Ground's composition theory - Revision history

Ground at 15:05, 10 July 2026

2026-07-10T15:05:34Z

← Older revision		Revision as of 15:05, 10 July 2026
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	I'm [[User:Ground]]. This document is going to be very long. Obviously it isn't done. I have more content to add and a need to revise the existing content. Don't expect it to make the most sense yet.		I'm [[User:Ground]]. This document is going to be very long. Obviously it isn't done. I have more content to add and a need to revise the existing content. Don't expect it to make the most sense yet.

	~~My music has had a distinctively shifting key center since about 2018. Even in 12edo, my simultaneous regard~~ and disregard for tonality may be confusing. This article is an attempt to explain how it works, with an emphasis on my other theories, [[Aberrisma\|aberrismic]] and [[Straddle_primes\|straddle-prime]]. I'm introducing a placeholder term for it, interval logic deviation theory (ILD), which can be replaced if this turns out to be something already described.		== Introduction and motivation ==

	In ILD, scales aren't a fixed set of notes, but a template for interval logic ~~that can~~ be deviated from. As such, their main features are probabilities in an interval sequence and bubble deviations from that interval sequence. ILD is best for music with a strong melodic focus, such as mine, where the melody informs the harmony instead of the reverse.		Much of my music has had a distinctively shifting tonality since 2018 or earlier, which started in 12edo. This article is an attempt to explain how it works, with an emphasis on my other theories, [[Aberrisma\|aberrismic]] and [[Straddle_primes\|straddle-prime]]. I'm introducing a placeholder term for it, interval logic deviation theory (ILD), which can be replaced if this turns out to be something already described.

			== Local tonality ==

			I have a simultaneous regard and disregard for standard Western tonality. This is because I view it as an important but strictly local property, meaning it fundamentally only applies on the scope of a single path from tension to release, however long that is. Thus, modulations are only generally uncommon because phrases usually resolve to the same key center they started from, but changing tonality is just as much of a choice as not changing it. Modulation flows just like any other melodic or harmonic movement.

			This flow is facilitated by ILD, in which scales aren't a fixed set of notes, but a template for interval logic to be rearranged and deviated from. As such, their main features are probabilities in an interval sequence and "bubble deviations" from that interval sequence. ILD is best for music with a strong melodic focus, such as mine, where the melody informs the harmony instead of the reverse. Other concepts may be used instead with the same general goal.

			Melodic interval sequences, or "words" of step sizes, are the most minimal expression of tonal tension and release. For example, if a diatonic melody were to play C then B, the listener is likely to expect A to be next and feel a small resolution upon hearing it. This is the descending sL word. Melodies are full of small sequences like this based on the scale that they are in. It's possible to use sequences with notes outside the scale while still feeling like they belong, and how much they belong can be predicted. The longer the word and the greater probability of occurring indicates that it's more likely to sound like it belongs in the scale.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Diatonic example of probabilities (up to word length 3)		\|+Diatonic example of probabilities (up to word length 3)
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	\|}		\|}

	Bubble deviations are named after the bubble sort algorithm, which repeatedly swaps adjacent items in an array. Steps in a base scale can be swapped in the same way to modify the scale with no requirement for a clear structure like a generator chain or lattice splotch, which is my term for a collection of generator chains in aberrismic theory. Suppose you want the scale word sLs in diatonic. This would require only one bubble deviation from the expected step order, turning sLLs to sLsL. While the probability of encountering it in the base diatonic scale is zero, it sounds more "probable" (less unexpected) than something like ssL.		== Axes of deviation ==

			"Bubble deviations" in ILD are named after the bubble sort algorithm, which repeatedly swaps adjacent items in an array. Steps in a base scale can be swapped in the same way to modify the scale with no requirement for a clear structure like a generator chain or lattice splotch, which is my term for a collection of generator chains in aberrismic theory. Suppose you want the scale word sLs in diatonic. This would require only one bubble deviation from the expected step order, turning sLLs to sLsL. While the probability of encountering it in the base diatonic scale is zero, it sounds more "probable" (less unexpected) than something like ssL.

