User:Overthink/Sandbox: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Overthink (talk | contribs)
autopatrolled
2,730 edits
subst?
Overthink (talk | contribs)
autopatrolled
2,730 edits
 
(37 intermediate revisions by the same user not shown)
Line 1: Line 1:
{{Infobox regtemp
{{Infobox interval|Monzo= -702 400 0 -99 100|debug=1}}
| Title = Marvel
The difference between 100 [[896/891]]'s and [[7/4]]
| Subgroups = 2.3.5.7, 2.3.5.7.11
| Comma basis = [[225/224]] (7-limit);<br>[[225/224]], [[385/384]] (11-limit)
| Edo join 1 = 19 | Edo join 2 = 22 | Edo join 3 = 31
| Mapping = 1; 1 0 2 -1; 0 1 2 -3
| Generator = 3/2, 5/4
| Generator tuning = 700.6, 383.5
| Optimization method = CWE
| Pergen = (P8, P5, ^1)
| Color name = Ruyoyoti
| Odd limit 1 = 9 | Mistuning 1 = 2.57 | Complexity 1 = ?
| Odd limit 2 = 11-limit 21 | Mistuning 2 = 3.86 | Complexity 2 = ?
}}
{{Clear}}
{{Clear}}
== Rank-3 tuning spectrum ==
9-odd-limit: 1/1, 10/9, 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, and complements


----
Single tunings fully defined by eigenmonzos (+ the octave):


[[User:Overthink/Test template]]
{10/9, 9/8, 6/5, 5/4, 4/3}, {10/9, 8/7}, {10/9, 7/6}, {10/9, 9/7, 7/5}, {9/8, 8/7, 7/6, 9/7, 4/3}, {9/8, 4/3, 7/5}, {8/7, 6/5}, {8/7, 5/4, 7/5}, {7/6, 6/5, 7/5}, {7/6, 5/4}, {6/5, 9/7}, {5/4, 9/7}


=== Marvel ===


{| class="wikitable center-1 right-2"
{10/9, 9/8, 6/5, 5/4, 4/3}:
 
~3/2: 701.955{{C}}, ~5/4: 386.314{{C}}
 
{10/9, 8/7}:
 
~3/2: 700.670{{C}}, ~5/4: 383.743{{C}}
 
{10/9, 7/6}:
 
~3/2: 700.413{{C}}, ~5/4: 383.229 {{C}}
 
{10/9, 9/7, 7/5}:
 
~3/2: 700.027{{C}}, ~5/4: 382.458{{C}}
 
{9/8, 8/7, 7/6, 9/7, 4/3}:
 
~3/2: 701.955{{C}}, ~5/4: 382.458{{C}}
 
{9/8, 4/3, 7/5}:
 
~3/2: 701.955{{C}}, ~5/4: 378.602{{C}}
 
{8/7, 6/5}:
 
~3/2: 700.027{{C}}, ~5/4: 384.386{{C}}
 
{8/7, 5/4, 7/5}:
 
~3/2: 698.099{{C}}, ~5/4: 386.314{{C}}
 
{7/6, 6/5, 7/5}:
 
~3/2: 699.384{{C}}, ~5/4: 383.743{{C}}
 
{7/6, 5/4}:
 
~3/2: 694.243{{C}}, ~5/4: 386.314{{C}}
 
{6/5, 9/7}:
 
~3/2: 698.099{{C}}, ~5/4: 382.458{{C}}
 
<s>{5/4, 9/7}</s> (impossible)
 
Additional eigenmonzo tunings up to 21-odd-limit (new intervals: 21/20, 16/15, 15/14, 21/16)
 
{21/20, 16/15}
 
{21/20, 5/4}
 
{21/20, 9/7}
 
<s>{16/15, 8/7}</s> (impossible)
 
{16/15, 7/6}
 
{16/15, 9/7}
 
{16/15, 7/5}
 
{15/14, ''Incomplete''
 
