User:Fitzgerald Lee/Sandbox: Difference between revisions

Line 1:

~~Minimal~~ edos to have N number of thirds (range is [[15/13]] to [[13/10]], closest JI interpretation that is consistent in the edo’s [[odd limit]] is shown):

First and second edos to have N number of consistent thirds (range is [[15/13]] to [[13/10]], closest JI interpretation that is consistent in the edo’s [[odd limit]] is shown):

{|class="wikitable"

!rowspan="1"|Number of thirds!!rowspan="1"|[[~~Edo~~]]!!rowspan="1"|Thirds

|-

|0||[[0edo|0]] or [[1edo|1]]||None

|0||[[0edo|0]] or [[1edo|1]]||None||1 or none||None

|-

|1||[[3edo|3]]||[[5/4]]

|1||[[3edo|3]]||[[5/4]]||[[4edo|4]]||[[6/5]]

|-

|2||[[5edo|5]]||[[7/6]], [[9/7]]

|2||[[5edo|5]]||[[7/6]], [[9/7]]||[[8edo|8]]||6/5, 5/4

|-

|3||[[15edo|15]]||7/6, [[6/5]], 5/4

|3||[[15edo|15]]||7/6, 6/5, 5/4||[[18edo|18]]||7/6, 6/5, 5/4

|-

|4||[[19edo|19]]||7/6, 6/5, 5/4, 9/7

|4||[[19edo|19]]||7/6, 6/5, 5/4, 9/7||[[22edo|22]]||7/6, 6/5, 5/4, 9/7

|-

|5||[[26edo|26]]||7/6, 6/5, [[16/13]], [[14/11]], [[13/10]]

|5||[[26edo|26]]||7/6, 6/5, [[16/13]], [[14/11]], [[13/10]]||[[31edo|31]]||7/6, 6/5, 5/4, [[11/9]], 14/11

|-

|6||[[29edo|29]]||[[15/13]], [[13/11]], 6/5, 16/13, 14/11, 13/10

|6||[[29edo|29]]||[[15/13]], [[13/11]], 6/5, 16/13, 14/11, 13/10||(41)||(~)

|-

|7||(41)||(~)

|7||(41)||(~)||(58)||(~)

|-

|8||(41)||(~)

|8||(41)||(~)||(58)||(~)

|-

|9||[[41edo|41]]||15/13, 7/6, 13/11, 6/5, [[11/9]], 5/4, 14/11, 9/7, 13/10

|9||[[41edo|41]]||15/13, 7/6, 13/11, 6/5, 11/9, 5/4, 14/11, 9/7, 13/10||(58)||(~)

|-

|10||[[58edo|58]]||15/13, 7/6, 13/11, 6/5, [[17/14]], 11/9, 5/4, 14/11, 9/7, 13/10||(72)||(~)

|-

|11||[[72edo|72]]||15/13, 7/6, [[20/17]], 6/5, 17/14, 11/9, 16/13, 5/4, 14/11, 9/7, [[22/17]]||(80)||(~)

|-

|12||(80)||(~)||(94)||(~)

|-

|13||[[80edo|80]]||[[22/19]], 7/6, 20/17, [[19/16]], 6/5, 17/14, 11/9, 16/13, 5/4, [[24/19]], 14/11, 9/7, 22/17||(94)||(~)

|-

|14||(94)||(~)

|-

|15||(94)||(~)

|-

|16||[[94edo|94]]||15/13, 22/19, 7/6, 20/17, 19/16, 6/5, [[23/19]], 11/9, 16/13, 26/21, 5/4, [[19/15]], [[23/18]], 9/7, 22/17, [[30/23]]

|}

This list could be used to get the minimal edos to add more flavours (of thirds).

@@ Line 1: / Line 1: @@
-Minimal edos to have N number of thirds (range is [[15/13]] to [[13/10]], closest JI interpretation that is consistent in the edo’s [[odd limit]] is shown):
+First and second edos to have N number of consistent thirds (range is [[15/13]] to [[13/10]], closest JI interpretation that is consistent in the edo’s [[odd limit]] is shown):
 {|class="wikitable"
-!rowspan="1"|Number of thirds!!rowspan="1"|[[Edo]]!!rowspan="1"|Thirds
+!rowspan="1"|Number of thirds!!rowspan="1"|First [[edo]]!!rowspan="1"|Thirds!!rowspan="1"|Second edo!!rowspan="1"|Thirds
 |-
-|0||[[0edo|0]] or [[1edo|1]]||None
+|0||[[0edo|0]] or [[1edo|1]]||None||1 or none||None
 |-
-|1||[[3edo|3]]||[[5/4]]
+|1||[[3edo|3]]||[[5/4]]||[[4edo|4]]||[[6/5]]
 |-
-|2||[[5edo|5]]||[[7/6]], [[9/7]]
+|2||[[5edo|5]]||[[7/6]], [[9/7]]||[[8edo|8]]||6/5, 5/4
 |-
-|3||[[15edo|15]]||7/6, [[6/5]], 5/4
+|3||[[15edo|15]]||7/6, 6/5, 5/4||[[18edo|18]]||7/6, 6/5, 5/4
 |-
-|4||[[19edo|19]]||7/6, 6/5, 5/4, 9/7
+|4||[[19edo|19]]||7/6, 6/5, 5/4, 9/7||[[22edo|22]]||7/6, 6/5, 5/4, 9/7
 |-
-|5||[[26edo|26]]||7/6, 6/5, [[16/13]], [[14/11]], [[13/10]]
+|5||[[26edo|26]]||7/6, 6/5, [[16/13]], [[14/11]], [[13/10]]||[[31edo|31]]||7/6, 6/5, 5/4, [[11/9]], 14/11
 |-
-|6||[[29edo|29]]||[[15/13]], [[13/11]], 6/5, 16/13, 14/11, 13/10
+|6||[[29edo|29]]||[[15/13]], [[13/11]], 6/5, 16/13, 14/11, 13/10||(41)||(~)
 |-
-|7||(41)||(~)
+|7||(41)||(~)||(58)||(~)
 |-
-|8||(41)||(~)
+|8||(41)||(~)||(58)||(~)
 |-
-|9||[[41edo|41]]||15/13, 7/6, 13/11, 6/5, [[11/9]], 5/4, 14/11, 9/7, 13/10
+|9||[[41edo|41]]||15/13, 7/6, 13/11, 6/5, 11/9, 5/4, 14/11, 9/7, 13/10||(58)||(~)
 |-
+|10||[[58edo|58]]||15/13, 7/6, 13/11, 6/5,  [[17/14]], 11/9, 5/4, 14/11, 9/7, 13/10||(72)||(~)
+|-
+|11||[[72edo|72]]||15/13, 7/6, [[20/17]], 6/5, 17/14, 11/9, 16/13, 5/4, 14/11, 9/7, [[22/17]]||(80)||(~)
+|-
+|12||(80)||(~)||(94)||(~)
+|-
+|13||[[80edo|80]]||[[22/19]], 7/6, 20/17, [[19/16]], 6/5, 17/14, 11/9, 16/13, 5/4, [[24/19]], 14/11, 9/7, 22/17||(94)||(~)
+|-
+|14||(94)||(~)
+|-
+|15||(94)||(~)
+|-
+|16||[[94edo|94]]||15/13, 22/19, 7/6, 20/17, 19/16, 6/5, [[23/19]], 11/9, 16/13, 26/21, 5/4, [[19/15]], [[23/18]], 9/7, 22/17, [[30/23]]
 |}
 This list could be used to get the minimal edos to add more flavours (of thirds).