	This explains why I used Dimininished[8] in 12edo more often than Augmented[6], because its stepwise interval logic has less deviation from diatonic. Diminished[8] is made of a repeating sequence of 1\12 and 2\12, common in diatonic, whereas Augmented[6]'s steps of 1\12 and 3\12 do not occur in diatonic at all. As a result, melodies in Diminished sound less exotic.		This explains why I used Dimininished[8] in 12edo more often than Augmented[6], because its stepwise interval logic has less deviation from diatonic. Diminished[8] is made of a repeating sequence of 1\12 and 2\12, common in diatonic, whereas Augmented[6]'s steps of 1\12 and 3\12 do not occur in diatonic at all. As a result, melodies in Diminished sound less exotic.

	Bubble deviations are only one axis of deviation. There is another axis which I've found to be exclusively useful in tuning systems with aberrismic-sized steps or smaller, the axis of microtonal deviation from expected intervals. This involves changing the pitch of an expected interval only slightly, so it is heard as a variation of the expected interval rather than a different interval entirely. This axis interacts with the base scale by introducing or modifying an aberrismic offset, for example diatonic being diasem or blackdye with the offset removed, 2.3.7 diasem having a larger offset than 2.3.23, or 2.3.5 blackdye having a smaller offset than 2.3.17/7. The intervals affected by the offset, usually thirds and sixths, differ microtonally when the offset is changed.		Bubble deviations are only one axis of deviation. There is another axis which I've found to be exclusively useful in tuning systems with aberrismic-sized steps or smaller: the axis of microtonal deviation from expected intervals. This involves changing the pitch of an expected interval only slightly, so it is heard as a variation of the expected interval rather than a different interval entirely. This axis interacts with the base scale by introducing or modifying an aberrismic offset, for example diatonic being diasem or blackdye with the offset removed, 2.3.7 diasem having a larger offset than 2.3.23, or 2.3.5 blackdye having a smaller offset than 2.3.17/7. The intervals affected by the offset, usually thirds and sixths, differ microtonally when the offset is changed.

	Straddling intervals that are stacked the most (usually 3/2) introduce a third axis that can be simplified into a combination of the other two. It's possible to have bubble deviation from a scale that isn't even in the tuning system being used, like how alternating <<3 and >3 in 37edo straddles 74edo meantone and results in trackdye.		Straddling intervals that are stacked the most (usually 3/2) introduce a third axis that can be simplified into a combination of the other two. It's possible to have bubble deviation from a scale that isn't even in the tuning system being used, like how alternating <<3 and >3 in 37edo straddles 74edo meantone and results in trackdye.

	{{UserTag\|KC\|Inthar\|000000\|Tens (stretching) and tract (compression) constitutes yet another axis of deviation separate from straddling. Diatonic-based example: This is important in 4L3s and 5L3s which are warped-diatonic MOSes. Note that dual-3 diatonic 5L1m1s is a subset of interleaved diatonic 7s(5L2m), tens-interleaved diatonic 6s(5L2m) ''and'' tract-interleaved diatonic 8s(5L2m).}}		{{UserTag\|KC\|Inthar\|000000\|Tens (stretching) and tract (compression) constitutes yet another axis of deviation separate from straddling. Diatonic-based example: This is important in 4L3s and 5L3s which are warped-diatonic MOSes. Note that dual-3 diatonic 5L1m1s is a subset of interleaved diatonic 7s(5L2m), tens-interleaved diatonic 6s(5L2m) ''and'' tract-interleaved diatonic 8s(5L2m).}}

Inthar at 19:12, 5 July 2026

2026-07-05T19:12:26Z

← Older revision		Revision as of 19:12, 5 July 2026
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	Straddling intervals that are stacked the most (usually 3/2) introduce a third axis that can be simplified into a combination of the other two. It's possible to have bubble deviation from a scale that isn't even in the tuning system being used, like how alternating <<3 and >3 in 37edo straddles 74edo meantone and results in trackdye.		Straddling intervals that are stacked the most (usually 3/2) introduce a third axis that can be simplified into a combination of the other two. It's possible to have bubble deviation from a scale that isn't even in the tuning system being used, like how alternating <<3 and >3 in 37edo straddles 74edo meantone and results in trackdye.

