User:BudjarnLambeth/The intervals I see as important: Difference between revisions
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== EDO Consonance Ratings (1–53edo) == | == EDO Consonance Ratings (1–53edo) == | ||
Table created using Claude, prompt listed below table. | Table created using Claude (I gave it a PDF of the EDO harmonic tables), prompt listed below table. | ||
{| class="wikitable sortable" style="text-align:center; font-size:80%;" | {| class="wikitable sortable" style="text-align:center; font-size:80%;" | ||
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! style="background:#fff0c8;" | 13/3<br/><small>lg tri neu 2nd^</small> | ! style="background:#fff0c8;" | 13/3<br/><small>lg tri neu 2nd^</small> | ||
|- | |- | ||
| '''1''' | | '''1''' | ||
| style="background:#90EE90;" | 0.0¢ ✓✓ | | style="background:#90EE90;" | 0.0¢ ✓✓ | ||
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| style="background:#FF9999;" | 231.0¢ ✗ | | style="background:#FF9999;" | 231.0¢ ✗ | ||
| style="background:#FF9999;" | 204.0¢ ✗ | | style="background:#FF9999;" | 204.0¢ ✗ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 267.0¢ ✗ | ||
| style="background:#FF9999;" | 884.0¢ ✗ | | style="background:#FF9999;" | 884.0¢ ✗ | ||
| style="background:#FF9999;" | 551.0¢ ✗ | | style="background:#FF9999;" | 551.0¢ ✗ | ||
| style="background:#FF9999;" | 617.0¢ ✗ | | style="background:#FF9999;" | 617.0¢ ✗ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 182.0¢ ✗ | ||
| style="background:#FF9999;" | 1049.0¢ ✗ | | style="background:#FF9999;" | 1049.0¢ ✗ | ||
| style="background:#FF9999;" | 359.0¢ ✗ | | style="background:#FF9999;" | 359.0¢ ✗ | ||
| style="background:#FF9999;" | 231.0¢ ✗ | | style="background:#FF9999;" | 231.0¢ ✗ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 139.0¢ ✗ | ||
| style="background:#90EE90;" | -9 | |||
|- | |- | ||
| '''2''' | | '''2''' | ||
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| style="background:#FF9999;" | 316.0¢ ✗ | | style="background:#FF9999;" | 316.0¢ ✗ | ||
| style="background:#FF9999;" | 49.0¢ ✗ | | style="background:#FF9999;" | 49.0¢ ✗ | ||
| style="background:# | | style="background:#90EE90;" | 17.0¢ ✓✓ | ||
| style="background:#FF9999;" | 418.0¢ ✗ | | style="background:#FF9999;" | 418.0¢ ✗ | ||
| style="background:#FF9999;" | 151.0¢ ✗ | | style="background:#FF9999;" | 151.0¢ ✗ | ||
| style="background:#FF9999;" | 241.0¢ ✗ | | style="background:#FF9999;" | 241.0¢ ✗ | ||
| style="background:#FF9999;" | 231.0¢ ✗ | | style="background:#FF9999;" | 231.0¢ ✗ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 139.0¢ ✗ | ||
| style="background:#90EE90;" | -8 | |||
|- | |- | ||
| '''3''' | | '''3''' | ||
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| style="background:#FFD700;" | 14.0¢ ✓ | | style="background:#FFD700;" | 14.0¢ ✓ | ||
| style="background:#FF9999;" | 98.0¢ ✗ | | style="background:#FF9999;" | 98.0¢ ✗ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 84.0¢ ✗ | ||
| style="background:#FF9999;" | 169.0¢ ✗ | | style="background:#FF9999;" | 169.0¢ ✗ | ||
| style="background:#FF9999;" | 196.0¢ ✗ | | style="background:#FF9999;" | 196.0¢ ✗ | ||
| style="background:#FF9999;" | 267.0¢ ✗ | | style="background:#FF9999;" | 267.0¢ ✗ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 84.0¢ ✗ | ||
| style="background:#FF9999;" | 151.0¢ ✗ | | style="background:#FF9999;" | 151.0¢ ✗ | ||
| style="background:#FF9999;" | 183.0¢ ✗ | | style="background:#FF9999;" | 183.0¢ ✗ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 182.0¢ ✗ | ||
| style="background:#FF9999;" | 249.0¢ ✗ | | style="background:#FF9999;" | 249.0¢ ✗ | ||
| style="background:#FF9999;" | 41.0¢ ✗ | | style="background:#FF9999;" | 41.0¢ ✗ | ||
| style="background:#FF9999;" | 169.0¢ ✗ | | style="background:#FF9999;" | 169.0¢ ✗ | ||
| style="background:#FF9999;" | 139.0¢ ✗ | | style="background:#FF9999;" | 139.0¢ ✗ | ||
