VECTORS, WAVES AND SPIKES
The identification and method of composition of them is based on the next concepts
1) As melody it has 3 layers (Simplicial submelody of the harmony, melodic arpeggio , diatonic chromatic arpeggio or ostinado)
2) Within each chord, it has
2.0) A single note from the simplicial submelody
2.1) A projected and simplified melodic arpeggio
2.2) The full diatonic chromatic ostinado, which consists from
a) Diatonic chromatic maxima VECTORS
b) Diatonic chromatic RIPPLES or waves or cycles or oscillations
c) SPIKES (jumps with intervals higher than 2nd)
THE KEY-WORD HERE IN THE 4TH GENERATION DIGITAL MUSIC FOR THE MUSICAL-THEORETIC IDEAS OF THIS POST (AS FAR AS MORDEN SOFTWARE FOR MUSIC MAKING IS ) IS MELODY-SEQUENCERS AND ARPEGGIATORS
THE TERM SEQUENCER MEANS HERE A LOOP OR RHYTHMIC CYCLE OF A MELODIC THEME THAT IS VARIATED INTERACTIVELY BY THE USER IN A MELODIC SEQUENCER.
THERE MANY GOOD SOFTWARE PROGRAMS FOR THIS COMPOSITION AND IMPROVISATION LIKE FUGUE MACHINE, YAMAHA MOBILE SEQUENCER, THUMPJAM ETC. ALSO ARPIO AND ARPEGGIONOME FOR GENERAL ARPEGGIOS ALTERNATED WITH MELODIC IMPROVISATIONS
THE MAIN IDEA TO COMPOSE AND IMPROVISE SUCH FAST DANCING SOLOING IS TO RESTRICT THE HARMONY, THE RHYTHM AND USED NOTES TO REALLY SIMPLEST POSSIBLE SCHEMES AND CONVERSELY ENHANCE THE COMPLEXITY IN WAVING OR ROTATING, VARIATIONAL PATTERNS
THE ANCIENT MUSICAL THEORY SIMPLE DESCRIPTION OF RAPSODY MUSIC STIL LIVING IN THE AEGEAN ISLANDS LIKE THAN OF CRETE IN GREECE :
Such music was created in ancient times it is mesmerizing with complicated melodic lines but in reality very simple musical description.
For these Aegean islands (Greece) improvisational folk melodies with violin or Lyra, the next factors prevail.
1) "Poetic meters" over the same note sometimes note up to 8 notes
3) Straight vectors ascending or descending usually of 4 or 5 notes so as to reach a new chord neighborhood.
2) Mainly waves by intervals of 2nds (chromatic) inside intervals of 3rds (melodic, either standing or ascending descending, and usually inside a chord so as to reach the neighborhood of a new chord.
A) THE UNDERLYNG CHORD OF THE SONG IS ONLY ONE AND IS A POWER CHORD AT ROOT POSITION OF SAY A DIATONIC SCALE (ALTHOUGH IN ANCIENT TIMES THEY DID NOT HAVE THE CONCEPT OF A 7-NOTES SCALE BUT ONLY OF A 4-NOTES SCALE THE TETRACHORD WHICH WAS A SCALE SPANING ONLY AN INTERVAL OF 4TH INSTEAD OF AN INTERVAL OF 8TH, THUS POWER CHORD WOULD BE THE ROOT POSITION ON THE TETRACHORD).
B) THE SOLOING IS ANY REPEATING PROGRESSION OF SHORT RYTHMIC MELODIC THEMES WITHIN A TETRACHORD WHICH IS USUALLY THE 1-2-2 IN SEMITONES THUS THE FRYGIAN TETRACHORD AT THE 3RD POSITION OF A DIATONIC SCALE WITH UNDERLYING POWER CHORD AT THE ROOT POSITION OF THE TETRACHORD OR THE 3RD POSITIONOF A MODERN 7-NOTES DIATONIC SCALE. (SOMETIMES ALTERNATING WITH ANOTHER TETRACHORD E.G. THE IONIAN TETARCHORD AT ROOT POSITION OF THE 7-NOTES DIATONIC SCALE , AND IN ANY CASE THE ACCOMPANYING CAN BE ALSO BY THE POWER CHORD AT THE ROOT POSITION OF THE 7-NOTES DIATONIC SCALE IN INSTEAD OF THE 3RD POSITION OF THE DIATONIC SCALE)
THE MORE COMPLICATED BUT NOT ALWAYS MORE ENLIGHTENING DESCRIPTION WITH MODERN SCALES AND CHORDS:
Some melodies would be very complicated shifting from natural minor to harmonic minor to double harmonic minor to diatonic major etc. Still all of the previous scales have commonnotes and the simplest type of chords that are called (neutral) power chords P5 (see post 35, that are essentially only an interval of fifth with doublingthe root one octave higher) are appropriate to accompany the melody if we want a relatively small number of chords .
