GeCo-Tool is a web application for generating and exploring musical sequences derived from the
interval matrix: a systematic representation of all transpositions of a given
interval sequence, analogous to the 12-tone row matrix used in serial composition.
The tool is designed for composers and music theorists interested in algorithmic and
constraint-based melodic generation.
Sequence Types
Binary — Each cycle alternates one interval and one leap.
The sequence repeats until the starting pitch-class is recovered.
Quaternary — Each cycle contains two interval/leap pairs
(Interval1+Leap1, Interval2+Leap2), producing longer periodic structures.
Senary — Three interval/leap pairs per cycle
(Int1+Lea1, Int2+Lea2, Int3+Lea3), yielding the richest harmonic variety.
Ternary — Three consecutive intervals per cycle (the 3D equivalent of Binary),
with the cycle repeating until the starting pitch-class returns.
Ternary — Three consecutive intervals per cycle (the 3D equivalent of Binary),
with the cycle repeating until the starting pitch-class returns.
Multidimensional — Any number of consecutive intervals per cycle (the N-dim equivalent of Binary),
with the cycle repeating until the starting pitch-class returns.
Intervals and leaps are expressed in semitones (positive = up, negative = down).
Tempo / Rhythm Mode
sequence-constrained — Duration changes occur at structurally significant
points of the sequence (e.g. at cycle boundaries).
length-constrained — Duration changes occur every N notes,
where N is chosen randomly from {2, 3, 5, 6}.
constant — All notes share the same duration, selectable from
whole to sixteenth note.
free — Each note receives an independently randomised duration
(quarter, eighth or sixteenth).
Pitch-Class Transformations
T — Transposes the melody by the selected number of semitones (−12 to +1).
I — Melodic inversion: each interval is reflected around the first pitch.
R — Retrograde: the sequence of pitches is reversed.
RI — Retrograde-Inversion: inversion followed by retrograde.
Rhythmic Transformations
S+ — Rhythmic shift forward: the duration pattern is cyclically advanced by two steps.
S− — Rhythmic shift backward: the duration pattern is cyclically retarded by two steps.
I — Rhythmic inversion: durations are ranked and replaced by their complementary rank.
R — Rhythmic retrograde: the sequence of durations is reversed.
Other Options
Harmony — Adds a left-hand accompaniment on the bass clef. Three styles available:
Classic (paired notes), On the beat, Off the beat.
Octaves — Constrains the melody to approximatively 1 or 2 octaves of range.
Bass Clef — Transposes the output two octaves down and notates in bass clef.
Metronome — When enabled, a click track sounds during playback: a stronger click on beat 1 of each bar, softer clicks on beats 2–4.
Swing — When enabled, eighth notes are played with a swing feel: the off-beat eighth is delayed, creating a long-short pattern.
Use the slider to set the intensity (50% = straight, 67% = full swing 2:1).
BPM — Sets the playback tempo (60–240 bpm).
R. Olmi & M. Bittelli — Generative Compositional Tool
