Otonal 17

Otonal 17 is a 7-tone mode of 17edo: 3 2 3 2 2 2 3

It approximates the chord 8:9:11:12:13 from the harmonic series. If you equate 17-equal with 17-Pythagorean, it is a rotation of Safi al-Din's Maqam Rahaw. In Pythagorean notation, it could be written G# A# C D D# F F# G#.

Moment of symmetry analysis

From a moment of symmetry perspective, Otonal 17 may be obtained by shuffling the 7-note neutral scale, or by taking a subset of the 10-note neutral scale. The generator is 5\17, 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]

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

Audio examples

• 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.