See also post 90 about the relavant tuning in 6-string guitar.
The next photo of the ipad shows in the program Muzix pro (https://www.youtube.com/watch?v=qfvHNmO1GoQ&t=26s ) the diatonic Isomorphic layout by alternating 3rds, at the diatonic scale C major .
We notice that
1) Each row is by intervals of 2nds
2) Ecah colomn is by alternating major-minor intervals of 3rds.
The layout has the nice property that vertically every 3 consecutive squares is a chord, either major minor or diminshed. That is why iti s an isomorphic layout as all chords ofthe same type have the same shape. Here it is even a strong isomorphic layout so that any chord of the diatonic scale in its normal position (1-3-5) has the same shape.
The advantages for melodic improvisation and chord accompanying are the next
1) Horizontally, as the layout is by 2nds , the horizontal motion is good for melodic themes made by 2nds
2) If we want a 2nd faster speed of up or down in the melodic improvisation then we move vertically by 3rds, which as if utilizing a chord as a gate to move fast.
3) If we want a 3rd faster speed of up or down in the melodic improvisation then we move diagonally by 4ths.
4) If we want to move by 5ths then we move vertically again but in the odd number of squares
5) Variations of an horizontal melodic theme is best if we shift one column up or down and repeat it (translation by a 3rd) or two rows up or down and repeat it: Translation by 5ths
6) When stopping at acenter note oft he melodic themes that last longer, then the accompaying chord, is vertically 3 squares that has the melodic center not in the middle or at one of its two ends. We may even try the first and then if not very much desired sound we shift one up or one down.
The Musix pro application allows for fast by a visisble button to change the scale or to have avaiable at 7 buttons the 7 chords of the scale. (here in the photo we have hide it).
MELODIC IMPROVISATION AND CHORD ACCOMPANYING WAS NEVER EASIER AND MORE MUSICALLY MEANINGFUL!
SOME RULES TO MAKE NICE MELODIC THEMES AND VARIATIONS OFTHEM ARE THE NEXT
(See also Max Martns maths of melodies in post 311)
1) We choose as melodic theme a symmetric pattern (square, triangle , polygone etc) or part of it as basic melodic theme and from the shape (and since each chord is always , due to the isomorphic layout, a vertical segment of 3 consecutive squares) we make sure it is harmonzed and accompanied by 1, 2 or 3 chords.The symmetric pattern of the melodic theme should make visible also the simplified substructure of its simplicial submelody corresponding melodic themes (in other terminology "Dolphin word")
2) We variate it by translating it vertically , horizontally, diagonally etc But not only translating but also transforming it with affine (linear) transformations and even topological transformations as a type of mutations discussed also in 4).
3) We variate it by inverting its times sequetioanl order in its notes, or taking a rfkection of the shape , relative to an axis or point
4) We mutate it (if it is part of a connected symmetric shape) by taking complementary or other parts of the same connected symmetric shape (or if its a full connected symmetric shape by taking an alternative symmetric shape).
5) We go on and loop as above in 1) 2) 3) 4).
I assume if Bach had this tool He would have composed even more and even more beatiful conterpoint musical pieces.
With this musical instrument the single unaccimpanied improvisation of altrnating chord and melodus is very well and efficient done! (see also post 102 THE METHOD OF UNACCOMPANIED IMPROVISATION BY ALTERNATION OF CHORDS VARIATIONS WITH SHORT MELODIC THEMES VARIATIONS and post 302. METHOD OF IMPROVISATION BY AN UNACOMPANIED SINGLE DIATONIC INSTRUMENT OR STRING INSTRUMENT WITH A SCALE MARKED ON THE FRETBOARD , BY SMALL MUSICAL THEMES AND PERPETUAL VARIATIONS BY TRANSLATION FROM S TRING TO STRING , INVERSION AND MUTATION. and post 295. THE 3 MAIN TYPES OF IMPROVISATION AND 3 BASIC PRINCIPLES )
The next photo of the ipad shows in the program Muzix pro (https://www.youtube.com/watch?v=qfvHNmO1GoQ&t=26s ) the diatonic Isomorphic layout by alternating 3rds, at the diatonic scale C major .
