The meaning of 3-1 is that we have a melody from 4 themes a1, a2,a3,b , where a1,a2,a3 are a repetition 3 times of a single theme or a similarity variation of a single theme, and then the melodic phrase closes with the theme b.
Similarly, it would be interpreted the 2-1 pattern, and 1-1 pattern.
The way to relate with the harmony of a chord progression is that each theme ai, is usually a chord R, or a chord transiton (R1, R2), or a double chord transition (R1,R2,R3).
The correspondence starts by requiring that te closure theme b is an harmonic transition resolution transition (R1,R2), e.g. R1=D7, R2=G, or R1=G7, R2=C.
Then if the underlying chords of a1,a2,a3 are (Rai, Ra(i+1)), then they could be
a) an inversion of a resolution
b) a melodic transition from major to minor or from minor to major
c) a chromatic transition
d) again a harmonic resolution
The 3-1 pattern is best fitting to poetry especially to 15-syllable poetry, and coresponds to 2-lines,
where a1, is 4 syllables, a2 4 sylables (together one line of 8 syllables ) , the a3 4 syllables and b 3 syllables (together the 2nd line of 7 syllables).
The 3-1 pattern fits also with teh andlauzian cadenca.
a1<-> 6m
a2<-> 5M
a3<-> 4M
b<-> 3M7
Once the chord transitions (Ri, R(i+1) are defined , we define also all the melodic themes and lines
m1, m2 , m3,...mk corresponding to them, and we represent them geometrically as horizontal lines
We choose the best diatonic scale to fit them (or fit a aprt of the chord progression) , and we denote the notes of teh scale by integer numbers 1,2,3,4,5,6,7.
This is in the context of chromatic tonality (in the sense thata we may change scale, but sill we write as if in asingle diatonic scale and all allouter notes are caled teh blue or chromatic notes, denoted by n# or nb .
For each melodic line mi, (which may be considered a riff too , see post 476) that corresponsd to the transition (Ri, R(i+1)) we write as optional starting note the middle (2nd note) of the 3-notes chord Ri, and as end note the middle of the chord R(i+1). It is optional because we could start and end at any note of the chords Ri, R(i+1).
Then on the melodic line mi, we write no other notes, and the timing of the notes exceps the chromatic or blue notes contained in the chord transition (Ri, R(i+1)) . It is recommended that the melodic line pass from the blue notes. In this way of pre-writing the compositon or improvisation, we leave space for free choice of the notes in the improvisation or composition, which is experimented with and chosen according to the emotions that that particular choice of intermediate notes creates. If it is palyed in a particular instrumemt, the convenience of palying also play a role in the choice. We do not also determine an up or down direction of the melodic line or a waving pattern. This may vary in the repetitions of the parts of the song or for the final choice in a composition after experimentation. Thus, as we see we do not use the pentagram , and the writing is more abstract than a final sequence of notes.
This sequence of geometric lines with abstract specifications , is called The melody geometic poem, or the RIFFS POEM.
A riff, that is all in a single chord, is usually a waving pattern, with initial and final notes sounding longer, and forming an interval of 3rd or 5th, and their complements. (very common in reels in folk Irish music)
The melodic-lines are grouped after the pattern 3-1, or 2-1, or 1-1, etc.
The final resolution 1 of the pattern 3-1, is not only in harmony a resolution but also a kind of inversion or resolution of the order-topoly shapes of the 3 melodic themes, in the 3-1 pattern.
Also they are classified after the harmony as, melodic, chromatic, harmonic, resolutions, and inverses of resolutions.
All these characterizations have of course emotional meaning.
But they are also classified according to their order topology shape. Ascending, descending, waving, stationary, spikes, etc.
As we see, we leave the order topology shape for the experiment and emotions to decide.
When in a keyboard (like the thumpjum digital harp) this way of writing makes it very-very easy to improvise for composition experimentation.
