(This post has not been written completely yet)
We have mentioned in previous posts in this book, that the diatonic scale has the optimal mathematical property of being the only 7-notes scale (within the chromatic Bach 12-notes scale) with he maximum number of major and minor chord-triads.
An interesting next question is what are the corresponding such scales with the same maximal property but with a smaller number of notes? E.g. 4,6, or 6 notes?
The answer was given in post 117 where the maximal such harmonic sb-scales are enumerated.
We highlight only the maximal harmonic 5-notes and 6-notes subscales as giving rise to the most popular in western songs chord progressions.
5-notes maximal harmonic pentatonic
intervals patterns 4-3-2-2-1 e.g. c4-e4-g4-a4-b4-c5
(It is essentially A chord with 7nth and with 6th)
Notice that this scale suggests the chord progression by taking chords of the full 7-notes diatonic scale based on the above notes of the maximal harmonic 5-notes scale which has the highest statistical frequency in popular songs: 1(7) 4 5 6m E.g. in C major scale it would be C7, F , G Am (=I7, IV, V, vi )=(1(7), 4, 5, 6m).
6-notes maximal harmonic
intervals patterns 2-2-3-2-2-1 e.g. c4-d4-e4-g4-a4-b4-c5
The answer was given in post 117 where the maximal such harmonic sb-scales are enumerated.
We highlight only the maximal harmonic 5-notes and 6-notes subscales as giving rise to the most popular in western songs chord progressions.
5-notes maximal harmonic pentatonic
intervals patterns 4-3-2-2-1 e.g. c4-e4-g4-a4-b4-c5
(It is essentially A chord with 7nth and with 6th)
Notice that this scale suggests the chord progression by taking chords of the full 7-notes diatonic scale based on the above notes of the maximal harmonic 5-notes scale which has the highest statistical frequency in popular songs: 1(7) 4 5 6m E.g. in C major scale it would be C7, F , G Am (=I7, IV, V, vi )=(1(7), 4, 5, 6m).
6-notes maximal harmonic
intervals patterns 2-2-3-2-2-1 e.g. c4-d4-e4-g4-a4-b4-c5
(It is essentially a chord with 7nth, 6th and 2nd. A mode of it is known also the raised Celtic minor scale of the hang-drums )
Notice that this scale also suggests a chord progression by taking chords of the full 7-notes diatonic scale based on the above notes of the maximal harmonic 5-notes scale which has highest statistical frequency in popular songs: 1(7) , 2m, 4 ,5, 6m E.g. in C major scale it would be C7,Dm, F , G Am. This progression includes both the Blues progression 1 2m 5 (=I , ii, V) , and the most popular 1,4,5,6m (=I, IV, V, vi) .
For the F major scale, which is common in Eastern Europe folk music , such a scale of chords would be
F7, Gm, Bb, C, Dm,
While for the Bb major scale , which is very common in Greek folk music, such a scale of chords would be
Bb, Cm, Eb , F , Gm.
This most popular chord progression has a variation:
Instead of 1M, 4M, 5M 6m , the 1M, 2m, 5M 6m (6m->2m->5M ->1M)
Or sometimes
5M->1M->4M->2m->5M
E.g. of (6m->2m->5M ->1M)
https://www.youtube.com/watch?v=gUNWjgaJEik
Notice that this scale also suggests a chord progression by taking chords of the full 7-notes diatonic scale based on the above notes of the maximal harmonic 5-notes scale which has highest statistical frequency in popular songs: 1(7) , 2m, 4 ,5, 6m E.g. in C major scale it would be C7,Dm, F , G Am. This progression includes both the Blues progression 1 2m 5 (=I , ii, V) , and the most popular 1,4,5,6m (=I, IV, V, vi) .
For the F major scale, which is common in Eastern Europe folk music , such a scale of chords would be
F7, Gm, Bb, C, Dm,
While for the Bb major scale , which is very common in Greek folk music, such a scale of chords would be
Bb, Cm, Eb , F , Gm.
This most popular chord progression has a variation:
Instead of 1M, 4M, 5M 6m , the 1M, 2m, 5M 6m (6m->2m->5M ->1M)
Or sometimes
5M->1M->4M->2m->5M
E.g. of (6m->2m->5M ->1M)
https://www.youtube.com/watch?v=gUNWjgaJEik
