Ground's composition theory - Revision history

Ground at 01:18, 31 August 2026

2026-08-31T01:18:40Z

← Older revision		Revision as of 01:18, 31 August 2026
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	This article is about composition and the practical considerations of tuning. I always have more content to add and revise. It has an emphasis on my other theories, [[Aberrisma\|aberrismic]] and [[Straddle_primes\|straddle-prime]], which may be useful to know.		This article is about composition and the practical considerations of tuning. I always have more content to add and revise. It has an emphasis on my other theories, [[Aberrisma\|aberrismic]] and [[Straddle_primes\|straddle-prime]], which may be useful to know.

	It should be kept in mind that my style is generally unrestrained and chaotic. My approach to writing chords is loosely based on non-functional jazz harmony. They usually outline and support the melody and have few defined cadences involving more than two chords; the most common is probably iv → i. As a result, I don't have much to say about harmonic functions, something which is also in dire need of thorough documentation.		It should be kept in mind that my style is generally unrestrained and chaotic, and I am in the [[Levels of tempering\|mesotempered category]]. My approach to writing chords is loosely based on non-functional jazz harmony. They usually outline and support the melody and have few defined cadences involving more than two chords; the most common is probably iv → i. As a result, I don't have much to say about harmonic functions, something which is also in dire need of thorough documentation.

	== Interval logic deviation theory ==		== Interval logic deviation theory ==
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	Example tier list of 37edo multiples:		Example tier list of 37edo multiples:
	* Base (37): S (~~one~~ of a kind)		* Base ([[37edo\|37]]): S (One of a kind.)
	* x2 (74): B (~~nothing~~ special besides the two meantone diasems and various Diashismic straddle temperaments)		* x2 ([[74edo\|74]]): B (Nothing special besides the two meantone diasems and various Diashismic straddle temperaments. A pretty straightforward extension of 37's interval set.)
	* x3 (111): A (~~very~~ good at approximating the 17-limit and containing a few temperaments I like)		* x3 ([[111edo\|111]]): A (Very good at approximating the 17-limit and containing a few temperaments I like. More of a self-contained microtemperament, very different from 74.)
	* x6 (222): D (~~has~~ extra approximations and generators, but too cumbersome to do much)		* x6 ([[222edo\|222]]): D (Has extra approximations and generators, but too cumbersome to do much.)
	This is a top-tier edo multiplication setup when you weight these based on their expected frequency, which is estimated based on existing projects:		This is a top-tier edo multiplication setup when you weight these based on their expected frequency, which is estimated based on existing projects:
	* Base: remainder		* Base: remainder

Ground at 01:00, 31 August 2026

2026-08-31T01:00:24Z

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	{{UTBox\|g_\|Ground\|7766ff}}		{{UTBox\|g_\|Ground\|7766ff}}

	This article is ~~going to be very long~~. I have more content to add and ~~a plan to~~ revise ~~the existing content eventually~~. It has an emphasis on my other theories, [[Aberrisma\|aberrismic]] and [[Straddle_primes\|straddle-prime]], which may be useful to know.		This article is about composition and the practical considerations of tuning. I always have more content to add and revise. It has an emphasis on my other theories, [[Aberrisma\|aberrismic]] and [[Straddle_primes\|straddle-prime]], which may be useful to know.

	My approach in writing chords is loosely based on non-functional jazz harmony. They ~~generally~~ outline the melody and have few defined cadences involving more than two chords; the most common is probably iv → i.		It should be kept in mind that my style is generally unrestrained and chaotic. My approach to writing chords is loosely based on non-functional jazz harmony. They usually outline and support the melody and have few defined cadences involving more than two chords; the most common is probably iv → i. As a result, I don't have much to say about harmonic functions, something which is also in dire need of thorough documentation.

	== Interval logic deviation theory ==		== Interval logic deviation theory ==

Ground at 00:46, 31 August 2026

2026-08-31T00:46:12Z

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	I consider 2/1, 3/2, and 5/4 to be the most important anchor concordances. If any two of them are approximated within a few cents, the tuning system will be capable of comfortably stable harmony. This is why I believe 12edo works so well, and why 25, 28, and 37edo are more capable than people expect. The original purpose of straddle primes was to account for the extreme variability of the reasonable tunings of 3/2 in 37edo and stacking both to approximate the pythagorean chain.		I consider 2/1, 3/2, and 5/4 to be the most important anchor concordances. If any two of them are approximated within a few cents, the tuning system will be capable of comfortably stable harmony. This is why I believe 12edo works so well, and why 25, 28, and 37edo are more capable than people expect. The original purpose of straddle primes was to account for the extreme variability of the reasonable tunings of 3/2 in 37edo and stacking both to approximate the pythagorean chain.

