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, (Shabach)
1-2-1
Harmonic minor (Hijazz,Huzam, Ancient Greek chromatic)
1-3-1
Harmonic double minor (Piraeus, Niavent)
1-2-3,
Diminished
Diminished
3-3-3 , (diminished 7nth)
3-3-1,
Pentatonic
3-3-2,
2-2-3
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,
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
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.
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.