Accompanying with power chords was the main use of 3-string instruments that are tuned in open (neutral) power chords like Greek Bouzouki D-A-D , Sazi D-A-D and Balalaika E-E-A.
Here is an example of Greek folk melody of minor Asia , which can be accompanied with only 3 power chords D5 (=D-A-D) , G5 (=G-D-G) and A5 (=A-E-A) .
When accompanying with power chords a melody in diatonic scale, any melody in the scale will create intervals with the notes of the power chord that the number of intervals of 2nds are as percentage much less in the average compared to intervals of 3rd and 4ths or 5ths. Thus the melody fits to the power chord. At the same time there is higher freedom ofthe elody relative to the power chord which stays same in a considerable time.
https://www.youtube.com/watch?v=2gcdVdzIqOU
Similar complicated but fast also melodies occur in Cretan folk music and Irish folk music and all of them have better harmonization with power chords.
E.g.
Cretan fast folk melodies
https://www.youtube.com/watch?v=XR4v7_itRm8
Irish fast folk melodies
https://www.youtube.com/watch?v=mpN36I9xr-o
A general scheme in improvisation of such fast (4* (45-65) beats/min) complicated melodies is to start from a high octave and "dance down" by intervals of 2nds but also 3rds to the lower octave same note and then "dance again up" to end to the initial higher octave note. We stop longer to the intermediate 5th note of the scale (in other words an arpeggio of the power chord is a simplicial submelody) and we may change power chords at the steps I ,IV, V. As we dance we translate melodic themes, invert and mutate. Or inversely we may go up and then down E.g. in a major mode diatonic scale we may go up with intervals 4-1-4-2-1 ( a Japanese 5-tonic called Akebono and the inverse of the Pelog 5-tonic scale) ) and return down with intervals 3-2-2-3-2 (a usual 5-tonic). Both these 5-tonic scales exist inside the 7 notes diatonic scale.
Irish fast melodies may use not the entire diatonic scale but the maximal 6-notes harmonic (see post 117) which is a mode of the Celtic raised minor , a kind of half pentatonic I, II, III, IV, V, VI, I with interval structure 2-2-1-2-2-3 or even better I, II, III, V, VI, VII, I with interval structure 2-2-3-2-2-1 . In Irish music it is used mainly straight descending or ascending alternated with static oscillations by 2nd and less often by 3rds or rotations (as if dancing steps) as contrasted to translated oscillations in oriental or even classical music (which in their turn correspond to cyclic such steps dancing). Static oscillations stall the ascending or descending and either temporarily reverse it or continues them. When there is much scale-space for melodic moves and we admit fast changes of the chords then translations of melodic themes is common. But when we are restricted to rather smaller parts of the scale and we have rather stable underlying chords then to accommodate the fast rhythm the "rotations" or harpisms inside an arpeggio or more generally a vector-chord (see below) is implemented.
A fundamental idea of the fast such fast soloing is that it is a 2-level waving or n-level waving n=2,3,4,5 . The smallest size waving is mainly by intervals of 2nds less often 3rds, and around notes of the larger waving. Also, the tempo is important. The beats of the small size waving is usually 4 or 2 or 8, and similarly, that of the larger and slower waving 4 beats, thus in total 8 or 16 or 32. In Cretan music the beats of the fast waving maybe 8 but 1-2 of them double thus as if from rhythm of 16 beats. The larger size waving could be an harpism of 3-notes chord but as the real underlying chord is a power P5 chord, it is not necessarily an arpeggio of a 3-notes major or minor chord but generally 4 notes (some times only 3) as subscale with total length an interval of 5th ,4th or of an octave. E.g. 3-2-3 or 4-3-2 or 3-4-2 or 5-2-5 or 4-1-4 or 4-2-4 etc Most often the 4-notes larger size waving is an arpeggio of the power chord 1-V-I' or another power chord of a scale. IT STARTS FROM V IT GOES UP (OR DOWN) TO I' AND THEN AGAIN THROUGH V TO I. THUS IT GOES UP A 5TH OR 4TH AND THEN DOWN A 4TH OR 5TH RESPECTIVELY. In a 6-holes wind instrument (like quena of andes or Cretan chabioli) this harpism of the power chord is very easy to visualize as the waving at the 1st 3 holes and then another at the higher 3 holes. In general it could be waving on 3 successive holes.
The larger size slower layer of the melody can be conceived as simplicial sub-melody of smaller size faster layer of the melody even though there is only one underlying power chord.
See e.g. 4. The Merrymaker's Club / The Acrobat at 7min in https://www.youtube.com/watch?v=BzQLitupNCY&t=1954s
Since in such fast melodies the simple factor is not a chord progression, in order to compose, improvise and play such melodis one may start with a base of variationally independent pitch-order topological shapes of melodic themes (in any layer) orbase of variationally independent Dolphin words or Melodic Seed (see post 106, 107, 92, 104, 136, 134, 40 ). The base of the pitch-order topological shapes of melodic themes are melodic themes that dominate statistically among other random shapes of melodic themes and cannot be derived by variations (translation, inversion , expansion) from other shapes of other melodic themes of the melody . By choosing the polarity of emotional positive-negative (e.g.ascending-descending expansive-contractive etc) of the pitch-order topological shape of the base of shapes of the melodic themes (in any layer) we may control if statistically the result would be emotional uplifting and happy or emotional more sad , in spite the fact that the tempo is always fast thus happy .
