User:2^67-1/Earth10

Prospective history

In the late 18th century British people gravitated towards equipentatonic scales for their pentatonic melodies, and hence they divided their pentatonic 'step' into two parts to allow for consonant triads. They discovered that the [0 3 6] triad was actually the most consonant in 10edo. Hence, the neopentatonicist style was the original method of 10edo composition when it first existed.

Then the French Revolution happened. France formed an alliance with Britain due to the former realizing the latter have a 10-tone system. Hence France, who decided to turn everything metric, promoted the British 10-note system to the rest of Europe. The British colonies at the time were the first to pick this up, then the rest of continental Europe, starting with the Netherlands.

The equivalent of the Second Viennese School in this universe, the New Pythagoreans, were a group of cultists from America and England who believed that the decimal sequences of irrational numbers held the key to greater understanding of the universe, because of 'music of the spheres' and whatnot. The first New Pythagorean composer was William Shanks who was in love with the sequence 4592307816, as it is the first pandigital sequence in pi, and used it as a tone row in his magnum opus, Symphony in Pi. To this day this sequence of intervals is known as the Shanks row or the Shanks motif.

Then, Arnold Schoenberg (who is American) took up Shanks' idea and, unlike Shanks, used other tone-rows. His students, Scott Mount and Anthony Weaver were also New Pythagorean composers.

Since some composers weren't happy with neopentatonicism, they decided to make their own style informed by Mozart, which was based on the Durmoll scale (what we call Kleeth), and a dicot-based harmonic system. Many neo-Baroque chorales and chorale collections were written using this system.

William Shanks viewed nationalism as a catalyst for war, hence he decided to turn to the universal and mathematical world, hence New Pythagoreanism being almost anti-Romanticist. As a result, France and the greater Slavic world decided to adopt New Pythagoreanism, with Les Six and the Five (or the Mighty Handful) becoming major international proponents.

This attracted many Christian musicians and composers (Scott Mount was one of them). Mount wrote a Mass in 10edo, which was half-dicot-based and half-neopentatonicist, with a few small sections in the New Pythagorean style.

Many African traditions (not sure which ones) developed equipentatonic systems. We take the fact that the French liked 10edo (what they call ‘metric tuning’) so much so that they even promoted it inside their colonies. This initially had more success than expected, due to a common arrangement by [TBD balafon player] who proposed the idea of two parallel balafons covering the entire 10edo gamut. This somehow eventually spread to America during the African slave trade and developed a new type of music (still called jazz), but Earth#10 jazz is more adventurous in the fact that they would regard each note of 10edo as equally important and thus they would regard the chromatic gamut as the scale itself. Equally interesting was the use of the [0 3 6 8] chord in 10edo as the main ‘primary’ chord in Earth#10 jazz music.

Earth#10 jazz music has more African influence in its instrumentation as well, with modern balafons being extremely common in jazz and other popular musical styles. As such, European wind instruments are not used at all, and hence the saxophone is more commonly used in the orchestra.

Sociopolitical structure of this world

There is a Northwestern European Union consisting of the Netherlands (called Holland in-universe), France, and the United Kingdom. Belgium did not gain independence from the Netherlands.

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Music theory

The notes are called 0 1 2 3 4 5 6 7 8 9. 0 of the 4th dekatave is written as 0_4 and has a frequency of 200*sqrt(2) Hz. Music is written with a jianpu-style notation which has been adopted worldwide in the early 20th century.

There are three main modes used in composition: dicot[7], called Durmoll (seen above), 5edo, and 10edo. Traditioanlly the main triad is taken to be [0 3 6]. Neopentatonicist composers use this triad on only the pentatonic notes on a certain mode, though more modern reincarnations of this style remove that requirement. Neopentatonic melodies are traditionally written in the equipentatonic mode and have a strong folk-like sound. Pieces or sections of pieces written in Durmoll or something similar have a strong resemblance to the music of the Classical period. Modern orchestral works from the Late Romantic onwards use both modes equally.

Instruments

Bowed string instruments

The New Violin Family was developed much, much earlier, around the early 19th century, and served as a new "metric" equivalent to the old violin family. However, its method of contsruction was to interpolate the old string family members and create new ones, rather than base all of its members on one single instrument. Its main members are:

• the soprano violin, tuned to 0_4 5_4 0_5 5_5
• the violin, tuned to 5_3 0_4 5_4 0_5
• the viola, tuned to 0_3 5_3 0_4 5_4
• the tenor viola, tuned to 5_2 0_3 5_3 0_4
• the violoncello, tuned to 0_2 5_2 0_3 5_3
• the bass violoncello, tuned to 5_1 0_2 5_2 0_3
• the contrabass, tuned to 0_1 5_1 0_2 5_2

Other surrogate members are:

• the alto violin, tuned to the same tuning as the viola with a slightly more violin-like tone
• the tenor violoncello, tuned to the same tuning as the tenor viola with a slightly more violin-like tone
• the subcontrabass, tuned a dekatave below the contrabass (this is a novelty, and the most famous one is at the Orchestre symphonique de Montréal) (yes, this is the octobass analogue)

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. (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. 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. That does not take into account the two "English" and "German" style key systems, which make classification of orchestral woodwind instruments in Earth#10 much more complicated than in our world.

The soprano wind instruments of each type are written in concert pitch (in the treble clef) with the exceptions of the bassoon and the nielsenphone, where the contra-alto instruments of each type are written in concert pitch (in the bass clef).

Brass instruments

Valved brass were not created and the main focus was on extending the trombone family and optimizing it to 10edo. However, it was found to be very difficult to near-impossible in the mid-1800s, and so brass instruments completely dies off in orchestral circles.

Percussion instruments

Timpani are still used to this day. However, they are smaller and are constructed like roto-toms, in sets of ten, in case they need to bring out melodies. Symphonic works/parts of works written in the "German" style need only have two timpani which are constructed more traditionally.

The glockenspiel has been enlarged to give an almost six-octave range to form an orchestral metallophone. An orchestral xylophone has the range of the upper four octaves of the orchestral metallophone.

Unpitched percussion are made the same way.

The Earth#10 symphony orchestra

The symphony orchestra in Earth#10, due to the lack of brass instruments, has a bloated wind section. Wind instruments are more commonly in groups of three, the most common grouping being, in the common orchestral score order:

• 1 piccolo, 2 flutes
• 2 oboes, 1 alto oboe (equivalent to the cor anglais in our timeline)
• 2 alto saxophones, 1 baritone saxophone
• 2 bassoons, 1 contrabassoon
• 2 clarinets, 1 bass clarinet
• 2 alto nielsenphones, 1 contra-alto nielsenphone

Traditionally the string section contains:

• 8 soprano violins
• 12 violins I
• 12 violins II
• 12 violas
• 12 tenor violas
• 10 violoncellos
• 8 bass violoncellos
• 8 contrabasses

Music

Introduction and Waltz, a short piece by Thomas Cunning, in the neopentatonicist style (dated to about 1790)