	{{UserTag\|KC\|Inthar\|000000\|Tens (stretching) and tract (compression) constitutes yet another axis of deviation. Diatonic-based example: This is important in 4L3s and 5L3s which are warped-diatonic MOSes. Note that dual-3 diatonic 5L1m1s is a subset of interleaved diatonic 7s(5L2m), tens-interleaved diatonic 6s(5L2m) ''and'' tract-interleaved diatonic 8s(5L2m).}}		{{UserTag\|KC\|Inthar\|000000\|Tens (stretching) and tract (compression) constitutes yet another axis of deviation separate from straddling. Diatonic-based example: This is important in 4L3s and 5L3s which are warped-diatonic MOSes. Note that dual-3 diatonic 5L1m1s is a subset of interleaved diatonic 7s(5L2m), tens-interleaved diatonic 6s(5L2m) ''and'' tract-interleaved diatonic 8s(5L2m).}}

Inthar at 19:02, 5 July 2026

2026-07-05T19:02:51Z

← Older revision		Revision as of 19:02, 5 July 2026
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	Straddling intervals that are stacked the most (usually 3/2) introduce a third axis that can be simplified into a combination of the other two. It's possible to have bubble deviation from a scale that isn't even in the tuning system being used, like how alternating <<3 and >3 in 37edo straddles 74edo meantone and results in trackdye.		Straddling intervals that are stacked the most (usually 3/2) introduce a third axis that can be simplified into a combination of the other two. It's possible to have bubble deviation from a scale that isn't even in the tuning system being used, like how alternating <<3 and >3 in 37edo straddles 74edo meantone and results in trackdye.

	{{UserTag\|KC\|Inthar\|000000\|Tens (stretching) and tract (compression) constitutes yet another axis of deviation. This is important in 4L3s and 5L3s which are warped-diatonic MOSes. Note that dual-3 diatonic 5L1m1s is a subset of interleaved diatonic 7s(5L2m), tens-interleaved diatonic 6s(5L2m) ''and'' tract-interleaved diatonic 8s(5L2m).}}		{{UserTag\|KC\|Inthar\|000000\|Tens (stretching) and tract (compression) constitutes yet another axis of deviation. Diatonic-based example: This is important in 4L3s and 5L3s which are warped-diatonic MOSes. Note that dual-3 diatonic 5L1m1s is a subset of interleaved diatonic 7s(5L2m), tens-interleaved diatonic 6s(5L2m) ''and'' tract-interleaved diatonic 8s(5L2m).}}

Inthar at 23:45, 4 July 2026

2026-07-04T23:45:14Z

← Older revision		Revision as of 23:45, 4 July 2026
Line 44:		Line 44:
	Straddling intervals that are stacked the most (usually 3/2) introduce a third axis that can be simplified into a combination of the other two. It's possible to have bubble deviation from a scale that isn't even in the tuning system being used, like how alternating <<3 and >3 in 37edo straddles 74edo meantone and results in trackdye.		Straddling intervals that are stacked the most (usually 3/2) introduce a third axis that can be simplified into a combination of the other two. It's possible to have bubble deviation from a scale that isn't even in the tuning system being used, like how alternating <<3 and >3 in 37edo straddles 74edo meantone and results in trackdye.

