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{{interwiki
| en = User:Dummy index
| ja = User:Dummy index
}}
Hello. I'm a engineer and weekend mathematician.
== 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"] ||
|}


===12ET-complementary comma pairs (e.g. syntonic-schismatic relation)===
{| 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
|}


{| class="wikitable"
9-odd-limit diamond (not care of beginning at 1)
! M3 or d4
{|
! A: 4*P5=M3+2*P8
|
! B: 8*P5+d4=5*P8
|
! Remarks
|
|
|9/5
|
|
|
|
|-
|-
! 32/27
|
| [[2187/2048]]={{monzo| -11 7 }}
|
| [[256/243]]={{monzo| 8 -5 }}
|
| A/B={{monzo| -19 12 }}, A: (7edo), B: (5edo)
|8/5
|
|<small>3/2</small>
|
|
|
|-
|-
! 6/5
|
| [[135/128]]={{monzo| -7 3 1 }}
|
| [[20480/19683|(64/63)^2*(245/243)]]={{monzo| 12 -9 1 }}
|7/5
| A/B={{monzo| -19 12 }}, A: [[Mavila]], B: [[Superpyth]]
|
|4/3
|
|9/7
|
|
|-
|-
! 11/9
|
| [[729/704]]={{monzo| -6 6 0 0 -1 }}
|6/5
| [[8192/8019|(64/63)^2/(99/98)]]={{monzo| 13 -6 0 0 -1 }}
|
| A/B={{monzo| -19 12 }}, A: [[Meantone family #Meanenneadecal|Meanenneadecal]]?, B: [[Archytas clan #Supra|Supra]]
|7/6
|
| 8/7
|
|9/8
|
|-
|-
! 8192/6561
|5/5
| [[531441/524288]]={{monzo| -19 12 }}
|
| 1/1
|3/3
| A: (12edo)
|
| 7/7
|
|1/1
|
|9/9
|-
|-
! 5/4
|
| [[81/80]]={{monzo| -4 4 -1 }}
|5/3
| [[32805/32768]]={{monzo| -15 8 1 }}
|
| A*B={{monzo| -19 12 }}, A: [[Meantone]], B: [[Schismatic]]
|12/7
|
|7/4
|
|16/9
|
|-
|-
! 81/64
|
| 1/1
|
| [[531441/524288]]={{monzo| -19 12 }}
|10/7
| B: (12edo)
|
|3/2
|
|14/9
|
|
|-
|-
! 9/7
|
| [[64/63]]={{monzo| 6 -2 0 -1 }}
|
| [[59049/57344]]={{monzo| -13 10 0 -1 }}
|
| B/A={{monzo| -19 12 }}, A: [[Archytas clan]], B: [[Septimal meantone]]
|5/4
|
|<small>4/3</small>
|
|
|
|-
|-
! 4/3
|
| [[256/243]]={{monzo| 8 -5 }}
|
| [[2187/2048]]={{monzo| -11 7 }}
|
| B/A={{monzo| -19 12 }}, A: (5edo), B: (7edo)
|
|10/9
|
|
|
|
|}
|}


Q: Mavila must have the fifth flatter than 7edo's, why be placed between 7edo and 5edo?
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
|
|
|
|
|}


A: I wrote the 32/27 in this table as a monzo-ish value. 32/27 constructed of P5 & P8 will much sharper when flatter P5 situation.
tritave 1.2.4.5.7 diamond
 
{|
{| class="wikitable"
|
! (3/2)^(1/2)
|
| [[2187/2048]]={{monzo| -11 7 }}
|
| [[17-comma]]={{monzo| 27 -17 }}
|
| A/B={{monzo| -38 24 }}, A: (7edo), B: (17edo)
|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)^(4/7)
|
| [[531441/524288]]={{monzo| -19 12 }}
|
| [[531441/524288]]={{monzo| -19 12 }}
|
| A*B={{monzo| -38 24 }}, A: (12edo), B: (12edo)
|3/2
|
|12/7
|
|
|
|-
|-
! (3/2)^(2/3)
|
| [[256/243]]={{monzo| 8 -5 }}
|
| {{monzo| -41 26 }}
|
| B/A={{monzo| -49 31 }}, A: (5edo), B: (26edo)
|
|9/7
|
|
|
|
|}
|}


