All 7-notes scales made from semitones, tones and at least one 3-semitone.
Many such scales are used in the Greek folk music with Buzuki, and have their origin in ancient Greece, Byzantine empire, and Arabic music. Many of them have Arabic names although they are played on the 12-semitone Bach equal temperament scale.
For the names of some of these scales see http://www.scales-chords.com/
Therefore its is worth finding them all. We have already found all of them that they do not contain a 3-semitone (see post 51, the diatonic, the melodic minor and the second melodic minor) . So let us find all that contain at least one 3-semitone We already know so far
1) the Harmonic minor= (1-3-1)-2-(-1-2-2), and
2)the Romani (or Hungarian /Ukrainian/Flamenco) double minor (modes also of Niavent and Hijaskar) also called Byzantine or Harmonic double minor scale (and by some also called abydos Egyptin scale)=(1-3-1)-2-(-1-3-1) (notice that the inverse order of it is identical with it).
The Romanian kaval flutes with 5 holes play the 6-notes scale 2-1-3-1-1-4 E.G. A4-B4-C5-D#5-E5-F5-A5 and by adding a 6th thump hole to play the G5# it becomes a Harmonic double minor scale A4-B4-C5-D#5-E5-F5-G5#-A5 or 2-1-3-1-1-3-1 which is a mode of the E5 harmonic double minor scale.
3) A slight alternation of it is the Persian scale or todi theta scale=(1-3-1-1-2-3-1)
4) Inverse Persian scale or Purvi Theta scale (3-1-1-3-2-1-1) or Byzantine parachromatic scale
The last 3 contain two 3-semitones, but only the Harmonic double minor two tetrachords 1-3-1 ! And the other two scales of post 50 are
This scale (as the harmonic double minor or Byzantine double minor too) too is directly derivable from the pentatonic scale e.g., the Egyptian mode of it 2-3-2-3-2 gives the
2-1-1-3-1-1-3 This scale can be easily played in the Shakuhachi minor pentatonic flutes.
5) the 2nd Harmonic minor or Kurdi or Kassigar=(1-3-1)-2-(-2-1-2) (which is the inverse order of the Harmonic minor),
6) and the 3rd Harmonic minor or Shamba (which is the inverse of the Neopolitan scale below) =(1-3-1)-2-(-2-2-1)
all of them containing the oriental tetra-chord 1-3-1.
We may take the inverse order of the Shamba which is called the Neopolitan scale
7) The 4th Harmonic minor or Neapolitan scale (different from the major and the minor Neopolitan)= (1-3-1)-1-(-2-2-2)
Notice that the Neapolitan scale is made by the inverses of 2 ancient Greek tetrachords the 1-1-3 and the 1-2-2 withe and in between tone 2 (disjunction of tetrachords or divorced tetrachords) . The 1-1-3 was called in ancient Greece the tonal tetrachor of the Chromatic Generation and the 1-2-2 the syntono tetrachord of the Diatonic generation.
Now are there more? Certainly there are! Many of them are modern versions in the 12-semitones scale realizations of ancient Byzantine 7-notes scales or "sounds" (ηχοι). If there are two 3-semitones as in the Romani double minor, we may have a permutation of it , which is not a cyclic permutation (mode of the Romani double minor) which are the next
8) (3-1-3-2-1-1-1)
9) Second Harmonic or Romani double minor=(3-1-3-1-2-1-1) or gypsy hexatonic or Mela Gayakapriya, Raga Kalakanti (see post 227 )
10) Third Harmonic or Romani double minor=(3-1-3-1-1-2-1) inverse of Mela Ganamurti, Raga Ganasamavarali (see post 227)
11) (3-1-3-1-1-1-2)
12) (3-1-2-3-1-1-1)
The next scales do not sound too much as minor scales as the 3-3 , or 3-2-3 is not sad and are mainly extrapolations of the western or Chinese/Mongolian pentatonic !
