Generate a random twelve-tone row and inspect Prime, Inversion, Retrograde, and Retrograde Inversion forms.
Create a twelve-tone row, inspect its prime, inversion, retrograde, and retrograde-inversion forms, then set register, duration, and BPM for playback or MIDI export.
A twelve-tone row presents all 12 pitch classes without repetition. It avoids tonal hierarchy and forms the basis for serial composition.
The original ordered row.
Intervals are mirrored around the first pitch.
The row played backward.
The inversion played backward.
All transpositions of the row and its inversion.
A twelve-tone row is an ordered succession of the twelve pitch classes C=0 through B=11 in equal temperament. Pitch class is octave-equivalent: C3, C4 and C5 share the same integer.
A row is not a chromatic scale. The chromatic aggregate says that all twelve classes are present; the row adds a specific order that can be transformed, partitioned and composed with.
Schoenberg systematized twelve-tone technique after free atonality; Webern explored compression, symmetry and timbre; Berg combined rows with dramatic, tonal and expressive references.
Pitch serialism is not the same as integral serialism. Later composers extended serial thinking to rhythm, dynamics and timbre, but no single procedure defines every twelve-tone composition.
P keeps the row order. I reflects every pitch class around an axis a with I_a(p)=(2a-p) mod 12. R reverses P, and RI reverses I.
JolyMusic labels matrix rows by transposition level relative to the first row head, and columns by the corresponding inversion-column head. The inversion convention is pitch-class-axis reflection.
The first row is the generated prime row. The first column is its inversion fixing the initial pitch class. Horizontal reading gives P forms; reverse horizontal reading gives R forms.
Vertical reading gives I forms; reverse vertical reading gives RI forms. Labels identify the transposition level of the form being read, not an index in the visual table.
The row constrains pitch organization, not every musical parameter. Register, rhythm, dynamics, articulation, instrumentation, texture and phrase structure remain compositional choices.
Local repetitions, doublings, trills or sustained tones can appear in real music; the analytical question is how they relate to the abstract row statement.
Source: Use the current row.
Instructions: Check that every integer 0-11 appears once.
Expected result: Twelve unique classes.
Musical interpretation: You have a complete chromatic aggregate.
Success criterion: No duplicate or missing class remains.
Source: 0 1 4 2 7 5 9 6 11 8 3 10
Instructions: Enter or compare the sequence as P.
Expected result: A valid ordered aggregate.
Musical interpretation: The order creates motivic identity.
Success criterion: Validation reports twelve unique classes.
Source: The example row.
Instructions: Read P from right to left.
Expected result: 10 3 8 11 6 9 5 7 2 4 1 0.
Musical interpretation: Contour order is reversed.
Success criterion: Your R matches the displayed retrograde.
Source: The example row around C=0.
Instructions: Apply (2a-p) mod 12 to each pitch class.
Expected result: 0 11 8 10 5 7 3 6 1 4 9 2.
Musical interpretation: Directed intervals are mirrored.
Success criterion: Your I0 matches the verified example.
Source: The example inversion.
Instructions: Reverse the inversion sequence.
Expected result: 2 9 4 1 6 3 7 5 10 8 11 0.
Musical interpretation: The mirror is heard backward.
Success criterion: Your RI0 matches the verified example.
Source: Current matrix.
Instructions: Select one row and one column, then compare forward and reverse reading.
Expected result: One P/R pair and one I/RI pair.
Musical interpretation: The same table supplies all four families.
Success criterion: The selected labels match the highlighted form.
Source: First two trichords.
Instructions: Compare prime forms and interval-class vectors.
Expected result: A set-theory comparison rather than a melodic interval list.
Musical interpretation: Segments can become motives or harmonies.
Success criterion: You distinguish ordered intervals from interval classes.
Source: Any P form plus a related I or R form.
Instructions: Assign register, rhythm and articulation to two forms.
Expected result: A two-phrase sketch using related row forms.
Musical interpretation: The row organizes pitch while musical parameters create shape.
Success criterion: The phrase uses the selected forms consistently.
The original row is the source for every displayed form; preserve its order when comparing transformations.
Register, note length, and BPM affect the playable result without changing the pitch-class logic of the row.