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. 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.
It can also be derived from tuning the tonic, dominant and subdominant chords as 5-limit just major chords (4:5:6): FAC – CEG – GBD.
! zarlino-RH.scl Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(<7 11 16|), or Dicot-meantone-mavila wakalix 1 ! ! 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 7 ! 9/8 5/4 4/3 3/2 5/3 15/8 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: 1/1 – 9/8 – 6/5 – 4/3 – 3/2 – 8/5 – 9/5 – 2/1.
! zarlino-LH.scl ! Ptolemy's Intense Diatonic Systonon, also Zarlino's scale, mavchrome7, Dwarf(<7 11 16|) 7 ! 10/9 5/4 4/3 3/2 5/3 15/8 2/1
Fokker blocks
The scale can be found in three different Fokker blocks, using the chromas 25/24, 81/80 and 135/128.
- Fokker block 1
Chroma basis: {81/80, 135/128}
Mode 5|1, dome 2|4 (LlsLlLs)
L = 9/8, l = 10/9, s = 16/15
- Fokker block 2
Chroma basis: {25/24, 81/80}
Mode 5|1, dome 4|2 (LlsLlLs)
L = 9/8, l = 10/9, S = 27/25, s = 16/15
- Fokker block 3
Chroma basis: {25/24, 135/128}
Mode 4|2, dome 4|2 (lSslSls)
L = 75/64, l = 9/8, S = 10/9, s = 16/15
See also
- Nicetone – regular 3L 2m 2s scale
- Superzarlino