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 & 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:

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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:

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 right-1 right-2"

|-

! ~~Degree~~

! Step# of scale<ref>In terms of the 10-note MOS scale, 1-based (unison=1)</ref>

! ~~Degree~~ of 17edo

! Steps of 17edo<ref>Amount of steps of 17edo, 0-based (often called "degree")</ref>

! Note name on C

! Harmonics approximated

! #Gens up

|-

~~| 6~~

~~| style="text-align:right;" | 9~~

~~| Gd~~

~~| '''23/16'''~~

~~| -5~~

|-

| 9

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| '''9/8'''

| +4

|-

| 6

| 8

| F+

| '''11/8'''

| +5

|}

The 6th degree can be ~~swapped for~~ a 11/8 (+5 generators) ~~by lowering it by a chroma~~. I prefer using the sharper ~~note~~ because it makes a 7/4 with the 8th degree.

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:

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]]

@@ Line 3: / Line 3: @@
 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:
@@ Line 40: / Line 40: @@
 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:
-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 right-1 right-2"
 |-
-! Degree
+! Step# of scale<ref>In terms of the 10-note MOS scale, 1-based (unison=1)</ref>
-! Degree of 17edo
+! Steps of 17edo<ref>Amount of steps of 17edo, 0-based (often called "degree")</ref>
 ! Note name on C
 ! Harmonics approximated
 ! #Gens up
-|-
-| 6
-| style="text-align:right;" | 9
-| Gd
-| '''23/16'''
-| -5
 |-
 | 9
@@ Line 112: / Line 104: @@
 | '''9/8'''
 | +4
+|-
+| 6
+| 8
+| F+
+| '''11/8'''
+| +5
 |}
-The 6th degree can be swapped for a 11/8 (+5 generators) by lowering it by a chroma. I prefer using the sharper note because it makes a 7/4 with the 8th degree.
+<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 ==
@@ Line 131: / Line 131: @@
 === 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"
@@ Line 299: / Line 301: @@
 == 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?
@@ Line 308: / Line 310: @@
 [[Category:17edo]]
 [[Category:Modes]]
-[[Category:Mos]]
+[[Category:MOS scales]]
 [[Category:Neutral]]
 [[Category:Neutral second]]
 [[Category:Neutral third]]