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=17edo neutral scale=
== 17edo neutral scale ==


A lovely system of Middle-Eastern flavored scales!
A lovely system of Middle-Eastern flavored scales!


We can call the [[MOSScales|Moment of Symmetry]] scale derived from a 5/17 generator & an octave repeat the '''17edo Neutral Scale'''. We build it by stacking neutral thirds, the generator of the [[maqamic|maqamic temperament]]. In 17edo that means the interval of five degrees of 17.
We can call the [[MOSScales|Moment of Symmetry]] scale derived from a 5/17 generator & an octave repeat the '''17edo Neutral Scale'''. It is an example of a [[neutral thirds scale]]. We build it by stacking neutral thirds, the generator of the [[neutrominant]] temperament. In [[17edo]] that means the interval of five degrees of 17.


Begin anywhere. Let's call our first pitch (& its octave transposition) 0:
Begin anywhere. Let's call our first pitch (& its octave transposition) 0:
Line 39: Line 39:
0 2 5 7 10 12 15 (0)
0 2 5 7 10 12 15 (0)


We have arrived again at a MOS scale, of type 3L+4s ("mosh" according to the [[MOSNamingScheme|MOSNamingScheme]]).
We have arrived again at a MOS scale, of type 3L+4s ("mosh" according to the [[MOSNamingScheme]]).


==7-note neutral scale:==
==Interval chain==
Viewing 17edo as a temperament on the 2.3.7.11.13 subgroup, we get the following interpretation for the 2122122212 mode of the 10-note MOS scale:
{| class="wikitable sortable right-1 right-2"
|-
! Step# of scale<ref>In terms of the 10-note MOS scale, 1-based (unison=1)</ref>
! Steps of 17edo<ref>Amount of steps of 17edo, 0-based (often called "degree")</ref>
! Note name on C
! Harmonics approximated
! #Gens up
|-
| 9
| 14
| Bb
| '''7/4'''
| -4
|-
| 2
| 2
| Dd
|
| -3
|-
| 5
| 7
| F
|
| -2
|-
| 8
| 12
| Ad
| '''13/8'''
| -1
|-
| 11
| 17
| C
| '''2/1'''
| 0
|-
| 4
| 5
| Ed
|
| +1
|-
| 7
| 10
| G
| '''3/2'''
| +2
|-
| 10
| 15
| Bd
|
| +3
|-
| 3
| 3
| D
| '''9/8'''
| +4
|-
| 6
| 8
| F+
| '''11/8'''
| +5
|}
<references/>
 
The 6th degree can be raised by a [[chroma]] to a 23/16 (-5 generators). Some may prefer using the sharper 6th degree because it makes a 7/4 with the 8th degree.
 
== 7-note neutral scale ==


degrees from 0: 0 2 5 7 10 12 15 (0)
degrees from 0: 0 2 5 7 10 12 15 (0)
Line 55: Line 129:
interval classes between: N2 M2 N2 M2 N2 M2 N2
interval classes between: N2 M2 N2 M2 N2 M2 N2


===modes of 7-note neutral scale===
=== modes of 7-note neutral scale ===


Naturally, with seven notes we have seven modes, depending on which note we make the starting pitch (tonic) of the scale. I have given these modes a one-syllable name for my own use. Feel free to name (or not name) these modes as you see fit:
{{Idiosyncratic terms|The 7 proposed mode names}}


==== ====
Naturally, with seven notes we have seven modes, depending on which note we make the starting pitch (tonic) of the scale. I ([[Andrew Heathwaite]]) have given these modes a one-syllable name for my own use. Feel free to name (or not name) these modes as you see fit:


{| class="wikitable"
{| class="wikitable"
! mode 1 : bish
! from bottom
! in between
|-
|-
| | mode 1 : bish
! degrees
| | from bottom
| 0 2 5 7 10 12 15 (0)
| | in between
| 2 3 2 3 2 3 2
|-
| | degrees
| | 0 2 5 7 10 12 15 (0)
| | 2 3 2 3 2 3 2
|-
|-
| | cents
! cents
| | 0 141 353 494 706 847 1059 (1200)
| 0 141 353 494 706 847 1059 (1200)
| | 141 212 141 212 141 212 141
| 141 212 141 212 141 212 141
|-
|-
| | interval classes
! interval classes
| | P1 N2 N3 P4 P5 N6 N7 (P8)
| P1 N2 N3 P4 P5 N6 N7 (P8)
| | N2 M2 N2 M2 N2 M2 N2
| N2 M2 N2 M2 N2 M2 N2
|-
|-
| | solfege
! solfege
| | do ru mu fa sol lu tu (do)
| do ru mu fa sol lu tu (do)
| | ru re ru re ru re ru
| ru re ru re ru re ru
|}
|}


