Decatonic scale

If the notes are ordered, a decatonic set has 3,628,800 permutations,[3] however, in twelve tone equal temperament only six unordered ten note sets exist, 10-1—10-6: Given that two of the notes from the chromatic scale are missing and only two whole tones are possible, all 10-note scales are cohemitonic scales.

This may be related to the seven notes of the diatonic scale as, "1 ♭2 ♮2 ♭3 ♮3 ♯4 ♮5 ♭6 ♮6 ♭7," and thus spelled, on C, as C, D♭, D♮, E♭, E♮, F♯, G, A♭, A♮, B♭.

This allows a dominant seventh chord to be built upon the tonic and a seventh sharp nine chord, and allows the tonic chord to have an altered ninth, eleventh, and thirteenth factors.

[1] However, pitch sets containing more than seven notes become increasingly similar to each other.

[4] A decatonic scale that has been used or considered by Kyle Gann and La Monte Young in 13-limit just intonation is 1/1, 12/11, 32/27, 9/7, 4/3, 132/91, 3/2, 18/11, 16/9, 176/91, and 2/1.