53edo: Difference between revisions
m Undo last edit. There's a note below the table explaining its meaning Tag: Undo |
Infobox precision, renew template for prime error table, make JI approximation table collapsed |
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{{Infobox ET | {{Infobox ET | ||
| Prime factorization = 53 (prime) | | Prime factorization = 53 (prime) | ||
| Step size = 22. | | Step size = 22.6415¢ | ||
| Fifth = 31\53 ( | | Fifth = 31\53 (701.9¢) | ||
| Major 2nd = 9\53 ( | | Major 2nd = 9\53 (203.8¢) | ||
| Semitones = 5:4 ( | | Semitones = 5:4 (113.2¢ : 90.6¢) | ||
| Consistency = 9 | | Consistency = 9 | ||
| Monotonicity = 23 | | Monotonicity = 23 | ||
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=== Prime harmonics === | === Prime harmonics === | ||
{{ | {{Harmonics in equal|53}} | ||
== Intervals == | == Intervals == | ||
{| class="wikitable center-all right-3 left-4 left-6" | {| class="wikitable center-all right-3 left-4 left-6" | ||
|- | |- | ||
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{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |- | ||
! | ! Interval | ||
! | ! Ratio | ||
! | ! Size | ||
! | ! Difference | ||
|- | |- | ||
| | | Perfect fifth | ||
| 3/2 | | 3/2 | ||
| 31 | | 31 | ||
| −0.07 cents | | −0.07 cents | ||
|- | |- | ||
| | | Major third | ||
| 5/4 | | 5/4 | ||
| 17 | | 17 | ||
| −1.40 cents | | −1.40 cents | ||
|- | |- | ||
| | | Minor third | ||
| 6/5 | | 6/5 | ||
| 14 | | 14 | ||
| +1.34 cents | | +1.34 cents | ||
|- | |- | ||
| | | Major tone | ||
| 9/8 | | 9/8 | ||
| 9 | | 9 | ||
| −0.14 cents | | −0.14 cents | ||
|- | |- | ||
| | | Minor tone | ||
| 10/9 | | 10/9 | ||
| 8 | | 8 | ||
| −1.27 cents | | −1.27 cents | ||
|- | |- | ||
| | | Diat. semitone | ||
| 16/15 | | 16/15 | ||
| 5 | | 5 | ||
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=== 15-odd-limit interval mappings === | === 15-odd-limit interval mappings === | ||
The following table shows how [[15-odd-limit intervals]] are represented in 53edo. Octave-reduced prime harmonics are '''bolded'''; inconsistent intervals are in ''italic''. | The following table shows how [[15-odd-limit intervals]] are represented in 53edo. Octave-reduced prime harmonics are '''bolded'''; inconsistent intervals are in ''italic''. | ||
{| class="wikitable center-all" | |||
{| class="wikitable center-all mw-collapsible mw-collapsed" | |||
|+style=white-space:nowrap| Direct mapping (even if inconsistent) | |||
|- | |- | ||
! Interval, complement | ! Interval, complement | ||
! Error (abs, [[Cent|¢]]) | ! Error (abs, [[Cent|¢]]) | ||
|- | |- | ||
| '''[[4/3]], [[ | | '''[[4/3]], [[3/2]]''' | ||
| '''0.068''' | | '''0.068''' | ||
|- | |- | ||
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| 2.724 | | 2.724 | ||
|- | |- | ||
| '''[[16/13]], [[ | | '''[[16/13]], [[13/8]]''' | ||
| '''2.792''' | | '''2.792''' | ||
|- | |- | ||