User:Fitzgerald Lee/Edo Thirds: Difference between revisions

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Created page with "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"|First edo!!rowspan="1"|Thirds!!rowspan="1"|Second edo!!rowspan="1"|Thirds |- |0||1||None||2||None |- |1||3||5/4||4||6/5 |- |2||5||7/6, 9/7||8||6/5, 5/4 |-..."
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First and second [[EDO|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):
First and second [[EDO|edos]] to have N number of thirds consistent in its [[odd limit]] (range is [[23/20]] to [[30/23]], closest JI interpretation that is consistent in the edo’s odd limit is shown):
{|class="wikitable"
{|class="wikitable"
!rowspan="1"|Number of thirds!!rowspan="1"|First edo!!rowspan="1"|Thirds!!rowspan="1"|Second edo!!rowspan="1"|Thirds
!rowspan="1"|Number of thirds!!rowspan="1"|First edo!!rowspan="1"|Thirds!!rowspan="1"|Second edo!!rowspan="1"|Thirds
Line 7: Line 7:
|1||[[3edo|3]]||[[5/4]]||[[4edo|4]]||[[6/5]]
|1||[[3edo|3]]||[[5/4]]||[[4edo|4]]||[[6/5]]
|-
|-
|2||[[5edo|5]]||[[7/6]], [[9/7]]||[[8edo|8]]||6/5, 5/4
|2||[[5edo|5]]||[[7/6]], [[9/7]]||[[6edo|6]]||7/6, 5/4
|-
|-
|3||[[15edo|15]]||7/6, 6/5, 5/4||[[18edo|18]]||7/6, 6/5, 5/4
|3||[[15edo|15]]||7/6, 6/5, 5/4||[[18edo|18]]||7/6, 6/5, 5/4
Line 13: Line 13:
|4||[[19edo|19]]||7/6, 6/5, 5/4, 9/7||[[22edo|22]]||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]]||[[31edo|31]]||7/6, 6/5, 5/4, [[11/9]], 14/11
|5||[[26edo|26]]||7/6, 6/5, [[16/13]], [[14/11]], [[13/10]]||(29)||(~)
|-
|-
|6||[[29edo|29]]||[[15/13]], [[13/11]], 6/5, 16/13, 14/11, 13/10||(41)||(~)
|6||[[29edo|29]]||[[15/13]], [[13/11]], 6/5, 16/13, 14/11, 13/10||(41)||(~)
|-
|-
|7||(41)||(~)||(58)||(~)
|7||(41)||(~)||(46)||(~)
|-
|-
|8||(41)||(~)||(58)||(~)
|8||(41)||(~)||[[46edo|46]]||7/6, 13/11, 6/5, [[11/9]], 16/13, 5/4, 14/11, 9/7
|-
|-
|9||[[41edo|41]]||15/13, 7/6, 13/11, 6/5, 11/9, 5/4, 14/11, 9/7, 13/10||(58)||(~)
|9||[[41edo|41]]||15/13, 7/6, 13/11, 6/5, 11/9, 5/4, 14/11, 9/7, 13/10||(58)||(~)
Line 37: Line 37:
|16||[[94edo|94]]||[[23/20]], 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]]||||
|16||[[94edo|94]]||[[23/20]], 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).
{|class="wikitable"
{|class="wikitable"
!rowspan="1"|Edo!!rowspan="1"|[[23/20]]!!rowspan="1"|[[15/13]]!!rowspan="1"|[[22/19]]!!rowspan="1"|[[7/6]]!!rowspan="1"|[[20/17]]!!rowspan="1"|[[13/11]]!!rowspan="1"|[[19/16]]!!rowspan="1"|[[6/5]]!!rowspan="1"|[[23/19]]!!rowspan="1"|[[17/14]]!!rowspan="1"|[[28/23]]!!rowspan="1"|[[11/9]]!!rowspan="1"|[[16/13]]!!rowspan="1"|[[21/17]]!!rowspan="1"|[[26/21]]!!rowspan="1"|[[5/4]]!!rowspan="1"|[[24/19]]!!rowspan="1"|[[19/15]]!!rowspan="1"|[[14/11]]!!rowspan="1"|[[23/18]]!!rowspan="1"|[[9/7]]!!rowspan="1"|[[22/17]]!!rowspan="1"|[[13/10]]!!rowspan="1"|[[30/23]]
