User:Overthink/Sandbox: Difference between revisions

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2,732 edits
→Marvel: fill in the rest
Line 59: Line 59:
{| class="wikitable center-all"
{| class="wikitable center-all"
! Gene-<br>rator
! Gene-<br>rator
! colspan=30 | ~3/2 <!-- placeholder colspan -->
! colspan=17 | ~3/2
|-
|-
! rowspan=30 | ~5/4 <!-- placeholder rowspan -->
! rowspan=17 | ~5/4
! colspan=3 | EDO tuning
! 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 | (↓↓↓)
! rowspan=2 | (↓↓↓)
! colspan=2 | Eigenmonzo
! colspan=2 | Eigenmonzo
| 112/75
| 112/75
|
|
| 25/14
| 25/14
| 25/21
| 25/21
|
| 63/50
| 63/50
| 189/100
| 189/100
| 567/400
| 567/400
|
| 3/2
| 3/2
|
|
|-
|-
! style="width: 60px;" | (↓↓↓)
! (↓↓↓)
! Size (¢)
! Size (¢)
| 694.243
| 694.243
| 694.737
| 696.774
| 698.099
| 698.099
| 699.384
| 699.384
| 700.000
| 700.027
| 700.027
| 700.413
| 700.413
| 700.670
| 700.670
| 701.887
| 701.955
| 701.955
| 702.439
| 709.091
|-
! colspan=3 |
! style="height: 5px;" |
! colspan=13 |
|-
|-
|
|
| 56/45
| 56/45
| 378.692
| 378.692
! rowspan=13 |
|
|
|
|
|  
|  
|  
|  
Line 101: Line 129:
|  
|  
| {3/2, 7/5}
| {3/2, 7/5}
|
|
|-
|-
| [[19edo|6\19]]
| [[19edo|6\19]]
|
|
| 378.947
| 378.947
|
| [[19edo]]
|
|
|
|
|  
|  
|  
|  
Line 122: Line 158:
|  
|  
|  
|  
|
|
|
|
|
| [[41edo]]
|  
|  
|-
|-
Line 134: Line 176:
|  
|  
|  
|  
|
|
|
|
|
| [[22edo]]
|-
|-
|
|
| 9/7
| 9/7
| 382.458
| 382.458
|
|
|  
|  
| {5/3, 9/7}
| {5/3, 9/7}
|
|  
|  
| {7/5, 9/5}
| {7/5, 9/5}
|
|  
|  
|  
|  
| {3/2, 7/4}
| {3/2, 7/4}
|
|
|-
|-
|
|
| 245/162
| 245/162
| 383.229
| 383.229
|
|
|
|  
|  
|  
|  
Line 154: Line 211:
|  
|  
| {7/6, 9/5}
| {7/6, 9/5}
|
|
|
|  
|  
|  
|  
Line 160: Line 220:
|
|
| 383.333
| 383.333
|
|
|
|
|
| [[72edo]]
|  
|  
|  
|  
Line 171: Line 237:
| 36/35
| 36/35
| 383.743
| 383.743
|
|
|  
|  
|  
|  
| {5/3, 7/6}
| {5/3, 7/6}
|
|  
|  
|  
|  
| {7/4, 9/5}
| {7/4, 9/5}
|
|
|
|  
|  
|-
|-
Line 182: Line 254:
| 175/144
| 175/144
| 384.386
| 384.386
|
|
|
|  
|  
|  
|  
|  
|  
| {5/3, 7/4}
| {5/3, 7/4}
|
|
|
|  
|  
|  
|  
Line 197: Line 275:
|  
|  
|  
|  
|
|
|
|
|
| [[53edo]]
|  
|  
|  
|  
Line 205: Line 289:
| 386.314
| 386.314
| {5/4, 7/6}
| {5/4, 7/6}
|
|
| {5/4, 7/4}
| {5/4, 7/4}
|
|
|  
|  
|  
|  
Line 211: Line 299:
|  
|  
| {3/2, 5/4}
| {3/2, 5/4}
|
|
|-
|-
| [[31edo|10\31]]
| [[31edo|10\31]]
|
|
| 387.097
| 387.097
|
|
| [[31edo]]
|
|
|
|  
|  
|  
|  
Line 226: Line 322:
|
|
| 400.000
| 400.000
|
|
|
|
|
| [[12edo]]
|  
|  
|  
|  

Revision as of 21:25, 14 March 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)

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
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