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Diaschismic–gothmic equivalence continuum: Difference between revisions

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Swap n and k following the organization of other continua, and rework the intro to better reflect this change. Reserve "m" for 1/n + 1/m = 1 and use "l" for the other relation
The mixed table looked pretty awful as it mixed temps of utterly different complexity levels. I'm making a separate table for fractional-numbered temps.
Line 35: Line 35:
| [[20000/19683]]
| [[20000/19683]]
| {{monzo| 5 -9 4 }}
| {{monzo| 5 -9 4 }}
|-
| 3/2
| 5/2
| [[Fifive]]
| 9765625/9565938
| {{monzo| -1 -14 10 }}
|-
|-
| 1
| 1
Line 47: Line 41:
| [[15625/15552]]
| [[15625/15552]]
| {{monzo| -6 -5 6 }}
| {{monzo| -6 -5 6 }}
|-
| 2/3
| 10/3
| [[Gammic]]
| (28 digits)
| {{monzo| -29 -11 20 }}
|-
| 3/5
| 17/5
| [[Chlorine]]
| (48 digits)
| {{monzo| -52 -17 34 }}
|-
| 1/2
| 7/2
| [[Vishnu]]
| [[6115295232/6103515625]]
| {{monzo| 23 6 -14 }}
|-
| 1/3
| 11/3
| [[Majvam]]
| (32 digits)
| {{monzo| 40 7 -22 }}
|-
|-
| 0
| 0
Line 77: Line 47:
| [[393216/390625]]
| [[393216/390625]]
| {{monzo| 17 1 -8 }}
| {{monzo| 17 1 -8 }}
|-
| -1/2
| 9/2
| [https://sintel.pythonanywhere.com/result?subgroup=2.3.5.13.17&reduce=on&weights=tenney&target=&edos=&commas=35184372088832%2F34332275390625%2C+289%2F288%2C+2197%2F2187&submit_comma=submit 34&142]
| (28 digits)
| {{monzo| 45 -2 -18 }}
|-
|-
| -1
| -1
Line 146: Line 110:
| [[1638400/1594323]]
| [[1638400/1594323]]
| {{monzo| 16 -13 2 }}
| {{monzo| 16 -13 2 }}
|}
{| class="wikitable"
|+ Temperaments with fractional ''m'' and ''n''
|-
! ''n'' !! ''m'' !! Temperament !! Comma
|-
| 5/2 = 2.5 || 5/3 = 1.{{overline|6}} || [[Fifive]] || {{monzo| -1 -14 10 }}
|-
| 13/4 = 3.25 || 13/9 = 1.{{overline|4}} || [[Quatracot]] || {{monzo| -33 -16 26 }}
|-
| 10/3 = 3.{{overline|3}} || 10/7 = 1.{{overline|428571}} || [[Gammic]] || {{monzo| -29 -11 20 }}
|-
| 17/5 = 3.{{overline|4}} || 17/12 = 1.41{{overline|6}} || [[Chlorine]] || {{monzo| -52 -17 34 }}
|-
| 7/2 = 3.5 || 7/5 = 1.4 || [[Vishnu]] || {{monzo| 23 6 -14 }}
|-
| 11/3 = 3.{{overline|6}} || 11/8 = 1.375 || [[Majvam]] || {{monzo| 40 7 -22 }}
|-
| 9/2 = 4.5 || 9/7 = 1.{{overline|285714}} || 34 & 142 || {{monzo| 45 -2 -18 }}
|}
|}


Line 214: Line 198:
|+ Temperaments with fractional ''k'' and ''l''
|+ Temperaments with fractional ''k'' and ''l''
|-
|-
! Temperament !! ''l'' !! ''k''
! ''l'' !! ''k'' !! Temperament !! Comma
|-
|-
| [[Majvam]] || 1/2 = 0.5 || 1/3 = 0.{{overline|3}}
| 1/2 = 0.5 || 1/3 = 0.{{overline|3}} || [[Majvam]] || {{monzo| 40 7 -22 }}
|-
|-
| [[Chlorine]] || 3/2 = 1.5 || 3/5 = 0.6
| 3/2 = 1.5 || 3/5 = 0.6 || [[Chlorine]] || {{monzo| -52 -17 34 }}
|-
|-
| [https://sintel.pythonanywhere.com/result?subgroup=2.3.5.13.17&reduce=on&weights=tenney&target=&edos=&commas=35184372088832%2F34332275390625%2C+289%2F288%2C+2197%2F2187&submit_comma=submit 34&142]
| -1/3 = -0.{{overline|3}} || -1/2 = -0.5 || 34 & 142 || {{monzo| 45 -2 -18 }}
| -1/3 = -0.{{overline|3}}
| -1/2 = -0.5
|}
|}


[[Category:34edo]]
[[Category:34edo]]
[[Category:Equivalence continua]]
[[Category:Equivalence continua]]
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