Ptolemy's intense diatonic

English Wikipedia has an article on:

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.

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 AKA dimeanmav1.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 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 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