13-limit: Difference between revisions
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The 13-prime-limit can be modeled in a 5-dimensional lattice, with the primes 3, 5, 7, 11, and 13 represented by each dimension. The prime 2 does not appear in the typical 13-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, a sixth dimension is need. | The 13-prime-limit can be modeled in a 5-dimensional lattice, with the primes 3, 5, 7, 11, and 13 represented by each dimension. The prime 2 does not appear in the typical 13-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, a sixth dimension is need. | ||
[[EDO|Edo]]s good for 13-limit are | [[EDO|Edo]]s good for 13-limit are 5, 6, 7, 9, 10, 15, 16, 17, 19, 20, 22, 24, 26, 31, 37, 46, 50, 53, 63, 77, 84, 87, 130, 140, 161, 183, 207, 217, 224, 270, 494, 851, 1075, 1282, 1578, 2159, 2190, 2684, 3265, 3535, 4573, 5004, 5585, 6079, 8269, 8539, 13854, 14124, 16808, 20203, 22887, 28742, 32007, 37011, 50434, 50928, 51629, 54624, 56202, 59467, 64471, 65052, ... . | ||
== Intervals == | |||
Here are all the 15-odd-limit intervals of 13: | |||
{| class="wikitable" | |||
| colspan="2" |[[Kite's color notation|Interval name]] | |||
|Ratio | |||
|Cents Value | |||
|- | |||
|3uz2 | |||
|thuzo 2nd | |||
|14/13 | |||
|128 | |||
|- | |||
|3o2 | |||
|tho 2nd | |||
|13/12 | |||
|139 | |||
|- | |||
|3uy2 | |||
|thuyo 2nd | |||
|15/13 | |||
|248 | |||
|- | |||
|3o1u3 | |||
|tholu 3rd | |||
|13/11 | |||
|289 | |||
|- | |||
|3u3 | |||
|thu 3rd | |||
|16/13 | |||
|359 | |||
|- | |||
|3og4 | |||
|thogu 4th | |||
|13/10 | |||
|454 | |||
|- | |||
|3u4 | |||
|thu 4th | |||
|18/13 | |||
|563 | |||
|- | |||
|3o5 | |||
|tho 5th | |||
|13/9 | |||
|637 | |||
|- | |||
|3uy5 | |||
|thuyo 5th | |||
|20/13 | |||
|746 | |||
|- | |||
|3o6 | |||
|tho 6th | |||
|13/8 | |||
|841 | |||
|- | |||
|3u1o6 | |||
|thulo 6th | |||
|22/13 | |||
|911 | |||
|- | |||
|3og7 | |||
|thogu 7th | |||
|26/15 | |||
|952 | |||
|- | |||
|3u7 | |||
|thu 7th | |||
|24/13 | |||
|1061 | |||
|- | |||
|3or7 | |||
|thoru 7th | |||
|13/7 | |||
|1072 | |||
|} | |||
See: [[Gallery of Just Intervals]] | |||
. | . | ||
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=See also= | =See also= | ||
[[Harmonic_Limit|Harmonic limit]] [[Category:13-limit]] | [[Harmonic_Limit|Harmonic limit]] | ||
[[Category:13-limit]] | |||
[[Category:limit]] | [[Category:limit]] | ||
[[Category:listen]] | [[Category:listen]] | ||
[[Category:prime_limit]] | [[Category:prime_limit]] | ||
[[Category:rank_6]] | [[Category:rank_6]] | ||