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26edo: Difference between revisions

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→Orgone Temperament: here it's better
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→Orgone Temperament: Do we really need to explain on the page for 26 how these EDOs are better than 26? This could be moved to its own page
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The primary triad for orgone temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates [[16/11|16:11]] and 3g approximates [[7/4|7:4]] (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.
The primary triad for orgone temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates [[16/11|16:11]] and 3g approximates [[7/4|7:4]] (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.


[[37edo]] is another orgone tuning, and [[89edo]] is better even than 26. If we take 11 and 26 to be the edges of the Orgone Spectrum, we may fill in the rest of the spectrum thus:


{| class="wikitable"
|-
| | 3\11
| |
| |
| |
| |
|-
| |
| |
| |
| |
| | 19\70
|-
| |
| |
| |
| | 16\59
| |
|-
| |
| |
| |
| |
| | 29\107
|-
| |
| |
| | 13\48
| |
| |
|-
| |
| |
| |
| |
| | 36\133
|-
| |
| |
| |
| | 23\85
| |
|-
| |
| |
| |
| |
| | 33\122
|-
| |
| | 10\37
| |
| |
| |
|-
| |
| |
| |
| |
| | 37\137
|-
| |
| |
| |
| | 27\100
| |
|-
| |
| |
| |
| |
| | 44\163
|-
| |
| |
| | 17\63
| |
| |
|-
| |
| |
| |
| |
| | 41\152
|-
| |
| |
| |
| | 24\89
| |
|-
| |
| |
| |
| |
| | 31\115
|-
| | 7\26
| |
| |
| |
| |
|}
Orgone has a minimax tuning which sharpens both 7 and 11 by 1/5 of an orgonisma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgonisma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.


[[File:orgone_heptatonic.jpg|alt=orgone_heptatonic.jpg|orgone_heptatonic.jpg]]
[[File:orgone_heptatonic.jpg|alt=orgone_heptatonic.jpg|orgone_heptatonic.jpg]]
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