Choose how many notes your row has — a dyad (2) up to eleven. This sets the size of the matrix; everything is analysed with the same tools, scaled to your row.
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0 / 12
Type a row or subset
Derive a row from this set
Allow
or keep adding notes to twelve for the matrix
Identity shown below — deriving a twelve-tone row needs a 2-, 3-, 4-, or 6-note set.
Generate a row
Source hexachord
DiscreteSet class
Set class
Click notes to build your row — used pitches lock so every class is used once.
Matrix
P down the left · I across the top · R down the right · RI across the bottom
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Build your row above, then press Generate.
constant diagonal — every cell on it is the matrix root (the top row's first note)your input rowRn / RIn = Pn / In read backwards — each is named after the form it reverses, so Rn ends on n
The 48 row forms
open a family to list its forms · click a form to hear it
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Rotational arrays
hexachordal rotation — each row rotates one place and transposes back to a constant first pitch (the centric note)
Subset analysis
discrete segments of your row · set classes & relationships
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Forte number ?A Forte number (e.g. 3-11 or 4-Z15) uniquely identifies a set class. The digit before the hyphen is the cardinality (how many pitch classes); the number after is the rank within that size. Z means two set classes share the same interval-class vector. Segments with the same Forte number are related by Tn or TnI and share identical interval content.PCS ?PCS = pitch-class set: the actual pitch classes in the segment, shown as note names or integers (0–11, with C = 0). Octave and spelling are ignored — it is the unordered collection of notes, e.g. E F G.normal form ?The most compact ordering of a pitch-class set — rotate it so the outer notes span the smallest interval (ties broken toward the left). Example: {0,4,9} → [9,0,4].prime form ?The normal form transposed to begin on 0, then compared with its inversion; the more left-packed of the two wins. Example: {0,4,9} → (037), the minor/major triad, set class 3-11.IC vector ?Interval-class vector: a six-slot tally of how many of each interval class (1–6) the set contains. Example: the major triad (037) → [001110].symmetry ?Degree of symmetry (Forte-style): T-n counts the transpositions (including T0) that map the set onto itself, and I-k counts the inversions that do. Asymmetric = only T0 fixes it (T-1, I-0); inversional = some TnI also fixes it; transpositional = a nonzero Tn does.combinatorial ?A row form is combinatorial with the prime when their first hexachords together use all twelve pitch classes, so the two forms can sound in parallel without repeating a note. An all-combinatorial hexachord does this under P, I, R and RI.
Compare two rows
order-position invariance & segmental overlap between two row forms (or a form vs. a row you type)
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Intervallic distances
Directed intervals in semitones (mod 12) between adjacent notes. Every P-, R-, I-, and RI-form shares the interval succession of its own family, so one representative of each is shown.