We notice that
1) Each row is by intervals of 2nds
2) Ecah colomn is by alternating major-minor intervals of 3rds.
The layout has the nice property that vertically every 3 consecutive squares is a chord, either major minor or diminshed. That is why iti s an isomorphic layout as all chords ofthe same type have the same shape. Here it is even a strong isomorphic layout so that any chord of the diatonic scale in its normal position (1-3-5) has the same shape.
The advantages for melodic improvisation and chord accompanying are the next
1) Horizontally, as the layout is by 2nds , the horizontal motion is good for melodic themes made by 2nds
2) If we want a 2nd faster speed of up or down in the melodic improvisation then we move vertically by 3rds, which as if utilizing a chord as a gate to move fast.
3) If we want a 3rd faster speed of up or down in the melodic improvisation then we move diagonally by 4ths.
4) If we want to move by 5ths then we move vertically again but in the odd number of squares
5) Variations of an horizontal melodic theme is best if we shift one column up or down and repeat it (translation by a 3rd) or two rows up or down and repeat it: Translation by 5ths
6) When stopping at acenter note oft he melodic themes that last longer, then the accompaying chord, is vertically 3 squares that has the melodic center not in the middle or at one of its two ends. We may even try the first and then if not very much desired sound we shift one up or one down.
The Musix pro application allows for fast by a visisble button to change the scale or to have avaiable at 7 buttons the 7 chords of the scale. (here in the photo we have hide it).
MELODIC IMPROVISATION AND CHORD ACCOMPANYING WAS NEVER EASIER AND MORE MUSICALLY MEANINGFUL!
SOME RULES TO MAKE NICE MELODIC THEMES AND VARIATIONS OFTHEM ARE THE NEXT
(See also Max Martns maths of melodies in post 311)
1) We choose as melodic theme a symmetric pattern (square, triangle , polygone etc) or part of it as basic melodic theme and from the shape (and since each chord is always , due to the isomorphic layout, a vertical segment of 3 consecutive squares) we make sure it is harmonzed and accompanied by 1, 2 or 3 chords.The symmetric pattern of the melodic theme should make visible also the simplified substructure of its simplicial submelody corresponding melodic themes (in other terminology "Dolphin word")
2) We variate it by translating it vertically , horizontally, diagonally etc But not only translating but also transforming it with affine (linear) transformations and even topological transformations as a type of mutations discussed also in 4).
3) We variate it by inverting its times sequetioanl order in its notes, or taking a rfkection of the shape , relative to an axis or point
4) We mutate it (if it is part of a connected symmetric shape) by taking complementary or other parts of the same connected symmetric shape (or if its a full connected symmetric shape by taking an alternative symmetric shape).
5) We go on and loop as above in 1) 2) 3) 4).
Because the beatiful melodies are reflected as beatiful geometric shapes,and the beatiful variations of them as beatiful geomotric motions and transformations, there is an open road to improvise amd compose an abundance of beatiful melodies with systematic symmetric structure in variatinosn ofthem and their harmony. The quality of the image in is symmetries and transformations is reflected in the quality of the melody structure and its harmony. In thiw way light and sound merge.
I assume if Bach had this tool He would have composed even more and even more beatiful conterpoint musical pieces.
With this musical instrument the single unaccimpanied improvisation of altrnating chord and melodus is very well and efficient done! (see also post 102 THE METHOD OF UNACCOMPANIED IMPROVISATION BY ALTERNATION OF CHORDS VARIATIONS WITH SHORT MELODIC THEMES VARIATIONS and post 302. METHOD OF IMPROVISATION BY AN UNACOMPANIED SINGLE DIATONIC INSTRUMENT OR STRING INSTRUMENT WITH A SCALE MARKED ON THE FRETBOARD , BY SMALL MUSICAL THEMES AND PERPETUAL VARIATIONS BY TRANSLATION FROM S TRING TO STRING , INVERSION AND MUTATION. and post 295. THE 3 MAIN TYPES OF IMPROVISATION AND 3 BASIC PRINCIPLES )
