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This is the page that I will use to just splatter my thoughts on; I think most of it will center around notation & regular temperaments. Some things you may see in specific are a notation for 14EDO around Titanium(9), a theory system for Orwell(22), and microtonal marimba layouts.
This is the page that I will use to just splatter my thoughts on; I think most of it will center around notation & regular temperaments.


== Titanium(9) Notation for 14EDO ==
== Titanium(9) Notation for 14EDO ==
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== Christopher Temperament ==
== Christopher Temperament ==
Christopher temperament is the name I give to the 2.5.7.11.13-limit temperament with a generator of a sharp [[7/6]] that tempers out [[99/98]], 44/43, 17496/16807, etc. It would be a generator of [[Orwell]] if it wasn't for the fact that its too sharp. Two generators give an 8c sharp [[11/8]], three of them make a 0.7c flat [[13/8]], and five make a 4c flat [[9/8]].
Christopher temperament is the name I give to the 2.5.7.9.11.13-limit temperament with a generator of a sharp [[7/6]] that tempers out [[99/98]], 44/43, 17496/16807, etc. It would be a generator of [[Orwell]] if it wasn't for the fact that its too sharp. Two generators give an 8c sharp [[11/8]], three of them make a 0.7c flat [[13/8]], and five make a 4c flat [[9/8]].


Using a [http://www.microtonalsoftware.com/scale-tree.html?left=13&right=17&rr=1200&ioi=279.944474 scale tree], you can find the EDOs that approximate the generator, starting with [[13edo|13]] & [[17edo|17EDO]]; you could also find a zigzag series of EDOs that approximate the generator, starting with 13 & [[30edo|30]].
Using a [http://www.microtonalsoftware.com/scale-tree.html?left=13&right=17&rr=1200&ioi=279.944474 scale tree], you can find the EDOs that approximate the generator, starting with [[13edo|13]] & [[17edo|17EDO]]; you could also find a zigzag series of EDOs that approximate the generator, starting with 13 & [[30edo|30]].
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== Resolutions in Temperaments ==
== Resolutions in Temperaments ==
As of 3/23/2020, I got really bored and I made a little resolution in the 4L5s scale of Christopher. I decided to try and record some progressions in various temperaments after realizing how easy it is to bust them out and sing microtonally. These are all using 4 voices of varying ranges. I hope you enjoy.
As of 3/23/2020, I got really bored and I made a little resolution in the [https://en.xen.wiki/w/User:CritDeathX/Sam%27s_Musings#4L5s 4L5s scale of Christopher]. I decided to try and record some progressions in various temperaments after realizing how easy it is to bust them out and sing microtonally. These are all using 4 voices of varying ranges. I hope you enjoy.


[https://en.xen.wiki/w/File:Christopher(9)_resolution.wav Christopher(9)]
[[File:Christopher(9) resolution.wav]] | Christopher 4L5s


[https://en.xen.wiki/w/File:Mavila_resolution.wav Mavila(9)]
[[File:Mavila resolution.wav]] | [[Mavila]] [[2L 5s|2L5s]]


[https://en.xen.wiki/w/File:Blackwood_resolution.wav Blackwood(10)]
[[File:Blackwood resolution.wav]] | [[Blackwood]] [[5L 5s|5L5s]]


== Halthird Temperament ==
== Halthird Temperament ==
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== Sothuyo Temperament ==
== Sothuyo Temperament ==
Sothuyo temperament is the name I give to the 2.3.5.13.17-limit temperament with a generator of a slightly sharp 13/10 that tempers out 170/169, '''[i am currently figuring this comma out; it should be fixed in a couple days]''', <small>6250000000/5931980229</small>, etc. The name for this temperament comes from the [[Color notation|colour notation]] name of 170/169, which is 17o13u<sup>2</sup>yb1.
Sothuyo temperament is the name I give to the 2.3.5.13.17-limit temperament with a generator of a slightly sharp 13/10 that tempers out 170/169, <small>6250000000/5931980229</small>, etc. The name for this temperament comes from the [[Color notation|colour notation]] name of 170/169, which is 17o3u<sup>2</sup>yb1.


