User:BudjarnLambeth/Polytriadic - Revision history

BudjarnLambeth: BudjarnLambeth moved page Polytriadic to User:BudjarnLambeth/Polytriadic

2025-05-07T02:56:06Z

BudjarnLambeth moved page Polytriadic to User:BudjarnLambeth/Polytriadic

← Older revision	Revision as of 02:56, 7 May 2025
(No difference)

BudjarnLambeth: added see also

2025-02-23T03:56:37Z

added see also

← Older revision		Revision as of 03:56, 23 February 2025
Line 43:		Line 43:

	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.		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.

	[[Category:Tuning]][[Category:Triad]]		[[Category:Tuning]][[Category:Triad]]

BudjarnLambeth: /* Example */

2025-02-23T03:29:55Z

Example

← Older revision		Revision as of 03:29, 23 February 2025
Line 36:		Line 36:

	There are many possible polytriadic tunings such a piece could use, but here is just one of them:		There are many possible polytriadic tunings such a piece could use, but here is just one of them:
	* 4 instruments total (standard string ~~quarter~~)		* 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 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)		* Violin 2 tuned to the scale 400c, 700c, 1200c (in the key of C major, that is: E, G, C)

BudjarnLambeth: /* Practical application */

2025-02-23T03:21:27Z

Practical application

← Older revision		Revision as of 03:21, 23 February 2025
Line 17:		Line 17:
	Polytriadic tunings can be a useful way to approach a tuning that does not possess any consonant small [[MOS scale]]s. This means that most high-complexity, high-accuracy temperaments, including [[microtemperament]]s, 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]].		Polytriadic tunings can be a useful way to approach a tuning that does not possess any consonant small [[MOS scale]]s. This means that most high-complexity, high-accuracy temperaments, including [[microtemperament]]s, 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]].

	~~They~~ can ~~also~~ 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 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.

	~~Polytriadic tunings could~~ 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.		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 ~~also naturally~~ 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.		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 ==		== Generalization of the idea ==

BudjarnLambeth at 03:20, 23 February 2025

2025-02-23T03:20:01Z

← Older revision		Revision as of 03:20, 23 February 2025
Line 1:		Line 1:
	A '''polytriadic tuning'''{{idiosyncratic}} is a [[tuning]] for an ensemble of 2 or more [[instrument]]s, where each instrument or group of instruments is tuned to a different [[triad]], and uses that triad as a [[scale]].		A '''polytriadic tuning'''{{idiosyncratic}} is a [[tuning]] for an ensemble of 2 or more [[instrument]]s, 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 a larger overarching scale or tuning.		All of the triads should be subsets of one larger overarching scale or tuning.

	'''Polytriadic music'''{{idiosyncratic}} is music that utilises such a tuning.		'''Polytriadic music'''{{idiosyncratic}} is music that utilises such a tuning.

BudjarnLambeth: As I was brainstorming how to approach the shoal temperament, this concept came to me, and I immediately realised it could be widely applicable across many tunings. I'm sure others have done it before, but I'm not sure if anyone has named it before.

2025-02-23T03:19:41Z

As I was brainstorming how to approach the shoal temperament, this concept came to me, and I immediately realised it could be widely applicable across many tunings. I'm sure others have done it before, but I'm not sure if anyone has named it before.

New page

A '''polytriadic tuning'''{{idiosyncratic}} is a [[tuning]] for an ensemble of 2 or more [[instrument]]s, 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 a larger overarching scale or tuning.

'''Polytriadic music'''{{idiosyncratic}} is music that utilises such a tuning.

The usage and/or study of such tunings could be referred to as '''polytriadicism'''.{{idiosyncratic}}

== 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 scale]]s. This means that most high-complexity, high-accuracy temperaments, including [[microtemperament]]s, 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]].

They can also 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.

Polytriadic tunings could 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 also naturally 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 ==
{{Idiosyncratic terms}}
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 quarter)
* 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.

[[Category:Tuning]][[Category:Triad]]