Nelinda: Difference between revisions

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[[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).

= Decimophone =

Unlike the saxophone, the nelinda is still viable as an instrument with its taper reversed (that is, narrower at the mouthpiece end and wider at the bell end). This will be the branch of the '''decimophone''' which highlights the 3n+''2'' harmonics (that is, harmonics 2, 5, 8, 11, 14 etc.)

This implies that overblowing at the major tenth, unlike other common full tubes, but instead like partial-tube trumpets, does not highlight the fundamental.

= Xenharmonic Systems for Decimophone =

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+2 spectrum like the decimophone can be developed, repeating at the 5/2 ratio (or ''major decade'').

2:5:8:11 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 2.5.8.11 JI subgroup, of which [[128/125]] is a notable comma.

Searching in Graham Breed's temperament finder for said comma, we quickly find the 4n (with respect to the major decade) [http://x31eq.com/cgi-bin/uv.cgi linear temperament], which we call ''[[Augmented family|augmented]].'' It is clear this is not a very interesting result, being nothing more than a less intuitively useful way of looking at [[12edo]].

@@ Line 12: / Line 12: @@
 [[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).
+= Decimophone =
+Unlike the saxophone, the nelinda is still viable as an instrument with its taper reversed (that is, narrower at the mouthpiece end and wider at the bell end).  This will be the branch of the '''decimophone''' which highlights the 3n+''2'' harmonics (that is, harmonics 2, 5, 8, 11, 14 etc.)
+This implies that overblowing at the major tenth, unlike other common full tubes, but instead like partial-tube trumpets, does not highlight the fundamental.
+= Xenharmonic Systems for Decimophone =
+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+2 spectrum like the decimophone can be developed, repeating at the 5/2 ratio (or ''major decade'').
+:5:8:11 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 2.5.8.11 JI subgroup, of which [[128/125]] is a notable comma.
+Searching in Graham Breed's temperament finder for said comma, we quickly find the 4n (with respect to the major decade) [http://x31eq.com/cgi-bin/uv.cgi linear temperament], which we call ''[[Augmented family|augmented]].'' It is clear this is not a very interesting result, being nothing more than a less intuitively useful way of looking at [[12edo]].