In Irish and Cretan such fast melodies , the variations of the melodic themes are more than 80% repetitions, inversions and mutations with rather static waving and less than 20% translations across the steps of a scale as in other types of folk music.
Such fast melodies with underlying harmony , only one power-5 chord is an ancient generation of music , when harmony was not discovered yet , that goes back 7,000 years ago. The tradition of many cultures of Mesopotamia, Egypt, minor Asia, Greece, Celtic music etc has preserved and reproduced such music with rich fast melody and practically no harmony.
POETIC MEASURE FOR THE PATTERN OF REPETITIONS
A good source for the pattern of repetitions of the melodic themes is the syllables poetic measure.
For example of an underlying poem exists for lyrics , with syllables measure pairs of lines with 8 syllables the first and 7 syllables the second, (8+7=15-syllables poetic measure) , the notation is repetitions of 8 and 7 beats one pause bear and then again.
Now the correspondence of the poetic measure to the melodic measure can be
1) Each line is one 8-beats musical measure of the melody
or
2) Each line is two consecutive 4-beats musical measures of the melody.
In the first case we have
two repetitions of melodic themes one
by 8 notes and one almost repeated
by 7 notes. In the second case we have
a repetition three times of a melodic theme of 4-notes and beats, which correspond to the two half parts of the first line and one first half part the second line while after these three repetitions occurs also a different melodic theme of 4 beats and 3 notes and one beat pause.
ORGANIZATION LAYERS OF FAST DANCING MELODIES
MELODIC ORGANIZATIONAL LAYERS FOR EACH POETIC-MUSICAL MEASURE.
Subscales defined by rhythm rather than harmony.
IN OTHER WORDS THE ORGANIZATIONAL STRUCTURE OF SUCH DANCING MELODIES IS MAINLY THROUGH THE RHYTHM RATHER , THAN HARMONY OR CHORD PROGRESSIONS OR SCALES.
1)
Layer 1:
Rule of 3-beats or 4-beats long-short micro-rhythmic themes,
In order to have a 3-layers fast melody, we may substitute each beat by 3 beats two of them in double the tempo and one in half the tempo (micro-rhythmic melodic themes as in post 92 ) In ancient Greek Poetry these themes might correspond to long -short vowel syllables of the poetic line.
E.g. the Poems of
Homer (Iliada, Odyssea) are written in this two level poetic syllabic measure
, where if the long beat is symbolized by - and the short by U it is 17 syllables (=9-8 but the beats are 12 per line, -=2 beats u-1 beat).
-UU-UU-UU-UU-UU-U or
-UU-UU-UU
-UU-UU-U
(Dactylico hexameter. The word daktylico in Greek means "by the fingers", and most probably indicated a rhythm by the fingers on the accompanying musical instrument or sound by the fingers when dancing.) Since the 9 is the smallest odd number divisible by 3, the poetic measure 9-8 is the simplest first to include rhythm divisible by 3 and 4.
Here the first line suggests 3 repetitions and the second line 2 repetitions (3-2)
The dance of syrtos (e.g. Kalamatianos) in Greece coming from ancient Greece dances is using the rhythm -UU (Dactylic hexameter) or in modern rhythm notation 1011 (1=beat 0=pause)
While if it is the Cretan poem
Erotocritos by V. Cornaros it is
15 syllables=8-7, while the 2nd layer micro-measure is tonic, not long-short syllables (0= one beat 1= one beat)
01000100
0100010
Here the suggested by the two poetic lines is 3 repetitions plus one different or alternation of two different (3-1) or (1-1)
Similarly, short 4-6 lines poems called in Creta mandinades suggest with their poetic micro-measure the micro-melodic themes of layer 3 and 4 of the melody.
2)
Layer 2: Rule of connected subscales or vector-intervals
2.1)In the first case to each of the two melodic measures we may correspond a 4-notes or 3-notes correspondingly connected subscale of the diatonic scale of total length an interval of 4th (5-semitones) or interval of 5th (7-semitones) , and play the 8 notes of the measure by the 4 different notes of the first subscale, and the second measure 7 notes by the 3 different notes of the second subscale.
The term vector-interval refers to that we use successive walk-though within the scale from the first note of the interval till its 2nd and last, including the intermediate notes of the scale. In case the interval is of 5 (that is 7 semitones) it is called also vector-chord or closure of chord in which case it is an extension of the concept of chord-arpeggio. Vector chords always assume the chord in normal position. Vector chords instead of arpeggios and as extensions of them is the usual way to improvise over a chord e.g. as Stephan Grappelli is doing with violin or as Chris Chille and Mike Marshall are doing with mandolin.
