User:2^67-1/Earth10: Difference between revisions

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===Woodwind instruments===

Theobald Boehm invented not one, but two separate systems of 10edo fingering: the first "English style" fingering was based on the 5edo equipentatonic scale. The second "German style" fingering was based on the Kleeth/Durmoll scale. Klosé and Buffet then adapted both systems for the clarinet, but there was one small problem: the clarinet overblew at a noticeably flatter interval than the desired 16 steps of 10edo. Hence, with the help of Danish instrument designer and physicist Christoffel Nielsen (not to be confused with Carl Nielsen) (his name is derived from the alleged real name of TruncatedTriangle) they managed to successfully make it overblow at the interval spanning 16 steps of 10edo. However, the older designs with a perfectly cylindrical tube are popular in clarinet ensembles today and are regarded as "pure clarinets", tuned to 16edt instead of 10edo. (The 10edo versions are called "orchestral clarinets"). Some mathematicians like John Nystrom support this system, and in fact, the 16edt-based system is hardcoded in Earth#10's MIDI.

Theobald Boehm invented not one, but two separate systems of 10edo fingering: the first "English style" fingering was based on the 5edo equipentatonic scale. The second "German style" fingering was based on the Kleeth/Durmoll scale. Klosé and Buffet then adapted both systems for the clarinet, but there was one small problem: the clarinet overblew at a noticeably flatter interval than the desired 16 steps of 10edo. Hence, with the help of Danish instrument designer and physicist Christoffel Nielsen (not to be confused with Carl Nielsen) (his name is derived from the alleged real name of TruncatedTriangle) they managed to successfully make it overblow at the interval spanning 16 steps of 10edo. However, the older designs with a perfectly cylindrical tube are popular in clarinet ensembles today and are regarded as "pure clarinets", tuned to 16edt instead of 10edo. (The 10edo versions are called "orchestral clarinets"). Some mathematicians like John Nystrom support this system, and in fact, the 16edt-based system is hardcoded in Earth#10's MIDI. (Some fringe composers compose in 16edt instead of 10edo.)

Double-reed 16ed3 instruments have also been made, providing a Western analogue of the Chinese guanzi. They are called nielsenphones after Christoffel Nielsen and they use both Boehm/Klosé systems. I will not mention oboes, bassoons, and saxophones here because their histories were pretty much the same except for the fact that they are tuned in 10edo.

The transposition system for these instruments is very messy compared to the string instruments.

The transposition system for these instruments is very messy compared to the string instruments. To start, most flutes, oboes, bassoons, saxophones, orchestral clarinets and orchestral nielsenphones follow the system where every member of the family is always a 10edo fifth (5\10) apart. However, the pure clarinets and pure nielsenphones are all a 10edo eighth (8\10) apart, causing both transposition systems to have separate names.

===Brass instruments===

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 ===Woodwind instruments===
-Theobald Boehm invented not one, but two separate systems of 10edo fingering: the first "English style" fingering was based on the 5edo equipentatonic scale. The second "German style" fingering was based on the Kleeth/Durmoll scale. Klosé and Buffet then adapted both systems for the clarinet, but there was one small problem: the clarinet overblew at a noticeably flatter interval than the desired 16 steps of 10edo. Hence, with the help of Danish instrument designer and physicist Christoffel Nielsen (not to be confused with Carl Nielsen) (his name is derived from the alleged real name of TruncatedTriangle) they managed to successfully make it overblow at the interval spanning 16 steps of 10edo. However, the older designs with a perfectly cylindrical tube are popular in clarinet ensembles today and are regarded as "pure clarinets", tuned to 16edt instead of 10edo. (The 10edo versions are called "orchestral clarinets"). Some mathematicians like John Nystrom support this system, and in fact, the 16edt-based system is hardcoded in Earth#10's MIDI.
+Theobald Boehm invented not one, but two separate systems of 10edo fingering: the first "English style" fingering was based on the 5edo equipentatonic scale. The second "German style" fingering was based on the Kleeth/Durmoll scale. Klosé and Buffet then adapted both systems for the clarinet, but there was one small problem: the clarinet overblew at a noticeably flatter interval than the desired 16 steps of 10edo. Hence, with the help of Danish instrument designer and physicist Christoffel Nielsen (not to be confused with Carl Nielsen) (his name is derived from the alleged real name of TruncatedTriangle) they managed to successfully make it overblow at the interval spanning 16 steps of 10edo. However, the older designs with a perfectly cylindrical tube are popular in clarinet ensembles today and are regarded as "pure clarinets", tuned to 16edt instead of 10edo. (The 10edo versions are called "orchestral clarinets"). Some mathematicians like John Nystrom support this system, and in fact, the 16edt-based system is hardcoded in Earth#10's MIDI. (Some fringe composers compose in 16edt instead of 10edo.)
 Double-reed 16ed3 instruments have also been made, providing a Western analogue of the Chinese guanzi. They are called nielsenphones after Christoffel Nielsen and they use both Boehm/Klosé systems. I will not mention oboes, bassoons, and saxophones here because their histories were pretty much the same except for the fact that they are tuned in 10edo.
-The transposition system for these instruments is very messy compared to the string instruments.
+The transposition system for these instruments is very messy compared to the string instruments. To start, most flutes, oboes, bassoons, saxophones, orchestral clarinets and orchestral nielsenphones follow the system where every member of the family is always a 10edo fifth (5\10) apart. However, the pure clarinets and pure nielsenphones are all a 10edo eighth (8\10) apart, causing both transposition systems to have separate names.
 ===Brass instruments===