Otonal 17: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,263 edits
m Categorised this uncategorised page
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,263 edits
Cleaned up the page
 
Line 1: Line 1:
Otonal 17 is a mode of 17 equal divisions of the octave. It has seven steps, here given in multiples of 17/oct:
Otonal 17 is a 7-tone mode of [[17edo]]: '''3 2 3 2 2 2 3'''


'''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#'''.


In pythagorean notation, the scale, beginning on G#: 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 [[17edo_neutral_scale#seven-note|7-note neutral scale]], or by taking a subset of the 10-note neutral scale. The generator is 5\17, its neutral third:


As understood by the harmonic series, an approximate 8:9:11:12:13 sonority is playable if you omit the 3rd note.
* '''[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 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 you can see, the 3's are all isolated from one another. You have to do two bubble-swaps to get otonal-17.  


As understood by the moment-of-symmetry paradigm, it is obtained by shuffling the [[17edo_neutral_scale#seven-note|7-note neutral scale]], or by taking a subset of the 10-note neutral scale. The generator is 5/17-oct, its neutral third:
Or, you can start over with a ''longer'' chain of neutral thirds, but with some holes:


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


'''[0 5 10 15 3 8 13]''' in ascending order yields:
As understood by the [[MOSNamingScheme]], this scale is a flavor of [[mosh]].


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


'''[3 2 3 2 3 2 2]'''
* A midi file of noodling in this scale - please excuse the pitchbend funniness in the first couple of seconds - it gets better - [[:File:17try.mid|17try.mid]]


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:
* For an example in a piece of music, see ''[[Fonala]]''.


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 - [[:File:17try.mid|17try.mid]]
for an example in a piece of music, see Fonala.
...As understood by the [[MOSNamingScheme|MOSNamingScheme]], this scale is a flavor of mosh!
[[Category:Todo:cleanup]]
[[Category:17edo]]
[[Category:17edo]]
[[Category:7-tone scales]]
[[Category:7-tone scales]]
[[Category:Pythagorean]]
[[Category:Maqam]]

Latest revision as of 07:34, 26 April 2023

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.
Retrieved from "https://en.xen.wiki/index.php?title=Otonal_17&oldid=109581"