List of octave-reduced harmonics: Difference between revisions
Changed the text to enable the inclusion of the octave in the chart for reference |
Recast lead section, fixed typo, added internal links (for convenience; same reason all edo mentions already have links), replaced 9 by 3 × 3 in factorization, categories |
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This is a list of overtones ([[harmonic]]s) up to 255, sorted by ascending pitch of their [[Octave reduction|octave-reduced]] equivalent (except the octave, which is not reduced). Prime overtones are in bold. | |||
{| class="wikitable center-1 right-2 sortable" | {| class="wikitable center-1 right-2 sortable" | ||
|- | |- | ||
! Overtone | ! Overtone | ||
! Size ([[cents|¢]])<ref>cent values are given for the | ! Size ([[cents|¢]])<ref>cent values are given for the octave reduced equivalent</ref> | ||
! class="unsortable" | Factorization | ! class="unsortable" | Factorization | ||
! class="unsortable" | Name | ! class="unsortable" | Name | ||
| Line 109: | Line 109: | ||
| 3 x 3 | | 3 x 3 | ||
| major whole-tone / Pythagorean whole tone | | major whole-tone / Pythagorean whole tone | ||
| 3-limit | | [[3-limit]] | ||
|- | |- | ||
| 145 | | 145 | ||
| Line 127: | Line 127: | ||
| 3 x 7 x 7 | | 3 x 7 x 7 | ||
| | | | ||
| 7-limit / close to 1 degree of [[5edo]], square root of 21 | | [[7-limit]] / close to 1 degree of [[5edo]], square root of 21 | ||
|- | |- | ||
| '''37''' | | '''37''' | ||
| Line 145: | Line 145: | ||
| 3 x 5 x 5 | | 3 x 5 x 5 | ||
| augmented second | | augmented second | ||
| 5-limit / close to 5 degrees of [[22edo]], 3 degrees of [[13edo]], square root of 11 | | [[5-limit]] / close to 5 degrees of [[22edo]], 3 degrees of [[13edo]], square root of 11 | ||
|- | |- | ||
| '''151''' | | '''151''' | ||
| Line 175: | Line 175: | ||
| 3 x 13 | | 3 x 13 | ||
| | | | ||
| 13-limit / close to 2 degrees of [[7edo]] | | [[13-limit]] / close to 2 degrees of [[7edo]] | ||
|- | |- | ||
| '''157''' | | '''157''' | ||
| Line 199: | Line 199: | ||
| '''prime''' | | '''prime''' | ||
| '''5-limit major third''' | | '''5-limit major third''' | ||
| '''5-limit / close to 10 degrees of [[31edo]]''' | | '''[[5-limit]] / close to 10 degrees of [[31edo]]''' | ||
|- | |- | ||
| '''161''' | | '''161''' | ||
| Line 209: | Line 209: | ||
| 81 | | 81 | ||
| 407.820 | | 407.820 | ||
| | | 3 x 3 × 3 × 3 | ||
| Pythagorean major third | | Pythagorean major third | ||
| 3-limit | | [[3-limit]] | ||
|- | |- | ||
| '''163''' | | '''163''' | ||
| Line 241: | Line 241: | ||
| 3 x 7 | | 3 x 7 | ||
| narrow fourth / septimal fourth | | narrow fourth / septimal fourth | ||
| 7-limit / close to 9 degrees of [[23edo]] | | [[7-limit]] / close to 9 degrees of [[23edo]] | ||
|- | |- | ||
| 169 | | 169 | ||
| Line 247: | Line 247: | ||
| 13 x 13 | | 13 x 13 | ||
| | | | ||
| 13-limit / close to 2 degrees of [[5edo]], square root of 7 | | [[13-limit]] / close to 2 degrees of [[5edo]], square root of 7 | ||
|- | |- | ||
| 85 | | 85 | ||
| Line 289: | Line 289: | ||
| '''prime''' | | '''prime''' | ||
| '''undecimal semi-augmented fourth / undecimal tritone''' | | '''undecimal semi-augmented fourth / undecimal tritone''' | ||
| '''11-limit / close to 11 degrees of [[24edo]]''' | | '''[[11-limit]] / close to 11 degrees of [[24edo]]''' | ||
|- | |- | ||
| 177 | | 177 | ||
| Line 313: | Line 313: | ||
| 3 x 3 x 5 | | 3 x 3 x 5 | ||
| high 5-limit tritone | | high 5-limit tritone | ||
| 5-limit / close to square root of 15 | | [[5-limit]] / close to square root of 15 | ||
|- | |- | ||
| '''181''' | | '''181''' | ||
| Line 325: | Line 325: | ||
| 7 x 13 | | 7 x 13 | ||
| | | | ||
| 13-limit | | [[13-limit]] | ||
|- | |- | ||
| 183 | | 183 | ||
| Line 367: | Line 367: | ||
| 3 x 3 x 3 x 7 | | 3 x 3 x 3 x 7 | ||
| | | | ||
| 7-limit / close to 9 degrees of [[16edo]], square root of 35 | | [[7-limit]] / close to 9 degrees of [[16edo]], square root of 35 | ||
|- | |- | ||
| 95 | | 95 | ||
| Line 385: | Line 385: | ||
| '''prime''' | | '''prime''' | ||
| '''just perfect fifth''' | | '''just perfect fifth''' | ||
| '''3-limit / close to 7 degrees of [[12edo]]''' | | '''[[3-limit]] / close to 7 degrees of [[12edo]]''' | ||
