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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 ==
Line 1,339: Line 1,339:
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]].
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 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]].
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.
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.
Line 1,891: Line 1,891:
s = 35.42 (-11x)
s = 35.42 (-11x)


c = 60.79 (-15x)
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"