right|Left-handed just minor scale on C, in [[HEJI]] notation.]]
+The left-handed version is most commonly encountered in its minor mode, 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}}.
+In the major mode, it only differs from the right-handed by having a 10/9 instead of 9/8 on the second degree. Reversing the steps of the right-handed major scale gives the left-handed phrygian mode.
+{| class="wikitable left-1" style="text-align:center"
+|+ Modes of Zarlino (left-handed)
+|-
+! Mode name
+! colspan=7 | Intervals
+|-
+| Lydian || 9/8 || 5/4 || 45/32 || 3/2 || 5/3 || 15/8 || 2/1
+|-
+| Ionian (major) || 10/9 || 5/4 || 4/3 || 3/2 || 5/3 || 15/8 || 2/1
+|-
+| Mixolydian || 10/9 || 5/4 || 4/3 || 40/27 || 5/3 || 16/9 || 2/1
+|-
+| Dorian || 9/8 || 6/5 || 27/20 || 3/2 || 27/16 || 9/5 || 2/1
+|-
+| Aeolian (minor) || 9/8 || 6/5 || 4/3 || 3/2 || 8/5 || 9/5 || 2/1
+|-
+| Phrygian || 16/15 || 6/5 || 4/3 || 3/2 || 8/5 || 16/9 || 2/1
+|-
+| Locrian || 16/15 || 32/27 || 4/3 || 64/45 || 8/5 || 16/9 || 2/1
+|}
+== Scala files ==
+Both are given in the major mode.
 <pre>
 ! zarlino-RH.scl
-Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(&lt;7 11 16|), or Dicot-meantone-mavila wakalix 1
+Ptolemy's Intense Diatonic Systonon, also Zarlino's scale
 !
-! wakalix info:
-! dicot: -2 to 4; meantone: -1 to 5; mavila: -4 to 2
-! dicot: LssLsLs; meantone: LLsLLLs; mavila: sLssLss
-! same as zarlino, Dwarf(<7 11 16|), mavchrome7, synchrome7, synmav7, ptolemy, yves, indian-magramma, even7a
 !
@@ Line 29: / Line 79: @@
 /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|)
+Ptolemy's Intense Diatonic Systonon, also Zarlino's scale
 !