	{{UserTag\|KC\|Inthar\|000000\|~~Since~~ dual-3 diatonic 5L1m1s is a subset of interleaved diatonic 7s(5L2m), tens-interleaved diatonic 6s(5L2m) ''and'' tract-interleaved diatonic 8s(5L2m)~~, tens (stretching) and tract (compression) constitutes yet another axis of deviation~~.}}		{{UserTag\|KC\|Inthar\|000000\|Tens (stretching) and tract (compression) constitutes yet another axis of deviation. This is important in 4L3s and 5L3s which are warped-diatonic MOSes. Note that dual-3 diatonic 5L1m1s is a subset of interleaved diatonic 7s(5L2m), tens-interleaved diatonic 6s(5L2m) ''and'' tract-interleaved diatonic 8s(5L2m).}}

Inthar at 23:43, 4 July 2026

2026-07-04T23:43:08Z

← Older revision		Revision as of 23:43, 4 July 2026
Line 43:		Line 43:

	Straddling intervals that are stacked the most (usually 3/2) introduce a third axis that can be simplified into a combination of the other two. It's possible to have bubble deviation from a scale that isn't even in the tuning system being used, like how alternating <<3 and >3 in 37edo straddles 74edo meantone and results in trackdye.		Straddling intervals that are stacked the most (usually 3/2) introduce a third axis that can be simplified into a combination of the other two. It's possible to have bubble deviation from a scale that isn't even in the tuning system being used, like how alternating <<3 and >3 in 37edo straddles 74edo meantone and results in trackdye.

			{{UserTag\|KC\|Inthar\|000000\|Since dual-3 diatonic 5L1m1s is a subset of interleaved diatonic 7s(5L2m), tens-interleaved diatonic 6s(5L2m) ''and'' tract-interleaved diatonic 8s(5L2m), tens (stretching) and tract (compression) constitutes yet another axis of deviation.}}

Inthar at 02:49, 4 July 2026

2026-07-04T02:49:37Z

← Older revision		Revision as of 02:49, 4 July 2026
Line 5:		Line 5:
	My music has had a distinctively shifting key center since about 2018. Even in 12edo, my simultaneous regard and disregard for tonality may be confusing. This article is an attempt to explain how it works, with an emphasis on my other theories, [[Aberrisma\|aberrismic]] and [[Straddle_primes\|straddle-prime]]. I'm introducing a placeholder term for it, interval logic deviation theory (ILD), which can be replaced if this turns out to be something already described.		My music has had a distinctively shifting key center since about 2018. Even in 12edo, my simultaneous regard and disregard for tonality may be confusing. This article is an attempt to explain how it works, with an emphasis on my other theories, [[Aberrisma\|aberrismic]] and [[Straddle_primes\|straddle-prime]]. I'm introducing a placeholder term for it, interval logic deviation theory (ILD), which can be replaced if this turns out to be something already described.

	In ILD, scales aren't a fixed set of notes, but a template for interval logic. As such, their main features are probabilities in an interval sequence and bubble deviations from that interval sequence. ILD is best for music with a strong melodic focus, such as mine, where the melody informs the harmony instead of the reverse.		In ILD, scales aren't a fixed set of notes, but a template for interval logic that can be deviated from. As such, their main features are probabilities in an interval sequence and bubble deviations from that interval sequence. ILD is best for music with a strong melodic focus, such as mine, where the melody informs the harmony instead of the reverse.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Diatonic example of probabilities (up to word length 3)		\|+Diatonic example of probabilities (up to word length 3)

Inthar at 02:46, 4 July 2026

2026-07-04T02:46:01Z

← Older revision		Revision as of 02:46, 4 July 2026
Line 38:		Line 38:
	Bubble deviations are named after the bubble sort algorithm, which repeatedly swaps adjacent items in an array. Steps in a base scale can be swapped in the same way to modify the scale with no requirement for a clear structure like a generator chain or lattice splotch, which is my term for a collection of generator chains in aberrismic theory. Suppose you want the scale word sLs in diatonic. This would require only one bubble deviation from the expected step order, turning sLLs to sLsL. While the probability of encountering it in the base diatonic scale is zero, it sounds more "probable" (less unexpected) than something like ssL.		Bubble deviations are named after the bubble sort algorithm, which repeatedly swaps adjacent items in an array. Steps in a base scale can be swapped in the same way to modify the scale with no requirement for a clear structure like a generator chain or lattice splotch, which is my term for a collection of generator chains in aberrismic theory. Suppose you want the scale word sLs in diatonic. This would require only one bubble deviation from the expected step order, turning sLLs to sLsL. While the probability of encountering it in the base diatonic scale is zero, it sounds more "probable" (less unexpected) than something like ssL.