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| '''4''' | | '''4''' | ||
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| style="background:#FF9999;" | 69.0¢ ✗ | | style="background:#FF9999;" | 69.0¢ ✗ | ||
| style="background:#FF9999;" | 96.0¢ ✗ | | style="background:#FF9999;" | 96.0¢ ✗ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 33.0¢ ✗ | ||
| style="background:# | | style="background:#90EE90;" | 16.0¢ ✓✓ | ||
| style="background:#FF9999;" | 49.0¢ ✗ | | style="background:#FF9999;" | 49.0¢ ✗ | ||
| style="background:# | | style="background:#90EE90;" | 17.0¢ ✓✓ | ||
| style="background:#FF9999;" | 182.0¢ ✗ | | style="background:#FF9999;" | 182.0¢ ✗ | ||
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| style="background:#FF9999;" | 69.0¢ ✗ | | style="background:#FF9999;" | 69.0¢ ✗ | ||
| style="background:#FF9999;" | 161.0¢ ✗ | | style="background:#FF9999;" | 161.0¢ ✗ | ||
| style="background:#90EE90;" | -6 | |||
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| '''5''' | | '''5''' | ||
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| style="background:#FF9999;" | 94.0¢ ✗ | | style="background:#FF9999;" | 94.0¢ ✗ | ||
| style="background:#FFD700;" | 18.0¢ ✓ | | style="background:#FFD700;" | 18.0¢ ✓ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 76.0¢ ✗ | ||
| style="background:#90EE90;" | 9.0¢ ✓✓ | | style="background:#90EE90;" | 9.0¢ ✓✓ | ||
| style="background:#FF9999;" | 36.0¢ ✗ | | style="background:#FF9999;" | 36.0¢ ✗ | ||
| style="background:#FF9999;" | 27.0¢ ✗ | | style="background:#FF9999;" | 27.0¢ ✗ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 76.0¢ ✗ | ||
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| style="background:#FF9999;" | 103.0¢ ✗ | | style="background:#FF9999;" | 103.0¢ ✗ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 58.0¢ ✗ | ||
| style="background:#FF9999;" | 89.0¢ ✗ | | style="background:#FF9999;" | 89.0¢ ✗ | ||
| style="background:#FF9999;" | 119.0¢ ✗ | | style="background:#FF9999;" | 119.0¢ ✗ | ||
| style="background:#90EE90;" | 9.0¢ ✓✓ | | style="background:#90EE90;" | 9.0¢ ✓✓ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 101.0¢ ✗ | ||
| style="background:#90EE90;" | -5 | |||
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| '''6''' | | '''6''' | ||
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| style="background:#FFD700;" | 13.7¢ ✓ | | style="background:#FFD700;" | 13.7¢ ✓ | ||
| style="background:#FF9999;" | 98.0¢ ✗ | | style="background:#FF9999;" | 98.0¢ ✗ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 84.3¢ ✗ | ||
| style="background:#FF9999;" | 31.2¢ ✗ | | style="background:#FF9999;" | 31.2¢ ✗ | ||
| style="background:#90EE90;" | 3.9¢ ✓✓ | | style="background:#90EE90;" | 3.9¢ ✓✓ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 66.8¢ ✗ | ||
| style="background:#FF9999;" | | | style="background:#FF9999;" | 84.3¢ ✗ | ||
| style="background:#FF9999;" | 48.7¢ ✗ | | style="background:#FF9999;" | 48.7¢ ✗ | ||
| style="background:# | | style="background:#90EE90;" | 17.5¢ ✓✓ | ||
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| style="background:#FF9999;" | | | style="background:#FF9999;" | 49.3¢ ✗ | ||
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| style="background:#FF9999;" | 138.5¢ ✗ | | style="background:#FF9999;" | 138.5¢ ✗ | ||
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| '''7''' | | '''7''' | ||
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| style="background:#FF9999;" | | | style="background:#FF9999;" | 27.3¢ ✗ | ||
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| style="background:#FF9999;" | 32.5¢ ✗ | | style="background:#FF9999;" | 32.5¢ ✗ | ||
| style="background:#FF9999;" | 75.9¢ ✗ | | style="background:#FF9999;" | 75.9¢ ✗ | ||
| style="background:# | | style="background:#FFD700;" | 27.3¢ ✓ | ||
| style="background:#FF9999;" | 37.0¢ ✗ | | style="background:#FF9999;" | 37.0¢ ✗ | ||