Random playing of the notes at equal time each, or "rotations" or permutations of a vector-chord , leads to a melody that the chord that fits to it harmonically to accompany it is the the chord of the vector-chord. Such "rotations" have also a projection trace as harping on the arpeggio of the underlying chord. In this way a pre-defined chord progression visualized as a progression of vector chords , defines an improvisational melody.
2.2) In the 2nd case to each of the first three melodic measures we may correspond a 4-notes connected subscale of the diatonic scale and for the 4th measure a 3-notes connected subscale of the diatonic scale. Then play the 4 notes of each measure by the 4 different notes of the first, second and third subscale, and of the fourth measure play the 3 notes by the 3 different notes of the fourth subscale.
In general if we use only intervals of 2nds 3rds and 4ths , the possible such connected 3-notes and 4-notes subscales of the 12-notes full scale , of total length in semitones at most 5 or 6 , are the next 9+6+10:
HERE WE LIST AND DISCUSS SHORT SUBSCALES OF THE CHROMATIC 12-TONE SCALE THAT CAN BE USED FOR REPETITIVE SOLOING. SOME OF THEM ARE KNOWN 4-CHORDS 5-CHORD 6-CHORDS OR SIMPLY CONNECTED PIECES FROM BEBOP SCALES DERIVED FROM THE SUPERPOSITION OF 32 OR 3 DIATONIC SCALES. THIS DOES NOT MEAN THAT THEY ARE MET ALL OF THEM IN CRETAN DACHTILIES AND IRISH REELS BUT THAT CAN BE USED FOR OUR OWN INSPIRED COMPOSITION AND IMPROVISATION
3-NOTES SUBSCALES (TRIADS E.G. VECTOR-INTERVALS OF 3 ), 16 IN TOTAL
THE TRIADS ESPECIALLY THE ONES
OF LENGTH AN INTERVAL OF 3 (vector-interval of 3)
ARE THE MAIN BUILDING BLOCK OF HARMONIC-MELODIC IMPROVISATIONS AS ALSO CHORDS ARE BUILD FROM INTERVALS OF 3.
WHEN WE SHIFT A MELODIC THEME BY A
CHROMATIC INTERVAL OF 2 USUALLY WE APPLY A
TRANSLATIONAL-VARIATION. WHEN WE SHIFT BY A
MELODIC INTERVAL OF 3 USUALLY WE APPLY AN
INVERSION -VARIATION. WHEN WE SHIFT BY AN
HARMONIC INTERVAL OF 4 OR 5 USUALLY WE APPLY A
MUTATION-VARIATION . IF WE STAY IN THE SAME INTERVAL WE HAVE A
ROTATION OR PERMUTATION VARIATION
By alternating major and minor such vector-intervals of 3 we impose also underlying hidden harmony of triad chords
Chromatic triad
1-1
Melodic triads:
minors 2-1, 1-2,
Majors 2-2 , 1-3, 3-1,
Blue :diminished chord 3-3
2-4, 4-2
If we want to avoid thinking about chords or arpeggios when playing, improvising or composing such solos, then the simplest idea is the triads of notes or intervals of 3rds with all their intermediate notes in some scale. By alternating such major and minor intervals of 3rds we may give the melody an underlying good harmonic content
(When improvising it is familiar melody if we alternate major-minor such vector-intervals of 3 because in diatonic scales this is the case and also in the formation of major and minor triad chords)
Harmonic triads
2-3 , 3-2,
4-1, 1-4 ,
Chords: major:4-3, minor: 3-4.
augmented chord 4-4
4-NOTES SUBSCALES (TETRADS) WITH TOTAL LENGTH 5 0R 7 SEMITONES
6+10 IN TOTAL
The most common are 2-2-1, 1-2-2. 1-3-1, 2-2-3, 3-2-2
TOTAL LENGTH 5 SEMITONES, 6 IN TOTAL
1-2-2, 2-2-1, 2-1-2,
3-1-1, 1-1-3, 1-3-1
The
1-1-3 is called by Aristoxenus the
tonal tetrachord of the Chromatic generation and it exists in the double harmonic minor scale.
