scales can be encoded as bitstrings over the octave - hence as integers - where each bit denotes the presence (1) or absence (0) of a pitch class.

derived from a sequence of intervals summing to one octave, key properties include:

• resolution: smallest interval unit; must evenly divide the octave into n parts
• leaps: minimum and maximum step sizes (optionally restricted to odd values)
• size: number of tones (the length of the interval set)
• leap limit: no single step exceeds one-third of the scale size

• scale-series: construct scales by chaining intervals, then convert those intervals into bitstring/integer form

• modes: distinct scales obtained by circularly rotating a scales interval sequence

• rotational symmetry: invariance under rotation (classified via a truncation hierarchy)
• prime scales: interval sequences irreducible to their reverse
• palindromic scales: symmetric under reversal (interval sequence reads identically forwards and backwards)
• chiral vs. achiral: absence vs. presence of reflective symmetry
• combined symmetry: scales possessing both rotational and reflective invariance

• balanced scales: pitch classes distributed as evenly as possible around the octave
• evenness: quantitative measure of interval uniformity
• deep scales: every interval class occurs with a unique multiplicity

• myhill property: each interval class appears exactly twice
• propriety: no two interval patterns within the scale are identical
• maximal area: greatest polygonal area when scale notes are plotted on a lattice
• proximity: minimal distance between adjacent scale degrees
• imperfection: aggregate deviation from an ideal uniform distribution

• theme: a recognizable musical idea or motif
• development: gradual transformation of that theme - variation of intervals, rhythm, instrumentation
• expansion & compression: stretching or contracting motifs in time or pitch space to create contrast

• pairs: coupling elements (melody+harmony, call+response) so one shapes the other
• sibling followers: choosing between parallel variations (e.g. two counter-melodies) to keep material fresh

• meter & meter alignment: fitting onsets to a grid (4/4, 7/8, etc.) and deliberately aligning or misaligning for groove
• beat-drive: the driving force of rhythmic repetition - kick-snare patterns, hi-hat subdivisions
• harmony periodicity: chord changes paced in relation to the meter

• quantized mapping: snapping parameters (pitch, timing, dynamics) to a predefined grid for stylistic consistency
• parameter: any controllable value (amp, frq, filter) that maps to musical expression

• frequency-bands: carving the spectrum into regions (bass/mid/high) and layering content in each
• noisiness: adding filtered noise or broadband components for texture and complexity

• loudness: overall energy contour - swells, fades, sudden hits
• richness: perceived fullness, often a combination of harmonic content, stereo width, and dynamic range

• melodic complexity: range and variety of intervals, use of diatonic vs. chromatic tones, ornamentation
• sound-durations: variety of note lengths (staccato vs. legato) to shape phrasing and momentum