Nelinda: Difference between revisions

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=Xenharmonic Systems for Nelinda=

Similar to the mutual affinity between the tritave-repeating [[Bohlen-Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 3n+1 spectrum like the nelinda can be developed, repeating at the 4/1 ratio~~, which could be called a~~ ''tetratave''.

Similar to the mutual affinity between the tritave-repeating [[Bohlen-Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 3n+1 spectrum like the nelinda can be developed, repeating at the 4/1 ratio (or ''tetratave'').

~~Operating on a single tetratave of~~ the ~~series gives us~~ a 4.7.10.13 JI subgroup, of which [[640/637]] serves as a notable comma.

4:7:10:13 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working with 4.7.10.13 JI subgroup, of which [[640/637]] serves as a notable comma.

Searching in Graham Breed's temperament finder, we quickly find the 27&20 (with respect to the tetratave) [http://x31eq.com/cgi-bin/rt.cgi?ets=14qddrrrfff_10p&limit=4_7_10_13 linear temperament], ~~tentatively called~~ ''Nelindic''~~, which tempers out the comma with aplomb~~. It has an approximate 16/13 as its generator and forms MOS of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale.

Searching in Graham Breed's temperament finder for said comma, we quickly find the 27&20 (with respect to the tetratave) [http://x31eq.com/cgi-bin/rt.cgi?ets=14qddrrrfff_10p&limit=4_7_10_13 linear temperament], which we could call ''Nelindic''. It has an approximate 16/13 as its generator and forms MOS of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale.

[[27ed4]] is an okay tuning for Nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).

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 =Xenharmonic Systems for Nelinda=
-Similar to the mutual affinity between the tritave-repeating [[Bohlen-Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 3n+1 spectrum like the nelinda can be developed, repeating at the 4/1 ratio, which could be called a ''tetratave''.
+Similar to the mutual affinity between the tritave-repeating [[Bohlen-Pierce]] scale and the clarinet, with its spectrum of odd harmonics, a tuning system specifically for a 3n+1 spectrum like the nelinda can be developed, repeating at the 4/1 ratio (or ''tetratave'').
-Operating on a single tetratave of the series gives us a 4.7.10.13 JI subgroup, of which [[640/637]] serves as a notable comma.
+:7:10:13 would serve as the basic chord for such a system, directly analogous to 4:5:6(:7) in "normal" ditave-repeating music and 3:5:7 for BP. This translates without issue to working with 4.7.10.13 JI subgroup, of which [[640/637]] serves as a notable comma.
-Searching in Graham Breed's temperament finder, we quickly find the 27&20 (with respect to the tetratave) [http://x31eq.com/cgi-bin/rt.cgi?ets=14qddrrrfff_10p&limit=4_7_10_13 linear temperament], tentatively called ''Nelindic'', which tempers out the comma with aplomb. It has an approximate 16/13 as its generator and forms MOS of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale.
+Searching in Graham Breed's temperament finder for said comma, we quickly find the 27&20 (with respect to the tetratave) [http://x31eq.com/cgi-bin/rt.cgi?ets=14qddrrrfff_10p&limit=4_7_10_13 linear temperament], which we could call ''Nelindic''. It has an approximate 16/13 as its generator and forms MOS of 6, 7, and 13 notes for starters, the latter of which yields a good albitonic scale.
 [[27ed4]] is an okay tuning for Nelindic (especially with compression), but [[47ed4]] ''really'' knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).