(This post has not been written completely yet)
See also posts 92, 103, 104 (concepts of chord-local 7-notes scale and chord-courtyard)
The chord-closure or vector-chord as defined in post 159 is only for the normal position of a chord.
The random playing of the notes at an equal time each, or "rotations" or permutations of a vector-chord (or chromatic and diatonic neighborhood of a chord) , leads to a melody that the chord that fits to it harmonically to accompany it, is the chord of the vector-chord. In this way, a pre-defined chord progression visualized as a progression of vector chords, defines almost completely an improvisational melody.
For improvisation in general over a known or unknown a tune we need two types of concepts
1) Simplifying to the melody concepts like chord-progression, simplicial sub-melody , bas etc
2) Enhancing to the melody concepts like counter-melody on the vector-chord underlying at that time the melody etc From the chord the middle (3rd note together with the root 1st note) is considered tobe the most characteristic from the chord as it differentiates it from major and minor.
Because 5 notes are played statistically almost equally in time and 3 are inside the chord while 2 only outside the overall result is harmonic with the chord. taking the middle note (3rd) ofthe chord as it its geometric center rather than its root, we have that this soloings is a kind of almost random "dancing" around the geometric center of the chordand inside the underlying scale. Since for each chord there is usually one note of a simplicial submelod, and we may take as note of the simplicial sub melody the geometric center (3rd in1-3-5) we may alsos say that this way of improvising is a "dancing" around the notes of this (middle note) simplicial submelody
Normally two triads are for the first poetic line (8 beats) and two more for the 2nd poetic line (7 syllables).
2ND LAYER FASTS HARMONIZATIONS OF VECTOR-CHORDS IMPROVISATIONS
Furthermore, when improvising by "waving" or "rotating" inside the vector chord, we may also add some harmony by playing the improvisational solo as 1st-2nd voice or doubles by intervals of 3 and of course changing them to major minor 3rds so that it belongs to the scale if the roots are in the scale or keeping it the same to the closest such that is in the scale. It can be with doubles or even triads (3-notes chords) which of course will create a fast-changing harmony which is reasonable to accompany with only stable power chord of 5 (interval of 5). Usually, the fast changing of the chords is of the chords I, IV, V (or substituting any one of them with its lower relative minor chord. see also post 159)
E.g. here is a good example of such melodic wavings in the next midi file. It can be considered as chromatic or diatonic waving around each note of the chord but in addition, harmonized with doubles by intervals of 3rds http://www.greeksongs.gr/midis/arampasperna.mid
Because 5 notes are played statistically almost equally in time and 3 are inside the chord while 2 only outside the overall result is harmonic with the chord. taking the middle note (3rd) ofthe chord as it its geometric center rather than its root, we have that this soloings is a kind of almost random "dancing" around the geometric center of the chordand inside the underlying scale.
Because 5 notes are played statistically almost equally in time and 3 are inside the chord while 2 only outside the overall result is harmonic with the chord. taking the middle note (3rd) ofthe chord as it its geometric center rather than its root, we have that this soloings is a kind of almost random "dancing" around the geometric center of the chordand inside the underlying scale.
We should notice that besides such "chromatic waving" or "rotating" within the closure of a triad chord in the normal position, we may have also waving ascending and waving descending or translating, if we expand the chord in two or 3 octaves. And this may be done again with fast-changing harmonization (I, IV, V) with doubles or triads , as long as the duration of the notes outside the chords (the initial and maybe two more within the pattern I, IV, V) are less than the duration of the notes inside the chords or as long as the intervals created by the notes of the melody and the notes of the chords have more 3rds 4ths and 5ths compared to intervals of 2nds.
We must remark here that if there is a melody in the song which is say using the chords X1, X2 X3,...Xn , the melodic improvisational fillings parallel and in between the parts of the melody with instruments like Bouzouki or mandolin or violin or lyre etc , need not keep the same chord-progression X1,...Xn but a permutation of it as well ,although in general, it will use the same chords and rarely more chords but of the same notes-scale or same scale of chords (chord-scale).
In all cases, a variational chord progression X(a1), ..., X(ak) will determine as above after determining the vector-chord wavings an improvisational solo.