|- | |- | ||
| '''193''' | | '''193''' | ||
| Line 403: | Line 403: | ||
| 3 x 5 x 13 | | 3 x 5 x 13 | ||
| | | | ||
| 13-limit / close to 19 degrees of [[31edo]], square root of 37 | | [[13-limit]] / close to 19 degrees of [[31edo]], square root of 37 | ||
|- | |- | ||
| 49 | | 49 | ||
| Line 409: | Line 409: | ||
| 7 x 7 | | 7 x 7 | ||
| | | | ||
| 7-limit / close to 8 degrees of [[13edo]] | | [[7-limit]] / close to 8 degrees of [[13edo]] | ||
|- | |- | ||
| '''197''' | | '''197''' | ||
| Line 421: | Line 421: | ||
| 3 x 3 x 11 | | 3 x 3 x 11 | ||
| | | | ||
| 11-limit / close to 5 degrees of [[8edo]] / 12 degrees of [[19edo]] | | [[11-limit]] / close to 5 degrees of [[8edo]] / 12 degrees of [[19edo]] | ||
|- | |- | ||
| '''199''' | | '''199''' | ||
| Line 433: | Line 433: | ||
| 5 x 5 | | 5 x 5 | ||
| augmented fifth | | augmented fifth | ||
| 5-limit / close to 9 degrees of [[14edo]] / 11 degrees of [[17edo]], square root of 39 | | [[5-limit]] / close to 9 degrees of [[14edo]] / 11 degrees of [[17edo]], square root of 39 | ||
|- | |- | ||
| 201 | | 201 | ||
| Line 481: | Line 481: | ||
| '''prime''' | | '''prime''' | ||
| '''overtone sixth, golden overtone''' | | '''overtone sixth, golden overtone''' | ||
| '''13-limit / close to 7 degrees of [[10edo]], golden ratio''' | | '''[[13-limit]] / close to 7 degrees of [[10edo]], golden ratio''' | ||
|- | |- | ||
| 209 | | 209 | ||
| Line 493: | Line 493: | ||
| 3 x 5 x 7 | | 3 x 5 x 7 | ||
| | | | ||
| 7-limit / close to 5 degrees of [[7edo]], square root of 43 | | [[7-limit]] / close to 5 degrees of [[7edo]], square root of 43 | ||
|- | |- | ||
| '''211''' | | '''211''' | ||
| Line 523: | Line 523: | ||
| 3 x 3 x 3 | | 3 x 3 x 3 | ||
| Pythagorean major sixth | | Pythagorean major sixth | ||
| 3-limit | | [[3-limit]] | ||
|- | |- | ||
| 217 | | 217 | ||
| Line 547: | Line 547: | ||
| 5 x 11 | | 5 x 11 | ||
| | | | ||
| 11-limit / close to 18 degrees of [[23edo]] | | [[11-limit]] / close to 18 degrees of [[23edo]] | ||
|- | |- | ||
| 221 | | 221 | ||
| Line 571: | Line 571: | ||
| '''prime''' | | '''prime''' | ||
| '''harmonic seventh / septimal minor seventh''' | | '''harmonic seventh / septimal minor seventh''' | ||
| '''7-limit / close to 17 degrees of [[21edo]] / 25 degrees of [[31edo]]''' | | '''[[7-limit]] / close to 17 degrees of [[21edo]] / 25 degrees of [[31edo]]''' | ||
|- | |- | ||
| 225 | | 225 | ||
| Line 577: | Line 577: | ||
| 3 x 3 x 5 x 5 | | 3 x 3 x 5 x 5 | ||
| 5-limit subminor seventh | | 5-limit subminor seventh | ||
| 5-limit / close to 11 degrees of [[16edo]] | | [[5-limit]] / close to 11 degrees of [[16edo]] | ||
|- | |- | ||
| '''113''' | | '''113''' | ||
| Line 631: | Line 631: | ||
| 3 x 3 x 13 | | 3 x 3 x 13 | ||
| | | | ||
| 13-limit / close to 13 degrees of [[15edo]] / 20 degrees of [[23edo]] | | [[13-limit]] / close to 13 degrees of [[15edo]] / 20 degrees of [[23edo]] | ||
|- | |- | ||
| 235 | | 235 | ||
| Line 667: | Line 667: | ||
| 3 x 5 | | 3 x 5 | ||
| 5-limit major seventh | | 5-limit major seventh | ||
| 5-limit / close to 19 degrees of [[21edo]] / 10 degrees of [[11edo]] | | [[5-limit]] / close to 19 degrees of [[21edo]] / 10 degrees of [[11edo]] | ||
|- | |- | ||
| '''241''' | | '''241''' | ||
| Line 679: | Line 679: | ||
| 11 x 11 | | 11 x 11 | ||
| | | | ||
| 11-limit / close to 11 degrees of [[12edo]], square root of 57 | | [[11-limit]] / close to 11 degrees of [[12edo]], square root of 57 | ||
|- | |- | ||
| 243 | | 243 | ||
| 1109.775 | | 1109.775 | ||
| 3 x 3 x 3 x | | 3 x 3 x 3 x 3 × 3 | ||
| Pythagorean major seventh | | Pythagorean major seventh | ||
| close to 12 degrees of [[13edo]] | | close to 12 degrees of [[13edo]] | ||
| Line 727: | Line 727: | ||
| 5 x 5 x 5 | | 5 x 5 x 5 | ||
| | | | ||
| 5-limit, close to square root of 61 | | [[5-limit]], close to square root of 61 | ||
|- | |- | ||
| '''251''' | | '''251''' | ||
| Line 739: | Line 739: | ||
| 3 x 3 x 7 | | 3 x 3 x 7 | ||
| | | | ||
| 7-limit | | [[7-limit]] | ||
|- | |- | ||
| 253 | | 253 | ||
| Line 767: | Line 767: | ||
<references /> | <references /> | ||
[[Category:Interval collection]] | [[Category:Interval collection]] | ||
[[Category: | [[Category:Harmonic]] | ||