| style="background:#FF9999;" | 103.2¢ ✗ | | style="background:#FF9999;" | 103.2¢ ✗ | ||
| style="background:# | | style="background:#90EE90;" | 11.0¢ ✓✓ | ||
| style="background:# | | style="background:#FFD700;" | 20.8¢ ✓ | ||
| style="background:#90EE90;" | 16.6¢ ✓✓ | | style="background:#90EE90;" | 16.6¢ ✓✓ | ||
| style="background:#FF9999;" | 59.7¢ ✗ | | style="background:#FF9999;" | 59.7¢ ✗ | ||
| style="background:#FF9999;" | 32.8¢ ✗ | | style="background:#FF9999;" | 32.8¢ ✗ | ||
| style="background:#90EE90;" | -3 | |||
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| '''8''' | | '''8''' | ||
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| style="background:#FF9999;" | 63.7¢ ✗ | | style="background:#FF9999;" | 63.7¢ ✗ | ||
| style="background:#FF9999;" | 48.0¢ ✗ | | style="background:#FF9999;" | 48.0¢ ✗ | ||
| style="background:# | | style="background:#FFD700;" | 15.7¢ ✓ | ||
| style="background:#FF9999;" | 68.8¢ ✗ | | style="background:#FF9999;" | 68.8¢ ✗ | ||
| style="background:#FF9999;" | 53.9¢ ✗ | | style="background:#FF9999;" | 53.9¢ ✗ | ||
| style="background:#FF9999;" | 116.8¢ ✗ | | style="background:#FF9999;" | 116.8¢ ✗ | ||
| style="background:# | | style="background:#90EE90;" | 15.7¢ ✓✓ | ||
| style="background:#FF9999;" | 48.7¢ ✗ | | style="background:#FF9999;" | 48.7¢ ✗ | ||
| style="background:#FF9999;" | 132.5¢ ✗ | | style="background:#FF9999;" | 132.5¢ ✗ | ||
| style="background:#FF9999;" | 117.6¢ ✗ | | style="background:#FF9999;" | 117.6¢ ✗ | ||
| style="background:# | | style="background:#90EE90;" | 0.7¢ ✓✓ | ||
| style="background:#FF9999;" | 59.5¢ ✗ | | style="background:#FF9999;" | 59.5¢ ✗ | ||
| style="background:#FF9999;" | 68.8¢ ✗ | | style="background:#FF9999;" | 68.8¢ ✗ | ||
| style="background:# | | style="background:#90EE90;" | 11.5¢ ✓✓ | ||
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| '''9''' | | '''9''' | ||
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| style="background:#FF9999;" | 49.0¢ ✗ | | style="background:#FF9999;" | 49.0¢ ✗ | ||
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| style="background:#FF9999;" | 49.2¢ ✗ | | style="background:#FF9999;" | 49.2¢ ✗ | ||
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| style="background:# | | style="background:#90EE90;" | 17.3¢ ✓✓ | ||
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| '''10''' | | '''10''' | ||
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| style="background:#FF9999;" | 79.6¢ ✗ | | style="background:#FF9999;" | 79.6¢ ✗ | ||
| style="background:#90EE90;" | 1 | |||
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| '''12''' | | '''12''' | ||
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| '''14''' | | '''14''' | ||
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For 2/1 all pure-octave tunings (eg EDOs) will be excellent. For any interval N/1 you can work it out by reading the absolute error from the Nth harmonic on the tables. For any interval L/M you can figure it out by reading the abs error of L and the abs error of M and then simply adding the two together. | For 2/1 all pure-octave tunings (eg EDOs) will be excellent. For any interval N/1 you can work it out by reading the absolute error from the Nth harmonic on the tables. For any interval L/M you can figure it out by reading the abs error of L and the abs error of M and then simply adding the two together. | ||
Please make a wikitext table which shows how well every hyperconsonance, consonance, and ambisonance is approximated in every EDO from 1edo to 53edo, as well as showing each of their estimated number of dissonances.</pre> | Please make a wikitext table which shows how well every hyperconsonance, consonance, and ambisonance is approximated in every EDO from 1edo to 53edo, as well as showing each of their estimated number of dissonances.</pre> | ||