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A '''rastmic chord''' is an [[Dyadic_chord #Essentially tempered dyadic chords|essentially tempered dyadic chord]] tempered by the rastma, [[243/242]], in the 2.3.11 subgroup in the 11 odd limit.
'''Rastmic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the rastma, [[243/242]], in the 2.3.11 [[subgroup]] in the [[11-odd-limit]].


The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16:
The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16.


* There are three ''rastmic triads'': the classic neutral triad 1-11/9-3/2 with steps 11/9-11/9-4/3, and an inversely related pair of triads, 1-9/8-11/6 with steps 9/8-18/11-12/11 and 1-9/8-11/9 with steps 9/8-12/11-18/11.
There are three rastmic triads: the classic neutral triad,
* 1–11/9–3/2 with steps of 11/9, 11/9, 4/3;


* ''Rastmic tetrads'' are seven in number: the palindromic classic [[neutral tetrad]] 1-11/9-3/2-11/6 with steps 11/9-11/9-11/9-12/11; the palindromic 1-3/2-18/11-11/6 with steps 3/2-12/11-9/8-12/11; the palindromic 1-9/8-11/9-11/8 with steps 9/8-12/11-9/8-16/11; the inverse pair 1-11/9-11/8-3/2 with steps 11/9-9/8-12/11-4/3 and 1-12/11-11/9-3/2 with steps 12/11-9/8-11/9-4/3; and the inverse pair 1-9/8-11/9-3/2 with steps 9/8-12/11-11/9-4/3 and 1-9/8-3/2-11/6 with steps 9/8-4/3-11/9-12/11.
and an inversely related pair of triads,
* 1–9/8–11/6 with steps of 9/8, 18/11, 12/11, and its inverse  
* 1–9/8–11/9 with steps of 9/8, 12/11, 18/11.


* There are five ''rastmic pentads'': the palindromic pentad 1-9/8-11/9-3/2-11/6 with steps 9/8-12/11-11/9-11/9-12/11; the pair 1-9/8-11/8-3/2-11/6 with steps 9/8-11/9-12/11-11/9-12/11 and 1-11/9-11/8-3/2-11/6 with steps 11/9-9/8-12/11-11/9-12/11; and the pair 1-9/8-11/9-11/8-3/2 with steps 9/8-12/11-9/8-12/11-4/3 and 1-9/8-3/2-18/11-11/6 with steps 9/8-4/3-12/11-9/8-12/11.
Rastmic tetrads are seven in number: three palindromic tetrads,
* 1–11/9–3/2–11/6 with steps of 11/9, 11/9, 11/9, 12/11 (→ [[neutral tetrad]]);  
* 1–3/2–18/11–11/6 with steps of 3/2, 12/11, 9/8, 12/11;  
* 1–9/8–11/9–11/8 with steps of 9/8, 12/11, 9/8, 16/11;


* There is also a ''rastmic hexad'': 1-9/8-11/9-11/8-3/2-11/6, with steps 9/8-12/11-9/8-12/11-11/9-12/11. This can be extended to the neutral diatonic scale, LsLsLss, which is [[Chromatic_pairs#Neutral|Neutral[7]]]. In neutral, with the neutral third (~11/9) as generator, the rastmic hexad is a chain of five neutral thirds rather than the six which give [[neutral7]], which therefore has two rastmic hexads and of course many more smaller rastmic chords.
and two inversely related pairs of tetrads,
* 1–11/9–11/8–3/2 with steps of 11/9, 9/8, 12/11, 4/3, and its inverse
* 1–12/11–11/9–3/2 with steps of 12/11, 9/8, 11/9, 4/3;
* 1–9/8–11/9–3/2 with steps of 9/8, 12/11, 11/9, 4/3, and its inverse
* 1–11/9–4/3–3/2 with steps of 11/9, 12/11, 9/8, 4/3.


Equal divisions of the octave with rastmic chords include 10, 17, 24, 31, 41, 58, 72, 130, 202, 736be, 938be, 1075be, 1116be, 1277be, 1318be.
There are five rastmic pentads: the palindromic pentad,
* 1–9/8–11/9–3/2–11/6 with steps of 9/8, 12/11, 11/9, 11/9, 12/11;
 
and two inversely related pairs of pentads,
* 1–9/8–11/8–3/2–11/6 with steps of 9/8, 11/9, 12/11, 11/9, 12/11, and its inverse
* 1–12/11–4/3–3/2–18/11 with steps of 12/11, 11/9, 9/8, 12/11, 11/9;
* 1–9/8–11/9–11/8–3/2 with steps of 9/8, 12/11, 9/8, 12/11, 4/3, and its inverse
* 1–12/11–11/9–4/3–3/2 with steps of 12/11, 9/8, 12/11, 9/8, 4/3.
 
There is also a unique rastmic hexad:
* 1–9/8–11/9–11/8–3/2–11/6 with steps of 9/8, 12/11, 9/8, 12/11, 11/9, 12/11.
 
[[Equal temperament]]s with rastmic chords include {{Optimal ET sequence| 10, 17, 24, 31, 41, 58, 72, 130, 202, 736be, 938be, 1075be, 1116be, 1277be and 1318be }}.