TOTAL LENGTH 7 SEMITONES, 10 IN TOTAL (We call such subscales
vector-chords as they contain the first and last note of 3-notes chord)
4-2-1, 2-4-1, 1-2-4, 1-4-2,
3-2-2. 2-3-2, 2-2-3
1-3-3, 3-3-1, 3-1-3
We must notice here that according to Aristoxenos (see post 25 page 40 of the manuscript) in ancient Greece there were the tetrachords (4 strings of the lyra) of total range an interval of 4 (5 semitones) that were tuned outside the Back 12-notes scale as follows
Enharmonic generation
1/4 of tone -- 1/4 of tone --2 tones
The closest in Bach scale would be or 1-1-3 in semitones
Chromatic generation
Soft: 1/3 of tone -1/3 tone - 11/6 tone=about 2 tones
The closest in Bach scale would be or 1-1-3 in semitones
3/8 tone --3/8 tone --7/4 tones
The closest in Bach scale would be 1-1-3 in semitones
tonal 1-1-3 in semitones
Diatonic generation
Uniform: 1-3/2-15/6 semitones
The closest in Bach scale would be 1-2-2 in semitones
Syntono 1-2-2 in semitones
5-NOTES SUBSCALES (INTERVALS OF 5) TOTAL LENGTH 7 SEMITONES 18 IN TOTAL
(We call such subscales
vector-chords as they contain the first and last note of a 3-notes chord)
1-2-2-2 (=a vector minor chord) , 2-2-2-1(=a vector major chord), 2-1-2-2(=a vector minor chord), 2-2-1-2=(=a vector major chord)
The 1-2-2-2 might be called the
syntono 5-chord of the Diatonic generation according to the terminology of
Aristoxenus for the ancient Greek music (actually it is mentioned the syntonon tetrachord 1-2-2)
1-1-2-3=(=a vector major chord), 1-1-3-2, 2-3-1-1, 3-2-1-1,
The
1-1-3-2, 2-3-1-1 might be also called tonal 5-chords of the Chromatic generation in the the terminology of
Aristoxenus for the ancient Greek music (actually it is mentioned the tonal tetrachord 1-1-3)
1-2-1-3(=a vector minor chord), 3-1-2-1(=a vector major chord), 1-3-1-2(=a vector major chord) , 2-1-3-1(=a vector minor chord),
1-2-3-1(=a vector minor chord), 1-3-2-1(=a vector major chord),
1-1-1-4(=a vector minor chord), 4-1-1-1(=a vector major chord), 1-4-1-1 1-1-4-1
We will formulate rules of combinations of intervals of 1,2,3,4,5,7 semitones (Intervals of 2 of 3 of 4 or of 5 as it is used to say) so as to compose beautiful melodic themes.
Obviously usually intervals of 1, 2 or 3,4 semitones are played horizontally on a single string while intervals of 3,4 of 5 of 7 are played vertically among strings.
(3,4)
1) Combination of intervals of 3, in other words of 3 or 4 semitones
We combine the 3+4=7 mostly as it gives arpeggios of minor major chords ans rarely the 3+3=6 and 4+4-8 that give arpeggios of diminished and augmented chords.
We also alternate the 3+4 with the 4+3 as so it mainly in the chords of a diatonic scale.
(3,4-5)
2) Combination of intervals of 3, in other words of 3 or 4 semitones and intervals of 5 in other words of 7 semitones.
We combine by alternating them around the 5 : 3-5-4 and 4-5-3, 4-5-3-5-4 etc
(3,4-7)
3) Combination of intervals of 4, in other words of 5 semitones and intervals of 5 in other words of 7 semitones
Similarly for the 7 : 3-7-4 and 4-7-3, 4-7-3-7-4 etc
(5-7)
4) Combination of intervals of 4, in other words of 5 semitones and intervals of 5 in other words of 7 semitones
We alternate 5 and 7 : 5-7-5 etc
(5-5)
5) Combination of intervals of 4, in other words of 5 semitones
We avoid repetitions of 5
6) (7-7)
Combination of intervals of 5, in other words of 7 semitones
We allow up to 3 repetitions of 7 7-7 , 7-7-7
(1,2-3,4)
7) Combination of intervals of 3, in other words of 3 or 4 semitones and intervals of 2 in other words of 1 or 2 semitones
We combine 1 freely with 3, 4 1-3, 1-4 as it gives intervals of minor 3 and of 4 that exist in arpeggios of major minor chords.
(1,2-5)
8) Combination of intervals of 4, in other words of 5 semitones and intervals of 2 in other words of 1 or 2 semitones
We combine only 2 with 5 2+5 =7, 5+2=7 as it gives intervals of 5 that exist in arpeggios of minor and major chords.
(1,2-7)
9) Combination of intervals of 4, in other words of 5 semitones and intervals of 2 in other words of 1 or 2 semitones
We combine freely the 1, 2 with 7 1+8= 2+7=9 as it gives intervals of 6 that exist in arpeggios of (inverted) minor and major chords.
10) (1,2-1,2)
We combine freely 1-2 and 2-2 as it gives intervals of 3 of the major minor chord arpeggios
Obviously usually intervals of 1, 2 or 3,4 semitones are played horizontally on a single string while intervals of 3,4 of 5 of 7 are played vertically among strings.
CONDILIES=WAVING ROTATIONS INSIDE A VECTOR-CHORD OR CONNECTED SUBSCALE (TETRACHORD, PENTACHORD, HEXACHORD ETC).THE VARIATIONS OF THE BASIC MICRO-THEMES (CALLED "STROFES" OR "GYRISMATA") ARE AS USUALLY TRANSLATION, INVERSION (IN TIME OR PITCH), EXPANSION-CONTRACTION AND MUTATION
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.