	This explains why I used Dimininished[8] in 12edo more often than Augmented[6], because its stepwise interval logic has less deviation from diatonic. Diminished is made of a repeating sequence of 1\12 and 2\12, common in diatonic, whereas Augmented's steps of 1\12 and 3\12 do not occur in diatonic at all. As a result, melodies in Diminished sound less exotic.		This explains why I used Dimininished[8] in 12edo more often than Augmented[6], because its stepwise interval logic has less deviation from diatonic. Diminished[8] is made of a repeating sequence of 1\12 and 2\12, common in diatonic, whereas Augmented[6]'s steps of 1\12 and 3\12 do not occur in diatonic at all. As a result, melodies in Diminished sound less exotic.

	Bubble deviations are only one axis of deviation. There is another axis which I've found to be exclusively useful in tuning systems with aberrismic-sized steps or smaller, the axis of microtonal deviation from expected intervals. This involves changing the pitch of an expected interval only slightly, so it is heard as a variation of the expected interval rather than a different interval entirely. This axis interacts with the base scale by introducing or modifying an aberrismic offset, for example diatonic being diasem or blackdye with the offset removed, 2.3.7 diasem having a larger offset than 2.3.23, or 2.3.5 blackdye having a smaller offset than 2.3.17/7. The intervals affected by the offset, usually thirds and sixths, differ microtonally when the offset is changed.		Bubble deviations are only one axis of deviation. There is another axis which I've found to be exclusively useful in tuning systems with aberrismic-sized steps or smaller, the axis of microtonal deviation from expected intervals. This involves changing the pitch of an expected interval only slightly, so it is heard as a variation of the expected interval rather than a different interval entirely. This axis interacts with the base scale by introducing or modifying an aberrismic offset, for example diatonic being diasem or blackdye with the offset removed, 2.3.7 diasem having a larger offset than 2.3.23, or 2.3.5 blackdye having a smaller offset than 2.3.17/7. The intervals affected by the offset, usually thirds and sixths, differ microtonally when the offset is changed.

	Straddling intervals that are stacked the most (usually 3/2) introduce a third axis that can be simplified into a combination of the other two. It's possible to have bubble deviation from a scale that isn't even in the tuning system being used, like how alternating <<3 and >3 in 37edo straddles 74edo meantone and results in trackdye.		Straddling intervals that are stacked the most (usually 3/2) introduce a third axis that can be simplified into a combination of the other two. It's possible to have bubble deviation from a scale that isn't even in the tuning system being used, like how alternating <<3 and >3 in 37edo straddles 74edo meantone and results in trackdye.

Inthar at 02:44, 4 July 2026

2026-07-04T02:44:08Z

← Older revision		Revision as of 02:44, 4 July 2026
Line 36:		Line 36:
	\|}		\|}

	Bubble deviations are named after the bubble sort, which repeatedly swaps adjacent items in an array. Steps in a base scale can be swapped in the same way to modify the scale with no requirement for a clear structure like a generator chain or lattice splotch, which is my term for a collection of generator chains in aberrismic theory. Suppose you want the scale word sLs in diatonic. This would require only one bubble deviation from the expected step order, turning sLLs to sLsL. While the probability of encountering it in the base diatonic scale is zero, it sounds more "probable" (less unexpected) than something like ssL.		Bubble deviations are named after the bubble sort algorithm, which repeatedly swaps adjacent items in an array. Steps in a base scale can be swapped in the same way to modify the scale with no requirement for a clear structure like a generator chain or lattice splotch, which is my term for a collection of generator chains in aberrismic theory. Suppose you want the scale word sLs in diatonic. This would require only one bubble deviation from the expected step order, turning sLLs to sLsL. While the probability of encountering it in the base diatonic scale is zero, it sounds more "probable" (less unexpected) than something like ssL.