13) (3-2-3-1-1-1-1) (with a very peculiar sound)
14) (3-2-1-3-1-1-1)
15) (3-3-2-1-1-1-1) (with a very peculiar sound)
16) (3-3-1-2-1-1-1)
17) (3-3-1-1-2-1-1)
18) (3-3-1-1-1-2-1)
19) (3-3-1-1-1-1-2) (this is the inverse order of scale 15)
While if it has only one 3-semitone we may take non-cyclic permutations of the 3) and 4) like the next fr which ma nor aware of names, but maybe there are in modern Arabic music (At first we make all possible combinations of different intervals around 3, and then all possible non-cyclic permutations of the rest of the intervals)
20) (1-3-2)-1-(-2-1-2)
21) (1-3-2)-1-(-1-2-2)
22) (1-3-2)-2-(-1-1-2)
23) Called Enigmatic (1-3-2)-2-(-2-1-1)
24) (1-3-2)-2-(-1-2-1) Anasazi flute scale or
| Mela Vanaspati, Raga Bhanumati |
26) (2-3-1)-1-(-2-1-2)
27) (2-3-1)-1-(-1-2-2) Inverse Anasazi flute scale or inverse
| Mela Vanaspati, Raga Bhanumati |
29) (2-3-1)-2-(-2-1-1)
30) Called Hungarian major scale (2-3-1)-2-(-1-2-1)
31) (2-3-1)-1-(-2-2-1) This scale is
refered in this video https://www.youtube.com/watch?v=mjttaiOq-8Q
as the 7-notes soul scale and is refred as the major pentatonic scale with added flat 3rd and flat 7nth!
32) (2-3-2)-1-(-2-1-1)
33) (2-3-2)-1-(-1-1-2)
34) (2-3-2)-1-(-1-2-1)
35) (2-3-2)-2-(-1-1-1)
It is clear that these scales can be ordered according to how many usual chords they define (like major, minor diminished, augmented). The more non-weird chords the higher in the list. In other words they are not all of them the same good from the point of view of harmony of the chords they define, although they may seem very similar from the melodic point of view.
There are also the 6 notes Hirajoshi scale
http://www.flutopedia.com/scale_Hirajoshi_Extended.htm
and the Miyako Bushi extended scale
There are also the 6 notes Hirajoshi scale
http://www.flutopedia.com/scale_Hirajoshi_Extended.htm
and the Miyako Bushi extended scale
It is clear that these scales can be ordered according to how many usual chords they define (like major, minor diminished, augmented). The more non-weird chords the higher in the list. In other words they are not all of them the same good from the point of view of harmony of the chords they define, although they may seem very similar from the melodic point of view.
Tetra-chords (all the next are diatonic tetra-chords)
Rast 2-2-1
Ussak 1-2-2
Kurdi 2-1-2
The next is from the second melodic minor or leading whole tone scale
Shamba 2-1-1
The next contain a 3-semitone
Niavent 2-1-3
Hijazz 1-3-1
Huzam 3-1-1
Piraeus 1-3-2
And the next are 5-notes sub-scales (penta-chords) that are essentially diatonic
Rast 2-2-1-2
Ussak 1-2-2-2
Kurdi 2-1-2-1 (this is from the melodic minor)
Minor 2-1-2-2
The next contain a 3-semitone
Shamba 2-1-1-3
Nikriz 2-1-3-1
Hijazz 1-3-1-2
Huzam 3-1-1-2
See also https://www.youtube.com/watch?v=B6xddWJFmt8
For Arabic names of many of the previous scales see
http://www.maqamworld.com/
And if we restrict to only 4-notes sub-scales (tetra-chords) , having inverse such scales not different, then we are left with a small number of 10 of such characteristic tetra-chords
They are also all such tetra-chords containing intervals of 1,2,3, and where inverses and cyclic permutations of them do not count as different . Obviously all of the above scales are compositions of two of them, with possibly an extra interval between them
Diatonic
They are also all such tetra-chords containing intervals of 1,2,3, and where inverses and cyclic permutations of them do not count as different . Obviously all of the above scales are compositions of two of them, with possibly an extra interval between them
Diatonic
2-2-1, (major, natural minor Rast, Ussak)
2-2-2, (major, augmented)
Melodic minor, double minor (Shabach)
1-2-1
Harmonic minor (Hijazz,Huzam)
1-3-1
Harmonic double minor
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
Ir is obvious also that by extrapolating the steps 3-semitones to 2+1 we get 8-notes and 9-notes scales that are made only from steps of 1 and 2 semitones.
