rawcog · Musikalisches Würfelspiel · Berlin, 1792

The Dice Waltz

Two dice, sixteen rolls, one waltz. This game was published in 1792 under Mozart's name: each roll picks one bar from a table of 176 pre-written fragments, and the result always holds together. There are 759,499,667,166,482 possible waltzes.

An example waltz is ready. Roll for your own.
Waltz No. –

The table

For each bar, add the two dice and look down that column. The number is the measure to play from the 176 printed fragments. Bar 8 never changes: all eleven options are the same G major chord, the halfway cadence. Bar 16 only changes on a roll of 11.

Rows are dice totals, with a bar showing how often each total comes up. Columns are bars of the waltz.

The score

Walzer

Why it never sounds wrong

The eleven options for each bar are variations on the same harmony. The plan of the piece is fixed in advance, and the dice only choose the surface. The real composer is whoever designed the table.

Not every roll is equal

A 7 comes up six times as often as a 2 or a 12, so the middle row of the table gets played far more than the edges. Chance here is weighted, not flat.

Same rolls, same waltz

Every waltz has a number. Roll the same sixteen totals and you get the same piece, note for note. The dice are a seed, and the table does the rest.