Stretching and compression - Revision history

Inthar: /* Chords */

2026-07-27T08:11:38Z

Chords

← Older revision		Revision as of 08:11, 27 July 2026
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	== Chords ==		== Chords ==
	Stretched versions of chords can be indicated by using the prefix ''tens-'', and compressed versions of chords can be indicated by using the prefix ''tract-''. (Example: [[oneirotonic]] tract-diatonic chords such as the tract-major triad which is 0s-M2s-M4s in TAMNAMS notation)		Stretched versions of chords can be indicated by using the prefix ''tens-'', and compressed versions of chords can be indicated by using the prefix ''tract-''. (Example: [[oneirotonic]] tract-diatonic chords such as the tract-major triad which is 0s-M2s-M4s in [[TAMNAMS]] notation)

	== Linear stretching and compression ==		== Linear stretching and compression ==

Inthar: /* Tens- and tractaberration */

2026-07-27T01:14:21Z

Tens- and tractaberration

← Older revision		Revision as of 01:14, 27 July 2026
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	=== Tens- and tractaberration ===		=== Tens- and tractaberration ===
	In [[aberrismic theory]], the ''tens-aberrated'' and ''tract-aberrated'' versions of a [[MOS]] scale aLbm are given by the [[MOS substitution]] operations [a+b-1]s(aLbm) and [a+b+1]s(aLbm) respectively. For example, sLsmsLsLsLsmsLs is a tractaberrated diatonic scale made from diatonic (a MOS substitution scale of type 8s(5L2m)).		In [[aberrismic theory]], the ''tens-aberrated'' and ''tract-aberrated'' versions of a [[MOS]] scale aLbm are given by the [[MOS substitution]] operations [a+b-1]s(aLbm) and [a+b+1]s(aLbm) respectively. For example, sLsmsLsLsLsmsLs is a tractaberrated diatonic scale made from diatonic (a MOS substitution scale of type 8s(5L2m)), also called trackdye.

	== Chords ==		== Chords ==

Inthar: /* Tens- and tractaberration */

2026-07-27T01:13:56Z

Tens- and tractaberration

← Older revision		Revision as of 01:13, 27 July 2026
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	=== Tens- and tractaberration ===		=== Tens- and tractaberration ===
	In [[aberrismic theory]], the ''tens-aberrated'' and ''tract-aberrated'' versions of a [[MOS]] scale aLbm are given by the [[MOS substitution]] operations [a+b-1]s(aLbm) and [a+b+1]s(aLbm) respectively.		In [[aberrismic theory]], the ''tens-aberrated'' and ''tract-aberrated'' versions of a [[MOS]] scale aLbm are given by the [[MOS substitution]] operations [a+b-1]s(aLbm) and [a+b+1]s(aLbm) respectively. For example, sLsmsLsLsLsmsLs is a tractaberrated diatonic scale made from diatonic (a MOS substitution scale of type 8s(5L2m)).

	== Chords ==		== Chords ==

Inthar: /* Tens- and tractaberration */

2026-07-27T01:13:07Z

Tens- and tractaberration

← Older revision		Revision as of 01:13, 27 July 2026
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	=== Tens- and tractaberration ===		=== Tens- and tractaberration ===
	In [[aberrismic theory]], the tens-aberrated and tract-aberrated versions of a [[MOS]] scale aLbm are given by the [[MOS substitution]] ~~patterns~~ [a+b-1]s(aLbm) and [a+b+1]s(aLbm) respectively.		In [[aberrismic theory]], the ''tens-aberrated'' and ''tract-aberrated'' versions of a [[MOS]] scale aLbm are given by the [[MOS substitution]] operations [a+b-1]s(aLbm) and [a+b+1]s(aLbm) respectively.

