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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:
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We have arrived again at a MOS scale, of type 3L+4s ("mosh" according to the [[MOSNamingScheme]]).
We have arrived again at a MOS scale, of type 3L+4s ("mosh" according to the [[MOSNamingScheme]]).
==Interval chain==
==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:
===Interval chain===
{| class="wikitable sortable right-1 right-2"
Viewing 17edo as a temperament on the 2.3.5.7.11.13.23.25 subgroup, we get the following interpretation for the 10-note MOS scale:
 
 
{| class="wikitable sortable sorted"
|-
|-
! style="text-align:right" | Degree
! Step# of scale<ref>In terms of the 10-note MOS scale, 1-based (unison=1)</ref>
! | Cents
! Steps of 17edo<ref>Amount of steps of 17edo, 0-based (often called "degree")</ref>
! | Note name on C
! Note name on C
! | Harmonics approximated
! Harmonics approximated
! | #Gens up
! #Gens up
|-
|-
| | 6
| 9
| style="text-align:right;" | 635.29
| 14
| | Gd
| Bb
| | '''23/16'''
| '''7/4'''
| | -5
| -4
|-
|-
| | 9
| 2
| style="text-align:right;" | 988.24
| 2
| | Bb
| Dd
| | '''7/4'''
|  
| | -4
| -3
|-
|-
| | 2
| 5
| style="text-align:right;" | 141.18
| 7
| | Dd
| F
| |  
|  
| | -3
| -2
|-
|-
| | 5
| 8
| style="text-align:right;" | 494.12
| 12
| | F
| Ad
| |
| '''13/8'''
| | -2
| -1
|-
|-
| | 8
| 11
| style="text-align:right;" | 1058.82
| 17
| | Ad
| C
| | '''13/8'''
| '''2/1'''
| | -1
| 0
|-
|-
| | 1
| 4
| style="text-align:right;" | 0, 1200
| 5
| | C
| Ed
| | '''1/1''', '''2/1'''
|  
| | 0
| +1
|-
|-
| | 4
| 7
| style="text-align:right;" | 352.94
| 10
| | Ed
| G
| |
| '''3/2'''
| | +1
| +2
|-
|-
| | 7
| 10
| style="text-align:right;" | 705.88
| 15
| | G
| Bd
| | '''3/2'''
|  
| | +2
| +3
|-
|-
| | 10
| 3
| style="text-align:right;" | 1058.82
| 3
| | Bd
| D
| |
| '''9/8'''
| | +3
| +4
|-
|-
| | 3
| 6
| style="text-align:right;" | 211.76
| 8
| | D
| F+
| | '''9/8'''
| '''11/8'''
| | +4
| +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 ==
== 7-note neutral scale ==
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=== 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"
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== 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?
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[[Category:17edo]]
[[Category:17edo]]
[[Category:Modes]]
[[Category:Modes]]
[[Category:Mos]]
[[Category:MOS scales]]
[[Category:Neutral]]
[[Category:Neutral]]
[[Category:Neutral second]]
[[Category:Neutral second]]
[[Category:Neutral third]]
[[Category:Neutral third]]
Retrieved from "https://en.xen.wiki/w/17edo_neutral_scale"