13edo: Difference between revisions
Cmloegcmluin (talk | contribs) →26edo subset: add Sagittal notation |
m →Regular temperament properties: cleanup |
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=== Commas === | === Commas === | ||
13et [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 13 21 30 36 45 48 }}.) | |||
{| class="commatable wikitable center-1 center-2 right-4 center-5" | {| class="commatable wikitable center-1 center-2 right-4 center-5" | ||
|- | |- | ||
! [[Harmonic limit|Prime <br> limit]] | ! [[Harmonic limit|Prime<br>limit]] | ||
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> | ! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> | ||
! [[Monzo]] | ! [[Monzo]] | ||
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| 43.41 | | 43.41 | ||
| Lazoyoyo | | Lazoyoyo | ||
| Avicennma, Avicenna's | | Avicennma, Avicenna's enharmonic diesis | ||
|- | |- | ||
| 7 | | 7 | ||
| Line 1,475: | Line 1,475: | ||
| 27.26 | | 27.26 | ||
| Ru | | Ru | ||
| Septimal | | Septimal comma, Archytas' comma, Leipziger Komma | ||
|- | |- | ||
| 7 | | 7 | ||
| Line 1,482: | Line 1,482: | ||
| 22.23 | | 22.23 | ||
| Laquadzo-atrigu | | Laquadzo-atrigu | ||
| Squalentine | | Squalentine comma | ||
|- | |- | ||
| 7 | | 7 | ||
| Line 1,489: | Line 1,489: | ||
| 21.18 | | 21.18 | ||
| Triru-aquinyo | | Triru-aquinyo | ||
| Gariboh | | Gariboh comma | ||
|- | |- | ||
| 7 | | 7 | ||
| Line 1,531: | Line 1,531: | ||
| 16.57 | | 16.57 | ||
| Thuzoyo | | Thuzoyo | ||
| Animist | | Animist comma | ||
|- | |- | ||
| 13 | | 13 | ||
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=== Animism === | === Animism === | ||
The animist comma, 105/104, appears whenever 3 | The animist comma, 105/104, appears whenever {{nowrap| ~3 × ~5 × ~7 = ~2<sup>3</sup> × ~13 }}… 13edo does not approximate 3 and 7 individually (26edo does), but 13edo has 21/16 (21 = 3*7) and is also an animist temperament. In 13edo, the 5th harmonic is tuned so flatly that 5/4 = 16/13, leading to some interesting identities. So two scales stand out through this construction: | ||
0 4 5 8 9 13 pentatonic | 0 4 5 8 9 13 pentatonic | ||