Sonic Twins

Symmetric and Asymmetric Trichord Pairs Over Common Chord Progressions

By Bruce Arnold — Muse Eek Publishing Inc. — ISBN 978-1-59489-180-9

The Concept

In Sonic Single, you work with one trichord at a time — learning to hear and execute each three-note structure over each chord type in every key. Sonic Twins takes the next step: instead of one trichord at a time, you work with pairs.

A trichord pair is two trichords chosen so that together they cover six distinct pitch classes — a hexachord. It is the same concept as two triad pairs but expands to include any 3 note combination. The two trichords share no notes. When you alternate between them over a chord progression, you produce a six-note sound world that is harmonically complete, intervalically rich, and recognizably different from any single trichord.

Symmetric and Asymmetric Pairs

Symmetric pairs use two transpositions of the same trichord prime form. The two trichords share no notes but have identical interval structures. Their combined hexachord is inversionally symmetric — it maps onto itself under inversion. Sonic Twins covers 69 symmetric pairs across all twelve trichord types.

Asymmetric pairs combine two different trichord prime forms. The hexachord produced may or may not be inversionally symmetric. Sonic Twins covers 259 asymmetric pairs. Together the 328 pairs represent the complete curated set of musically useful trichord pairings across all eight chord types.

The 249 Symmetric Hexatonic Pairs

Within the symmetric pairs, 249 produce inversionally symmetric hexatonic scales when considered over specific chord types. The table below shows the count of symmetric hexatonic pairs available for each trichord type over each chord type:

Trichord Pairs in Practice: Compositions

The fastest way into the sound of a trichord pair is to listen to music built from it. The compositions below use specific trichord pairs consistently throughout — the melodies and harmonies derive from the two trichords moving through the chord changes.

Example Files

Each file type in the Sonic Twins library is shown below with a representative example. The complete library contains files for all 328 trichord pairs across all twelve keys — these examples show the format and sound of each type.

Download Complete Sets

Every file type is available as a complete zip download from right inside the PDF. These downloads are extensive and covering all 328 trichord pairs across all twelve keys. Various types of exercises are presented. Below is a list:

Recommended Practice Sequence

1. Listen to the vamp accompaniment to establish harmonic context.
2. Study the chord voicings — learn the shapes, then transpose through all twelve keys.
3. Play the trichord pair arpeggios — hear the voicings as lines.
4. Run the hexachord scale — hear the full six-note pitch collection linearly.
5. Practice the étude without rests — slow enough to hear each note against the drone.
6. Practice the étude with rests — let the rests create phrasing.
7. Listen to the vamp étude — hear the result in full musical context.
8. Practice dyad sequencing — isolate each two-note subset across registers.

Ear Training Path

Not sure where to start? The free Ear Training Guided Tour maps the full curriculum.

Recommended Companion Volumes

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