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Point Set

A rootless arrangement of semitone offsets from the lowest note. Its shape stays the same when a MIDI voicing is transposed.

Try it

Give a rootless shape an anchor

Select offsets from the lowest note. Transposition moves the MIDI notes and their pitch classes, while the relative point shape remains unchanged.

Transpose0 st

MIDI notes

48-52-55

Note names

C3-E3-G3

Pitch-class set

0-4-7

Rootless point shape

0-4-7

Range: C3–G3, 7 semitones. The point shape needs the shown C3 anchor before it becomes MIDI notes.

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

Variable-length binary string where 1s represent included positions. Unlike pc-set's fixed 12-bit pattern, this can extend to represent wider intervals.

  • 10001001
  • 1000100100001

steps

Comma-separated sequence of relative positions from a reference point

  • 0-4-7
  • 0-3-7-10

chord name

Traditional chord quality names without specific root

  • maj
  • min7
  • dim7

scale name

Traditional scale quality names without specific root

  • major
  • dorian
  • phrygian
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.

Concept connections

Note setA group of concrete MIDI pitches with octaves. It specifies one voicing and can be reduced to pitch classes or a rootless point shape.Pitch-class setA selection of the twelve pitch classes, independent of octave and order. It says which pitches are present without choosing a chord root or voicing.Note RangeThe span between a lowest and highest MIDI note. It describes a register boundary, not every note inside it.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.Point Set CollectionA collection of interval patterns (point sets) that are transposition-invariantPoint Set Sequence CollectionAn unordered, transposition-invariant collection of point-set progressions — a library of progression shapes independent of key. Its `groupOf` is point-set-sequence.
Sources and playback

Concept descriptions and examples were adapted from Codex Music Mono’s typed catalog and concept examples. The Code Sequencer plays MIDI through a connected instrument; Symbolic does not synthesize sound.