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 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.)

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.

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=Xenharmonic Systems for Nelinda=

Similar to the mutual affinity between the Bohlen-Pierce scale

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''.

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.

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.

[[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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-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 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.)
 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.
@@ Line 5: / Line 5: @@
 =Xenharmonic Systems for Nelinda=
-Similar to the mutual affinity between the Bohlen-Pierce scale
+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''.
+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.
+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.
+[[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).