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Dummy index

Joined 12 October 2021
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Hello. I'm a engineer and weekend mathematician, not for music.
{{interwiki
| en = User:Dummy index
| ja = User:Dummy index
}}
Hello. I'm a engineer and weekend mathematician.


==List of subpages==
== List of subpages ==


{{Special:Prefixindex|prefix=User:Dummy_index/|hideredirects=1|stripprefix=1}}
{{Special:Prefixindex|prefix=User:Dummy_index/|hideredirects=1|stripprefix=1}}


==Memo==
== Memo ==
{| class="wikitable"
|+ Partialpyths
|-
! basis including !! examples !! remarks
|-
| 2.9 || [[Subgroup temperaments #2.9.5.7 subgroup]] ||
|-
| 4.3 || [[Subgroup temperaments #4.3.5 subgroup]],<br />not meanquad (p=4/1, g=4/3 or 3/1) -> named tetrameantone,<br />[https://x31eq.com/pyscript/rt.html?ets=q87_q111&limit=4_3_5_7 "mistyquad"], [https://x31eq.com/pyscript/rt.html?ets=q111_q144&limit=4_3_5_7 "mirquad"] ||
|-
| 4.6 = 4.3/2 = 6.3/2<br /> = 6.9 = 3/2.9 || [[meanquad]] (p=4/1, g=3/2), [https://x31eq.com/pyscript/rt.html?ets=q99_q144&limit=4_6_5_7 "ennealimmalquad"] || plain weave
|-
| 4.9 || [[Subgroup temperaments #Meansquared]] || 4.9.25 meansquared is [[Sane and insane temperaments|insane]]
|-
| 4/3.9 = 12.9 = 16.12 || [[39ed9]] ||
|-
| 4.9/2 = 4.18 || [https://x31eq.com/pyscript/rt.html?ets=q25_q12&limit=4_18_5_7 "israquad"] ||
|-
| 4/3.9/2 = 8.6 = 6.27 ||  || twill weave
|-
| 12.18 = 12.3/2 = 8.3/2<br /> = 18.3/2 = 27.3/2 = 8.12 || [https://x31eq.com/pyscript/rt.html?ets=q31_q26&limit=8_12_5_7 "septimal meanocto"] || twill weave
|-
| 12.9/2 = 8/3.9/2 = 8/3.12<br /> = 9/2.54 = 9/2.243<br /> = 8/3.32 = 12.32 ||  || satin weave
|-
| 4/3.18 = 4/3.27/2 = 18.27/2<br /> = 4/3.24 = 4/3.32 = 24.32 ||  || satin weave
|-
| 8.9 = 72.9 = 72.6<sup>6</sup><br /> = 9/8.9 = 9/8.(3/2)<sup>6</sup> || [[Subgroup temperaments #Sixscared]], [https://x31eq.com/pyscript/rt.html?ets=q19_q18&limit=8_9_10_14 "israocto"] ||
|}
 
{| class="wikitable"
|9/7||5/4|| 11/9||6/5||13/11||7/6||15/13||8/7
|-
|13/10||14/11||16/13||17/14||19/16||20/17||22/19||23/20
|-
|17/13||19/15||21/17||23/19||25/21||27/23
|-
| colspan="2" |<small>21/16 22/17 24/19</small>|| colspan="2" |26/21 27/22 || colspan="2" |32/27 33/28
|-
| colspan="2" |<small>32/25 33/26 34/27</small>|| colspan="2" |39/32 40/33
|}
 
9-odd-limit diamond (not care of beginning at 1)
{|
|
|
|
|
|9/5
|
|
|
|
|-
|
|
|
|8/5
|
|<small>3/2</small>
|
|
|
|-
|
|
|7/5
|
|4/3
|
|9/7
|
|
|-
|
|6/5
|
|7/6
|
| 8/7
|
|9/8
|
|-
|5/5
|
|3/3
|
| 7/7
|
|1/1
|
|9/9
|-
|
|5/3
|
|12/7
|
|7/4
|
|16/9
|
|-
|
|
|10/7
|
|3/2
|
|14/9
|
|
|-
|
|
|
|5/4
|
|<small>4/3</small>
|
|
|
|-
|
|
|
|
|10/9
|
|
|
|
|}
 
1.3.9.11.17 diamond, for 24edo (not cover 1\24, 5\24, 6\24, 8\24, ...)
{|
|
|
|
|
|18/11
|
|
|
|
|-
|
|
|
|17/11
|
|<small>3/2</small>
|
|
|
|-
|
|
|16/11
|
|17/12
|
|9/8
|
|
|-
|
|12/11
|
|4/3
|
|17/16
|
|18/17
|
|-
|11/11
|
|3/3
|
|1/1
|
|17/17
|
|9/9
|-
|
|11/6
|
|3/2
|
|32/17
|
|17/9
|
|-
|
|
|11/8
|
|24/17
|
|16/9
|
|
|-
|
|
|
|22/17
|
|<small>4/3</small>
|
|
|
|-
|
|
|
|
|11/9
|
|
|
|
|}


