🎵 Triadic Arpeggios

Introduction

GeCo-Tool is based on interval generation within the pitch-class space ℤ₁₂. In previous documents, scales were represented as ordered semitone sequences and triads were represented as harmonic structures derived from those scales. In this document, each scale or collection is transformed into a single continuous melodic chain.

Two related procedures are used:

(a) For collections that naturally generate tertian harmony, a triadic arpeggio is built on every degree by selecting:

The resulting arpeggios are concatenated into a single continuous melodic sequence. Within each three-note structure the motion is always ascending. Between one structure and the next, the line returns downward to the first note of the following structure.

Thus:

rather than:

(b) For collections that do not naturally generate tertian harmony, the same geometric process is applied:

The resulting structures should not necessarily be interpreted as traditional triads. Instead, they are generalized cyclic objects generated by the same skip-one-note process. As for the scales, a zipped file containing the presets is provided.

Arpeggio Chains from Tertian Collections

Skip-One-Note Chains

Negative values indicate descending motion; positive values indicate ascending intervals (semitones).