	In 37edo, both 4:5:>6 and 4:5:<<6 (a very close approximation of 1/(40:32:27)) serve as reasonable consonances. I've never been able to observe different functions between them. The same applies to the different tunings of 6:8:9, besides <<6:8:<<<<9 = 6:>>8:<<9 which just doesn't sound good. This is most obviously useful when an accurate 3 isn't available, but it's also beneficial for altering intervals to follow a melody with optimal step sizes for my compositional goal. Using a very flat 3 ~~for example widens~~ 16/15 ~~considerably~~.		In 37edo, both 4:5:>6 and 4:5:<<6 (a very close approximation of 1/(40:32:27)) serve as reasonable consonances. I've never been able to observe different functions between them. The same applies to the different tunings of 6:8:9, besides <<6:8:<<<<9 = 6:>>8:<<9 which just doesn't sound good. This is most obviously useful when an accurate 3 isn't available, but it's also beneficial for altering intervals to follow a melody with optimal step sizes for my compositional goal:
			* Using the very flat <<3 results in >>16/15, quite audibly wider while keeping some semblance of 4:5:6.
			* <<6/5 is found in the [[Pentagoth]] triad, which uses the exaggerated quality of the minor third and the stability of the major third.

	Compare the different optimizations of 2.3.5 Meantone which I have noticed sound better than those immediately around them:		Compare the different optimizations of 2.3.5 Meantone which I have noticed sound better than those immediately around them:

Ground at 00:40, 31 August 2026

2026-08-31T00:40:25Z

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 |Doubling ed4s is very annoying, but it's the only way for me to practically reach large prime edos. 67 is the only one significant enough to be worth the trouble.
 |}
 == Anchor concordances ==
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 For example, the patent 3/2 in 25 and 28edo is far off, but their representations of 4:5:6 mask the beating with an accurate 5/4. I prefer to have anchor concordances be 3/2, thirds, or sometimes sixths because they show up the most often in tertian chords, and major thirds in particular. My theory is that this is because the major third range has stronger concordance wells than minor thirds, which have something close to a plateau on the harmonic entropy curve. My favorites to have are 5/4, 9/7, and 13/10.
 Compare the different optimizations of 2.3.5 Meantone which I have noticed sound better than those immediately around them:

Ground at 04:16, 24 August 2026

2026-08-24T04:16:56Z

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	For example, the patent 3/2 in 25 and 28edo is far off, but their representations of 4:5:6 mask the beating with an accurate 5/4. I prefer to have anchor concordances be 3/2, thirds, or sometimes sixths because they show up the most often in tertian chords, and major thirds in particular. My theory is that this is because the major third range has stronger concordance wells than minor thirds, which have something close to a plateau on the harmonic entropy curve. My favorites to have are 5/4, 9/7, and 13/10.		For example, the patent 3/2 in 25 and 28edo is far off, but their representations of 4:5:6 mask the beating with an accurate 5/4. I prefer to have anchor concordances be 3/2, thirds, or sometimes sixths because they show up the most often in tertian chords, and major thirds in particular. My theory is that this is because the major third range has stronger concordance wells than minor thirds, which have something close to a plateau on the harmonic entropy curve. My favorites to have are 5/4, 9/7, and 13/10.

			Compare the different optimizations of 2.3.5 Meantone which I have noticed sound better than those immediately around them:
			* ~69edo: DR 4:5:6, 10:12:15
			* ~31edo: 5/4 anchor concordance
			* ~74edo: DR 3:4:5
			* ~67edo: 1/6-comma (equal error on 9 and 5, around where 3 becomes truly stackable by my standards)

	== Quartertone composition ==		== Quartertone composition ==

Ground at 04:07, 24 August 2026

2026-08-24T04:07:08Z

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	== Anchor concordances ==		== Anchor concordances ==

	~~Hiiiiiiiiiiiiiiii another incomplete section :3~~		We conventionally make the distinction between consonance, which is dependent on musical context, and concordance, which is not. This gives the false impression that concordance does not vary significantly between people, and based on register and timbre. Dyadic harmonic entropy is the most well-known measure of concordance, and it works pretty well for me, but not everyone. Triadic harmonic entropy fits less well because I've personally noticed that having at least one interval in a chord tuned close to LCJI sounds more concordant than balancing the errors of multiple LCJI intervals. I refer to this special interval as an '''anchor concordance''' because it stabilizes the whole chord. This way of optimization is opposed to delta-rational, which I also find useful.

