Polytriadic

A polytriadic tuning^{[idiosyncratic term]} is a tuning for an ensemble of 2 or more instruments, where each instrument or group of instruments is tuned to a different triad, and uses that triad as a scale.

All of the triads should be subsets of one larger overarching scale or tuning.

Polytriadic music^{[idiosyncratic term]} is music that utilises such a tuning.

The usage and/or study of such tunings could be referred to as polytriadicism.^{[idiosyncratic term]}

Sources of consonance and dissonance

The consonance in a polytriadic piece of music emerges from the consonance within each triad, and from the shared notes the the triads have in common with one another.

The dissonance, harmonic complexity and harmonic richness comes from the differences between the triads, which create the equivalent of 'tensions' in conventional 12-tone equal (12edo) music.

Practical application

Polytriadic tunings lend themselves to arpeggios, counter-melodies, and interweaving voice lines. Composers who like such techniques might be drawn to polytriadicism.

Polytriadic tunings can be a useful way to approach a tuning that does not possess any consonant small MOS scales. This means that most high-complexity, high-accuracy temperaments, including microtemperaments, could be well suited to polytriadic approaches. This could include some of the temperaments in the columns towards the right of the tables in the survey of efficient temperaments by subgroup.

Polytriadicism can be a useful way to explore very large just intonation scales, such as very large combination product sets or primodal scales, which might not otherwise have an intuitive way to subdivide them, especially if they haven't yet been studied or explored much.

Polytriadicism can also be a useful way to explore xenrythmic concepts, such as polyrhythms or unusual time signatures, as each triad could be used to harmonically 'label' or 'flag' one particular rhythmic element, helping to more clearly distinguish the different rhythmic lines or concepts in a piece from one another.

Polytriadic tunings lend themselves to algorithmic, generative music, using modular synthesizers or something similar. They can help to distill consonance out of random or semi-random atmospheric noise.

Generalization of the idea

This article or section contains multiple idiosyncratic terms. Such terms are used by only a few people and are not regularly used within the community.

Along similar lines to polytriadic tunings, one could imagine:

• Polydyadic tunings (each instrument/instrument group is tuned to a different dyad subset of a larger overarching scale)
• Polytetradic tunings (each instrument/instrument group is tuned to a different tetrad subset of a larger overarching scale)
• Polypentadic tunings (each instrument/instrument group is tuned to a different pentad subset of a larger overarching scale)
• Polyhexadic tunings (each instrument/instrument group is tuned to a different hexad subset of a larger overarching scale)
• And so on...

Example

One could imagine a polytriadic piece in any tuning system, but this example imagines a polytriadic piece in 12edo because all readers are likely to be familiar with it.

There are many possible polytriadic tunings such a piece could use, but here is just one of them:

• 4 instruments total (standard string quartet)
• Violin 1 tuned to the scale 300c, 700c, 1200c (in the key of C major, that is: Eb, G, C)
• Violin 2 tuned to the scale 400c, 700c, 1200c (in the key of C major, that is: E, G, C)
• Viola tuned to the scale 900c, 1000c, 1200c (in the key of C major, that is: Ab, A, C)
• Cello tuned to the scale 500c, 700c, 1200c (in the key of C major, that is: F, G, C)

This should give some idea of what a polytriadic tuning can look like. But of course there can be as few as two instruments/voices, or as many as tens or even hundreds. There can be multiple instruments tuned to the same triad. And there can be any parent tuning or scale, not just 12edo.

See also

• Shoal17: Lists some triads specifically for use in polytriadicism.