User:Overthink/Sandbox: Difference between revisions

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


== Header test ==
== Stuff ==
=== 11-limit ===
=== Orwell as 9-form ===
R
(Note that 13/10 and 20/13 are mapped via tridecimal orwell)
a
n
d
o
m
=== 11-limit 2 ===
R
a
n
d
o
m
=== 11-limit ===
Wrong place
 
=== 11-limit 3 ===
R
a
n
d
o
m
=== Filler characters ===
 
| class="wikitable center-all"
 
 
! Gene-<br>rator
 
! colspan=17 | ~3/2


{| 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
|-
|-
 
! Cents
! rowspan=17 | ~5/4
| 43
 
| 200
! colspan=3 | EDO tuning
| 314
 
| 471
! rowspan=3 |
| 586
 
| 743
| 857
| 1014
| 1129
|  
|  
 
|-
| [[19edo|11\19]]
! Ratios
 
| style="background-color: white;" | 36/35~33/32
| [[31edo|18\31]]
| style="background-color: white;" | 9/8
 
| 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
| [[12edo|7\12]]
| style="background-color: white;" | 9/5
 
| style="background-color: white;" | 27/14~48/25
|
| style="background-color: white;" |
 
|-
! Cents
| 0
| 157
| 271
| 429
| 543
| 700
| 814
| 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;" |
|-
! Cents
|  
|  
 
| 114
| [[53edo|31\53]]
| 229
 
| 386
|  
| 500
 
| 657
| [[41edo|24\41]]
| 771
 
| 929
| [[22edo|1\22]]
| 1043
 
| 1200
|-
! Ratios
| style="background-color: white;" |  
| style="background-color: white;" | 15/14~16/15
| 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
|-
|-
 
! Cents
! rowspan=2 | (↓↓↓)
 
! colspan=2 | Eigenmonzo
 
| 112/75
 
|
 
 
|
 
| 25/14
 
 
| 25/21
 
|  
|  
| 63/50
| 71
 
| 186
| 189/100
| 343
 
| 457
| 567/400
| 614
 
| 729
|
| 886
 
| 1000
| 3/2
| 1157
 
|
 
|
 
|-
|-
 
! Ratios
! (↓↓↓)
| style="background-color: white;" |
 
| style="background-color: white;" | 25/24~28/27
! Size (¢)
| style="background-color: white;" | 10/9
 
| style="background-color: white;" | 11/9
| 694.243
| style="background-color: white;" | (13/10)
 
| style="background-color: white;" | 10/7
| 694.737
| style="background-color: white;" | 32/21
 
| style="background-color: white;" | 5/3
| 696.774
| style="background-color: white;" | 16/9
 
| style="background-color: white;" | 35/18~64/33
| 698.099
|}
 
| 699.384
 
| 700.000
 
| 700.027
 
| 700.413
 
| 700.670
 
| 701.887
 
| 701.955
 
| 702.439
 
| 709.091

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
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