{| class="wikitable"
{| class="wikitable"
! mode 2 : dril
! from bottom
! in between
|-
|-
| | mode 2 : dril
! degrees
| | from bottom
| 0 3 5 8 10 13 15 (0)
| | in between
| 3 2 3 2 3 2 2
|-
| | degrees
| | 0 3 5 8 10 13 15 (0)
| | 3 2 3 2 3 2 2
|-
|-
| | cents
! cents
| | 0 212 353 565 706 918 1059 (1200)
| 0 212 353 565 706 918 1059 (1200)
| | 212 141 212 141 212 141 141
| 212 141 212 141 212 141 141
|-
|-
| | interval classes
! interval classes
| | P1 M2 N3 A4 P5 M6 N7 (P8)
| P1 M2 N3 A4 P5 M6 N7 (P8)
| | M2 N2 M2 N2 M2 N2 N2
| M2 N2 M2 N2 M2 N2 N2
|-
|-
| | solfege
! solfege
| | do re mu fu sol la tu (do)
| do re mu fu sol la tu (do)
| | re ru re ru re ru ru
| re ru re ru re ru ru
|}
|}


{| class="wikitable"
{| class="wikitable"
! mode 3 : fish
! from bottom
! in between
|-
|-
| | mode 3 : fish
! degrees
| | from bottom
| 0 2 5 7 10 12 14 (0)
| | in between
| 2 3 2 3 2 2 3
|-
|-
| | degrees
! cents
| | 0 2 5 7 10 12 14 (0)
| 0 141 353 494 706 847 988 (1200)
| | 2 3 2 3 2 2 3
| 141 212 141 212 141 141 212
|-
|-
| | cents
! interval classes
| | 0 141 353 494 706 847 988 (1200)
| P1 N2 N3 P4 P5 N6 m7 (P8)
| | 141 212 141 212 141 141 212
| N2 M2 N2 M2 N2 N2 M2
|-
|-
| | interval classes
! solfege
| | P1 N2 N3 P4 P5 N6 m7 (P8)
| do ru mu fa sol lu te (do)
| | N2 M2 N2 M2 N2 N2 M2
| ru re ru re ru ru re
|-
| | solfege
| | do ru mu fa sol lu te (do)
| | ru re ru re ru ru re
|}
|}


{| class="wikitable"
{| class="wikitable"
! mode 4 : gil
! from bottom
! in between
|-
|-
| | mode 4 : gil
! degrees
| | from bottom
| 0 3 5 8 10 12 15 (0)
| | in between
| 3 2 3 2 2 3 2
|-
|-
| | degrees
! cents
| | 0 3 5 8 10 12 15 (0)
| 0 212 353 565 706 847 1059 (1200)
| | 3 2 3 2 2 3 2
| 212 131 212 141 141 212 141
|-
|-
| | cents
! interval classes
| | 0 212 353 565 706 847 1059 (1200)
| P1 M2 N3 A4 P5 N6 N7 (P8)
| | 212 131 212 141 141 212 141
| M2 N2 M2 N2 N2 M2 N2
|-
|-
| | interval classes
! solfege
| | P1 M2 N3 A4 P5 N6 N7 (P8)
| do re mu fu sol lu tu (do)
| | M2 N2 M2 N2 N2 M2 N2
| re ru re ru ru re ru
|-
| | solfege
| | do re mu fu sol lu tu (do)
| | re ru re ru ru re ru
|}
|}


{| class="wikitable"
{| class="wikitable"
! mode 5 : jwl
! from bottom
! in between
|-
|-
| | mode 5 : jwl
! degrees
| | from bottom
| 0 2 5 7 9 12 14 (0)
| | in between
| 2 3 2 2 3 2 3
|-
|-
| | degrees
! cents
| | 0 2 5 7 9 12 14 (0)
| 0 141 353 494 635 847 988 (1200)
| | 2 3 2 2 3 2 3
| 141 212 141 141 212 141 212
|-
|-
| | cents
! interval classes
| | 0 141 353 494 635 847 988 (1200)
| P1 N2 N3 P4 d5 N6 m7 (P8)
| | 141 212 141 141 212 141 212
| N2 M2 N2 N2 M2 N2 M2
|-
|-
| | interval classes
! solfege
| | P1 N2 N3 P4 d5 N6 m7 (P8)
| do ru mu fa su lu te (do)
| | N2 M2 N2 N2 M2 N2 M2
| ru re ru ru re ru re
|-
| | solfege
| | do ru mu fa su lu te (do)
| | ru re ru ru re ru re
|}
|}


{| class="wikitable"
{| class="wikitable"
! mode 6 : kleeth
! from bottom
! in between
|-
|-
| | mode 6 : kleeth
! degrees
| | from bottom
| 0 3 5 7 10 12 15 (0)
| | in between
| 3 2 2 3 2 3 2
|-
|-
| | degrees
! cents
| | 0 3 5 7 10 12 15 (0)
| 0 212 353 494 706 847 1059 (1200)
| | 3 2 2 3 2 3 2
| 212 141 141 212 141 212 141
|-
|-
| | cents
! interval classes
| | 0 212 353 494 706 847 1059 (1200)
| P1 M2 N3 P4 P5 N6 N7 (P8)
| | 212 141 141 212 141 212 141
| M2 N2 N2 M2 N2 M2 N2
|-
|-
| | interval classes
! solfege
| | P1 M2 N3 P4 P5 N6 N7 (P8)
| do re mu fa sol lu tu (do)
| | M2 N2 N2 M2 N2 M2 N2
| re ru ru re ru re ru
|-
| | solfege
| | do re mu fa sol lu tu (do)
| | re ru ru re ru re ru
|}
|}


