User:Overthink/13-limit interval flavors: Difference between revisions
Created page with "In this article, we will cover the various flavors of 13-limit intervals. We consider intervals that differ by a pythagorean interval to have the same flavor. {| class="wikitable" |+13-limit flavors !D\N !1/3/9 !5 !7 !11 !13 |- |1/3/9 |1/1 | | | | |- |5 | |1/1 |7/5 |11/10 |13/10 |- |7 | | |1/1 | | |- |11 | | | |1/1 | |- |13 | | | | |1/1 |}" |
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In this article, we will cover the various flavors of 13-limit intervals. We consider intervals that differ by a pythagorean interval to have the same flavor. | In this article, we will cover the various flavors of 13-limit intervals. We consider intervals that differ by a pythagorean interval to have the same flavor. The flavor of an interval depends on the primes higher than 3 in its prime factorization. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+13-limit flavors | |+13-limit flavors | ||
| Line 9: | Line 9: | ||
!13 | !13 | ||
|- | |- | ||
!1/3/9 | |||
|[[1/1]] | |[[1/1]] (wa) | ||
| | |[[5/4]] (yo) | ||
| | |[[7/4]] (zo) | ||
| | |[[11/8]] (ilo) | ||
| | |[[13/8]] (tho) | ||
|- | |- | ||
!5 | |||
| | |[[8/5]] (gu) | ||
|1/1 | |1/1 | ||
|[[7/5]] | |[[7/5]] (zogu) | ||
|[[11/10]] | |[[11/10]] (logu) | ||
|13/10 | |[[13/10]] (thogu) | ||
|- | |- | ||
!7 | |||
| | |[[8/7]] (ru) | ||
| | |[[10/7]] (yoru) | ||
|1/1 | |1/1 | ||
| | |[[11/7]] (loru) | ||
| | |[[13/7]] (thoru) | ||
|- | |- | ||
!11 | |||
| | |[[16/11]] (lu) | ||
| | |[[20/11]] (yolu) | ||
| | |[[14/11]] (zolu) | ||
|1/1 | |1/1 | ||
| | |[[13/11]] (tholu) | ||
|- | |- | ||
!13 | |||
| | |[[16/13]] (thu) | ||
| | |[[20/13]] (yothu) | ||
| | |[[14/13]] (zothu) | ||
| | |[[22/13]] (lothu) | ||
|1/1 | |1/1 | ||
|} | |||
== The flavors of intervals == | |||
{| class="wikitable" | |||
|+Pythagorean (wa) | |||
!Cents | |||
!Ratio | |||
!FJS Name | |||
!Color name | |||
|- | |||
|0.000 | |||
|1/1 | |||
|P1 | |||
|wa 1sn | |||
|- | |||
|90.225 | |||
|256/243 | |||
|m2 | |||
|sawa 2nd | |||
|- | |||
|203.910 | |||
|9/8 | |||
|M2 | |||
|wa 2nd | |||
|- | |||
|294.135 | |||
|32/27 | |||
|m3 | |||
|wa 3rd | |||
|- | |||
|407.820 | |||
|81/64 | |||
|M3 | |||
|lawa 3rd | |||
|- | |||
|498.045 | |||
|4/3 | |||
|P4 | |||
|wa 4th | |||
|- | |||
|588.270 | |||
|1024/729 | |||
|d5 | |||
|sawa 5th | |||
|- | |||
|611.730 | |||
|729/512 | |||
|A4 | |||
|lawa 4th | |||
|- | |||
|701.955 | |||
|3/2 | |||
|P5 | |||
|wa 5th | |||
|- | |||
|792.180 | |||
|128/81 | |||
|m6 | |||
|sawa 6th | |||
|- | |||
|905.865 | |||
|27/16 | |||
|M6 | |||
|wa 6th | |||
|- | |||
|996.090 | |||
|16/9 | |||
|m7 | |||
|wa 7th | |||
|- | |||
|1109.775 | |||
|243/128 | |||
|M7 | |||
|lawa 7th | |||
|- | |||
|1200.000 | |||
|2/1 | |||
|P8 | |||
|wa 8ve | |||
|} | |} | ||