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For example, in 4L1s, the L is 1 generator up; s is 4 generators down. The chroma is 9 generators up, and is also the L of 4L5s.
For example, in 4L1s, the L is 1 generator up; s is 4 generators down. The chroma is 9 generators up, and is also the L of 4L5s.
As of 3/29/2020, I'm realizing this may be evident in all of temperaments; if not all, then a lot of them.


== Resolutions in Temperaments ==
== Resolutions in Temperaments ==
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[https://en.xen.wiki/w/File:Blackwood_resolution.wav Blackwood(10)]
[https://en.xen.wiki/w/File:Blackwood_resolution.wav Blackwood(10)]
== Trififth Temperament ==
Trififth temperament is the name I've given to the 2.3.7-limit temperament with a generator of a sharp [[8/7]] that tempers out 1029/1024. The simplest primes it can give are 7/4 down one generator and 3/2 up 3 generators, hence the name. Other primes are in the double digits, with 5 being 17 generators.
This is the closest [http://www.microtonalsoftware.com/scale-tree.html?left=13&right=17&rr=1200&ioi=279.944474 scale tree] I could find for EDOs that support the generator, starting with [[5edo|5]] and [[16edo|16EDO]]. To my knowledge, there's no zigzag pattern for the generator.
=== Interval Chain ===
{| class="wikitable"
!991.96
!26.63
!261.30
!495.98
!730.65
!965.33
!0.0
!234.67
!469.35
!704.02
!938.69
!1173.37
!208.04
|-
|16/9 -4c
|64/63
|7/6 +6c
|4/3
|32/21
|7/4 +4c
|1/1
|8/7 -4c
|21/16
|3/2
|12/7 -6c
|63/32
|9/8 +4c
|}
=== MOS Scales ===
==== [[1L 4s|1L4s]] ====
{| class="wikitable"
!0
!1
!2
!3
!4
|-
|0.0
|
|
|
|
|-
|
|234.67
|
|
|
|-
|
|
|469.35
|
|
|-
|
|
|
|704.02
|
|-
|
|
|
|
|938.69
|}
L = 261.30 (-4x)
s = 234.67 (1x)
c = 26.63 (-5x)
==== [[5L 1s|5L1s]] ====
{| class="wikitable"
!0
!1
!2
!3
!4
!5
|-
|0.0
|
|
|
|
|
|-
|
|234.67
|
|
|
|
|-
|
|
|469.35
|
|
|
|-
|
|
|
|704.02
|
|
|-
|
|
|
|
|938.69
|
|-
|
|
|
|
|
|1173.37
|}
L = 234.67 (1x)
s = 26.63 (-5x)
c = 208.04 (6x)
==== [[5L 6s|5L6s]] ====
{| class="wikitable"
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
|-
|0.0
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|208.04
|
|
|
|
|-
|
|234.67
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|442.72
|
|
|
|-
|
|
|469.35
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|677.39
|
|
|-
|
|
|
|704.02
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|912.07
|
|-
|
|
|
|
|938.69
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|1146.74
|-
|
|
|
|
|
|1173.37
|
|
|
|
|
|}
L= 208.04 (6x)
s = 26.63 (-5x)
c = 181.41 (11x)
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