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The Stack Archive

New music notation system could render modern musical instruments ‘useless’

Tue 1 Sep 2015

Musical notes and harmonies are not ‘final discoveries’, like a periodic table of elements, but rather are defined both by the limitations of physical instruments which are able to play them and by the ability of musical notation to transcribe a score into a realistically readable system.

Until four centuries ago the use of the mathematics of periodic waves in the tuning of musical instruments was a common and venerated practice in world music, but gradually gave way to ‘tempered tunings’ – limitations of note frequency which became necessary for the tuning of keyboard instruments and the facility of musical transcription.

In terms of potential range this minimisation of scope can be likened to the difference between the full richness of the English language and the clipped tokenism of Orwell’s newspeak. But the richer musical world of ‘Just Intonation’ (JI) – any system of tuning whereby note frequency is expressed by ratios of small whole integers – was lost to most western music for pragmatic reasons; physical musical instruments were logarithmic in relation to JI, and even those capable of better expressing a more complete range of notes had to live, so to speak, in harmony with the ‘lowest common denominators’ in the orchestra, whose limitations defined the potential harmonic range.

In the age of the computer, this limitation is meaningless, and now Edinburgh-based researcher and Systems Developer David Ryan has presented [PDF*] a new JI-based system of music notation. The author warns: “much of modern harmony will be undone by this theory, and many musical instruments will be rendered useless when culture as a whole decides to embrace the infinite harmonies and beautiful musical purity made possible under the new regime.”

JI pitch has no standard notation; there is not enough room on a stave – which represents frequency – to display JI-based gradations, and neither can existing digital notation schemes such as midi pitch represent these potential JI tonalities, since it is only capable of individuating 50-60 notes.

Ryan’s system of JI notation specifies a base frequency at C, and allows multiplication in the same way that rational numbers do. Perhaps a little confusingly it proposes to retain but redefine the existing note-name system (C, D, E, F, G, A, B), wherein notations could now express every 3-limit JI note, with a separate system for 5-limit (and higher) notes.

The system allows for keyboard input via ASCII characters, and Ryan has achieved a system that does not need any bespoke input device or intermediary software.

3D lattice of 7-limit notations up to octave equivalence - David Ryan, 'A new Computer Friendly Notation for Musical Composition in Just Intonation allowing Easy Transposition by Multiplication of Notations', http://arxiv.org/pdf/1508.07739v1

3D lattice of 7-limit notations up to octave equivalence – David Ryan, ‘A new Computer Friendly Notation for Musical Composition in Just Intonation allowing Easy Transposition by Multiplication of Notations’, http://arxiv.org/pdf/1508.07739v1

Ryan is not a lone voice in musical history as regards curiosity about the ultra-harmonic potential of music. American composer and music theorist Harry Partch (1901-1974) developed a series of specialized instruments to express music with the range of Just Intonation. However his researches and techniques were applicable only to the instruments that he made – a pattern which tends to repeat across other researchers and musicians who have experimented with JI.

There is a certain experimental interest in JI in the fringe and semi-commercial music and performance scene. Paul J. Gallagher’s The Kingdom of Mescal, a multi-cultural work composed using Just Intonation, will shortly be performed in New York. Machine-intelligence designer and prototype at Google Kenric McDowell (aka ‘Big Phone’) applies a JI approach to his techno output, noting “I was so fixated on using [JI] to make techno that I stopped using acoustic instruments in my tracks except for flute and things that are tonally flexible.”

Ryan has made his music sequencer available via GitHub, and presents examples of his own JI-based compositions at SoundCloud.

*At the author’s request I changed the original link with that of a more recent version of the paper.

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