All the next chords are superposition of 2-notes relatives chords of types major, minor, diminished, and augmented.
Discussion of the defnition-creation and roles of the 8 basic such chords (in root position)
The next equations show how such chords are composed from minor, major, diminished and augmented triads or chords
433=maj+dim=R7
434=maj+min=Rmaj7
343=min+maj=Rm7=R'6, where R' the root of a relative chord
333=dim+dim=Rdim7
334=dim+min=Rm6=R'm7b5 , called also half diminished where R' the root of a relative chord
444=aug+aug=Raug
344=min+aug=Rminmaj7
443=aug+maj=Rmaj7#5
4 of the above chords can be 4-notes chords of the diatonic scale e.g. the R7, Rmaj7, Rm7, Rm7b5. But the Rdim7, Raug, Rminmaj7, Rmaj7#5 cannot be 4-note chords of the diatonic scale. Nevertheless there exist in other scales as we shall see like Harmonic minor, and harmonic double minor Melodic minor (Hindu)and Melodic double minor (Arabic) and other oriental scales as in the scales of post 52.
Similarly we might classify the 5 notes chords of a single diatonic scale e,g. chords like dominant 7th with sixth one octave lower e.g. C6,7 =min+maj+min with structure 3-4-3-4.
Some of the above chords appear as chords of the LONG SCALE (see post 42, and 34)
(successive distance in semitones) (434343434343434343434343)
Besides the long scale we may define the HARMONIC MAJOR DIATONIC 7 SCALE of 7 notes that spans 2 octaves, and every 3 or 4 successive notes is a chord of the above types
Here it is (STARTING FROM THE C3)
etc -C4-E3-G3-B3-D4-F4-A4-C5- etc
Constructing therapeutic harps, or similar instruments (e. thump pianos) or such keyboards with this scale, has the property that almost what ever we play sounds harmonic as 3 or 4 notes in sequence are well known cords, and overlapping such triads , are relative chords. In fact we may design such an harmonic double row keyboard
as follows
-D3-F3-A3-C3- E4-G4-B4-
-C4-E3-G3-B3-D4-F4-A4-C5-
There are exactly 12 of characteristic tetra-chords (4-notes sub-scales) containing intervals of 1,2,3, and where inverses and cyclic permutations of them do not count as different
Diatonic
2-2-1, (major)
2-2-2, (major, augmented)
2-1-2 (natural minor)
Melodic minor
1-2-1
Melodic double minor
2-1-1,
Harmonic minor
1-3-1
Harmonic double minor
1-2-3,
Diminished
3-3-3 , (diminished 7nth)
3-3-1,
Pentatonic
3-3-2,
2-2-3
2-2-3
Other
1-1-1, (Chromatic)
The above classification is also a classification of 4-notes scales made from intervals of semitone, tone, 3-semitones and 2-tones. They are the arpeggios of the previous chords
4-3-3-2
4-3-4-1
3-4-3-2
3-3-3-3
3-3-4-2
3-4-4-1
4-4-3-1
In addition if the intervals 4 are extrapolated to 2-2 or 3-1, 1-3 , and the 3 to 2-1, 1-2, then are shaped 5-notes pentatonic scales.
We also list also here the classification of the 4-string shapes of all the main of above 8-chords with roots, on the 6th, 5th and 4th string of the guitar.
The main value of this classification is when improvising with a melody while simultaneously we play a background 3-strings chord which is a major , minor, diminished or augmented chord, and together with the note of the melody they make as composite chord one of the above chords. This is valuable in chord-melody improvisation.
Such 4-notes chords are met as 4-notes chords of the melodic minor scale, harmonic minor scale, second melodic minor scale (or leading whole tone scale , ), Romani or Hungarian (Gypsy) minor scale , Greek Buzuki Arabic scales etc ( see posts 46, 50,51,52).
As such 4-notes chords create mostly the feeling of anxiety and resolve at a major or minor chord, this also means that the anxiety-serenity resolutions are realized by modulations from such scales like melodic minor leading whole tone (second melodic minor), harmonic minor , Romani minor etc, to ordinary diatonic scale (major scale).
Such 4-notes chords are met as 4-notes chords of the melodic minor scale, harmonic minor scale, second melodic minor scale (or leading whole tone scale , ), Romani or Hungarian (Gypsy) minor scale , Greek Buzuki Arabic scales etc ( see posts 46, 50,51,52).
As such 4-notes chords create mostly the feeling of anxiety and resolve at a major or minor chord, this also means that the anxiety-serenity resolutions are realized by modulations from such scales like melodic minor leading whole tone (second melodic minor), harmonic minor , Romani minor etc, to ordinary diatonic scale (major scale).
The ways to play them on the guitar fretboard are plenty and very well known (see post 14 ,46 ) We present here only the not very usual types of
Rmmaj7 and Rm7#5
1)Rmmaj7 e.g. R=E
2) Rm7#5 e.g. R=E
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.
