Nelinda: Difference between revisions

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The '''nelinda''' is a ~~conceptual~~ family of single-reed instruments developed by [https://www.youtube.com/user/TruncatedTriangle/ TruncatedTriangle]. In contrast to the conical-bore saxophone, which produces all ~~(1n+1)~~ harmonics, and the cylindrical-bore clarinet, which produces mostly odd-numbered (2n+1) harmonics, the nelinda has a taper opposite in direction to the saxophone (that is, wider at the mouthpiece end and narrower at the bell end) designed to highlight the ''3n+1'' harmonics (that is, harmonics 1, 4 ,7, 10, 13, etc.)

The '''nelinda''' is a hypothetical family of single-reed instruments developed by [https://www.youtube.com/user/TruncatedTriangle/ TruncatedTriangle]. In contrast to the conical-bore saxophone, which produces all harmonics, and the cylindrical-bore clarinet, which produces mostly odd-numbered ({{nowrap| 2''n'' + 1 }}) harmonics, the nelinda has a taper opposite in direction to the saxophone (that is, wider at the mouthpiece end and narrower at the bell end) designed to highlight the {{nowrap| 3''n'' + 1 }} harmonics (that is, harmonics 1, 4, 7, 10, 13, etc.)

This implies that it will overblow not at the octave/ditave (2/1) or the twelfth/tritave (3/1) like other single-reeds, but instead at the fifteenth or double octave (4/1), giving it a wide range.

=Xenharmonic ~~Systems~~ for ~~Nelinda~~=

== 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 (3''n'' + 1) spectrum like the nelinda can be developed, repeating at the 4/1 ratio (or ''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~~, which ~~could be called~~ a ~~''tetratave''~~.

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 within a 4.7.10.13 JI subgroup, of which [[640/637]] is a notable comma.

~~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~~.

The {{nowrap| 20 & 27 }} (with respect to the tetratave) [https://sintel.pythonanywhere.com/result?subgroup=4.7.10.13&reduce=on&weights=weil&target=&edos=20%2C27&submit_edo=submit&commas= linear temperament] is a notable entry that tempers out the said comma, which we could call ''nelindic'', and corresponds to [[huntington]] excluding every other peiod. 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). Note that 20ed4 is just 10edo, where 5/4 (and possibly also 7/4) is tuned too flat,.

~~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.

[[Category:Instruments]]

[[Category:Nonoctave]]

[[~~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).~~

[[Category:Subgroup]]

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-The '''nelinda''' is a conceptual family of single-reed instruments developed by [https://www.youtube.com/user/TruncatedTriangle/ TruncatedTriangle]. In contrast to the conical-bore saxophone, which produces all (1n+1) harmonics, and the cylindrical-bore clarinet, which produces mostly odd-numbered (2n+1) harmonics, the nelinda has a taper opposite in direction to the saxophone (that is, wider at the mouthpiece end and narrower at the bell end) designed to highlight the ''3n+1'' harmonics (that is, harmonics 1, 4 ,7, 10, 13, etc.)
+The '''nelinda''' is a hypothetical family of single-reed instruments developed by [https://www.youtube.com/user/TruncatedTriangle/ TruncatedTriangle]. In contrast to the conical-bore saxophone, which produces all harmonics, and the cylindrical-bore clarinet, which produces mostly odd-numbered ({{nowrap| 2''n'' + 1 }}) harmonics, the nelinda has a taper opposite in direction to the saxophone (that is, wider at the mouthpiece end and narrower at the bell end) designed to highlight the {{nowrap| 3''n'' + 1 }} harmonics (that is, harmonics 1, 4, 7, 10, 13, etc.)
 This implies that it will overblow not at the octave/ditave (2/1) or the twelfth/tritave (3/1) like other single-reeds, but instead at the fifteenth or double octave (4/1), giving it a wide range.
-=Xenharmonic Systems for Nelinda=
+== 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 (3''n'' + 1) spectrum like the nelinda can be developed, repeating at the 4/1 ratio (or ''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, which could be called a ''tetratave''.
+: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 within a 4.7.10.13 JI subgroup, of which [[640/637]] is a notable comma.
-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.
+The {{nowrap| 20 & 27 }} (with respect to the tetratave) [https://sintel.pythonanywhere.com/result?subgroup=4.7.10.13&reduce=on&weights=weil&target=&edos=20%2C27&submit_edo=submit&commas= linear temperament] is a notable entry that tempers out the said comma, which we could call ''nelindic'', and corresponds to [[huntington]] excluding every other peiod. 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). Note that 20ed4 is just 10edo, where 5/4 (and possibly also 7/4) is tuned too flat,.
-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.
+[[Category:Instruments]]
+[[Category:Nonoctave]]
-[[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).
+[[Category:Subgroup]]