Otonal 17

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Otonal 17 is a mode of 17 equal divisions of the octave. It has seven steps, here given in multiples of 17/oct:

3 2 3 2 2 2 3

In pythagorean notation, the scale, beginning on G#: G# A# C D D# F F# G#

As understood by the harmonic series, an approximate 8:9:11:12:13 sonority is playable if you omit the 3rd note.

As understood by the scale archive, it is a rotation of Safi al-Din's maqam Rahawi, but only if you equate 17-equal with 17-pythagorean.

As understood by the moment-of-symmetry paradigm, it is obtained by shuffling the 7-note neutral scale, or by taking a subset of the 10-note neutral scale. The generator is 5/17-oct, its neutral third:

[0 5 10 15 20 25 30] wrapped around at 17 yields:

[0 5 10 15 3 8 13] in ascending order yields:

[0 3 5 8 10 13 15] expressed in terms of consecutive intervals:

[3 2 3 2 3 2 2]

As you can see, the 3's are all isolated from one another. You have to do two bubble-swaps to get otonal-17. Or, you can start over with a longer chain of neutral thirds, but with some holes:

this time going both directions from zero: [-20 -15 -10 -5 0 5 10 15 20 25]

now with X's on the omitted notes: [-20 X X -5 0 5 10 X 20 25]

wrapped and ordered: [0 3 5 8 10 12 14]

A midi file of noodling in this scale - please excuse the pitchbend funniness in the first couple of seconds - it gets better - 17try.mid

for an example in a piece of music, see Fonala.

...As understood by the MOSNamingScheme, this scale is a flavor of mosh!