User:2^67-1/Earth10 scratchpad
Prospective history
During the French Revolution, the music of earlier French composers was abandoned in favour of a purer, "more French", decimal music. The 10-note "French" system spread throughout the entirety of continental Europe within thirty years, with younger composers picking it up and older composers who were accustomed to the older 12edo-adjacent systems vehemently despising it.
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 some Temitope Ayokunle 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 and electric (and acoustic) koras being extremely common in jazz and other popular musical styles. As such, European instruments are sparingly used in jazz, and hence the saxophone is more commonly used in the orchestra.
Due to the influence of Nystrom, hexadecimal (called nystromal in this universe, to distinguish it from "tonal" referring to music) is used as an official number base across the larger cities in Northern Europe, the Northwestern European Union, and some formerly colonial cities in Asia.
Sociopolitical structure of this world
Most importantly, there was only one world war, due to von Stauffenberg successfully killing Hitler. This caused the world in Earth#10 to be much more peaceful than it is today, especially with more advances in art.
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 Holland.
The People's Republic of China never forms, due to a successful Mao Zedong assassination attempt. China in this world is the ROC.
Decolonization of Africa was never attempted (so Zimbabwe is still called Rhodesia) though the decolonization of Asia was more successful than it is in our world. However, colonial influence led to a new "Euro-Asian" culture of art and music. To this day, colonial languages in Asia are still widely learned: French in Lata (formerly French Indochina), Dutch in Indonesia, and English in India and Singapore.
Distribution of the languages across the world
The official languages of the USA are English, French, German, Dutch, and Mandarin Chinese. However, Louisiana has decided to have Cajun as its sole official language. Canada (called Greater Quebec in-universe) is a Francophone country. The official languages of Australia and New Zealand are now English and Dutch.
Zwischensprache is a minority language in England, Holland, and France. Scots is not a vulnerable language due to Scotland having Scots as its sole official language.
English does not remain a global language, with a more-or-less equal distribution of Mandarin Chinese, English, French, and Dutch-language (and to a lesser extent Indonesian, Tamil, German, and Russian) websites. Mandarin Chinese, in particular, is a commonly-learned language due to its influence in the Earth#10 scientific community.
Languages of this world that are not in our world
Zwischensprache (debatable)
Called variously Interlangue, Tussentaal, the Betweenspeak, and Zwischensprache (the name used in this article), it originally was formed as a pidgin language in the 19th to 20th centuries due to frequent contact of people of France, Holland, and Britain. It has several names due to there not being a standardized grammar or lexicon for the language yet, however, there were a few attempts to do so. It has also been theorized that this forms a dialect continuum with the French and Dutch dialects forming the ends thereof, with the British dialect somewhat in the middle.
Cajun
Cajun (formerly Louisiana French) diverged far enough from French that it can be considered a separate language. It is mainly spoken in Louisiana with other Cajun-speaking communities in South America.
Lenka Kutu
This is the equivalent of Toki Pona in this universe. It has exactly 256 words, equally distributed between Germanic, Romance, Austronesian, and Sino-Tibetan, with some words from other language families. It is also the official language of the New Pythagorean movement since its adoption in 2011.
Music theory
The notes are called 0 1 2 3 4 5 6 7 8 9. 0 of the 4th dekatave is written as 0₄ and has a frequency of 200*sqrt(2) Hz. Music is written with a jianpu-style notation (called the ciphersystem) 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. Traditionally 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 relatively 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 0₄ 5₄ 0₅ 5₅
- the violin, tuned to 5₃ 0₄ 5₄ 0₅
- the viola, tuned to 0₃ 5₃ 0₄ 5₄
- the tenor viola, tuned to 5₂ 0₃ 5₃ 0₄
- the violoncello, tuned to 0₂ 5₂ 0₃ 5₃
- the bass violoncello, tuned to 5₁ 0₂ 5₂ 0₃
- the contrabass, tuned to 0₁ 5₁ 0₂ 5₂
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 cello-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)
Plucked string instruments
The harp is constructed similarly though harps in Earth#10 are much wider than in our timeline, as the harp has no pedals and thus there is a string for every note in the 10edo gamut. It has a range from between 0₀ to 5₇. In addition, they are shaped more like psalteries. (Red strings signify note 0 and blue strings signify note 5.)
Smaller "half-size" harps (derogatorily called "Celtic harps") are lever harps tuned in 5edo where the levers shift by 10edo steps and are oftentimes used as teaching materials for children.
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 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 a 16edt-based system instead of 10edo.)
Double-reed 16edt 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 similar except for the fact that they are tuned in 10edo.
The transposition system for these instruments is messy compared to that of 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 16edt eighth (8\16<3/1> or sqrt(3)) apart, causing both transposition systems to have separate names for each register. 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/high 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).
Here is a table of all the wind instruments used in orchestras and wind ensembles in Earth#10. Instruments in italics are much rarer.
| Flutes | Oboes | Saxophones | Bassoons | Orchestral clarinets | Orchestral nielsenphones | Pure clarinets | Pure nielsenphones |
|---|---|---|---|---|---|---|---|
|
|
|
|
|
|
|
|
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 die 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 (range 0₂ to 0₈). An orchestral xylophone has the range of 0₄ to 0₈.
Unpitched percussion are made the same way as in our world.
The Earth#10 symphony orchestra
The symphony orchestra in Earth#10 which has been standardized around the middle to late Romantic period, 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
- 1 harp
The pitched percussion section contains, at the minimum, 1 set of 10 timpani, and 1 metallophone.
Music
Introduction and Waltz, a short piece by Thomas Cunning, in the neopentatonicist style (dated to about 1820)