26edo: 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 * 13 | | Prime factorization = 2 * 13 | ||
| Subgroup = 2.3.5.7.11.13 | | Subgroup = 2.3.5.7.11.13 | ||
| Step size = 46. | | Step size = 46.154¢ | ||
| Fifth type = flattone 15\26 692.31¢ | | Fifth type = flattone 15\26 = 692.31¢ | ||
| Major 2nd = 4\26 = 185¢ | |||
| Minor 2nd = 3\26 = 138¢ | |||
| Augmented 1sn = 1\26 = 46¢ | |||
| Common uses = flattone diatonic<br/>orgone | | Common uses = flattone diatonic<br/>orgone | ||
| Important MOS = diatonic ([[flattone]]) 5*4-2*3 (15\26, 1\1)<br/>[[orgone]] 4*5-3*2 (7\26, 1\1)<br/>[[lemba]] 4*5-2*3 (5\26, 1\2) | | Important MOS = diatonic ([[flattone]]) 5*4-2*3 (15\26, 1\1)<br/>[[orgone]] 4*5-3*2 (7\26, 1\1)<br/>[[lemba]] 4*5-2*3 (5\26, 1\2) | ||
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== Theory == | == Theory == | ||
{| class="wikitable center-all" | |||
|- | |||
|+Approximation of [[primary interval]]s in 26 EDO | |||
|- | |||
! colspan="2" | Prime number ---> | |||
!2 | |||
! 3 | |||
! 5 | |||
! 7 | |||
! 11 | |||
! 13 | |||
! 17 | |||
! 19 | |||
! 23 | |||
|- | |||
! rowspan="2" | Error | |||
! absolute ([[cent|¢]]) | |||
|0 | |||
| -9.65 | |||
| -17.1 | |||
| +0.4 | |||
| +2.5 | |||
| -9.8 | |||
| -12.6 | |||
| -20.6 | |||
| +17.9 | |||
|- | |||
![[Relative error|relative]] (%) | |||
|0 | |||
| -21 | |||
| -37 | |||
| +0.9 | |||
| +5 | |||
| -21 | |||
| -27 | |||
| -45 | |||
| +39 | |||
|- | |||
! colspan="2" | [[nearest edomapping]] | |||
|26 | |||
| 15 | |||
| 8 | |||
| 21 | |||
| 12 | |||
| 18 | |||
| 2 | |||
| 6 | |||
| 14 | |||
|- | |||
! | |||
![[fifthspan]] | |||
|0 | |||
| +1 | |||
| +4 | |||
| -9 | |||
| +6 | |||
| -4 | |||
| -12 | |||
| -10 | |||
| -6 | |||
|} | |||
In the [[7-limit]], it tempers out 50/49, 525/512 and 875/864, and supports [[injera]], [[flattone]], [[Jubilismic clan#Lemba|lemba]] and [[Jubilismic clan#Doublewide|doublewide]] temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13 odd limit]] [[consistent|consistently]]. 26edo has a very good approximation of the harmonic seventh ([[7/4]]). | In the [[7-limit]], it tempers out 50/49, 525/512 and 875/864, and supports [[injera]], [[flattone]], [[Jubilismic clan#Lemba|lemba]] and [[Jubilismic clan#Doublewide|doublewide]] temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13 odd limit]] [[consistent|consistently]]. 26edo has a very good approximation of the harmonic seventh ([[7/4]]). | ||
| Line 314: | Line 379: | ||
== Selected just intervals approximated == | == Selected just intervals approximated == | ||
=== 15-odd-limit interval mappings === | === 15-odd-limit interval mappings === | ||