![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/8/81/Carter_all-interval_sets.png/640px-Carter_all-interval_sets.png&w=640&q=50)
All-interval twelve-tone row
From Wikipedia, the free encyclopedia
In music, an all-interval twelve-tone row, series, or chord, is a twelve-tone tone row arranged so that it contains one instance of each interval within the octave, 1 through 11 (an ordering of every interval, 0 through 11, that contains each (ordered) pitch-interval class, 0 through 11). A "twelve-note spatial set made up of the eleven intervals [between consecutive pitches]."[1] There are 1,928 distinct all-interval twelve-tone rows.[4] These sets may be ordered in time or in register. "Distinct" in this context means in transpositionally and rotationally normal form (yielding 3856 such series), and disregarding inversionally related forms.[5] These 1,928 tone rows have been independently rediscovered several times, their first computation probably was by Andre Riotte in 1961.[6]
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Lyric_Suite_Movement_I_tone_row.svg/350px-Lyric_Suite_Movement_I_tone_row.svg.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/8/81/Carter_all-interval_sets.png/640px-Carter_all-interval_sets.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Nono_-_Il_Canto_sospeso_all-interval_series.png/320px-Nono_-_Il_Canto_sospeso_all-interval_series.png)
Since the sum of numbers 1 through 11 equals 66, an all-interval row must contain a tritone between its first and last notes,[7] as well as in their middle.