{| class="wikitable center-all"
! Gene-<br>rator
! colspan=17 | ~3/2
|-
! rowspan=17 | ~5/4
! colspan=3 | EDO tuning
! rowspan=3 |
|
| [[19edo|11\19]]
| [[31edo|18\31]]
|
|
| [[12edo|7\12]]
|
|
|
| [[53edo|31\53]]
|
| [[41edo|24\41]]
| [[22edo|1\22]]
|-
! rowspan=2 | (↓↓↓)
! colspan=2 | Eigenmonzo
| 112/75
|
|
| 25/14
| 25/21
|
| 63/50
| 189/100
| 567/400
|
| 3/2
|
|
|-
! (↓↓↓)
! Size (¢)
| 694.243
| 694.737
| 696.774
| 698.099
| 699.384
| 700.000
| 700.027
| 700.413
| 700.670
| 701.887
| 701.955
| 702.439
| 709.091
|-
! colspan=3 |
! style="height: 5px;" |
! colspan=13 |
|-
|
| 56/45
| 378.692
! rowspan=13 |
|
|
|
|
|
|
|
|
|
|
| {3/2, 7/5}
|
|
|-
| [[19edo|6\19]]
|
| 378.947
|
| [[19edo]]
|
|
|
|
|
|
|
|
|
|
|
|-
| [[41edo|13\41]]
|
| 380.488
|
|
|
|
|
|
|
|
|
|
|
| [[41edo]]
|
|-
| [[22edo|7\22]]
|
| 381.818
|
|
|
|
|
|
|
|
|
|
|
|
| [[22edo]]
|-
|
| 9/7
| 382.458
|
|
|
| {5/3, 9/7}
|
|
| {7/5, 9/5}
|
|
|
| {3/2, 7/4}
|
|
|-
|
| 245/162
| 383.229
|
|
|
|
|
|
|
| {7/6, 9/5}
|
|
|
|
|
|-
| [[72edo|23\72]]
|
| 383.333
|
|
|
|
|
| [[72edo]]
|
|
|
|
|
|
|
|-
|-
! Steps
|
! Cents
| 36/35
! Approximate ratios
| 383.743
! [[Ups and downs notation]]
|
|
|
|
| {5/3, 7/6}
|
|
|
| {7/4, 9/5}
|
|
|
|
|-
|-
| 0
|
| 0
| 175/144
| [[1/1]]
| 384.386
| D
|
|
|
|
|
|
| {5/3, 7/4}
|
|
|
|
|
|  
|-
|-
| 1
| [[53edo|17\53]]
| 100
|
| [[15/14]], [[16/15]], [[17/16]], [[18/17]], [[19/18]], [[20/19]], [[21/20]], [[22/21]]
| 384.906
| D♯, E♭
|
|
|
|
|
|
|
|
|
| [[53edo]]
|  
|
|
|-
|-
| 2
|
| 200
| 5/4
| [[9/8]], [[10/9]], [[17/15]], [[19/17]], [[21/19]]
| 386.314
| E
| {5/4, 7/6}
|
|
| {5/4, 7/4}
|
|
|
|
|
|
| {3/2, 5/4}
|
|  
|-
|-
| 3
| [[31edo|10\31]]
| 300
|
| [[6/5]], [[19/16]], [[20/17]]
| 387.097
| F
|
|  
| [[31edo]]
|  
|
|
|
|
|
|
|
|
|
|-
|-
| 4
| [[12edo|4\12]]
| 400
|
| [[5/4]], [[14/11]], [[19/15]], [[23/18]]
| 400.000
| F♯, G♭
|
|
|
|
|
| [[12edo]]
|
|
|
|
|
|
|
|}
 
11-odd-limit adds 12/11, 11/10, 11/9, 14/11, 11/8
 
15-odd-limit: 16/15, 15/14, 15/11
 
21-odd-limit: 22/21, 21/20, 21/16
 
== Stuff ==
=== Orwell as 9-form ===
(Note that 13/10 and 20/13 are mapped via tridecimal orwell)
 