!rowspan="1"|Edo!!rowspan="1"|[[7/6]]!!rowspan="1"|[[6/5]]!!rowspan="1"|[[11/9]]!!rowspan="1"|[[5/4]]!!rowspan="1"|[[14/11]]!!rowspan="1"|[[9/7]]
|-
|[[1edo|1]]||||||||||||
|-
|[[2edo|2]]||||||||||||
|-
|[[3edo|3]]||||1|| ||1|| ||
|-
|[[4edo|4]]||1||1|| ||1|| ||
|-
|[[5edo|5]]||1||1|| ||2|| ||2
|-
|[[6edo|6]]||1||2|| ||2|| ||
|-
|[[7edo|7]]||||2|| ||2|| ||
|-
|[[8edo|8]]||||2|| ||3|| ||
|-
|[[9edo|9]]||||2|| ||3|| ||
|-
|[[10edo|10]]||||3|| ||3|| ||
|-
|[[11edo|11]]||||||||||||
|-
|[[12edo|12]]||3||3|| ||4|| ||4
|-
|[[13edo|13]]||||||||||||
|-
|[[14edo|14]]||||||||||||
|-
|[[15edo|15]]||3||4|| ||5|| ||
|-
|[[16edo|16]]||4||4|| ||5|| ||
|-
|[[17edo|17]]||||||||||||
|-
|[[18edo|18]]||4||5|| ||6|| ||
|-
|[[19edo|19]]||4||5|| ||6|| ||7
|-
|[[20edo|20]]||||||||||||
|-
|[[21edo|21]]||||||||||||
|-
|[[22edo|22]]||5||6||6||7||8||8
|-
|[[23edo|23]]||||6|| ||7|| ||
|-
|[[24edo|24]]||||6|| ||8|| ||
|-
|[[25edo|25]]||||7|| ||8|| ||
|}
{|class="wikitable"
!rowspan="1"|Edo!!rowspan="1"|[[15/13]]!!rowspan="1"|[[7/6]]!!rowspan="1"|[[13/11]]!!rowspan="1"|[[6/5]]!!rowspan="1"|[[11/9]]!!rowspan="1"|[[16/13]]!!rowspan="1"|[[5/4]]!!rowspan="1"|[[14/11]]!!rowspan="1"|[[9/7]]!!rowspan="1"|[[13/10]]
|-
|[[26edo|26]]||||6||6||7||8||8||8||9||9||10
|-
|[[27edo|27]]||||6|| ||7|| ||||9|| ||10||10
|-
|[[28edo|28]]||||||||7|| ||||9|| ||||
|-
|[[29edo|29]]||6||6||7||8||8||9||9||10||11||11
|-
|[[30edo|30]]||||||||8|| ||||10|| ||||
|-
|[[31edo|31]]||||7|| ||8||9|| ||10||11||11||
|-
|[[32edo|32]]||||||||||||||||||||
|-
|[[33edo|33]]||||||||||||||||||||
|-
|[[34edo|34]]||||||||9|| ||||11|| ||||
|-
|[[35edo|35]]||||8|| ||9|| ||||11|| ||||
|-
|[[36edo|36]]||||8|| ||9|| ||||12|| ||||
|-
|[[37edo|37]]||||8|| ||10|| ||||12|| ||||
|-
|[[38edo|38]]||||||||10|| ||||12|| ||||
|-
|[[39edo|39]]||||||||10|| ||||13|| ||||
|-
|[[40edo|40]]||||||||||||||||||||
|-
|[[41edo|41]]||8||9||10||11||12||12||13||14||15||16
|-
|[[42edo|42]]||||9|| ||11|| ||||14|| ||||
|-
|[[43edo|43]]||||10|| ||11|| ||||14|| ||||
|-
|[[44edo|44]]||||||||12|| ||||14|| ||||
|-
|[[45edo|45]]||||10|| ||12|| ||||14|| ||||
|-
|[[46edo|46]]||||10||11||12||13||14||15||16||17||17
|-
|[[47edo|47]]||||||||12|| ||||15|| ||||
|-
|[[48edo|48]]||||||||13|| ||||15|| ||||
|-
|[[49edo|49]]||||11|| ||13|| ||||16|| ||||
|-
|[[50edo|50]]||||11|| ||13|| ||||16|| ||18||
|}
{|class="wikitable"
!rowspan="1"|Edo!!rowspan="1"|[[15/13]]!!rowspan="1"|[[7/6]]!!rowspan="1"|[[20/17]]!!rowspan="1"|[[13/11]]!!rowspan="1"|[[6/5]]!!rowspan="1"|[[17/14]]!!rowspan="1"|[[11/9]]!!rowspan="1"|[[16/13]]!!rowspan="1"|[[5/4]]!!rowspan="1"|[[14/11]]!!rowspan="1"|[[9/7]]!!rowspan="1"|[[22/17]]!!rowspan="1"|[[13/10]]
|-
|[[51edo|51]]||||||||||||||||||||||||||
|-
|[[52edo|52]]||||||||||||||||||||||||||
|-
