View source for Stretching and compression

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'''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 ==
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]] 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 ==
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 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).

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.