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 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 patterns [a+b-1]s(aLbm) and [a+b+1]s(aLbm) respectively.
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.
