User:2^67-1/Earth10
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This page is part of a worldbuilding project. It describes musical tuning concepts from a fictional alternate world, rather than the real world.
It may contain references to people, cultures, or places that do not actually exist, or events that did not actually happen. This does not mean that it can’t be used to make real music—it still could be; it just means this article shouldn’t be used as a factual source about real history or traditions, or as a source of terminology and principle compatible with real established common practices and conventions. |
Music theory
The notes are called 0 1 2 3 4 5 6 7 8 9. 0 of the 2nd dekatave is written as 0₂ and has a frequency of 115.741 Hz, which is 100 vibrations per new second (1/100000 of a day). 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 in most classical and folk-style music is taken to be [0 3 6], or what is known here as the neutral triad. This triad on note X is called Xt. Degree arithmetic is assumed to be modulo 10.
Neopentatonic melodies are traditionally written in the equipentatonic mode and have a strong folk-like sound. Traditionally, triads are placed to harmonize the melody such that they produce the most harmonious sound. Here are the rules for selecting a chord to harmonize some notes:
- Use Xt or (X-6)t when there is only one note, X.
- If there are two distinct notes a tone apart in the part you want to harmonize, use the 1st rule on the note which receives the most stress.
- If there are three distinct notes each a tone apart use the triad corresponding with the root of the topmost or bottommost note (though the latter is rare).
Nowadays neopentatonicism is more liberal and allows the (X-3)t triad for the first rule.
Pieces or sections of pieces written in Durmoll or something similar have a strong resemblance to the music of the Classical period and traditional Western harmony is applied accordingly. Modern orchestral works from the Late Romantic onwards use both modes relatively equally.
Intervals are called the unison, first, second... ninth, dekatave, first-and-dekatave, second-and-dekatave... ninth-and-dekatave, double dekatave.
The Italian sixth on 0 is [7 0 5], the French sixth is [7 0 2 5], and the German sixth [7 0 3 5]. All resolve to the triad on the sixth above 0.
Notation in modern Earth#10 Ciphersystem
- The treble clef is written as a stylized, cursive "4".
- The alto clef is written as a stylized, cursive "3".
- The bass clef is written as a stylized, cursive "2".
Notes are written exactly like in jianpu, but with no accidentals and using the numerals 0 to 9 for the note names. The default dekatave number is taken to be the number of the dekatave prescribed by the clef.
4-part harmony
- A fifth must always be succeeded with a first in the opposite direction.
- Parallel dekataves and sixths are not allowed (in the usual manner as exposed octaves and fifths in OTL harmony).
- Exposed dekataves and sixths are not allowed (in the usual manner as exposed octaves and fifths in OTL harmony).
- Overlapping of voices in similar motion as well as crossing of voices are not allowed (as is in OTL harmony).
Instruments
Keyboard instruments
There are two keyboard layouts commonly used today for modern music, the 'English' and 'German' layouts. The 'English' layout is used in New Pythagorean (see below) works and jazz works but the 'German' keyboard is used for classical-style works. Both may be used in the course of a single work.
Bowed string instruments
The "New Violin Family" was developed around the early 19th century by the Mirecourt school, and served as a new "metric" equivalent to the old violin family. It was commissioned by the French government. However, its method of construction 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 treble violin, tuned a dekatave above the ordinary violin
- 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)
It is slightly less common for the lower instruments to be tuned in fourths, like the traditional tuning for double basses.
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.
Modern balalaikas, called "metric balalaikas" are a mainstay of Eastern European folk music ensembles and often feature in orchestras and orchestral works by composers in eastern Europe. Their tunings are:
- prima: 5₃ 5₃ 0₄
- secunda: 0₄ 0₄ 5₄
- alto: 5₃ 5₃ 0₄
- tenor: 0₃ 0₃ 5₃
- bass: 5₂ 0₃ 5₃
- contrabass: 5₁ 0₂ 5₂
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) 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 same fingering systems are used for the flute, oboe, bassoon, and saxophone (the two Boehm systems), as well as for the clarinet and nielsenphone (the two Boehm-Klosé systems).
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. (Despite this, the English-style fingerings are much more commonly-learned.) Instruments look very similar to their Earth#12 counterparts. The nielsenphone is made out of red wood, redder than the bassoon, and usually has silver keys. Lower nielsenphones are bent like low clarinets.
