User:M-yac/Neutral Intervals and the FJS: Difference between revisions
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FilterNashi (talk | contribs) →Comparing the FJS and Neutral FJS: maintenance: this might a typo Tags: Mobile edit Mobile web edit Advanced mobile edit |
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* Lowering the FJS radius of tolerance. This ensures the formal comma of the 11th harmonic is a neutral interval (in particular, a semi-augmented fourth) which lets us write "n2_11" for [[12/11]], "n3^11" for [[11/9]], etc. | * Lowering the FJS radius of tolerance. This ensures the formal comma of the 11th harmonic is a neutral interval (in particular, a semi-augmented fourth) which lets us write "n2_11" for [[12/11]], "n3^11" for [[11/9]], etc. | ||
I call this modification the '''Neutral FJS''', and you can experiment with it [https://www.yacavone.net/fjs-explorer/?rotPreset=3&fifthSeqPreset=2 here] or in [https://www.yacavone.net/xen-calc/ xen-calc]. Be sure to check out the table | I call this modification the '''Neutral FJS''', and you can experiment with it [https://www.yacavone.net/fjs-explorer/?rotPreset=3&fifthSeqPreset=2 here] or in [https://www.yacavone.net/xen-calc/ xen-calc]. Be sure to check out the [[#nfjs-examples|table of examples]] at the end of the third section. | ||
In the first section, I precisely define what a Pythagorean interval is, and in the second, show how to extend this definition naturally to include neutral intervals. If you don't care about the details, skip to the table at the end of the second section. In the third second, I give a brief overview of the FJS and discuss how to modify it. In the last two sections, we discuss the pros and cons of this modification and preview some generalizations. | In the first section, I precisely define what a Pythagorean interval is, and in the second, show how to extend this definition naturally to include neutral intervals. If you don't care about the details, skip to the table at the end of the second section. In the third second, I give a brief overview of the FJS and discuss how to modify it. In the last two sections, we discuss the pros and cons of this modification and preview some generalizations. | ||
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{| class="wikitable" | {| class="wikitable" | ||
|+ FJS vs. Neutral FJS symbols in the 13-limit | |+id="nfjs-examples"| FJS vs. Neutral FJS symbols in the 13-limit | ||
|- | |- | ||
! Ratio !! Name !! FJS Symbol !! Neutral FJS Symbol || Cents | ! Ratio !! Name !! FJS Symbol !! Neutral FJS Symbol || Cents | ||
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| 8ve - diesis || 1140c - 1170c || sd8 || 1143.16c - 1166.62c | | 8ve - diesis || 1140c - 1170c || sd8 || 1143.16c - 1166.62c | ||
|- | |- | ||
| 8vs - commas || 1170c - 1200c || | | 8vs - commas || 1170c - 1200c || P8 || 1166.62c - 1200c | ||
|} | |} | ||