RHYTHMIC MICRO-THEMES AND IMPROVISATION OF THEM.
At another side nevertheless, such fast dancing solos have a "projection trace" to the rhythm exclusively as note durations and position in time irrespectively of what pitch is each note. Then the melodic micro-themes or "rotations" ("gyrismata" or "strofes") become rhythmic micro-themes, and the melodic improvisation of them becomes rhythmic improvisation. Such rhythmic improvisations obviously could be carried out with single note or on percussion instrument only (see Djembe music). When one tries to compose or improvise such melodic "rotations" the underlying rhythmic micro-themes and their variations are of primary importance as they choose where in time you put a note and how long it would sound. having chosen the rhythmic micro-themes and their variations will greatly make easy the final choice of the pitch too of each not and the melodic patterns. The rhythm here will be like a road of the mountains where we eventually drive our melodic vehicle, and this "road" is not straight by changing directions and slopes. The rhythmic variations are similar to the melodic themes variations: They have inversions in time, translation of patterns in rhythms increased or decreased by powers of 2, and mutations.
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 .
In temporal order it will be of course 2-2-1 or 2-2-2-1. A kind of happy inverse of it it would be the pattern 1-2-5 .g. III->IV->V->I'.
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 4th note of the major diatonic scale with a sharp and apply wavings by intervals of 2nd going up and down it.
Or we may combine two or 3 diatonic scales deriving a bebop 8-notes or 9-notes scale.
Other examples of subscales from here http://mantolinokrhth.blogspot.com/2012/08/blog-post.html give in semitones
1-1-2-2-1
2-2-1-2-2-1
2-1-1-1-2-2-1-2
1-1-1-2-2-1
2-1-1-1-2-2
Somewhere in the wavings by 2nds we double the speed of waving for 2-3 such oscillations
Usual rhythms are, Cretan dance (pidichtos) and reels dancing (1110). But also (1010100010001000)
POETIC MEASURE FOR THE PATTERN OF REPETITIONS IN DACHTILIES (CONDILIES).
The dactilies are correlated with poetic improvisation as well, called in Creta mandinades (mandiniades) that are usually pairs of poetic lines in iambic 15-syllables poetic measure.
Somehow all dactilies (condilies) could be considered "the same big tune" with unlimited variations, open to continuing by the players and also with known words (maninades) but also open to unlimited variations and be continued by the players and singers.
This is similar to songs of Portuguese fado, where a single chord progression patterned on the intervals 1-2-2 makes an unlimited pattern of tunes and variations.
Here in dactlilies (condilies) also there are unique characteristic morphological patterns which are 2 or 3 waving by intervals of 2nd cadenzas of 3-4 notes , and all of them within an interval of 4 or 5th (1-2-2 or 1-2-2-2).
This some how determine repetition patterns of rotations (gyrismata or strifes) .
A good source for the pattern of repetitions of the melodic themes is the syllables poetic measure.
For example of an underlying poem exists for lyrics , with syllables measure pairs of lines with 8 syllables the first and 7 syllables the second, (8+7=15-syllables poetic measure) , the notation is repetitions of 8 and 7 beats one pause bear and then again.
Now the correspondence of the poetic measure to the melodic measure can be
1) Each line is one 8-beats musical measure of the melody
or
2) Each line is two consecutive 4-beats musical measures of the melody.
In the first case we have two repetitions of melodic themes one by 8 notes and one almost repeated by 7 notes. In the second case we have a repetition three times of a melodic theme of 4-notes and beats, which correspond to the two half parts of the first line and one first half part the second line while after these three repetitions occurs also a different melodic theme of 4 beats and 3 notes and one beat pause.
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 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.
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). Thus multi-octave-scales that cover all notes of the diatonic scale and are made exclusively from intervals of 3, 4, 5 , 7 , 8 or 9 semitones are of interest and there is a special post 200 for this technique.
3)
Layer 3: Rule of the poetic line and repetition pattern.
Each poetic line, as beats (e.g. 8 or 7+1 ορ 9-8 ορ 6-5) will correspond to a melodic theme realized in one or two or three connected subscales (vector-intervals). In this way, a repetition pattern is created by two successive poetic lines. If the repetitions are substituted with a translation of the melodic themes across connected subscales then a
full harpism of the partition of the octave (usually corresponding to a triad chord) by the connected subscales
is created by two successive poetic lines. In such cases, the layer 2 of the "harping" or "rotation" of connected subscales of the octave partition and the layer 3 of the pattern of repetitions are practically identical. This rotation of melodic themes on such vector-intervals, may be translations , but may be mutations too. Usually in Irish music it is mutation. The translation occurs at layer 4 (below) when translating the whole rotation inside such a vector chord of layer 3 when such vector-chords change. E.g.in a diatonic scale it may be the chords 5, 1, 4 etc. or in intervals of semitones 7-5-2 etc. Such larger layer translations of progressions of themes can be considered also as modulations in the sense of change mode inside the diatonic scale but not the scale, and repeating the progressions of melodic themes.