{| class="wikitable"
{| class="wikitable"
! mode 7 : led
! from bottom
! in between
|-
|-
| | mode 7 : led
! degrees
| | from bottom
| 0 2 4 7 9 12 14 (0)
| | in between
| 2 2 3 2 3 2 3
|-
|-
| | degrees
! cents
| | 0 2 4 7 9 12 14 (0)
| 0 141 282 494 635 847 988 (1200)
| | 2 2 3 2 3 2 3
| 141 141 212 141 212 141 212
|-
|-
| | cents
! interval classes
| | 0 141 282 494 635 847 988 (1200)
| P1 N2 m3 P4 d5 N6 m7 (P8)
| | 141 141 212 141 212 141 212
| N2 N2 M2 N2 M2 N2 M2
|-
|-
| | interval classes
! solfege
| | P1 N2 m3 P4 d5 N6 m7 (P8)
| do ru me fa su lu te (do)
| | N2 N2 M2 N2 M2 N2 M2
| ru ru re ru re ru re
|-
| | solfege
| | do ru me fa su lu te (do)
| | ru ru re ru re ru re
|}
|}


Line 232: Line 299:
If you continue stacking neutral thirds, you will soon come to a rather lovely 10-note neutral scale. I (or someone) will come back to that sooner or later.
If you continue stacking neutral thirds, you will soon come to a rather lovely 10-note neutral scale. I (or someone) will come back to that sooner or later.


==Some brief note on the 3, 7 and 10 note MOS.==
== Some brief note on the 3, 7 and 10 note MOS ==
You can also take call the neutral sixth the generator, which I personally favour as it is an (approximate) harmonic rather than a subharmonic. But that's because it's how I use it, you might not. If you see it this way, the 3rd harmonic is harmonically opposite to the 13th harmonic, because, (13/8)^2 ~ 4/3, the perfect fourth being an upside down perfect fifth.
 
You can also take call the neutral sixth the generator, which I ([[Andrew Heathwaite]]) personally favour as it is an (approximate) harmonic rather than a subharmonic. But that's because it's how I use it, you might not. If you see it this way, the 3rd harmonic is harmonically opposite to the 13th harmonic, because, (13/8)^2 ~ 4/3, the perfect fourth being an upside down perfect fifth.


You might also find that the 10-note scale can be formed by two 17-tone pythagoresque pentatonic scales a neutral interval apart, implying something of a different approach. And one of the loveliest things I find about them is the ease with which one can play 8:11:13 chords, so there are some frightening blues licks in this decatonic scale. R'lyeh blues anyone?
You might also find that the 10-note scale can be formed by two 17-tone pythagoresque pentatonic scales a neutral interval apart, implying something of a different approach. And one of the loveliest things I find about them is the ease with which one can play 8:11:13 chords, so there are some frightening blues licks in this decatonic scale. R'lyeh blues anyone?


(Note that you will come up with similarly structured scales by using ''other neutral thirds'' as generators, although some of them will sound quite different. A neutral sixth about sharp of the 13th harmonic leads to 7L+3s like in 17-tone, whereas going flat of the 13th harmonic can lead to 7s+3L. (This boast is possible because 10-edo sits right on it.) Some equal divisions of the octave containing neutral scales: [[10edo|10edo]], [[13edo|13edo]], [[16edo|16edo]], [[19edo|19edo]], [[24edo|24edo]], [[31edo|31edo]]....)
(Note that you will come up with similarly structured scales by using ''other neutral thirds'' as generators, although some of them will sound quite different. A neutral sixth about sharp of the 13th harmonic leads to 7L+3s like in 17-tone, whereas going flat of the 13th harmonic can lead to 7s+3L. (This boast is possible because 10-edo sits right on it.) Some equal divisions of the octave containing neutral scales: [[10edo]], [[13edo]], [[16edo]], [[19edo]], [[24edo]], [[31edo]]....)
 
[[Category:13-limit]]
[[Category:13-limit]]
[[Category:17edo]]
[[Category:17edo]]
[[Category:modes]]
[[Category:Modes]]
[[Category:mos]]
[[Category:MOS scales]]
[[Category:neutral]]
[[Category:Neutral]]
[[Category:neutral_2nd]]
[[Category:Neutral second]]
[[Category:neutral_3rd]]
[[Category:Neutral third]]
Retrieved from "https://en.xen.wiki/w/17edo_neutral_scale"