|[[53edo|53]]||||12|| ||||14|| ||||||17|| ||19|| ||
|-
|[[54edo|54]]||||||||||||||||||||||||||
|-
|[[55edo|55]]||||||||||14|| ||||||18|| ||||||
|-
|[[56edo|56]]||||12|| ||||15|| ||||||18|| ||||||
|-
|[[57edo|57]]||||13|| ||||15|| ||||||18|| ||||||
|-
|[[58edo|58]]||12||13||14||14||15||16||17||17||19||20||21||22||22
|-
|[[59edo|59]]||||13|| ||||16|| ||||||19|| ||||||
|-
|-
|[[1edo|1]]||||||||||||||||||||||||||||||||||||||||||||||||
|[[60edo|60]]||||13|| ||||16|| ||||||19|| ||22|| ||
|-
|-
|[[2edo|2]]||||||||||||||||||||||||||||||||||||||||||||||||
|[[61edo|61]]||||||||||16|| ||||||20|| ||||||
|-
|-
|[[3edo|3]]||||||||||||||||1||||||||||||||||1||||||||||||||||
|[[62edo|62]]||||14|| ||||16|| ||||||20|| ||||||
|-
|-
|[[4edo|4]]||||||||1||||||||1||||||||||||||||1||||||||||||||||
|[[63edo|63]]||||14|| ||||17|| ||||||20|| ||||||
|-
|-
|[[5edo|5]]||||||||1||||||||1||||||||||||||||2||||||||||2||||||
|[[64edo|64]]||||||||||||||||||||||||||
|-
|-
|[[8edo|8]]||||||||||||||||2||||||||||||||||3||||||||||||||||
|[[65edo|65]]||||||||||17|| ||||||21|| ||||||
|-
|-
|[[15edo|15]]||||||||3||||||||4||||||||||||||||5||||||||||||||||
|[[66edo|66]]||||||||||||||||||||||||||
|-
|-
|[[18edo|18]]||||||||4||||||||5||||||||||||||||6||||||||||||||||
|[[67edo|67]]||||||||||||||||||||||||||
|-
|-
|[[19edo|19]]||||||||4||||||||5||||||||||||||||6||||||||||7||||||
|[[68edo|68]]||||15|| ||||18|| ||||||22|| ||25|| ||
|-
|-
|[[22edo|22]]||||||||5|| ||||||6|| ||||||6|| ||||||7|| ||||||||8|| ||||
|[[69edo|69]]||||||||||18|| ||||||22|| ||||||
|-
|-
|[[26edo|26]]||||||||6|| ||6|| ||7|| ||||||8||8|| ||||8|| ||||9|| ||9|| ||10||
|[[70edo|70]]||||16|| ||||18|| ||||||23|| ||25|| ||
|-
|-
|[[29edo|29]]||||6|| ||6|| ||7|| ||8|| ||||||8||9|| ||||9|| ||||10|| ||11|| ||11||
|[[71edo|71]]||||||||||19|| ||||||23|| ||||||
|-
|-
|[[31edo|31]]||||||||7|| ||||||8|| ||||||9|| ||||||10|| ||||11|| ||11|| ||||
|[[72edo|72]]||15||16||17||17||19||20||21||22||23||25||26||27||27
|-
|-
|[[41edo|41]]||||8|| ||9|| ||10|| ||11|| ||||||12||12|| ||||13|| ||||14|| ||15|| ||16||
|[[73edo|73]]||||16|| ||||19|| ||||||24|| ||||||
|-
|-
|[[58edo|58]]||||12|| ||13||14||14|| ||15|| ||16|| ||17||17|| ||||19|| ||||20|| ||21|| ||22||
|[[74edo|74]]||||||||||19|| ||||||24|| ||||||
|-
|-
|[[72edo|72]]||||15|| ||16||17||17|| ||19|| ||20|| ||21||22|| ||||23|| ||||25|| ||26|| ||27||
|[[75edo|75]]||||||||||20|| ||||||24|| ||||||
|}
{|class="wikitable"
!rowspan="1"|Edo!!rowspan="1"|[[23/20]]!!rowspan="1"|[[15/13]]!!rowspan="1"|[[22/19]]!!rowspan="1"|[[7/6]]!!rowspan="1"|[[20/17]]!!rowspan="1"|[[13/11]]!!rowspan="1"|[[19/16]]!!rowspan="1"|[[6/5]]!!rowspan="1"|[[23/19]]!!rowspan="1"|[[17/14]]!!rowspan="1"|[[28/23]]!!rowspan="1"|[[11/9]]!!rowspan="1"|[[16/13]]!!rowspan="1"|[[21/17]]!!rowspan="1"|[[26/21]]!!rowspan="1"|[[5/4]]!!rowspan="1"|[[24/19]]!!rowspan="1"|[[19/15]]!!rowspan="1"|[[14/11]]!!rowspan="1"|[[23/18]]!!rowspan="1"|[[9/7]]!!rowspan="1"|[[22/17]]!!rowspan="1"|[[13/10]]!!rowspan="1"|[[30/23]]