In Irish reels the "rotation" of layer 3 is a waving inside vector-interval of 5 (vector chord) and its complementary to the octave vector-interval of 4 E.g. if the chord is C3 major, the waving is inside the C3-G3 and G3-C4 which is a vector-interval of 4. This is done with the poetic lines repetition structure. This type of old and fast melodies were not accompanied by 3-notes chords as in later centuries but only by an interval of 5 (in the example the C3-G3) . It is a technique similar to the finger picking but for 3 strings only!
This is the reason why tuning by intervals of 5 was optimal in playing such melodies! Another reason is that tuning the strings by intervals of 4 or 5 allows an easy and conscious shifting of a melodic theme by such an interval (usually this is equivalent with changing chord e.g.among the I, IV, V) and at the same time mutating the melodic theme. Intervals of 2 or 3 are conducted horizontally on the same string.
In this layer 3, a repetition pattern common to some Irish reels is A1A2A1A3 B1B2B1B3
E.g, a melodic rotation as A1 part at 5-2' (corresponding to the chord V) then the A2 part as 1-5 corresponding to the chord I, and A3 part as 4-1' corresponding to the chord IV. Nevertheless all are accompanied not with the chords I, IV, V but with only a power chord 1-5(-1') or only the interval of 5th of each of the chords I IV, V. Similarly for the rotations and parts B1 , B2 , B3.
In case we have an instrument tuned by 5ths like mandolin, mandola, mandocello and preferably of 5 courses instead of 4, we may apply the theme A1 in the highest string and across an octave instead of 5th, and then the A2 in the next lower string in the same way across an octave and A3 in the next lower string across an octave , and always accompany with the next two lower strings which make an interval of 5. In this way the range of the melody is a bit more than 2 octaves: 1-2'' This requires a bit mores space with strings, but we may tune a 6-string guitar by 5ths on at least 5 consecutive strings instead of using an octave mandolin.
4)
Layer 3:Rule of the partition of the octave and "harping" or "rotation" of the octave.
Each octave is partitioned by the connected subscales. One of the best ways is to partition the octave to 3 connected subscales two of triads and one of a tetrad, which corresponds to the partition of the octave by the notes of a 3-notes chord (major or minor). This chords also can be used as an underlying chord, besides the static power-5 chord, while the melody plays within these 3 connected subscales. If a1 a2 a3 is a partition of the octave the "harping" or "rotation" is a progression of subscales a1a3a2a1a1a2a3a2a3a1 etc If e.g the partition of the c major scale is the a1=C3-D3-E3, a2=E3-F3-G3 , a3=G3-A3-B3-C4, then an "harping" of the partition a1a3a2a1a1 corresponds also to a harping of the extended 4-notes Chord C major=C3 E3, G3 C4 .
This rotation of melodic themes on such vector-intervals, may be translations , but may be mutations too. Usually in Irish music it is mutation. The translation occurs at layer 4 (below) when translating the whole rotation inside such a vector chord of layer 3 when such vector-chords change. E.g.in a diatonic scale it may be the chords 5, 1, 4 etc. or in intervals in semitones 7-5-2 etc. Such larger layer translations of progressions of themes can be considered also as modulations in the sense of change mode inside the diatonic scale but not the scale, and repeating the progressions of melodic themes.
In Irish reels the "rotation" of layer 3 is a waving inside vector-interval of 5 (vector chord) and its complementary to the octave vector-interval of 4 E.g. if the chord is C3 major, the waving is inside the C3-G3 and G3-C4 which is a vector-interval of 4. This is done with the poetic lines repetition structure. This type of old and fast melodies were not accompanied by 3-notes chords as in later centuries but only by an interval of 5 (in the example the C3-G3) . It is a technique similar to the finger picking but for 3 strings only!
This is the reason why tuning by intervals of 5 was optimal in playing such melodies!
5) Layer 4: Rule of parts of the song. This is practically defining the parts A, B C etc of the song. that is larger scale repetitions. The translation occurs at layer 4 , here when translating the whole rotation inside such a vector chord of layer 3 ,when such vector-chords change. E.g.in a diatonic scale it may be the chords 5, 1, 4 etc. or in intervals of semitones 7-5-2 etc. Such larger layer translations of progressions of themes can be considered also as modulations in the sense of change mode inside the diatonic scale but not the scale, and repeating the progressions of melodic themes. A reason for tuning the strings by intervals of 4 or 5 is that it allows an easy and conscious shifting of a melodic theme by such an interval (usually this is equivalent with changing chord or mode inside the scale e.g.among the I, IV, V) and at the same time mutating the melodic theme. Intervals of 2 or 3 are conducted horizontally on the same string
We recommend melodic improvisation with overtones tuning as in post 191 that the intervals escalate from 8 to 5 to 4 to 3M and finally 3m. This is also an organizational structure of melodies in C major mainly in the ancient mode of isocratic harmony and played mainly across a single string..