{| class="wikitable"
{| class="wikitable"
|-  
|-  
! chord by pitches
! Chord by Pitches
! chord by intervals
! Chord by Intervals
|-  
|-  
| 1 - 11/9 - 3/2
| 1–11/9–3/2
| 11/9 - 11/9 - 4/3
| 11/9, 11/9, 4/3
|-  
|-  
| 1 - 9/8 - 11/6
| 1–9/8–11/6
| 9/8 - 18/11 - 12/11
| 9/8, 18/11, 2/11
|-  
|-  
| 1 - 9/8 - 11/9
| 1–9/8–11/9
| 9/8 - 12/11 - 18/11
| 9/8, 12/11, 18/11
|-  
|-  
| 1 - 11/9 - 3/2 - 11/6
| 1–11/9–3/2–11/6
| 11/9 - 11/9 - 11/9 - 12/11
| 11/9, 11/9, 11/9, 12/11
|-  
|-  
| 1 - 3/2 - 18/11 - 11/6
| 1–3/2–18/11–11/6
| 3/2 - 12/11 - 9/8 - 12/11
| 3/2, 12/11, 9/8, 12/11
|-  
|-  
| 1 - 9/8 - 11/9 - 11/8
| 1–9/8–11/9–11/8
| 9/8 - 12/11 - 9/8 - 16/11
| 9/8, 12/11, 9/8, 16/11
|-  
|-  
| 1 - 11/9 - 11/8 - 3/2
| 1–11/9–11/8–3/2
| 11/9 - 9/8 - 12/11 - 4/3
| 11/9, 9/8, 12/11, 4/3
|-  
|-  
| 1 - 12/11 - 11/9 - 3/2
| 1–12/11–11/9–3/2
| 12/11 - 9/8 - 11/9 - 4/3
| 12/11, 9/8, 11/9, 4/3
|-  
|-  
| 1 - 9/8 - 11/9 - 3/2
| 1–9/8–11/9–3/2
| 9/8 - 12/11 - 11/9 - 4/3
| 9/8, 12/11, 11/9, 4/3
|-  
|-  
| 1 - 9/8 - 3/2 - 11/6
| 1–11/9–4/3–3/2
| 9/8 - 4/3 - 11/9 - 12/11
| 11/9, 12/11, 9/8, 4/3
|-  
|-  
| 1 - 9/8 - 11/9 - 3/2 - 11/6
| 1–9/8–11/9–3/2–11/6
| 9/8 - 12/11 - 11/9 - 11/9 - 12/11
| 9/8, 12/11, 11/9, 11/9, 12/11
|-  
|-  
| 1 - 9/8 - 11/8 - 3/2 - 11/6
| 1–9/8–11/8–3/2–11/6
| 9/8 - 11/9 - 12/11 - 11/9 - 12/11
| 9/8, 11/9, 12/11, 11/9, 12/11
|-  
|-  
| 1 - 11/9 - 11/8 - 3/2 - 11/6
| 1–12/11–4/3–3/2–18/11
| 11/9 - 9/8 - 12/11 - 11/9 - 12/11
| 12/11, 11/9, 9/8, 12/11, 11/9
|-  
|-  
| 1 - 9/8 - 11/9 - 11/8 - 3/2
| 1–9/8–11/9–11/8–3/2
| 9/8 - 12/11 - 9/8 - 12/11 - 4/3
| 9/8, 12/11, 9/8, 12/11, 4/3
|-  
|-  
| 1 - 9/8 - 3/2 - 18/11 - 11/6
| 1–12/11–11/9–4/3–3/2
| 9/8 - 4/3 - 12/11 - 9/8 - 12/11
| 12/11, 9/8, 12/11, 9/8, 4/3
|-  
|-  
| 1 - 9/8 - 11/9 - 11/8 - 3/2 - 11/6
| 1–9/8–11/9–11/8–3/2–11/6
| 9/8 - 12/11 - 9/8 - 12/11 - 11/9 - 12/11
| 9/8, 12/11, 9/8, 12/11, 11/9, 12/11
|}
|}


[[Category:11-limit]]
== Rastgross heptad ==
[[Category:Chords]]
Rastmic chords can be extended to the [[neutralization|neutralized]] [[5L 2s|diatonic]] scale, [[3L 4s|LsLsLss]], which is [[neutral7|Neutral[7]]]. In [[rastmic clan #Neutral|neutral]], with the neutral third (~11/9) as generator, the rastmic hexad is a chain of five neutral thirds rather than the six which give Neutral[7], which therefore has two rastmic hexads and of course many more smaller rastmic chords.
[[Category:Dyadic]]
 
In the 2.3.11.13 subgroup, this scale is interpreted as an essentially tempered heptad, the '''rastgross heptad''', tempered by [[144/143]] (grossma) and 243/242. This heptad is 1–9/8–11/9–11/8–3/2–22/13–11/6 with steps of 9/8, 12/11, 9/8, 12/11, 9/8, 12/11, 12/11 (→ [[rastgross1]]).
 
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Rastmic]]
[[Category:Rastmic]]
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