User:Overthink/Sandbox: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Overthink (talk | contribs)
note this
Overthink (talk | contribs)
attempt rank-3 tuning spectrum
Line 1: Line 1:
{{Infobox interval|Monzo= -702 400 0 -99 100}}
{{Infobox interval|Monzo= -702 400 0 -99 100|debug=1}}
The difference between 100 [[896/891]]'s and [[7/4]]
The difference between 100 [[896/891]]'s and [[7/4]]
{{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):
{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}
{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}
<s>{5/4, 9/7}</s>

Revision as of 22:06, 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}

{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}