Nelinda: Difference between revisions

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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.

2:5:8:11(:14) 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(.14) JI subgroup, of which 125/121 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~~]].

Searching in Graham Breed's temperament finder for said comma, we quickly find the 9&8/7 (with respect to the major decade) [http://x31eq.com/cgi-bin/uv.cgi?uvs=125%3A121&page=2&limit=2_5_8_11 linear temperament], which we could call ''Major Decimophonic.'' It has an approximate 19/17 or 4/3 as its generator and forms MOS of 7 or 8, 9 and 16 or 17 notes for starters, the latter of which yields a good albitonic scale.

Unlike the nelinda, the decimophone has branches. The most important one beside that already mentioned will have a taper designed to highlight the ''4n+3'' harmonics (that is, the other harmonics of the clarinet.)

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 4n+3 spectrum like the decimophone can be developed, repeating at the 7/3 ratio (or ''minor decade'').

3:7:11:15(:19) 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 3.7.11.15(.19) JI subgroup, of which 135/133 is a notable comma.

Searching in Graham Breed's temperament finder for said comma, we quickly find, beside more convoluted definitions of [[Bohlen-Pierce]], in top-down order, the 8&3, 17&8, 10&8, 8&7, and 14&8 (with respect to the minor decade) [http://x31eq.com/cgi-bin/uv.cgi?uvs=125%3A121&page=2&limit=2_5_8_11 linear temperaments], which we could call ''Minor Decimophonic.'' They have either the 7/3 or an approximate 14/9 as their period and form MOS of 5 through 7, or 8, 9 through 11, 13 through 15 and 17 or 18 notes for starters, the latter of which yield good albitonic scales.

17ed of either tenth is an okay tuning for either Decimophonic (especially with stretching), but 25ed of either tenth knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).

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 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.
+:5:8:11(:14) 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(.14) JI subgroup, of which 125/121 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]].
+Searching in Graham Breed's temperament finder for said comma, we quickly find the 9&8/7 (with respect to the major decade) [http://x31eq.com/cgi-bin/uv.cgi?uvs=125%3A121&page=2&limit=2_5_8_11 linear temperament], which we could call ''Major Decimophonic.'' It has an approximate 19/17 or 4/3 as its generator and forms MOS of 7 or 8, 9 and 16 or 17 notes for starters, the latter of which yields a good albitonic scale.
+Unlike the nelinda, the decimophone has branches. The most important one beside that already mentioned will have a taper designed to highlight the ''4n+3'' harmonics (that is, the other harmonics of the clarinet.)
+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 4n+3 spectrum like the decimophone can be developed, repeating at the 7/3 ratio (or ''minor decade'').
+:7:11:15(:19) 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 3.7.11.15(.19) JI subgroup, of which 135/133 is a notable comma.
+Searching in Graham Breed's temperament finder for said comma, we quickly find, beside more convoluted definitions of [[Bohlen-Pierce]], in top-down order, the 8&3, 17&8, 10&8, 8&7, and 14&8 (with respect to the minor decade) [http://x31eq.com/cgi-bin/uv.cgi?uvs=125%3A121&page=2&limit=2_5_8_11 linear temperaments], which we could call ''Minor Decimophonic.'' They have either the 7/3 or an approximate 14/9 as their period and form MOS of 5 through 7, or 8, 9 through 11, 13 through 15 and 17 or 18 notes for starters, the latter of which yield good albitonic scales.
+ed of either tenth is an okay tuning for either Decimophonic (especially with stretching), but 25ed of either tenth knocks it out of the park (similar to 12ed2 vs 31ed2 for 2.3.5).