Using a [http://www.microtonalsoftware.com/scale-tree.html?left=8&right=13&rr=1200&ioi=458.873648 scale tree], you can find EDOs that support this generator, starting with [[8edo|8]] and 13EDO. There's a zigzag pattern between 13 and [[21edo|21EDO]].
Using a [http://www.microtonalsoftware.com/scale-tree.html?left=8&right=13&rr=1200&ioi=458.873648 scale tree], you can find EDOs that support this generator, starting with [[8edo|8]] and 13EDO. There's a zigzag pattern between 13 and [[21edo|21EDO]].
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c = 34.64258 (-13x)
c = 34.64258 (-13x)
== Ocean Temperament ==
Ocean temperament is the name I give to the 13-limit temperament with a generator of a slightly sharp [[6/5]] that tempers out [[100/99]], 875/864, 21875/21384, etc. Two generators give 16/11, three give [[7/4]], and five give [[14/11]].
Using a [http://www.microtonalsoftware.com/scale-tree.html?left=11&right=15&rr=1200&ioi=324.052766 scale tree], you can find EDOs that support this generator, starting with [[11edo|11]] and [[15edo|15EDO]]. Using my slightly better knowledge about zigzags in scale trees, the zigzag of EDOs start with 11-15-[[26edo|26]].
On a side note, I believe I have found a better way to find new generators; usually, I would type something like 927.927364 into Scale Workshop and pray to whatever god there is that the MOS scales are good. The problem with this method is that these would usually give ''very'' small s steps (sometimes around 3 cents or so) or the generator is Orwell. How I found this temperament is focusing on EDO steps (something like 52\107); this is slightly better for me, as there's a bit more of a good sense as to if it will cause small s steps or not.
=== Interval Chain ===
{| class="wikitable"
!131.63
!455.68
!779.74
!1103.79
!227.84
!551.89
!875.95
!0.0
!324.05
!648.11
!972.16
!96.21
!420.26
!744.32
!1068.37
|-
|[[14/13]] +4c
|13/10
|[[11/7]]
|[[17/9]] +3c
|8/7 -3c
|11/8
|[[5/3]] -8c
|1/1
|6/5 +8c
|16/11
|7/4 +3c
|[[18/17]] -3c
|14/11
|20/13
|[[13/7]] -4c
|}
=== Eigenmonzos ===
{| class="wikitable"
|7/4
|322.94196882304163
|-
|14/11
|323.50159282087367
|-
|3/2
|323.64441181561097
|-
|13/8
|324.0527661769311
|-
|5/4
|324.1446071165522
|-
|16/11
|324.3410288176217
|-
|9/8
|325.48875021634683
|}
=== MOS Scales ===
''(note; these scales would be better with equal generators up & down [for example, the first scale could be 3|3 in [[Modal UDP Notation]]])''
==== [[4L 3s|4L3s]] ====
{| class="wikitable"
!0
!1
!2
!3
!4
!5
!6
|-
|0.0
|
|
|
|
|
|
|-
|
|
|
|
|96.21
|
|
|-
|
|324.05
|
|
|
|
|
|-
|
|
|
|
|
|420.26
|
|-
|
|
|648.11
|
|
|
|
|-
|
|
|
|
|
|
|744.32
|-
|
|
|
|972.16
|
|
|
|}
L = 227.84 (-3x)
s = 96.21 (4x)
c = 131.63 (-7x)
==== [[4L 7s|4L7s]] ====
{| class="wikitable"
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
|-
|0.0
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|96.21
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|192.42
|
|
|-
|
|324.05
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|420.26
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|516.48
|
|-
|
|
|648.11
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|744.32
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|840.53
|-
|
|
|
|972.16
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|1068.37
|
|
|
|}
L = 131.63 (-7x)
s = 96.21 (4x)
c = 35.42 (-11x)
==== [[4L 11s|4L11s]] ====
{| class="wikitable"
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
|-
|0.0
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|96.21
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|192.42
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|
|288.63
|
|
|-
|
|324.05
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|420.26
