Complete Harmony CanonsCanons which results in all possible harmonies, once and only once, ignoring pitch doublings, based on the number of voices and the number of pitches that are used, with no grand pauses. Ones I have found1 canon with 2 voices and 2 pitches 24 canons with 2 voices and 4 pitches 615856 canons with 2 voices and 6 pitches 97806 canons with 3 voices and 5 pitches 14 canons with 4 voices and 4 pitches 85258 canons with 4 voices and 5 pitches 2020 canons with 5 voices and 5 pitches Explanation:With a few exceptions, the canons listed in the links above are represented as strings of numbers. Each string of numbers represents an individual musical canon. I decided to (mostly) use number notation and not musical notation simply to save space. An example of how to translate between the numbers and actual music is below on this page. Each canon is meant for a certain number of voices and contains a specific limited number of possible pitches (represented by the numbers) plus rests (represented by an underscore). For these canons, the pitches and rests all have the duration of one beat. The delays between the voices in the canons are measured in beats, and are listed in the headers. The resulting canons will contain every possible harmony, producible by however many voices and pitches are available, once and only once, ignoring pitch doublings. For example:The number string: 01_2_23010414230423143___can be represented musically using any collection of 5 pitches. If for simplicity's sake we use the first 5 notes of a C major scale (0=C, 1=D, 2=E, 3=F, 4=G, underscore=rest) we get the melody: This numbers-string/melody happens to be found in the collection of canons with 3 voices and 5 pitches, under the subsection delay #1 = 1 beat; delay #2 = 2 beatsSo we can put that musical melody in canon with a delay between the voices of 1 then 2 beats, and it produces this piece: which contains all possible harmonies once and only once (ignoring pitch doublings). |