	~~I have found that tempered chords can be substantially stabilized by having a somewhat accurate LCJI ratio.~~ For example, the patent 3/2 in 25 and 28edo is far off, but their representations of 4:5:6 mask the beating with an accurate 5/4. I prefer to have ~~these intervals~~ be thirds or sometimes sixths because they show up the most often chords, ~~especially~~ major thirds. My theory is that this is because the major third range has stronger concordance wells than minor thirds, which have something close to a plateau on the harmonic entropy curve. My favorites to have are 5/4, 9/7, and 13/10.		For example, the patent 3/2 in 25 and 28edo is far off, but their representations of 4:5:6 mask the beating with an accurate 5/4. I prefer to have anchor concordances be 3/2, thirds, or sometimes sixths because they show up the most often in tertian chords, and major thirds in particular. My theory is that this is because the major third range has stronger concordance wells than minor thirds, which have something close to a plateau on the harmonic entropy curve. My favorites to have are 5/4, 9/7, and 13/10.

	== Quartertone composition ==		== Quartertone composition ==

Ground at 21:46, 21 August 2026

2026-08-21T21:46:25Z

Show changes

Ground at 03:26, 18 August 2026

2026-08-18T03:26:31Z

← Older revision		Revision as of 03:26, 18 August 2026
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	== 9-note diatonic analogue ==		== 9-note diatonic analogue ==

			ModMOSes and ternary scales based on them are the best. I haven't used them extensively since my first two albums (2014-2015), so I'm going to challenge myself to use one as often as possible. It's easier if the scale being modified is very familiar, such as quasi-diatonic. There's actually nothing about ILD that prefers MOSes over any other type of scale. This will need to be a whole section eventually.

	When it comes to extending the diatonic scale's circle of fifths as seen in ILD, there's no alteration more important than the modes of the melodic minor scale, which I'll be referring to together as '''melodiatonic'''. It's the only non-diatonic scale that's possible to construct by making a single bubble deviation from diatonic, and it makes sense looking at the circle of fifths. Assume that some altered diatonic scale must contain only L and s steps to preserve as much step logic as possible. To do this, only ordinals following a semitone may be sharpened (C and F when the unaltered notes are all naturals), and only ordinals preceding a semitone may be flattened (B and E). Sharpening F or flattening B just changes the key signature and the result is still diatonic. Sharpening C or flattening E results in melodiatonic. I have found melodiatonic to be a remarkably reliable way to make diatonic tunings (including 12edo) sound exotic yet familiar enough to hit the same emotional beats diatonic can provide. After diatonic, it has the smallest span across the chain of fifths without duplicating a diatonic ordinal, meaning that it contains no pairs of notes that are 7 generators apart. Just like how diatonic is the framework for all quasi-diatonic scales, melodiatonic can be used as the framework for certain alterations of those quasi-diatonic scales. {{adv\|Unconventional uses of melodiatonic I can think of off the top of my head are parts of Undertale's Heartache in Bb Dorian b2 and the main theme of Animusic's Harmonic Voltage in C Mixolydian b6.}}		When it comes to extending the diatonic scale's circle of fifths as seen in ILD, there's no alteration more important than the modes of the melodic minor scale, which I'll be referring to together as '''melodiatonic'''. It's the only non-diatonic scale that's possible to construct by making a single bubble deviation from diatonic, and it makes sense looking at the circle of fifths. Assume that some altered diatonic scale must contain only L and s steps to preserve as much step logic as possible. To do this, only ordinals following a semitone may be sharpened (C and F when the unaltered notes are all naturals), and only ordinals preceding a semitone may be flattened (B and E). Sharpening F or flattening B just changes the key signature and the result is still diatonic. Sharpening C or flattening E results in melodiatonic. I have found melodiatonic to be a remarkably reliable way to make diatonic tunings (including 12edo) sound exotic yet familiar enough to hit the same emotional beats diatonic can provide. After diatonic, it has the smallest span across the chain of fifths without duplicating a diatonic ordinal, meaning that it contains no pairs of notes that are 7 generators apart. Just like how diatonic is the framework for all quasi-diatonic scales, melodiatonic can be used as the framework for certain alterations of those quasi-diatonic scales. {{adv\|Unconventional uses of melodiatonic I can think of off the top of my head are parts of Undertale's Heartache in Bb Dorian b2 and the main theme of Animusic's Harmonic Voltage in C Mixolydian b6.}}
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	\|1200		\|1200
	\|}		\|}

			== Adaptive diatonic modification system ==

			This section is incomplete.