{| class="wikitable center-all"
! Degree
! 0-step
! 1-step
! 2-step
! 3-step
! 4-step
! 5-step
! 6-step
! 7-step
! 8-step
! 9-step
|-
|-
| 5
! Cents
| 500
| 43
| [[4/3]], [[23/17]]
| 200
| G
| 314
| 471
| 586
| 743
| 857
| 1014
| 1129
|  
|-
|-
| 6
! Ratios
| 600
| style="background-color: white;" | 36/35~33/32
| [[7/5]], [[10/7]], [[17/12]], [[23/16]]
| style="background-color: white;" | 9/8
| G♯, A♭
| style="background-color: white;" | 6/5
| style="background-color: white;" | 21/16
| style="background-color: white;" | 7/5
| style="background-color: white;" | (20/13)
| style="background-color: white;" | 18/11
| style="background-color: white;" | 9/5
| style="background-color: white;" | 27/14~48/25
| style="background-color: white;" |
|-
|-
| 7
! Cents
| 0
| 157
| 271
| 429
| 543
| 700
| 700
| [[3/2]]
| 814
| A
| 971
| 1086
|
|-
! Ratios
| style="background-color: white;" | 1/1
| style="background-color: white;" | 11/10~12/11
| style="background-color: white;" | 7/6
| style="background-color: white;" | 9/7~14/11
| style="background-color: white;" | 11/8~15/11
| style="background-color: white;" | 3/2
| style="background-color: white;" | 8/5
| style="background-color: white;" | 7/4
| style="background-color: white;" | 15/8~28/15
| style="background-color: white;" |
|-
|-
| 8
! Cents
| 800
|
| [[8/5]], [[11/7]], [[19/12]]
| 114
| A♯, B♭
| 229
| 386
| 500
| 657
| 771
| 929
| 1043
| 1200
|-
|-
| 9
! Ratios
| 900
| style="background-color: white;" |
| [[5/3]], [[17/10]]
| style="background-color: white;" | 15/14~16/15
| B
| style="background-color: white;" | 8/7
| style="background-color: white;" | 5/4
| style="background-color: white;" | 4/3
| style="background-color: white;" | 16/11~22/15
| style="background-color: white;" | 11/7~14/9
| style="background-color: white;" | 12/7
| style="background-color: white;" | 11/6~20/11
| style="background-color: white;" | 2/1
|-
|-
| 10
! Cents
|  
| 71
| 186
| 343
| 457
| 614
| 729
| 886
| 1000
| 1000
| [[9/5]], [[16/9]], [[23/13]]
| 1157
| C
|-
| 11
| 1100
| [[15/8]], [[17/9]], [[19/10]], [[21/11]], [[23/12]]
| C♯, D♭
|-
|-
| 12
! Ratios
| 1200
| style="background-color: white;" |  
| [[2/1]]
| style="background-color: white;" | 25/24~28/27
| D
| style="background-color: white;" | 10/9
| style="background-color: white;" | 11/9
| style="background-color: white;" | (13/10)
| style="background-color: white;" | 10/7
| style="background-color: white;" | 32/21
| style="background-color: white;" | 5/3
| style="background-color: white;" | 16/9
| style="background-color: white;" | 35/18~64/33
|}
|}

Latest revision as of 01:49, 24 May 2026

Interval information
Factorization 2-702 × 3400 × 7-99 × 11100
Monzo [-702 400 0 -99 100⟩
Size in cents 0.02984219¢
Name(s) missing ? 
Special properties reduced
Tenney norm (log2 nd) 1959.86
Weil norm (log2 max(n, d)) 1959.86
Wilson norm (sopfr(nd)) 4397

Audio demonstration

Open this interval in xen-calc

The difference between 100 896/891's and 7/4

Rank-3 tuning spectrum

9-odd-limit: 1/1, 10/9, 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, and complements

Single tunings fully defined by eigenmonzos (+ the octave):

{10/9, 9/8, 6/5, 5/4, 4/3}, {10/9, 8/7}, {10/9, 7/6}, {10/9, 9/7, 7/5}, {9/8, 8/7, 7/6, 9/7, 4/3}, {9/8, 4/3, 7/5}, {8/7, 6/5}, {8/7, 5/4, 7/5}, {7/6, 6/5, 7/5}, {7/6, 5/4}, {6/5, 9/7}, {5/4, 9/7}

