User:Overthink/Sandbox: Difference between revisions

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=== Marvel ===
=== Marvel ===


{10/9, 9/8, 6/5, 5/4, 4/3}: ~3/2: 701.955{{C}}, ~5/4: 386.314{{C}}
{10/9, 9/8, 6/5, 5/4, 4/3}:


{10/9, 8/7} ~3/2: 700.670{{C}}, ~5/4: 383.743{{C}}
~3/2: 701.955{{C}}, ~5/4: 386.314{{C}}


{10/9, 7/6} ~3/2: 700.413{{C}}, ~5/4: 383.229 {{C}}
{10/9, 8/7}:


{10/9, 9/7, 7/5} ~3/2: 700.027{{C}}, ~5/4: 382.458{{C}}
~3/2: 700.670{{C}}, ~5/4: 383.743{{C}}


{9/8, 8/7, 7/6, 9/7, 4/3} ~3/2: 701.955{{C}}, ~5/4: 382.458{{C}}
{10/9, 7/6}:


{9/8, 4/3, 7/5} ~3/2: 701.955{{C}}, ~5/4: 378.602{{C}}
~3/2: 700.413{{C}}, ~5/4: 383.229 {{C}}


{8/7, 6/5} ~3/2: 700.027{{C}}, ~5/4: 384.386{{C}}
{10/9, 9/7, 7/5}:


{8/7, 5/4, 7/5} ~3/2: 698.099{{C}}, ~5/4: 386.314{{C}}
~3/2: 700.027{{C}}, ~5/4: 382.458{{C}}


{7/6, 6/5, 7/5} ~3/2: 699.384{{C}}, ~5/4: 383.743{{C}}
{9/8, 8/7, 7/6, 9/7, 4/3}:


{7/6, 5/4} ~3/2: 694.243{{C}}, ~5/4: 386.314{{C}}
~3/2: 701.955{{C}}, ~5/4: 382.458{{C}}


{6/5, 9/7} ~3/2: 698.099{{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)
<s>{5/4, 9/7}</s> (impossible)
{| class="wikitable"
! Gene-<br>rator
! colspan=8 | ~3/2
|-
! rowspan=7 | ~5/4
! Size (¢)
| 694.243
| 698.099
| 699.384
| 700.027
| 700.413
| 700.670
| 701.955
|-
| 378.692
|-
| 382.458
|-
| 383.229
|-
| 383.743
|-
| 384.386
|-
| 386.314
|}

Revision as of 22:42, 13 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 Size (¢) 694.243 698.099 699.384 700.027 700.413 700.670 701.955
378.692
382.458
383.229
383.743
384.386
386.314
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