24edo: Difference between revisions
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added M2, m2 and A1 to the template, made the primes-error table |
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| Prime factorization = 2<sup>3</sup> * 3 | | Prime factorization = 2<sup>3</sup> * 3 | ||
| Subgroup = 2.3.11.13.17.19 | | Subgroup = 2.3.11.13.17.19 | ||
| Step size = | | Step size = 50¢ | ||
| Fifth type = Meantone 7\12 700¢ | | Fifth type = Meantone 7\12 = 700¢ | ||
| Major 2nd = 4\24 = 200¢ | |||
| Minor 2nd = 2\24 = 100¢ | |||
| Augmented 1sn = 2\24 = 100¢ | |||
| Common uses = Hyperchromatic 12edo, Westernized maqam, semaphore | | Common uses = Hyperchromatic 12edo, Westernized maqam, semaphore | ||
| Important MOS = semaphore 4L1s 55455 (generator: 5\24)<br/> semaphore 5L4s 414144141 (generator: 5\24) <br> mohajira 3L4s 3434343 (generator: 7\24) <br> mohajira 7L3s 3313313313 (generator: 7\24) | | Important MOS = semaphore 4L1s 55455 (generator: 5\24)<br/> semaphore 5L4s 414144141 (generator: 5\24) <br> mohajira 3L4s 3434343 (generator: 7\24) <br> mohajira 7L3s 3313313313 (generator: 7\24) | ||
| Line 17: | Line 20: | ||
=Theory= | =Theory= | ||
{| class="wikitable" | |||
|+ | |||
! colspan="2" |Prime number ---> | |||
!2 | |||
!3 | |||
!5 | |||
!7 | |||
!11 | |||
!13 | |||
!17 | |||
!19 | |||
|- | |||
! rowspan="2" |Error | |||
!absolute ([[Cent|¢]]) | |||
|0 | |||
| -1.96 | |||
|13.7 | |||
| -18.8 | |||
| -1.3 | |||
|9.5 | |||
| -5.0 | |||
|2.5 | |||
|- | |||
![[Relative error|relative]] (%) | |||
|0 | |||
| -4 | |||
|27 | |||
| -38 | |||
| -3 | |||
|19 | |||
| -10 | |||
|5 | |||
|- | |||
! colspan="2" |[[nearest edomapping]] | |||
|24 | |||
|14 | |||
|8 | |||
|19 | |||
|11 | |||
|17 | |||
|2 | |||
|6 | |||
|} | |||
The 24edo system divides the octave into 24 equal parts of exactly 50 cents each. It is also known as '''quarter-tone tuning''', since it evenly divides the 12-tone equal tempered semitone in two. Quarter-tones are the most commonly used microtonal tuning due to its retention of the familiar 12 tones and since it is the smallest microtonal equal temperament that contains all the 12 notes, and also because of its use in theory and occasionally in practice in [[Arabic,_Turkish,_Persian|Arabic]] music. It is easy to jump into this tuning and make microtonal music right away using common 12 equal software and even instruments as illustrated in ''[[DIY Quartertone Composition with 12 equal tools]]''. | The 24edo system divides the octave into 24 equal parts of exactly 50 cents each. It is also known as '''quarter-tone tuning''', since it evenly divides the 12-tone equal tempered semitone in two. Quarter-tones are the most commonly used microtonal tuning due to its retention of the familiar 12 tones and since it is the smallest microtonal equal temperament that contains all the 12 notes, and also because of its use in theory and occasionally in practice in [[Arabic,_Turkish,_Persian|Arabic]] music. It is easy to jump into this tuning and make microtonal music right away using common 12 equal software and even instruments as illustrated in ''[[DIY Quartertone Composition with 12 equal tools]]''. | ||