"(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. but... around 698 cents I can hardly any contribute."
tritave 1.2.4.5.7 diamond
{|
|
|
|
|
|7/3
|
|
|
|
|-
|
|
|
|2/1
|
|7/4
|
|
|
|-
|
|
|5/3
|
|<small>3/2</small>
|
|7/5
|
|
|-
|
|4/3
|
|5/4
|
|6/5
|
|7/6
|
|-
|1/1
|
|4/4
|
|5/5
|
|2/2
|
|7/7
|-
|
|9/4
|
|12/5
|
|5/2
|
|18/7
|
|-
|
|
|9/5
|
|<small>2/1</small>
|
|15/7
|
|
|-
|
|
|
|3/2
|
|12/7
|
|
|
|-
|
|
|
|
|9/7
|
|
|
|
|}


"[[Color notation]], parhaps trizo ≈ yo? Hmm, Marvel*Sensamagic=[[10976/10935]]=(32/15)/(9/7)^3. Straight path to g2 16/15, if 9/7 were in the position of 8/7."
~~ hoge ~~
 
*[https://sintel.pythonanywhere.com/result?subgroup=3.7.31.127&reduce=on&weights=weil&target=&edos=3799%261324%268&submit_edo=submit&commas=] Mersenne prime basis


{| class="wikitable"
{| class="wikitable"
| 4/3 || 9/7 || 5/4 || 11/9 || 6/5 || 13/11 || 7/6 || 15/13
|+Caption text
|-
!Subgroup!!Chord<br>(w/o implicit eqave)
!Condition
!Comma!!Temperament
|-
|2.3||1:2:3:4
|3/2~4/3
|[[9/8|S3]]||2et
|-
|4.3.5||1:3:4:5
|4/3~5/4
|[[16/15|S4]]||tetrafather
|-
|2.3.5||
|(extension)
| ||father
|-
|4.6.5
|1:4:5:6
|5/4~6/5
|[[25/24|S5]]
|dicotquad
|-
|8.9.7
|1:7:8:9
|8/7~9/8
|[[64/63|S8]]
|sixscared
|-
|8.9.10
|1:8:9:10
|9/8~10/9
|[[81/80|S9]]
|israocto
|-
|
|
|
|
|
|-
|2.3
|1:2:3:4
|(2/1)/(3/2)~(3/2)/(4/3)
|[[32/27|S2/S3]]
|3et
|-
|2.3.5
|2:3:4:5
|(3/2)/(4/3)~(4/3)/(5/4)
|[[135/128|S3/S4]]
|mavila
|-
|2.3.5
|3:4:5:6
|(4/3)/(5/4)~(5/4)/(6/5)
|[[128/125|S4/S5]]
|augmented
|-
|3/2.5/4.7/4
|4:5:6:7
|(5/4)/(6/5)~(6/5)/(7/6)
|[[875/864|S5/S6]]
|
|-
|4.6.5.7
|
|(higher-rank expansion)
|
|supermagicquad
|-
|-
| 13/10 || 14/11 || 16/13 || 17/14 || 19/16 || 20/17 || 22/19 || 23/20
|10/7.20/11.20/17
|[[11:14:17:20]]
|(14/11)/(17/14)~(17/14)/(20/17)
|54880/54043
|
|-
|-
| 17/13 || 19/15 || 21/17 || 23/19 || 25/21 || 27/23
|4.14/5.11/5.17/5
|
| + 7''p''~4/1
| + ***
|
|-
|-
| 21/16 || 22/17 || 26/21 || 27/22 || 32/27 || 33/28 || 38/33
|2.7/5.11/5.17/5
|
| (extension, 7''p''~2/1)
|  
|non-over-1 greenwood
|}
|}
* 360edz 5ed12/11 10ed25/21 15ed13/10 36ed15/8 59ed14/5 69ed10/3 84ed13/3 95ed21/4 105ed25/4 278ed128
* I don't remember how I found it: 43-limit 1820105/1820104
* some cubismas: 61-limit 103823/103822 67-limit 50653/50652 300763/300762 79-limit 493039/493038
temperaments of [[7L 2s (3/1-equivalent)]]
* hyposoft:
** g = ~13/7, 2g = ~(8/7)*3, 6g = ~(3/2)*27
** 1029/1024, [[lemba]]
* hypohard:
** g = ~13/7, 2g = ~(15/13)*3, 4g = ~(4/3)*9
** b16&b23, [https://x31eq.com/pyscript/rt.html?ets=b16%26b23&limit=3.4.5.7.13 3.4.5.7.13], 3.5.7->enfactored canopus, [https://x31eq.com/pyscript/rt.html?ets=b16%26b23&limit=3.5.7.13 3.5.7.13], [https://x31eq.com/pyscript/rt.html?ets=b16%26b46cd&limit=2.3.5.7 2.3.5.7]


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