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|516.48
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|
|
|612.69
|
|-
|
|
|648.11
|
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|744.32
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|840.53
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|936.74
|-
|
|
|
|972.16
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|1068.37
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|1164.58
|
|
|
|}
L = 96.21 (4x)
s = 35.42 (-11x)
c = 61.79 (-15x)
== Worell Temperament ==
Worell temperament is the name I give to the 11-limit temperament with a generator of a slightly flat 7/6 that tempers out 343/324, 117649/116640, 9058973/8957952, etc. Six generators give 5/4, seven generators give 16/11, ten generators give 8/7, and eleven generators give 4/3. It is named worell temperament because of the perceived similarity to orwell, except for higher complexity for its primes; for example, orwell takes three generators to get to 5/4, while worell takes twice as many generators.
Using a [http://www.microtonalsoftware.com/scale-tree.html?left=9&right=14&rr=1200&ioi=264.05999884615005 scale tree], you can find EDOs that support this generator, starting with [[9edo|9]] & [[14edo|14EDO]]. Admittedly, I don't enjoy 14EDO's approximation of 7/6, but the website I'm using can only go up to [[19edo|19 notes]].
Its not a temperament that I'm too proud of, mainly from the fact I realized while writing this that this was already a generator for [https://en.xen.wiki/w/User:CritDeathX/Sam's_Musings#Halthird_Temperament halthird temperament]. Also, the L:s ratio gets a bit wonky at the 14-note scale.
=== Interval Chain ===
{| class="wikitable"
|815.640
|1079.700
|143.760
|407.820
|671.880
|935.940
|0.0
|264.060
|528.120
|792.180
|1056.240
|120.300
|384.360
|-
|8/5
|28/15
|12/11 -7c
|81/64
|40/27 -9c
|12/7
|1/1
|7/6
|[[27/20]] +9c
|128/64
|11/6 +7c
|15/14
|5/4
|}
=== Eigenmonzos ===
{| class="wikitable"
|40/27
|259.77564436566377
|-
|7/4
|263.1174093530875
|-
|3/2
|263.45863628496477
|-
|81/64
|264.05999884615005
|-
|11/8
|264.09743680503476
|-
|5/4
|264.38561897747246
|-
|7/6
|266.87090560373764
|}
=== MOS Scales ===
==== 4L1s ====
{| class="wikitable"
!0
!1
!2
!3
!4
|-
|0.0
|
|
|
|
|-
|
|264.060
|
|
|
|-
|
|
|528.120
|
|
|-
|
|
|
|792.180
|
|-
|
|
|
|
|1056.240
|}
L = 264.060 (1x)
s = 143.760 (-4x)
c = 120.300 (5x)
==== 4L5s ====
{| class="wikitable"
!0
!1
!2
!3
!4
!5
!6
!7
!8
|-
|0.0
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|120.300
|
|
|
|-
|
|264.060
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|384.360
|
|
|-
|
|
|528.120
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|648.420
|
|-
|
|
|
|792.180
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|912.480
|-
|
|
|
|
|1056.240
|
|
|
|
|}
L = 143.760 (-4x)
s = 120.300 (5x)
c = 23.460 (-9x)
==== 9L5s ====
{| class="wikitable"
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
|-
|0.0
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|120.300
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|240.600
|
|
|
|-
|
|264.060
|
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|384.360
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|504.660
|
|
|-
|
|
|528.120
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|648.420
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|
|768.720
|
|-
|
|
|
|792.180
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|912.480
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|
|
|1032.780
|-
|
|
|
|
|1056.240
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|1176.540
|
|
|
|
|}
L = 120.300 (5x)
s = 23.460 (-9x)
c = 96.960 (14x)
Retrieved from "https://en.xen.wiki/w/User:CritDeathX/Sam%27s_Musings"