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 |
|---|---|---|---|---|---|---|---|
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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 treble flute, 2 alto flutes
- 2 alto oboes, 1 contra-alto oboe
- 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
Usually, if a theorbo is not found, a contrabass (metric) balalaika is used for the continuo part in Baroque works.
The pitched percussion section contains, minimally, 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)
History of Earth#10 music
Classical music
During the French Revolution, the music of earlier French composers was abandoned in favour of a purer, "more French", decimal music. The French decimal time caught on and was successful in this timeline and they also decimalized music. The Institution for the Decimal Music in France then "decimalized" several Bach works, as well as Mozart and Haydn sonatas and symphonies though these never caught on.
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.
Hence, works commonly performed by symphony orchestras are from the Romantic onwards, with Classical-period works sparingly performed. Folk music, especially European, American, and African, is also commonly performed, with symphonic versions of these works composed.
Jazz music
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 and kamele ngoni 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.
Non-musical worldbuilding
Mathematics
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. Nystromal is also used and accepted in most dual-mode calculators and is even used and accepted in many large research journals.
Sociopolitical structure of this world
IMPORTANT NOTE: Anything shown here is meant for this alternate history project, and are not influenced by past, current, or future world affairs.
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 map of Europe is similar to inter-War Europe, with the exceptions of Luxembourg and Belgium never gaining independence.
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 "Eurasian" 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.
The only other differences in territories other than Europe are that Lata is a single country, and that China and Taiwan are united under the ROC.
Distribution of the languages across the world
The most spoken languages in this world are French, Mandarin, Hindi, English, Spanish, Arabic, Bengali, Portuguese, Dutch, Ewe, Russian, and Indonesian.
The official languages of the USA are English, French, German, Dutch, and Mandarin Chinese. However, Louisiana has Cajun as its sole official language. Ewe is a trade language in the USA and is a commonly spoken language in the more urban cities.
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, a puppet state of the United Kingdom, 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 the United Kingdom. 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.
Scots
Unlike in Earth#12, Scots has a standardized orthography and is a recognized official language of Scotland, and the Scottish community in Earth#10.
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.
Notable people
People with an Earth#12 equivalent
(Earth#12 equivalents are in brackets.)
- Johan/John Nystrom, inventor, engineer, and author, unlike in Earth#12, he is also a composer, popularised 16ed3 (John Nystrom)
- Frederick Quart, 19th century British pianist and composer, one of the first composers for the new piano (Frederic Chopin)
- Gust Schilder, 19th century Dutch composer of symphonic works (Gustav Mahler)
- William Shanks, mathematician and composer, unlike in Earth#12, he is not only a mathematician (William Shanks)
- Arnold Schoenberg, American composer, invented serialism (Arnold Schoenberg)
- Bela Bartók, Hungarian ethnomusicologist and xenharmonic composer, one of the earliest Earth#10 xenharmonicists (Bela Bartók)
- Scott Mount, American composer, student of Arnold Schoenberg (Alban Berg)
- Anthony Weaver, American composer, student of Arnold Schoenberg (Anton Webern)
- Carl Orff, German music educator and ethnomusicologist, unlike Earth#12 Carl Orff, he is not a composer and is an ethnomusicologist in Earth#10, popularised equipentatonic instruments in the West (Carl Orff)
- Trevelyan Grausson, 21st century American 16ed3 supporter, clarinet and nielsenphone player (Monocrad)
- Fitzgerald Sweelinck, 21st century Indonesian-British xenharmonic composer, pioneered the use of the blackwood scale (Fitzgerald Lee)
- Himmel R. Friedman, American xenharmonic theorist (CompactStar)
- Hackett Cole, 21st century British music theorist, and unlike in Earth#12 does not work in xenharmonics at all (2^67-1 alias Cole)
People without an Earth#12 equivalent
- Thomas Cunning, early 19th century English composer
- Christoffel Nielsen, Danish inventor, invented the nielsenphone family
- Temitope Ayokunle, Malian balafon player, popularised an arrangement of two balafons to produce 10edo, picked up by Carl Orff in the West
See also
Introduction and Waltz, a short piece by Thomas Cunning, in the neopentatonicist style