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altered_chord_ic_histogram.md

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Interval-class histogram for altered dominant chord

An interesting thing.

  • take altered chord - X7#9
  • its interval class histogram is 111111
    • {1: 1, 2: 1, 3: 1, 4: 1, 5:1, 6:1}
  • it contains each interval class exactly once
  • interval class
    • the shortest distance between two tones on the 12-tone circle
    • range: 0-6
  • in the above example we omit the unison (interval class 0)
    • however it is trivial to add it and the histogram's property keeps holding