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Dummy index

Joined 12 October 2021
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606 edits
No edit summary
Line 79: Line 79:


{| class="wikitable"
{| class="wikitable"
! rowspan="2"|
!  
! colspan="4"|[[Fifthspan]]
! colspan="4"|Ratios
! rowspan="2"|Remarks
! rowspan="2"|Remarks
! rowspan="2"|Mapping development
! rowspan="2"|Mapping development
|-
|-
! [[Fifthspan]]
! -8
! -8
! -6
! -6
Line 240: Line 241:
|  
|  
| [{{val| 1 0 ... }}, {{val| 0 1 no-five -2 -6 }}] -17
| [{{val| 1 0 ... }}, {{val| 0 1 no-five -2 -6 }}] -17
|-
! [[Superpyth]]
| 6/5
| 15/11
| 9/7
| 22/15
|
| [{{val| 1 0 ... }}, {{val| 0 1 9 -2 16 }}] +22
|-
! [[Archytas clan#Ultrapyth|Ultrapyth]]
| 33/28
| 112/81
| 9/7
| 81/56
|
| [{{val| 1 0 ... }}, {{val| 0 1 14 -2 -11 }}] +5-25
|}
|}


Line 245: Line 262:


{| class="wikitable"
{| class="wikitable"
! rowspan="2"|
!  
! rowspan="2"|Generator
! rowspan="2"|Generator
! colspan="2"|Fifth(?)span
! colspan="2"|Ratios
! rowspan="2"|Remarks
! rowspan="2"|Remarks
! rowspan="2"|Mapping
! rowspan="2"|Mapping
|-
|-
! Fifth(?)span
! 1
! 1
! 2
! 2
|-
! [[Pluto]]
| 7/5
| 10/7
| 81/80
|
| [{{val| 1 0 ... }}, {{val| 0 -7 -26 -25 }}]
|-
|-
! [[Tritonic]]
! [[Tritonic]]
Line 267: Line 292:
|  
|  
| [{{val| 1 0 ... }}, {{val| 0 3 12 11 }}]
| [{{val| 1 0 ... }}, {{val| 0 3 12 11 }}]
|-
! [[Maquila]]
| 15/11
| 22/15,35/24
| 77/72
|
| [{{val| 1 0 ... }}, {{val| 0 17 -6 22 10 }}]
|-
|-
! Pelogic
! Pelogic
Line 277: Line 309:
! Septimal mavila
! Septimal mavila
| 3/2
| 3/2
| 3/2,64/45
| 3/2,16/11,22/15,64/45
| 9/8,16/15
| 12/11,11/10,9/8,16/15
|  
|  
| [{{val| 1 0 ... }}, {{val| 0 1 -3 -11 }}]
| [{{val| 1 0 ... }}, {{val| 0 1 -3 -11 -1 }}]
|-
|-
! [[Gravity family|Larry]]
! [[Gravity family|Larry]]
Line 323: Line 355:
|  
|  
| [{{val| 1 0 ... }}, {{val| 0 1 9 -2 }}]
| [{{val| 1 0 ... }}, {{val| 0 1 9 -2 }}]
|-
! [[Hemiseven]]
| 320/243
| 243/160
| 8/7,55/48
|
| [{{val| 1 0 ... }}, {{val| 0 -6 -29 2 21 }}]
|-
|-
! [[Father]]
! [[Father]]
Line 423: Line 462:
| at -5(m2)
| at -5(m2)
| 700.209
| 700.209
| don't know regular temperament with nominal 18/17 at m2, but it will have {{map| 0 1 * * * * 7 }} in the mapping.
| for regular temperament with nominal 18/17 at m2, see [[No-sevens subgroup temperaments#Photia]] for example.
|-
|-
| 17/16
| 17/16
Line 464: Line 503:
| 695.869
| 695.869
| this interpretation is by the [[Syntonic-enneadecal equivalence continuum|Lalayo]].
| this interpretation is by the [[Syntonic-enneadecal equivalence continuum|Lalayo]].
|-
| 256/243
| at -5(m2)
| rowspan="5"|701.955
| rowspan="5"|any 3-limit eigenmonzo results in the pythagorean tuning.
|-
| 1024/729
| at -6(d5)
|-
| 2187/2048
| at +7(A1)
|-
| 8192/6561
| at -8(d4)
|-
| {{monzo| 27 -17 }}
| at -17(dd3)
|-
| 256/243
| at +7(A1)
| 698.604
| flatten 2187/2048 of +7(A1) by {{monzo| -19 12 }}. (-1 pythagorean comma / +7 step)
|-
| 1024/729
| at +6(A4)
| 698.045
| flatten 729/512 of +6(A4) by {{monzo| -19 12 }}. (-1 pythagorean comma / +6 step)
|-
| 2187/2048
| at -5(m2)
| 697.263
| sharpen 256/243 of -5(m2) by {{monzo| -19 12 }}. (+1 pythagorean comma / -5 step)
|-
| 8192/6561
| at +4(M3)
| 696.090
| flatten 81/64 of +4(M3) by {{monzo| -19 12 }}. (-1 pythagorean comma / +4 step)
|-
| {{monzo| 27 -17 }}
| at +7(A1)
| 695.252
| flatten 2187/2048 of +7(A1) by two {{monzo| -19 12 }}. (-2 pythagorean comma / +7 step)
|}
|}


"(14/11)*(13/11) is for [[gentle region]], then what is for meantone? 33/28, thrice, 99/84, flatly approx., 100/85, [[20/17]], (14/11)*(20/17)*(2/3)=[[561/560|560/561]]. Oh, 33/28 is the [[mediant]] of 13/11 and 20/17."
"(14/11)*(13/11) is for [[gentle region]], then what is for meantone? 33/28, thrice, 99/84, flatly approx., 100/85, [[20/17]], (14/11)*(20/17)*(2/3)=[[561/560|560/561]]. Oh, 33/28 is the [[mediant]] of 13/11 and 20/17."
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