For a list of scales with their chords see http://www.scales-chords.com/
We may compare these scales with the 6-notes minor blue scale with interval structure
3-2-1-1-3-2 (see e.g. http://www.jazzguitar.be/minor-blues-scale.html )
or https://en.wikipedia.org/wiki/Hexatonic_scale
which is analysis of the western pentatonic below.
The 6-tone scale 1-3-3-1-3-1, the inverse which is 1-3-1-3-3-1 and the
1-3-1-3-1-3
And the 6-tone scale of the Hang instrument (raised Celtic minor )(see https://en.wikipedia.org/wiki/Hang_(instrument) )
2-1-2-2-2-3
This 6-tone Hang-scale can be derived from the dominant pentatonic
3-3-2-2-2 by splitting the 3 o 2-1, or can be derived also
from the 7-tone diatonic scale 2-1-2-2-2-1-2 by merging 1-2 to 3.
Or the 5-tone Egyptian / Mongolian mode of the western pentatonic 2-3-2-3-2
The pentatonic scale is the arpeggio of a major chord with 6th and 9th (or 2nd) which is the usual pentatonic scale
2-2-3-2-3.
Here also we may mention the blue arpeggio (arpeggio of both minor and major chord) of a chord with 6th, which is a pentatonic scale of the next structure
3-1-3-2-3
which can be considered as the harmonic minor that we subtracted the 4th and 7nth note!
The 6-tone Prometheus 2-2-2-3-1-2
The 6-tones inverse Prometheus 2-1-3-2-2-2
or the 6-tone 2-3-2-2-1-2 (raised Celtic Minor ) which is extrapolation of the 5-tonic
We may compare these scales with the Western pentatonic scale that has also two 3-semitones, that is of interval step structure 2-2-3-2-3 (also known as Egyptian/Mongolian).
Or compare them with the oriental 6-note scale 1-3-1-3-1-3
Or compare them with other 4-notes scales like 3-3-3-3
the 3-5-3-1 and 2-1-4-5 or 3-2-2-5 or 4-2-1-5, and 2-2-3-5 that extrapolations to 4-notes scales of 3-notes major or minor chords arpeggios-scales
Or the 8-notes Algerian=2-1-2-1-1-1-3-1
Or the 8-notes extrapolation of the Romani double minor
1-3-1-1-1-1-3-1
Or the Chinese 5-notes scale that have 2-tones steps , in other words interval structure
Interval fro the root : 1, 3, #4, 5, 7
Intervals in steps: 4 - 2 - 1 - 4 - 1 (the tetra-chord 1-4-1 is used instead of the oriental
1-3-1)
Formula: Quadra-step, Whole, Half, Quadra-step, Half 4 - 2 - 1 - 4 - 1
See e.g.
http://www.pianoscales.org/chinese.html
C: C, E, F#, G, B, C (we notice that it is a sub-scale of the F-major 7-notes scale)
For example if we take the mode of the diatonic scale starting from F
F G A B C D E F , a Chinese scale will be shaped by keeping the semitones B C,, E, F, but eliminating the notes G, D , Thus it will be
F, A, B, C, E, / F
Somehow all the above scales may be considered extrapolations of arpeggios of 3-notes chords of the type major,minor, diminished and augmented.
If we ask to find all scales that use steps of only 2 or 3 semitones, then they must be 5-tonic or 6-notes and the next are all the possible cases
5-tonic
3-3-2-2-2 dominant pentatonic
2-3-2-3-2 pentatonic
6-notes
2-2-2-2-2-2 (Whole tone)