If we are composing e.g. in a midi editor the above perceptions are adequate for easy composition of melodies. But if we are playing an instrument and we want to improvise, then instead of having as center the arpeggio of a chord to improvise diatonically or chromatically around it it ir ending at it it is easier to think of waving around or ending at centers that are not chords but notes that are away by intervals of 3rd, 4th, 5th 8th (e.g. the notes of a simplistic sub-melody).
See also post 159
CRETAN CONDILIES AND IRISH REELS WAVING ROTATIONS INSIDE A VECTOR-CHORD
Very often the rotational waving inside a vector chord (in Creta it is called condilies as it was played with wind instruments from cane and the thicker rings of it are called Condili) (e.g. major chord 1-3-5 as root chord of a diatonic scale) is a waving by intervals of 2nds of a full walkthrough of the vector chord 3-4-5-4-3-2-1-1 , which restricted to the notes of the chord is 3-5-3-1 .Other times as cycle waving starting and ending on the same note of the chord (e.g. 3rd middle note). For every type of "Condilies" there is a "projection trace" of it as an almost repetitive harping on the arpeggio of an underlying chord. It is almost certain though that it includes notes outside the arpeggio of the chord.
Another insight about Condilies is the next: Let us remember the well known Andalusian cadenza patterned on the sub-scale 1-2-2 semitones (See post 17 and also above about Ancient Greek syntono tetrachord ) which is played by chord e.g. iv->V->IV->III . Here for condilies we may have a melodic version of it where instead of chords we play waving patterns around the notes of pitch order 1-2-2 in semitones .
Or so as to have a pure interval of 5 , 1-2-2-2 or 2-2-2-1 . And also an interval of
minor 6 : 1-2-2-2-1
If we combine the 6-notes 1-2-2-2-1 with the 4 notes 1-2-2 at one semitone distance we get the 1-2-2-2-1-1-1-2-2 which is a modulation to 2 different diatonic scales. We may also combine a diatonic scale with a 6-notes blues scale by having the 4 note of the major diatonic scale with a sharp and apply wavings by intervals of 2nd going up and down it.Somewhere in the wavings by 2nds we double the speed of waving for 2-3 such oscillations
The harmonization of the Condillies in the 5-chordo 1-2-2-2 is not a iii minor chord (1-2)-(2-2) (e.g. Em in C major scale or F#m in D major) but two major chord V=5M and I=1M (G-C in C major or D-A in D major), Where the upper -(2-2) part is the lower major 3rd of V=5M chord and the lower (1-2)- is the upper minor 3rd ofthe I-1M chord. In general this might be a way also to substitute a minor chord in a melody in a diatonic scale with two major chords. If we want to accompany it with intervals of 5th strictly speaking it should be two intervals of 5th 4-1! and 1-5 as steps of the diatonic scale. An harmonization of the Condillies in the 4-chord 1-2-2 , it could be an upper part -(2-2) which is the lower major 3rd of the IV=4M chord (in D major it would be G major) andthe (1-2)- (overlapping with the 2-2 part) it would be the upper minor 3rd of the I =1M chord (In D major the D major chord).
Of course in some cases depending on the waving we may use the chords progression
I->V->IV->I,where the 3rd chord is of very short duration.
More generally see below about 2 or 3 only chords harmonization.
If we want to accompany such condillies melodies not with one power chord but with major or minor triads then they should be as few as possible e.g. 2 or 3. For happy melodies obviously, they are the I, IV, V. According to the degree of sadness we want to impose, we substitute any of the major chords with its lower minor relative. In other words vi for I, ii for IV and iii for V.