Marvel

{10/9, 9/8, 6/5, 5/4, 4/3}:

~3/2: 701.955 ¢, ~5/4: 386.314 ¢

{10/9, 8/7}:

~3/2: 700.670 ¢, ~5/4: 383.743 ¢

{10/9, 7/6}:

~3/2: 700.413 ¢, ~5/4: 383.229  ¢

{10/9, 9/7, 7/5}:

~3/2: 700.027 ¢, ~5/4: 382.458 ¢

{9/8, 8/7, 7/6, 9/7, 4/3}:

~3/2: 701.955 ¢, ~5/4: 382.458 ¢

{9/8, 4/3, 7/5}:

~3/2: 701.955 ¢, ~5/4: 378.602 ¢

{8/7, 6/5}:

~3/2: 700.027 ¢, ~5/4: 384.386 ¢

{8/7, 5/4, 7/5}:

~3/2: 698.099 ¢, ~5/4: 386.314 ¢

{7/6, 6/5, 7/5}:

~3/2: 699.384 ¢, ~5/4: 383.743 ¢

{7/6, 5/4}:

~3/2: 694.243 ¢, ~5/4: 386.314 ¢

{6/5, 9/7}:

~3/2: 698.099 ¢, ~5/4: 382.458 ¢

{5/4, 9/7} (impossible)

Additional eigenmonzo tunings up to 21-odd-limit (new intervals: 21/20, 16/15, 15/14, 21/16)

{21/20, 16/15}

{21/20, 5/4}

{21/20, 9/7}

{16/15, 8/7} (impossible)

{16/15, 7/6}

{16/15, 9/7}

{16/15, 7/5}

{15/14, Incomplete

Gene-
rator 		~3/2
~5/4 EDO tuning 11\19 18\31 7\12 31\53 24\41 1\22
(↓↓↓) Eigenmonzo 112/75 25/14 25/21 63/50 189/100 567/400 3/2
(↓↓↓) Size (¢) 694.243 694.737 696.774 698.099 699.384 700.000 700.027 700.413 700.670 701.887 701.955 702.439 709.091
56/45 378.692 {3/2, 7/5}
6\19 378.947 19edo
13\41 380.488 41edo
7\22 381.818 22edo
9/7 382.458 {5/3, 9/7} {7/5, 9/5} {3/2, 7/4}
245/162 383.229 {7/6, 9/5}
23\72 383.333 72edo
36/35 383.743 {5/3, 7/6} {7/4, 9/5}
175/144 384.386 {5/3, 7/4}
17\53 384.906 53edo
5/4 386.314 {5/4, 7/6} {5/4, 7/4} {3/2, 5/4}
10\31 387.097 31edo
4\12 400.000 12edo

11-odd-limit adds 12/11, 11/10, 11/9, 14/11, 11/8

15-odd-limit: 16/15, 15/14, 15/11

21-odd-limit: 22/21, 21/20, 21/16

Stuff

Orwell as 9-form

(Note that 13/10 and 20/13 are mapped via tridecimal orwell)

Degree 0-step 1-step 2-step 3-step 4-step 5-step 6-step 7-step 8-step 9-step
Cents 43 200 314 471 586 743 857 1014 1129
Ratios 36/35~33/32 9/8 6/5 21/16 7/5 (20/13) 18/11 9/5 27/14~48/25
Cents 0 157 271 429 543 700 814 971 1086
Ratios 1/1 11/10~12/11 7/6 9/7~14/11 11/8~15/11 3/2 8/5 7/4 15/8~28/15
Cents 114 229 386 500 657 771 929 1043 1200
Ratios 15/14~16/15 8/7 5/4 4/3 16/11~22/15 11/7~14/9 12/7 11/6~20/11 2/1
Cents 71 186 343 457 614 729 886 1000 1157
Ratios 25/24~28/27 10/9 11/9 (13/10) 10/7 32/21 5/3 16/9 35/18~64/33
Retrieved from "https://en.xen.wiki/index.php?title=User:Overthink/Sandbox&oldid=230810"