2025-05-10

melody and composition

musical semantics over pitch and form

melody

melody describes a sequence of pitches over time. its core dimensions include:

  • tuning: the mapping of pitch classes to frequencies
  • scale: an ordered set of pitch intervals anchored by a root note
  • direction: melodic contour (ascending, descending, arch, wave, etc)
  • harmony: vertical combinations of pitches that support or contrast the melody
  • repetition: recurring motifs, sequences, and ostinatos
  • chords: simultaneous pitch groupings that enrich or underline a melodic line

scales

see also ian ring - a study of scales

representation

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.

interval structure

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

series generation

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

modes

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

symmetry & classification

  • 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

balance & uniformity

  • 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

advanced metrics

  • 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

song composition

localized & balanced features

  • domain: which musical parameter space youre working in (pitch, rhythm, timbre, dynamics)
  • harmonization: how events in one domain (e.g. melody) relate to or balance against another (e.g. harmony or rhythm)
  • balance: distributing attention or energy so no single feature overwhelms the rest

emphasis

  • pitch emphasis: highlighting certain scale degrees or melodic peaks
  • onset emphasis: placing accents on particular beats or off-beats
  • parameter emphasis: boosting key parameters (filter cutoff, resonance, stereo panning) for moments of interest

theme and development

  • 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

dependency and variation

  • 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

periodicity and alignment

  • 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

  • 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

timbral richness

  • 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

dynamics and loudness

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

melodic & structural complexity

  • 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