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| Prime factorization
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32 × 11 × 19 × 53
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| Step size
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0.012037 ¢
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| Fifth
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58317\99693 (701.959 ¢) (→ 19439\33231)
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| Semitones (A1:m2)
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9447:7494 (113.7 ¢ : 90.2 ¢)
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| Dual sharp fifth
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58317\99693 (701.959 ¢) (→ 19439\33231)
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| Dual flat fifth
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58316\99693 (701.947 ¢)
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| Dual major 2nd
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16940\99693 (203.906 ¢) (→ 1540\9063)
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| Consistency limit
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7
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| Distinct consistency limit
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7
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99693 equal divisions of the octave (99693edo) is the tuning that divides the octave into 99693 equal steps of about 0.012 cents. It is notable for being the edo below 100000 with the lowest maximum error, using direct approximation for each harmonic, for the first 547 harmonics (547 being the 100th prime number).
Theory
Approximation of odd harmonics in 99693 EDO
| Odd harmonic
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3
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5
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7
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9
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11
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13
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15
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17
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19
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21
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23
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25
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27
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29
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31
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| Error
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absolute (¢)
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+0.004
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+0.000
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+0.004
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-0.004
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-0.001
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+0.001
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+0.004
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-0.005
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+0.004
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-0.004
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-0.006
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+0.001
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+0.000
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+0.004
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+0.004
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| relative (%)
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+33
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+2
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+37
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-33
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-12
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+6
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+36
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-43
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+36
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-30
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-46
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+4
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+0
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+30
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+31
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| Steps (reduced)
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158010 (58317)
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231480 (32094)
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279874 (80488)
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316019 (16940)
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344881 (45802)
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368908 (69829)
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389490 (90411)
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407491 (8719)
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423489 (24717)
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437883 (39111)
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450967 (52195)
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462960 (64188)
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474029 (75257)
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484307 (85535)
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493899 (95127)
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