There is small number of exactly

**10 characteristic tetra-chords (=4-notes sub-scales)**containing intervals of 1,2,3, semitones and**where inverses and cyclic permutations of them do not count as different**(e.g. the 2-2-1, the cyclic permutation of it as 2-1-2, and the inverse of the first as 1-2-2 are considered the same tetra-chord)**Diatonic**

**2-2-1, (major, natural minor, Ancient Greek syntono, Rast, Ussak, Kurdi)**

**2-2-2, (major, augmented)**

**Melodic minor or Hindu, Melodic double minor or Arabic, (S**

**habach)**

**1-2-1**

**Harmonic minor (Hijazz,**

**Huzam, Ancient Greek chromatic**

**)**

**1-3-1**

**Harmonic double minor (Piraeus, Niavent)**

**1-2-3,**

**Diminished**

**3-3-3 , (diminished 7nth)**

**3-3-1,**

**Pentatonic**

**3-3-2,**

**2-2-3**

**Chromatic**

**1-1-1**

**We should be also familiar with the ways we can play them in 1 , 2 or 3 strings.**

**If we are interested for 5-chords that have length exactly a pure 5th (7 semitones) so that it is within a classical 3 chord major or minor then the only cases are the next 3 (always here cyclic permutations and inversions are counted as the same 5-chord)**

**1) 2-2-2-1 (diatonic)**

**2) 1-2-1-3 (Harmonic minor)**

**3) 2-3-1-1 (Piraeus, Hungarian)**

**If on the other hand we set the restrictions**

**a) 4-notes sub-scales (tetra-hords)**

**b) Made from steps of 1,2,3 or 4 semitones**

**c) Make total sum 5 (interval of pure 4th) or 7**

**(interval of pure 5th) then all the possible combinations**

**where inverses and cyclic permutations of them do not count as different**

**are the next**

__5 only,__

**Diatonic**

**2-2-1, (major, natural minor, Ancient Greek syntono, Rast, Ussak, Kurdi)**

**Harmonic minor (Hijazz,**

**Huzam, Ancient Greek chromatic**

**)**

**1-3-1**

**Diminished**

**3-3-1,**

**Pentatonic**

**2-2-3**

**Chinese**

**1-2-4**

**THE CLASSIFICATION OF ALL SUB-SCALES OF TOTAL LENGTH AN INTERVAL OF PURE 5TH (7-SEMITONES).**

**We make here this classification of all 1 note, 2 notes, 3 notes, 4 notes, 5 notes, 6 notes and 7 notes sub-scales of total length a pure interval of 5th (7-semitones) . As usually we use the convention that cyclic permutations of a scale are modes and not a different scale. The numbers denote semitones.**

The classification is the next

**8-scales**

**1) 1 note scale: 7 That is an interval of pure 5th. This is actually not counting as a scale**

**2) 2-notes scales 4-3 , Intervals of 3rd ( 3 or 4 semitones)**

**3) 3-notes scales a) 2-3-2 It occurs as sub-scale in the standard pentatone scale**

**b) 1-3-1-2 It occurs in the Harmonic minor scale, and has oriental sound**

**c) 1-1-3-2**

**4) 4-notes scales 2-2-1-2 It occurs in the diatonic scale.**

**5) 6-tones scales a) 1-1-1-2-2 Small chromatic sound**

**b) 2-1-2-1-1 Hebrew scales sound**

**6) 7-notes scale 1-1-1-1-1-1-1-1 Full chromatic scale sound.**