ROOT/POWER CHORD/ ROOT MAJOR CHORD/CHORD PROGRESSION IMPROVISATION METHOD.
We notice that the intervals escalate from 8 to 5 to 4 to 3M and finally 3m. This is also an organizational structure of melodies in C major mainly in the ancient mode of isocratic harmony and played mainly across a single string..
1) At first melodies within an interval of 8 accompanied with a single note the root C.
In general we may also have a melodic theme starting at the first note of string and ending at its other end note , in other words one octave. Then translate , invert and mutate it by playing it on another string and by the tuning all strings are only 3 notes , in intervals of 8, 5, 4, 3M, 3m apart, thus plenty many variations! All themes and variations are isocratically accompanied by the root of the scale C (or interval C-G).
2) Then melodies within an interval of 8 accompanied with a pair of notes at different octaves that are the root C.
2) Then melodies within an interval of 7 accompanied with a power chord 1-5-1'of 3 notes C3-G4-C4
Again in general we may also have a melodic theme starting at the first note of string and ending at 7 fret note , in other words one 5th. Then translate , invert and mutate it by playing it on another string and by the tuning all strings are only 3 notes , in intervals of 8, 5, 4, 3M, 3m apart, thus plenty many variations! All themes and variations are isocratically accompanied by the power chord 1-5-1'of 3 notes C3-G4-C4
3) Then melodies within an interval of 4 accompanied with a power chord 1-5-1'of 3 notes C3-G4-C4
Again in general we may also have a melodic theme starting at the first note of string and ending at 5th fret note , in other words one 4th. Then translate , invert and mutate it by playing it on another string and by the tuning all strings are only 3 notes , in intervals of 8, 5, 4, 3M, 3m apart, thus plenty many variations! All themes and variations are isocratically accompanied by the power chord 1-5-1'of 3 notes C3-G4-C4
4) Then melodies within the arpeggio or vector-chord of a chord 1-3-5 (see post 159) accompanied by the major chord 1-3-5 C major
Again in general we may also have a melodic theme starting at the first note of the chord 1-3-5 C major of a string and ending 7th frets higher, in other words one 5th or vector-chord . Then translate , invert and mutate it by playing it on another string and by the tuning all strings are only 3 notes , in intervals of 8, 5, 4, 3M, 3m apart, thus plenty many variations! All themes and variations are isocratically accompanied by the major chord 1-3-5 C major.
5)
Finally a chord progression by triads or tetrads on the last 3 or 4 strings of the tuning (major minor diminished augmented) alternated with melodic bridges among them.
In improvising-composing such solos, the next factors control the next aspects
Mind: Controls the awareness of the 3 layers of the melody and the repetition pattern created by two poetic lines.
Emotions: Control the shape of the dolphin words or shapes of melodic themes in mid-fast and slow layer.
Fingers: Control the rhythm and continuity of the conduction.
PROGRESSIONS OF VECTOR INTERVALS AT FIRST OF 3 AND THEN ORGANIZED AS VECTOR CHORDS OF VECTOR INTERVALS OF 5 AS MAIN MIDDLE LAYER (LAYER 3) MELODIC ORGANIZING PRINCIPLE OF SUCH MELODIES
A 2nd approach to improvise and organize such melodies is to forget the layers 4, 3 as above and use only layers 2, 1,in other words create melodic themes through vector-intervals (when the interval is of 5 notes and total length 7 semitones we call it vector-chord while if it is e.g. of length an interval of 3 a vector-interval of 3) and "dance" a walkthrough from the first note to neighboring and intermediate till the 2nd and last with a rhythmic pattern. The first and last note sound more times or more time. If it is an interval of 5 notes and length 7 semitones it is essentially a melodic theme with underlying chord a power chord or a major/minor chord. Thus such vector-intervals play the simplicity role of chords. But it may as well be vector intervals of intervals of 3 notes and length 3 or 4 semitones, or other intervals. The practice gives that vector-intervals of 3 are the minimal basic building block of good melodies By alternating major and minor such vector-intervals of 3 we impose also underlying hidden harmony of triad chords. Still the vector-intervals play a simplifying role as the chord in a melody play, although they do not play the harmonic role athata chord plays. Then we repeat the melodic theme over the vector-interval as we strum a chord a guitar. We inverse and mutate the melodic theme of vector-interval and change vector intervals When we change vector-intervals we may translate invert or mutate the melodic theme.
Thus the main factor to organize such an improvisation is
1) The dancing rhythm and poetic micro-rhythm (e.g. 1011 or -UU daktylico or 101 -U- etc)
2) the progression of the vector intervals of 3
Such organizing techniques in melodic improvisation with traditional musical instruments are done best when the tuning of the strings is by intervals of 7 semitones which is when we have to mutate the melodic theme. E.g. Viola, Cello, Mandola, Mandocello, Irish bouzouki, Oud, Lute , Tambouras, Saz etc.
