17edo neutral scale: Difference between revisions
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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 [[ | 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: | |||
Viewing 17edo as a temperament on the 2.3 | {| class="wikitable sortable right-1 right-2" | ||
{| class="wikitable sortable | |||
|- | |- | ||
! | ! 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 | |||
|} | |} | ||
The 6th degree can be | <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: | [[Category:MOS scales]] | ||
[[Category:Neutral]] | [[Category:Neutral]] | ||
[[Category:Neutral second]] | [[Category:Neutral second]] | ||
[[Category:Neutral third]] | [[Category:Neutral third]] | ||