# 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](https://ianring.com/musictheory/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