|-
|-
|[[80edo|80]]||||17||17||18||19||19||20||21|| ||22|| ||23||24|| ||||26||27||27||28|| ||29||30||30||
|[[80edo|80]]||||17||17||18||19||19||20||21|| ||22|| ||23||24|| ||||26||27||27||28|| ||29||30||30||
|-
|-
|[[94edo|94]]||19||19||20||21||22||23||23||25||26||26||27||27||28||29||29||30||32||32||33||33||34||35||36||36
|[[94edo|94]]||19||19||20||21||22||23||23||25||26||26||27||27||28||29||29||30||32||32||33||33||34||35||36||36
|-
|}
|}

Latest revision as of 02:14, 13 November 2025

First and second edos to have N number of thirds consistent in its odd limit (range is 23/20 to 30/23, closest JI interpretation that is consistent in the edo’s odd limit is shown):

Number of thirds First edo Thirds Second edo Thirds
0 1 None 2 None
1 3 5/4 4 6/5
2 5 7/6, 9/7 6 7/6, 5/4
3 15 7/6, 6/5, 5/4 18 7/6, 6/5, 5/4
4 19 7/6, 6/5, 5/4, 9/7 22 7/6, 6/5, 5/4, 9/7
5 26 7/6, 6/5, 16/13, 14/11, 13/10 (29) (~)
6 29 15/13, 13/11, 6/5, 16/13, 14/11, 13/10 (41) (~)
7 (41) (~) (46) (~)
8 (41) (~) 46 7/6, 13/11, 6/5, 11/9, 16/13, 5/4, 14/11, 9/7
9 41 15/13, 7/6, 13/11, 6/5, 11/9, 5/4, 14/11, 9/7, 13/10 (58) (~)
10 58 15/13, 7/6, 13/11, 6/5, 17/14, 11/9, 5/4, 14/11, 9/7, 13/10 (72) (~)
11 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 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 94 23/20, 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
Edo 7/6 6/5 11/9 5/4 14/11 9/7
1
2
3 1 1
4 1 1 1
5 1 1 2 2
6 1 2 2
7 2 2
8 2 3
9 2 3
10 3 3
11
12 3 3 4 4
13
14
15 3 4 5
16 4 4 5
17
18 4 5 6
19 4 5 6 7
20
21
22 5 6 6 7 8 8
23 6 7
24 6 8
25 7 8
Edo 15/13 7/6 13/11 6/5 11/9 16/13 5/4 14/11 9/7 13/10
26 6 6 7 8 8 8 9 9 10
27 6 7 9 10 10
28 7 9
29 6 6 7 8 8 9 9 10 11 11
30 8 10
31 7 8 9 10 11 11
32
33
34 9 11
35 8 9 11
36 8 9 12
37 8 10 12
38 10 12
39 10 13
40
41 8 9 10 11 12 12 13 14 15 16
42 9 11 14
43 10 11 14
44 12 14
45 10 12 14
46 10 11 12 13 14 15 16 17 17
47 12 15
48 13 15
49 11 13 16
50 11 13 16 18
Edo 15/13 7/6 20/17 13/11 6/5 17/14 11/9 16/13 5/4 14/11 9/7 22/17 13/10
51
52
53 12 14 17 19
54
55 14 18
56 12 15 18
57 13 15 18
58 12 13 14 14 15 16 17 17 19 20 21 22 22
59 13 16 19
60 13 16 19 22
61 16 20
62 14 16 20
63 14 17 20
64
65 17 21
66
67
68 15 18 22 25
69 18 22
70 16 18 23 25
71 19 23
72 15 16 17 17 19 20 21 22 23 25 26 27 27
73 16 19 24
74 19 24
75 20 24
Edo 23/20 15/13 22/19 7/6 20/17 13/11 19/16 6/5 23/19 17/14 28/23 11/9 16/13 21/17 26/21 5/4 24/19 19/15 14/11 23/18 9/7 22/17 13/10 30/23
80 17 17 18 19 19 20 21 22 23 24 26 27 27 28 29 30 30
94 19 19 20 21 22 23 23 25 26 26 27 27 28 29 29 30 32 32 33 33 34 35 36 36
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