	== Chords ==		== Chords ==

Inthar: /* Scales */

2026-07-27T01:12:19Z

Scales

← Older revision		Revision as of 01:12, 27 July 2026
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	== Scales ==		== Scales ==
	A scale pattern can be compressed by inserting a(n arbitrary but usually small) step size; this is how [[oneirotonic]] is obtained from MOS diatonic (LLsLLLs -> LLsLsLLs), and similarly [[pinedye]] (LLmLLLm -> LLmLLsLm). A scale pattern may be stretched by removing a step (MOS diatonic LLsLLLs -> machinoid LLLLLs) or making it smaller (MOS diatonic LLsLLLs -> smitonic LLsLsLs).		A scale pattern can be compressed by inserting a(n arbitrary but usually small) step size; this is how [[oneirotonic]] is obtained from MOS diatonic (LLsLLLs -> LLsLsLLs), and similarly [[pinedye]] (LLmLLLm -> LLmLLsLm). A scale pattern may be stretched by removing a step (MOS diatonic LLsLLLs -> machinoid LLLLLs) or making it smaller (MOS diatonic LLsLLLs -> smitonic LLsLsLs).

			=== Tens- and tractaberration ===
			In [[aberrismic theory]], the tens-aberrated and tract-aberrated versions of a [[MOS]] scale aLbm are given by the [[MOS substitution]] patterns [a+b-1]s(aLbm) and [a+b+1]s(aLbm) respectively.

	== Chords ==		== Chords ==

Inthar at 01:09, 27 July 2026

2026-07-27T01:09:32Z

← Older revision		Revision as of 01:09, 27 July 2026
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	{{stub}}		{{stub}}
	'''Stretching and compression''' are (usually logarithmic or approximately logarithmic) operations that can be done on melodies, scales, or chords. Stretching can be called '''tens''' and compression can be called '''tract'''; these ~~morphemes~~ may be prefixed to chords or scales to indicate stretching and compression~~; for~~ example, [[13edo]]'s 0-4-7\13 (0c-369c-646c) may be called a tractmajor chord since it is a compressed version of the [[12edo]] major chord 0-4-7\12 (0c-400c-700c), whereas [[11edo]]'s 0-4-7\11 (0c-436c-763c) is a tensmajor chord.		'''Stretching and compression''' are (usually logarithmic or approximately logarithmic) operations that can be done on melodies, scales, or chords. Stretching can be called '''tens''' and compression can be called '''tract'''; these may be prefixed to chords or scales to indicate stretching and compression. For example, [[13edo]]'s 0-4-7\13 (0c-369c-646c) may be called a tractmajor chord since it is a compressed version of the [[12edo]] major chord 0-4-7\12 (0c-400c-700c), whereas [[11edo]]'s 0-4-7\11 (0c-436c-763c) is a tensmajor chord.

	== Scales ==		== Scales ==

Inthar at 01:08, 27 July 2026

2026-07-27T01:08:26Z

← Older revision		Revision as of 01:08, 27 July 2026
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	{{stub}}		{{stub}}
	'''Stretching and compression''' are (usually logarithmic or approximately logarithmic) operations that can be done on melodies, scales, or chords. Stretching can be called '''tens''' and compression can be called '''tract'''; these morphemes may be prefixed to chords or scales to indicate stretching and compression; for example, [[13edo]]'s 0-4-7\13 (0c-369c-646c) may be called a tractmajor chord since it is a compressed version of the [[12edo]] major chord 0-4-7\12 (0c-400c-700c).		'''Stretching and compression''' are (usually logarithmic or approximately logarithmic) operations that can be done on melodies, scales, or chords. Stretching can be called '''tens''' and compression can be called '''tract'''; these morphemes may be prefixed to chords or scales to indicate stretching and compression; for example, [[13edo]]'s 0-4-7\13 (0c-369c-646c) may be called a tractmajor chord since it is a compressed version of the [[12edo]] major chord 0-4-7\12 (0c-400c-700c), whereas [[11edo]]'s 0-4-7\11 (0c-436c-763c) is a tensmajor chord.