About the symbols: In a C major scale the symbols denote the next chords
I=1M=C
ii=2m=Dm
iii=3m=Em
IV=4M=F
V=5M=G
vi=6m=Am
vii=7d=Bdim
So the possible combinations are
I, IV, V or only I, V
vi , IV, V or only vi, V
I , ii, V
I, IV, iii or only I, iii
iv , ii, V or only iv, V
I , ii, iii or only I, iii
vi, IV, iii or only I, iii
vi, ii, iii or only vi, iii
We must understand that the dancing melodies of melodic improvisation that are of a high degree of freedom in changes and are accompanied only by a root power chord 1-5-1' are a different class of melodies of harmonic improvisation that are those that during not very short intervals of time are accompanied by a 3-notes chord of the scale. An example of a melody that the only reasonable accompanying chord is a root power chord is to go up and down several times all the 7 notes scale and fast enough. Theoretically, one could accompany it with very fast changing 3-notes chords but exactly because it is very fast changing it is meaningless and it is better only a root power chord. On the other hand, singing melodies that can be divided into a small number and of significant duration time intervals during which they have clear 3-notes major or minor or diminished accompanying chord (preferably with another instrument than the soloing instrument) have better harmony if accompanied by such major or minor chords rather than a single root power chord.
Another insight about Condilies is the next: Let us remember the well known Andalusian cadenza patterned on the sub-scale 1-2-2 semitones (See post 17 and also above about Ancient Greek syntono tetrachord ) which is played by chord e.g. iv->V->IV->III . Here for condilies we may have a melodic version of it where instead of chords we play waving patterns around the notes of pitch order 1-2-2 in semitones .
Or so as to have a pure interval of 5 , 1-2-2-2 or 2-2-2-1 . And also an interval of
minor 6 : 1-2-2-2-1
If we combine the 6-notes 1-2-2-2-1 with the 4 notes 1-2-2 at one semitone distance we get the 1-2-2-2-1-1-1-2-2 which is a modulation to 2 different diatonic scales. We may also combine a diatonic scale with a 6-notes blues scale by having the 4 note of the major diatonic scale with a sharp and apply wavings by intervals of 2nd going up and down it.Somewhere in the wavings by 2nds we double the speed of waving for 2-3 such oscillations
Of course in some cases depending on the waving we may use the chords progression
I->V->IV->I,where the 3rd chord is of very short duration.
More generally see below about 2 or 3 only chords harmonization.
If we want to accompany such condillies melodies not with one power chord but with major or minor triads then they should be as few as possible e.g. 2 or 3. For happy melodies obviously, they are the I, IV, V. According to the degree of sadness we want to impose, we substitute any of the major chords with its lower minor relative. In other words vi for I, ii for IV and iii for V.
About the symbols: In a C major scale the symbols denote the next chords
I=1M=C
ii=2m=Dm
iii=3m=Em
IV=4M=F
V=5M=G
vi=6m=Am
vii=7d=Bdim
So the possible combinations are
I, IV, V or only I, V
vi , IV, V or only vi, V
I , ii, V
I, IV, iii or only I, iii
iv , ii, V or only iv, V
I , ii, iii or only I, iii
vi, IV, iii or only I, iii
vi, ii, iii or only vi, iii
We must understand that the dancing melodies of melodic improvisation that are of a high degree of freedom in changes and are accompanied only by a root power chord 1-5-1' are a different class of melodies of harmonic improvisation that are those that during not very short intervals of time are accompanied by a 3-notes chord of the scale. An example of a melody that the only reasonable accompanying chord is a root power chord is to go up and down several times all the 7 notes scale and fast enough. Theoretically, one could accompany it with very fast changing 3-notes chords but exactly because it is very fast changing it is meaningless and it is better only a root power chord. On the other hand, singing melodies that can be divided into a small number and of significant duration time intervals during which they have clear 3-notes major or minor or diminished accompanying chord (preferably with another instrument than the soloing instrument) have better harmony if accompanied by such major or minor chords rather than a single root power chord.
WAVING AROUND THE SIMPLICIAL SUBMELODY AS IMPROVISATIONAL PARALLEL DIALOGUE COUNTER-MELODY OF THE MELODY
The previous remark about waving an improvisation across the vector-chords and around or ending specific center-notes can be enhanced by having these center-notes to be the notes of the simplicial sub- melody of the singing melody (the simplicial sub-melody has about one note per underlying chord). Thus such a waving diatonic improvisation (or slightly chromatic waving sometimes with the two blue notes 5# , 2# of the harmonic minor and double harmonic minor) is the parallel dialogue to the melody with a more dense and filling counter-melody
