29edo: 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 = 29 | | Prime factorization = 29 | ||
| Subgroup = 2.3.5.7.11.13 | | Subgroup = 2.3.5.7.11.13 | ||
| Step size = 41. | | Step size = 41.379¢ | ||
| Fifth type = [[leapfrog]] 17\29 703.448¢ | | Fifth type = [[leapfrog]] 17\29 = 703.448¢ | ||
| Major 2nd = 5\29 = 207¢ | |||
| Minor 2nd = 2\29 = 83¢ | |||
| Augmented 1sn = 3\29 = 124¢ | |||
| Common uses = neogothic | | Common uses = neogothic | ||
| Important MOS = [[leapfrog]] diatonic 5*5-2*2 (17\29, 1\1)<br/> porcupine 1*2-7*4 (4\29, 1\1)<br/> semaphore 5*5-4*1 (6\29, 1\1) <br/> nautilus 14*2-1*1 (4\29, 2\1) | | Important MOS = [[leapfrog]] diatonic 5*5-2*2 (17\29, 1\1)<br/> porcupine 1*2-7*4 (4\29, 1\1)<br/> semaphore 5*5-4*1 (6\29, 1\1) <br/> nautilus 14*2-1*1 (4\29, 2\1) | ||
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== Theory == | == Theory == | ||
{| class="wikitable center-all" | |||
! colspan="2" | | |||
! prime 2 | |||
! prime 3 | |||
! prime 5 | |||
! prime 7 | |||
! prime 11 | |||
! prime 13 | |||
|- | |||
! rowspan="2" |Error | |||
! absolute (¢) | |||
| 0 | |||
| +1.49 | |||
| -13.9 | |||
| -17.1 | |||
| -13.4 | |||
| -12.9 | |||
|- | |||
![[Relative error|relative]] (%) | |||
| 0 | |||
| +4 | |||
| -34 | |||
| -41 | |||
| -32 | |||
| -31 | |||
|- | |||
! colspan="2" |[[nearest edomapping]] | |||
|29 | |||
|17 | |||
|9 | |||
|23 | |||
|13 | |||
|20 | |||
|- | |||
! colspan="2" |[[fifthspan]] | |||
|0 | |||
| +1 | |||
| -8 | |||
| -14 | |||
| +11 | |||
| +8 | |||
|} | |||
29 is the lowest edo which approximates the [[3/2]] just fifth more accurately than [[12edo]]: 3/2 = 701.955… cents; 17 degrees of 29edo = 703.448… cents. Since the fifth is slightly sharp, 29edo is a [[Erv Wilson's Linear Notations|positive temperament]] – a Superpythagorean instead of a Meantone system. | 29 is the lowest edo which approximates the [[3/2]] just fifth more accurately than [[12edo]]: 3/2 = 701.955… cents; 17 degrees of 29edo = 703.448… cents. Since the fifth is slightly sharp, 29edo is a [[Erv Wilson's Linear Notations|positive temperament]] – a Superpythagorean instead of a Meantone system. | ||
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== Just approximation == | == Just approximation == | ||
=== Selected just intervals by error === | === Selected just intervals by error === | ||
==== 15-odd-limit interval mappings ==== | ==== 15-odd-limit interval mappings ==== | ||
The following table shows how [[15-odd-limit intervals]] are represented in 29edo. Prime harmonics are in '''bold'''. | The following table shows how [[15-odd-limit intervals]] are represented in 29edo. Prime harmonics are in '''bold'''. | ||