===temperaments with septimal tritones===
~~ 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"
! [[Fifthspan]]
|+Caption text
! -8
|-
! -6
!Subgroup!!Chord<br>(w/o implicit eqave)
! 4
!Condition
! 6
!Comma!!Temperament
! Remarks
|-
|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
|-
|-
! [[Septimal meantone]]
|3/2.5/4.7/4
| 32/25
|4:5:6:7
| 10/7
|(5/4)/(6/5)~(6/5)/(7/6)
| 5/4
|[[875/864|S5/S6]]
| 7/5
|
| Good 4:5:7 in 10 fifthspan<sub>p-p</sub>
|-
|-
! [[Meantone family#Dominant|Dominant]]
|4.6.5.7
| 32/25
|
| 7/5
|(higher-rank expansion)
| 5/4
|
| 10/7
|supermagicquad
| inaccurate
|-
|-
! [[Schismatic family#Schism|Schism]]
|10/7.20/11.20/17
| 5/4
|[[11:14:17:20]]
| 10/7
|(14/11)/(17/14)~(17/14)/(20/17)
| 80/63
|54880/54043
| 7/5
|
| inaccurate
|-
|-
! [[Garibaldi temperament|Garibaldi]]
|4.14/5.11/5.17/5
| 5/4
|
| 7/5
| + 7''p''~4/1
| 80/63
| + ***
| 10/7
|
| Good 4:5:6:7 in 15 fifthspan<sub>p-p</sub><br>Good 4:6 & 5:7 in 6 fifthspan<sub>p-p</sub>
|-
|-
! [[Hemififths]]
|2.7/5.11/5.17/5
|
| (extension, 7''p''~2/1)
|  
|  
| 7/5
|non-over-1 greenwood
|
| 10/7
| 5/4 is at 12.5 fifthspan
|}
|}
* 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]
[[Category:User en-1]]
[[Category:User ja-N]]

Latest revision as of 15:05, 13 September 2025

Hello. I'm a engineer and weekend mathematician.

List of subpages

Memo

Partialpyths
basis including examples remarks
2.9 Subgroup temperaments #2.9.5.7 subgroup
4.3 Subgroup temperaments #4.3.5 subgroup,
not meanquad (p=4/1, g=4/3 or 3/1) -> named tetrameantone,
"mistyquad", "mirquad"
4.6 = 4.3/2 = 6.3/2
= 6.9 = 3/2.9		 meanquad (p=4/1, g=3/2), "ennealimmalquad" plain weave
4.9 Subgroup temperaments #Meansquared 4.9.25 meansquared is insane
4/3.9 = 12.9 = 16.12 39ed9
4.9/2 = 4.18 "israquad"
4/3.9/2 = 8.6 = 6.27 twill weave
12.18 = 12.3/2 = 8.3/2
= 18.3/2 = 27.3/2 = 8.12		 "septimal meanocto" twill weave
12.9/2 = 8/3.9/2 = 8/3.12
= 9/2.54 = 9/2.243
= 8/3.32 = 12.32		 satin weave
4/3.18 = 4/3.27/2 = 18.27/2
= 4/3.24 = 4/3.32 = 24.32		 satin weave
8.9 = 72.9 = 72.66
= 9/8.9 = 9/8.(3/2)6		 Subgroup temperaments #Sixscared, "israocto"
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
21/16 22/17 24/19 26/21 27/22 32/27 33/28
32/25 33/26 34/27 39/32 40/33

9-odd-limit diamond (not care of beginning at 1)

9/5
8/5 3/2
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 4/3
10/9

1.3.9.11.17 diamond, for 24edo (not cover 1\24, 5\24, 6\24, 8\24, ...)

18/11
17/11 3/2
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 4/3
11/9

tritave 1.2.4.5.7 diamond

7/3
2/1 7/4
5/3 3/2 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 2/1 15/7
3/2 12/7
9/7

~~ hoge ~~

  • [1] Mersenne prime basis
Caption text
Subgroup Chord
(w/o implicit eqave) 		Condition Comma Temperament
2.3 1:2:3:4 3/2~4/3 S3 2et
4.3.5 1:3:4:5 4/3~5/4 S4 tetrafather
2.3.5 (extension) father
4.6.5 1:4:5:6 5/4~6/5 S5 dicotquad
8.9.7 1:7:8:9 8/7~9/8 S8 sixscared
8.9.10 1:8:9:10 9/8~10/9 S9 israocto
2.3 1:2:3:4 (2/1)/(3/2)~(3/2)/(4/3) S2/S3 3et
2.3.5 2:3:4:5 (3/2)/(4/3)~(4/3)/(5/4) S3/S4 mavila
2.3.5 3:4:5:6 (4/3)/(5/4)~(5/4)/(6/5) S4/S5 augmented
3/2.5/4.7/4 4:5:6:7 (5/4)/(6/5)~(6/5)/(7/6) S5/S6
4.6.5.7 (higher-rank expansion) supermagicquad
10/7.20/11.20/17 11:14:17:20 (14/11)/(17/14)~(17/14)/(20/17) 54880/54043
4.14/5.11/5.17/5 + 7p~4/1 + ***
2.7/5.11/5.17/5 (extension, 7p~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:
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