47edo: Difference between revisions
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{{Infobox ET | {{Infobox ET | ||
| Prime factorization = 47 | | Prime factorization = 47 is prime | ||
| Step size = 25. | | Step size = 25.53191¢ | ||
| Fifth = 27\47 | | Fifth = 27\47 (689¢) | ||
| Major 2nd = 7\47 | | Major 2nd = 7\47 (179¢) | ||
| Minor 2nd = 6\47 | | Minor 2nd = 6\47 (153¢) | ||
| Augmented 1sn = 1\47 | | Augmented 1sn = 1\47 (26¢) | ||
}} | }} | ||
==Theory== | == Theory == | ||
'''47-EDO''' divides the octave into 47 equal parts of 25. | '''47-EDO''' divides the octave into 47 equal parts of 25.5 cents each. It has a fifth which is 12.5933 cents flat, unless you use the alternative fifth which is 12.9386 cents sharp, similar to 35edo. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[k*N_subgroups|2*47 subgroup]] of the [[23-limit|23-limit]], on which it tempers out the same commas as [[94edo|94edo]]. It provides a good tuning for [[Chromatic_pairs#Baldy|baldy]] and [[Chromatic_pairs#Silver|silver]] temperaments and relatives. | ||
47edo is the 15th [[prime_numbers|prime]] edo, following [[43edo|43edo]] and preceding [[53edo|53edo]]. | 47edo is the 15th [[prime_numbers|prime]] edo, following [[43edo|43edo]] and preceding [[53edo|53edo]]. | ||
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D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats. | D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats. | ||
==Intervals== | == Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||