19edo: Difference between revisions
m cat sorting |
added M2, m2 and A1 to the template, moved the primes-error table up to the top |
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| Prime factorization = 19 | | Prime factorization = 19 | ||
| Subgroup = 2.3.5.7.13 | | Subgroup = 2.3.5.7.13 | ||
| Step size = 63. | | Step size = 63.158¢ | ||
| Fifth type = [[Meantone]] 11\19 694.737¢ | | Fifth type = [[Meantone]] 11\19 694.737¢ | ||
| Major 2nd = 3\19 = 189¢ | |||
| Minor 2nd = 2\19 = 126¢ | |||
| Augmented 1sn = 1\19 = 63¢ | |||
| Common uses = extended third-comma meantone, semaphore | | Common uses = extended third-comma meantone, semaphore | ||
| Important MOS = [[meantone]] diatonic 5*3-2*2 (11\19, 1\1)<br/>[[semaphore]] 5*3-4*1 (4\19, 1\1)<br/>[[sensi]] 3*3-5*2 (7\19, 1\1) | | Important MOS = [[meantone]] diatonic 5*3-2*2 (11\19, 1\1)<br/>[[semaphore]] 5*3-4*1 (4\19, 1\1)<br/>[[sensi]] 3*3-5*2 (7\19, 1\1) | ||
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In music, '''19 equal temperament''', called 19-TET, 19-[[EDO]], or 19-ET, is the scale derived by dividing the [[octave]] into 19 [[Equal|equally]] large steps. Each step represents a frequency ratio of the 19th root of 2, or 63.16 [[cent|cents]]. It is the 8th [[prime numbers|prime]] [[prime EDO|edo]], following [[17edo]] and coming before [[23edo]]. | In music, '''19 equal temperament''', called 19-TET, 19-[[EDO]], or 19-ET, is the scale derived by dividing the [[octave]] into 19 [[Equal|equally]] large steps. Each step represents a frequency ratio of the 19th root of 2, or 63.16 [[cent|cents]]. It is the 8th [[prime numbers|prime]] [[prime EDO|edo]], following [[17edo]] and coming before [[23edo]]. | ||
== Theory == | == Theory == | ||
{| class="wikitable" style="text-align:center;" | |||
! colspan="2" | | |||
! prime 2 | |||
! prime 3 | |||
! prime 5 | |||
! prime 7 | |||
! prime 11 | |||
! prime 13 | |||
! prime 23 | |||
|- | |||
! rowspan="2" | Error | |||
! absolute ([[cent|¢]]) | |||
| 0.0 | |||
| -7.22 | |||
| -7.4 | |||
| -21.5 | |||
| +17.1 | |||
| -19.5 | |||
| +3.3 | |||
|- | |||
![[Relative error|relative]] (%) | |||
| 0.0 | |||
| -11 | |||
| -12 | |||
| -34 | |||
| +27 | |||
| -31 | |||
| +5 | |||
|- | |||
! colspan="2" |[[nearest edomapping]] | |||
|19 | |||
|11 | |||
|6 | |||
|15 | |||
|9 | |||
|13 | |||
|10 | |||
|- | |||
! colspan="2" |[[fifthspan]] | |||
| 0 | |||
| +1 | |||
| +4 | |||
| -9 | |||
| +6 | |||
| -4 | |||
| -6 | |||
|} | |||
=== History === | === History === | ||
| Line 332: | Line 383: | ||
=== Selected just intervals by error === | === Selected just intervals by error === | ||
==== 15-odd-limit interval mappings ==== | ==== 15-odd-limit interval mappings ==== | ||