Pitch interval¶
The semitone separation between two octave-specified musical pitches, directed or undirected without octave reduction.
Core Idea¶
A pitch interval in chromatic music analysis compares two octave-specified pitches by semitone separation. The ordered form is signed: y−x is positive for an upward move and negative for a downward one. The unordered form uses the absolute value, keeping size but dropping orientation. Unlike pitch-class intervals, both retain octave position; C4 to C5 is twelve semitones, not zero.
A semitone count does not alone fix the interval's diatonic spelling: six semitones may be an augmented fourth or diminished fifth according to notation. The official music21 guide illustrates a perfect fifth with seven semitones, a descending reverse, and a separate reduced intervalClass of five. These are different queries of pitch information, not competing answers to one question. The target assumes a stated chromatic frame; a raw frequency difference without a musical pitch representation is not the same object.
Scope of Application¶
These uses retain pitch register while choosing whether direction matters.
- Melodic analysis. Retain upward and downward displacement across successive pitches.
- Harmonic comparison. Compare unordered semitone spans while retaining register.
- Computational music theory. Keep chromatic semitone counts separate from interval-class reductions.
- Notation interpretation. Distinguish a numerical span from its diatonic spelling.
Clarity¶
Name both octave-specified pitches and the semitone frame. From C4 to E5 the directed difference is +16; backward it is −16; unordered magnitude is 16. A pitch-class interval is the closest miss because modulo-12 reduction discards register. State separately whether the analysis preserves direction, octave, and diatonic spelling.
Manages Complexity¶
The word interval can conceal four transformations: choose a chromatic frame, retain or drop direction, retain or reduce octave, and assign a diatonic spelling. Keeping these transformations explicit explains why music21 reports a perfect fifth as seven semitones but an intervalClass of five. It also prevents a melodic contour analysis from silently becoming a pitch-class inventory.
Abstract Reasoning¶
- Specify the two pitches with octave positions and one semitone coordinate system.
- Subtract endpoint coordinates for an ordered signed interval.
- Take absolute value only if direction is intentionally discarded.
- Preserve the unreduced span before any modulo-12 pitch-class comparison.
- Keep diatonic spelling and enharmonic interpretation separate from chromatic semitone size.
Knowledge Transfer¶
The signed/absolute separation distinction transfers among melody analysis, harmony comparison, and music software when endpoints and tuning frame are preserved. music21's exact interval-class result should not be copied as an unreduced distance, and its notation spelling conventions need not transfer to another tuning system. Outside musical pitch space, a signed number difference is only a structural analogy, not this pitch interval.
Neighborhood in Abstraction Space¶
Pitch interval sits in a moderately populated region (42nd percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Musical & Poetic Form (11 abstractions)
Nearest neighbors
- Transposition (Music) — 0.92
- Strähle construction — 0.88
- Musical Interval — 0.87
- Boogie — 0.87
- Major Limma — 0.86
Computed from structural-signature embeddings · 2026-10-08