structural / Symbolic

Point Set Sequence

An ordered sequence of point-sets that may contain duplicates

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Resolve a progression in a key

Roman numerals describe functions relative to a selected key. Change the key to reinterpret the same numerals, or transpose the resulting MIDI notes by a fixed number of semitones. These are different operations.

KeyRoman progression

Transpose0 st

Selected chord: Cmaj7 · octave-free set

Key

C major

Scale notes

C-D-E-F-G-A-B

Pitch classes

0-4-7-11

Resolved chord symbols (before shift)

Cmaj7 - G7 - Am7 - Fmaj7

C is the tonic; major supplies the scale. Roman numerals resolve to diatonic seventh chords where available. The semitone control moves the resolved notes after that interpretation.

Written forms

Ways to write this concept

Each notation describes the same underlying object. Load a playable example to hear one MIDI realization in the Code Sequencer.

binary

Comma-separated list of variable-length binary patterns

10001001,10000101
1000100100001,1000100010001

steps

Comma-separated list of step sequences

0-4-7,0-3-7
0-4-7-11,0-3-7-10

roman

Traditional roman numeral analysis without specific key center, representing abstract progression patterns

Imaj7-V7-IV
ii7-V7-Imaj7

binary pc steps

12-bit binary PC set with scale steps

2:100010010000,7:100010010000,0:100010010000
2:100010001000,7:100010010000,0:100010001000

binary stack

Variable-length binary representing vertical stacking of intervals from root

1000100100000000,1000100100000,100010010000
100010001,10001001000,1000100

binary num stack

Base-10 representation of binary-stack

34064,4368,2192
273,1097,70

relative notes

Full note sets with relative octave positions

2:[0,4,7,11,-1], 7:[0,4,7,10,14], 0:[0,4,7,11]
2:[-12,0,4,7], 7:[0,4,7,10], 0:[-12,0,3,7]

Choose Load beside a convertible example to open its live player. Some catalog formats describe analysis or a display label and have no note realization yet.

Note Set SequenceAn ordered sequence of note sets (chords) that may contain duplicates Pc Set SequenceAn ordered sequence of pitch class sets that may contain duplicates Song formA chord progression arranged by labeled section (intro, verse, chorus, bridge…) — the harmonic skeleton of a lead sheet or guitar-chord chart. An ordered, named sequence whose sections are chord progressions (its `groupOf` is note-set-sequence). Forget the labels/order and it becomes a collection of progressions; forget pitch and it becomes a point-song-form (a key-independent structural shape for comparing songs).Pc song formA song form whose section progressions are octave-free (pitch-class) — the octaveless abstraction of a song-form. Keeps section labels, order, and harmony but drops register. Its `groupOf` is pc-set-sequence.Point sequenceAn ordered, rootless pitch contour. An anchor note turns its relative positions into a concrete line.Point scoreA key-independent polyphonic shape — simultaneous point-sequences (offset lines). The transposition-invariant fingerprint of a counterpoint: two passages in different keys with the same voice motion land on the same point-score, so it is the natural representation for contrapuntal similarity. Its `groupOf` is point-sequence.