			In order to make modified diatonic scales easier to use and quickly understand the intervals I use in my head, I have a proposal for an interval scheme based on splitting diatonic or quasi-diatonic intervals, somewhat similar to [[Adaptive diatonic interval names\|ADIN]].

			First specify which is the default diatonic or quasi-diatonic quality. This is usually pental (4:5:6), pyth, or septal (6:7:9).

			Neutral seconds are about 3/7 to 4/7 of the minor third.

	== Structural tuning selection ==		== Structural tuning selection ==

Inthar: /* Song structure */

2026-08-17T10:29:54Z

Song structure

← Older revision		Revision as of 10:29, 17 August 2026
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	I've noticed that I write more "disjointed" songs than I would like, and fewer "straightforward" and "episodic". This system is intended to keep track of what I'm doing and help me work toward a better result.		I've noticed that I write more "disjointed" songs than I would like, and fewer "straightforward" and "episodic". This system is intended to keep track of what I'm doing and help me work toward a better result.

	{\| class="wikitable"		{\| class="wikitable sortable"
	\|+Song Structure Types of The Gralbums		\|+Song Structure Types of The Gralbums
	!Track		!Track

Ground at 06:18, 17 August 2026

2026-08-17T06:18:42Z

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	The size of the aberrisma presents other issues.		The size of the aberrisma presents other issues.

			== Song structure ==

			This is my system for categorizing the songs I write by structure. Something similar can be applied to other people's music, but the standards will be different due to the unusual complexity of my music.

			* '''straightforward''': The simplest type, being in a similar style throughout. Always works.
			* '''opposing sections''': Two straightforward parts that are very different.
			* '''medium''': Somewhat straightforward, somewhat disjointed.
			* '''episodic''': Containing many different sections with themes and a progression throughout the song. The most desirable when done well and in moderation.
			* '''disjointed''': Containing many different sections with no clear pattern. The least desirable.

			I've noticed that I write more "disjointed" songs than I would like, and fewer "straightforward" and "episodic". This system is intended to keep track of what I'm doing and help me work toward a better result.

			{\| class="wikitable"
			\|+Song Structure Types of The Gralbums
			!Track
			!Title
			!Type
			\|-
			\|g1t1
			\|The Lake Reflects a Black Sky
			\|'''disjointed'''
			\|-
			\|g1t2
			\|The Art of It
			\|'''episodic'''
			\|-
			\|g1t3
			\|Rail Twinge
			\|'''straightforward'''
			\|-
			\|g1t4
			\|Back Stalk
			\|'''medium'''
			\|-
			\|g1t5
			\|Superior Intermedial
			\|'''episodic'''
			\|-
			\|g1t6
			\|Snowboard Index
			\|'''straightforward'''
			\|-
			\|g1t7
			\|Winter's Mortal Hope
			\|'''medium'''
			\|-
			\|g1t8
			\|Transpiration
			\|'''opposing sections'''
			\|-
			\|g1t9
			\|Revelation of Your Forever
			\|'''medium'''
			\|-
			\|g2t1
			\|The Life Unreachable
			\|'''disjointed'''
			\|-
			\|g2t2
			\|Monolithium
			\|'''opposing sections'''
			\|-
			\|g2t3
			\|Nocturne Paranoia
			\|'''disjointed'''
			\|-
			\|g2t4
			\|Glimmer Extrication
			\|'''episodic'''
			\|-
			\|g2t5
			\|Not This Time
			\|'''straightforward'''
			\|-
			\|g2t6
			\|Sakura Blade Minivan
			\|'''medium'''
			\|-
			\|g2t7
			\|Resolute Prelude
			\|'''straightforward'''
			\|-
			\|g2t8
			\|Life and Limb
			\|'''straightforward'''
			\|-
			\|g2t9
			\|Residual Soliloquy
			\|'''disjointed'''
			\|}