	== Scales ==		== Scales ==

Inthar at 01:07, 27 July 2026

2026-07-27T01:07:17Z

← Older revision		Revision as of 01:07, 27 July 2026
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	{{stub}}		{{stub}}
	'''Stretching and compression''' are (usually logarithmic or approximately logarithmic) operations that can be done on melodies, scales, or chords. Stretching can be called '''tens''' and compression can be called '''tract'''; these morphemes may be prefixed to chords or scales to indicate stretching and compression, for example 0-4-7\13 (0c-369c-646c) is a tractmajor chord since it is a compressed version of 0-4-7\12 (0c-400c-700c).		'''Stretching and compression''' are (usually logarithmic or approximately logarithmic) operations that can be done on melodies, scales, or chords. Stretching can be called '''tens''' and compression can be called '''tract'''; these morphemes may be prefixed to chords or scales to indicate stretching and compression; for example, [[13edo]]'s 0-4-7\13 (0c-369c-646c) may be called a tractmajor chord since it is a compressed version of the [[12edo]] major chord 0-4-7\12 (0c-400c-700c).

	== Scales ==		== Scales ==

Inthar at 01:06, 27 July 2026

2026-07-27T01:06:26Z

← Older revision		Revision as of 01:06, 27 July 2026
Line 1:		Line 1:
	{{stub}}		{{stub}}
	'''Stretching and compression''' are (usually logarithmic or approximately logarithmic) operations that can be done on melodies, scales, or chords. Stretching can be called '''tens''' and compression can be called '''tract'''; these morphemes may be prefixed to chords or scales to indicate stretching and compression.		'''Stretching and compression''' are (usually logarithmic or approximately logarithmic) operations that can be done on melodies, scales, or chords. Stretching can be called '''tens''' and compression can be called '''tract'''; these morphemes may be prefixed to chords or scales to indicate stretching and compression, for example 0-4-7\13 (0c-369c-646c) is a tractmajor chord since it is a compressed version of 0-4-7\12 (0c-400c-700c).

	== Scales ==		== Scales ==

Inthar: /* Linear stretching and compression */

2026-07-27T01:03:35Z

Linear stretching and compression

← Older revision		Revision as of 01:03, 27 July 2026
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	== Linear stretching and compression ==		== Linear stretching and compression ==
	Linear stretching and compression involves adding a uniform linear increment to a chord written in frequency ratios: for example, 4.1:5.1:6.1 (= 41:51:61) is a linearly compressed 4:5:6, and 3.9:4.9:5.9 (= 39:49:59) is a linearly stretched 4:5:6.		Linear stretching and compression involves subtracting or adding a uniform linear increment to a chord written in frequency ratios: for example, 4.1:5.1:6.1 (= 41:51:61) is a linearly compressed 4:5:6, and 3.9:4.9:5.9 (= 39:49:59) is a linearly stretched 4:5:6.

	The psychoacoustic significance of linearly stretching is that it preserves a chord's [[delta signature]], unlike logarithmic stretching, which preserves the logarithmic ratios between intervals (ratios between cent values) in a chord. Note that all the chords in the examples above are isodifferential (+1+1).		The psychoacoustic significance of linearly stretching is that it preserves a chord's [[delta signature]], unlike logarithmic stretching, which preserves the logarithmic ratios between intervals (ratios between cent values) in a chord. Note that all the chords in the examples above are isodifferential (+1+1).

	A small logarithmic stretch nevertheless ''approximates'' a small linear stretch. This can be useful when hunting for approximate DR chords in equal divisions: for example, the 19edo major triad 0-6-11\19 can be logarithmically stretched to 0-6-11\18 and logarithmically compressed to 0-6-11\20. All of these chords are roughly +1+1.		A small logarithmic stretch nevertheless ''approximates'' a small linear stretch. This can be useful when hunting for approximate DR chords in equal divisions: for example, the 19edo major triad 0-6-11\19 can be logarithmically stretched to 0-6-11\18 and logarithmically compressed to 0-6-11\20. All of these chords are roughly +1+1.