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[https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(264.292863%2C%20600.0)&data=50.050041%0A121.464315%0A192.878589%0A264.292863%0A314.342904%0A385.757178%0A457.171452%0A528.585726%0A600.000000&freq=261.625565&midi=60&vert=5&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white%20white%20black%20white%20black&waveform=triangle&ampenv=organ 7L2s]
[https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(264.292863%2C%20600.0)&data=50.050041%0A121.464315%0A192.878589%0A264.292863%0A314.342904%0A385.757178%0A457.171452%0A528.585726%0A600.000000&freq=261.625565&midi=60&vert=5&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white%20white%20black%20white%20black&waveform=triangle&ampenv=organ 7L2s]
== Stepped Temperament ==
Stepped temperament is the name I give to the '''2.3.5.9.10.11.13.29.31'''-limit temperament with a generator of a flat 5/4 that tempers out <small>967458816/847425747</small>, <small>16325867520/13841287201</small>, <small>823543/629856</small>, etc. Obviously, this is a high complexity temperament, though the good thing is that you have two major thirds that you can choose from; a 12c sharp third (appears after 13 generators) or a 15c flat third (the generator). I tried to demonstrate this fact in the limit, though I have a feeling there's a more accurate way of writing it. A similar occurrence happens in [[pseudo-semaphore]], where the 3rd harmonic has 2 different mappings.
Another thing you may notice is the size of the limit; this is the largest limit that I've seen as of 4/8/2020. Considering I'm only sticking under 31, this is still a sizable limit.
Using a [http://www.microtonalsoftware.com/scale-tree.html?left=13&right=16&rr=1200&ioi=371.301736 scale tree], you can find EDOs that have this generator, starting with 13 & [[16edo|16EDO]]. There's a zigzag pattern starting with 13 & [[42edo|42EDO]], though if you want a more linear pattern, there's one between 13 and [[29edo|29EDO]].
=== Interval Chain ===
{| class="wikitable"
|258.28
|629.59
|1000.89
|172.19
|543.49
|914.79
|86.09
|457.40
|828.70
|0.0
|371.30
|742.60
|1113.91
|285.21
|656.51
|1027.81
|199.11
|570.41
|941.72
|-
|[[22/19]] -4c
|[[36/25]]
|16/9 +5c
|32/29
|11/8 -8c
|[[22/13]]
|[[20/19]]
|13/10
|8/5 +15c
|1/1
|5/4 -15c
|20/13
|[[19/10]]
|[[13/11]] +4c
|16/11 +8c
|[[29/16]]
|9/8 -5c
|[[25/18]]
|[[19/11]] +4c
|}
=== MOS Scales ===
==== [[3L 4s|3L4s]] ====
{| class="wikitable"
!0
!1
!2
!3
!4
!5
!6
|-
|0.0
|
|
|
|
|
|
|-
|
|
|
|
|285.21
|
|
|-
|
|371.30
|
|
|
|
|
|-
|
|
|
|
|
|656.51
|
|-
|
|
|742.60
|
|
|
|
|-
|
|
|
|
|
|
|1027.81
|-
|
|
|
|1113.91
|
|
|
|}
L = 285.21 (4x)
s = 86.09 (-3x)
c = 199.11 (7x)
==== [[3L 7s|3L7s]] ====
{| class="wikitable"
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
|-
|0.0
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|199.11
|
|
|-
|
|
|
|
|285.21
|
|
|
|
|
|-
|
|371.30
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|570.41
|
|-
|
|
|
|
|
|656.51
|
|
|
|
|-
|
|
|742.60
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|941.72
|-
|
|
|
|
|
|
|1027.81
|
|
|
|-
|
|
|
|1113.91
|
|
|
|
|
|
|}
L = 199.11 (7x)
s = 86.09 (-3x)
c = 113.02 (10x)
==== [[3L 10s|3L10s]] ====
{| class="wikitable"
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
|-
|0.0
|
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|113.02
|
|
|-
|
|
|
|
|
|
|
|199.11
|
|
|
|
|
|-
|
|
|
|
|285.21
|
|
|
|
|
|
|
|
|-
|
|371.30
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|484.32
|
|-
|
|
|
|
|
|
|
|
|570.41
|
|
|
|
|-
|
|
|
|
|
|656.51
|
|
|
|
|
|
|
|-
|
|
|742.60
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|
|855.62
|-
|
|
|
|
|
|
|
|
|
|941.72
|
|
|
|-
|
|
|
|
|
|
|1027.81
|
|
|
|
|
|
|-
|
|
|
|1113.91
|
|
|
|
|
|
|
|
|
|}
L = 113.02 (10x)
s = 86.09 (-3x)
c = 26.92 (13x)
Retrieved from "https://en.xen.wiki/w/User:CritDeathX/Sam%27s_Musings"