18edo: Difference between revisions
m Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot |
added M2, m2 and A1 to the template, moved the primes-error table up to the top |
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| Prime factorization = 2 * 3<sup>2</sup> | | Prime factorization = 2 * 3<sup>2</sup> | ||
| Subgroup = 2.5.9.21.13/3.17/3.23/3.29/3, 2.9.75.21.55.39.51 | | Subgroup = 2.5.9.21.13/3.17/3.23/3.29/3, 2.9.75.21.55.39.51 | ||
| Step size = 66. | | Step size = 66.667¢ | ||
| Fifth type = father 11\18 733.33¢ | | Fifth type = father 11\18 = 733.33¢ | ||
| Major 2nd = 4\18 = 267¢ | |||
| Minor 2nd = -1\18 = -67¢ | |||
| Augmented 1sn = 5\18 = 333¢ | |||
| Common uses = | | Common uses = | ||
| Important MOS = oneirotonic ([[A-Team]]) 5L3s 33133131 (7\18, 1\1) | | Important MOS = oneirotonic ([[A-Team]]) 5L3s 33133131 (7\18, 1\1) | ||
| Line 19: | Line 22: | ||
== Theory == | == Theory == | ||
{| class="wikitable" | |||
! colspan="2" | | |||
!prime 2 | |||
!prime 3 | |||
!prime 5 | |||
!prime 7 | |||
!prime 11 | |||
!prime 13 | |||
|- | |||
! rowspan="2" |Error | |||
!absolute ([[Cent|¢]]) | |||
|0 | |||
|31.38 | |||
|13.7 | |||
|31.2 | |||
| -18.0 | |||
|26.1 | |||
|- | |||
![[Relative error|relative]] (%) | |||
|0 | |||
|47 | |||
|21 | |||
|47 | |||
| -27 | |||
|39 | |||
|- | |||
! colspan="2" |[[nearest edomapping]] | |||
|18 | |||
|11 | |||
|6 | |||
|15 | |||
|8 | |||
|13 | |||
|- | |||
! colspan="2" |[[fifthspan]] | |||
|0 | |||
| +1 | |||
| -6 | |||
| +3 | |||
| +4 | |||
| -7 | |||
|} | |||
18 Equal Divisions of the Octave, also known as The Third-Tone System, divides the octave into 18 equal parts of ~66.667 cents each. It does not approximate the 3rd harmonic at all, unless a >30¢-error is considered acceptable, and it approximates the 5th, 7th and 9th harmonics equally well (or equally poorly) as 12-TET does. It does, however, render more accurate tunings of 7/6, 21/16, 15/11, 12/7, and 13/7. It is also the smallest EDO to approximate the harmonic series chord 5:6:7 without tempering out 36/35 (and thus without using the same interval to approximate both 6/5 and 7/6). | 18 Equal Divisions of the Octave, also known as The Third-Tone System, divides the octave into 18 equal parts of ~66.667 cents each. It does not approximate the 3rd harmonic at all, unless a >30¢-error is considered acceptable, and it approximates the 5th, 7th and 9th harmonics equally well (or equally poorly) as 12-TET does. It does, however, render more accurate tunings of 7/6, 21/16, 15/11, 12/7, and 13/7. It is also the smallest EDO to approximate the harmonic series chord 5:6:7 without tempering out 36/35 (and thus without using the same interval to approximate both 6/5 and 7/6). | ||