	This explains why I used Dimininished[8] in 12edo more often than Augmented[6], because its stepwise interval logic has less deviation from diatonic. Diminished is made of a repeating sequence of 1\12 and 2\12, common in diatonic, whereas Augmented's steps of 1\12 and 3\12 do not occur in diatonic at all. As a result, melodies in Diminished sound less exotic.		This explains why I used Dimininished[8] in 12edo more often than Augmented[6], because its stepwise interval logic has less deviation from diatonic. Diminished is made of a repeating sequence of 1\12 and 2\12, common in diatonic, whereas Augmented's steps of 1\12 and 3\12 do not occur in diatonic at all. As a result, melodies in Diminished sound less exotic.

Inthar at 02:41, 4 July 2026

2026-07-04T02:41:34Z

← Older revision		Revision as of 02:41, 4 July 2026
Line 36:		Line 36:
	\|}		\|}

	Bubble deviations are named after the bubble sort, which repeatedly swaps adjacent items in an array. Steps in a base scale can be swapped in the same way to modify the scale with no requirement for a clear structure like a generator chain or lattice splotch, which is my term for a collection of generator chains in aberrismic theory. Suppose you want the scale word sLs in diatonic. This would require only one bubble deviation from the expected step order, turning sLLs to sLsL. While the probability of encountering it in the base diatonic scale is zero, it sounds more "probable" (~~expected~~) than something like ssL.		Bubble deviations are named after the bubble sort, which repeatedly swaps adjacent items in an array. Steps in a base scale can be swapped in the same way to modify the scale with no requirement for a clear structure like a generator chain or lattice splotch, which is my term for a collection of generator chains in aberrismic theory. Suppose you want the scale word sLs in diatonic. This would require only one bubble deviation from the expected step order, turning sLLs to sLsL. While the probability of encountering it in the base diatonic scale is zero, it sounds more "probable" (less unexpected) than something like ssL.

	This explains why I used Dimininished[8] in 12edo more often than Augmented[6], because its stepwise interval logic has less deviation from diatonic. Diminished is made of a repeating sequence of 1\12 and 2\12, common in diatonic, whereas Augmented's steps of 1\12 and 3\12 do not occur in diatonic at all. As a result, melodies in Diminished sound less exotic.		This explains why I used Dimininished[8] in 12edo more often than Augmented[6], because its stepwise interval logic has less deviation from diatonic. Diminished is made of a repeating sequence of 1\12 and 2\12, common in diatonic, whereas Augmented's steps of 1\12 and 3\12 do not occur in diatonic at all. As a result, melodies in Diminished sound less exotic.

Inthar at 02:41, 4 July 2026

2026-07-04T02:41:02Z

← Older revision		Revision as of 02:41, 4 July 2026
Line 7:		Line 7:
	In ILD, scales aren't a fixed set of notes, but a template for interval logic. As such, their main features are probabilities in an interval sequence and bubble deviations from that interval sequence. ILD is best for music with a strong melodic focus, such as mine, where the melody informs the harmony instead of the reverse.		In ILD, scales aren't a fixed set of notes, but a template for interval logic. As such, their main features are probabilities in an interval sequence and bubble deviations from that interval sequence. ILD is best for music with a strong melodic focus, such as mine, where the melody informs the harmony instead of the reverse.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Diatonic ~~Example~~ of ~~Probabilities~~ (up to word length 3)		\|+Diatonic example of probabilities (up to word length 3)
	!Sequence		!Sequence
	!Next ~~Interval Probability~~		!Next step probability
	\|-		\|-
	\|s		\|s