17edo neutral scale: Difference between revisions

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 A lovely system of Middle-Eastern flavored scales!
-We can call the [[MOSScales|Moment of Symmetry]] scale derived from a 5/17 generator &amp; 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 &amp; 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 (&amp; 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]]).
+==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 ==
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 === 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"
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 == 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?
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 [[Category:17edo]]
 [[Category:Modes]]
-[[Category:Mos]]
+[[Category:MOS scales]]
 [[Category:Neutral]]
 [[Category:Neutral second]]
 [[Category:Neutral third]]