There are an infinite number of musical notes, the ancient Greeks discovered, yet we use just a fraction of them because of the limitations of modern instruments.
Now an Edinburgh researcher claims that a new computer-based system of music notation will render traditional instruments obsolete and herald a new age of harmony.
Western music took a wrong turn with the introduction of “tempered tuning”, a system which made tuning keyboard instruments easier and helped keep fixed-pitch orchestral instruments in tune with each other, argues Dr David Ryan, an Edinburgh-based music and mathematics expert.
Tempered tuning, which divides an octave into 12 equal parts and made scores easily transcribable, “reduces the number of potential notes available, none of which (apart from the octave) are actually in tune,” Dr Ryan claims.
However technological advances now allows music to return to Just Intonation (JI), a theory which applies the mathematics of periodic waves to the science of instrument tuning, and ensures that two notes in the same interval share the same harmonic series.
In a research paper, Dr Ryan writes: “JI was known by the ancient Chinese and Greeks, being used to tune instruments until around four centuries ago, when tempered tunings started to be used for their greater convenience, especially that of tuning keyboard instruments.
“Just Intonation is a desirable tuning philosophy since it has a mathematical grounding in the physics of sound, and subjectively (to most people) its harmonies sound better and purer than the tempered approximations.”
The artificial restrictions that have been placed on instruments are meaningless when a computer programme can exploit the limitless harmonic potential of Just Intonation.
Dr Ryan, an Oxford maths graduate who works as a database programmer, has created a “new notation system for note frequencies in Justly Intoned musical composition, in a format which can be inputted into a computer using an ASCII (coding) keyboard, to aid computer sequencing of JI music.”
He wrote: “Music sounds better when its notes are in harmony with each other. On a piano keyboard certain combinations of notes, such as major triads (C E G), sound good together. However, the 12-note piano scale gives little explanation of why this is, or why a different chord (B D F) sounds less good.
“Fortunately, there is a scientific and mathematical explanation for quantifying how harmonious a chord will sound.”
“However, let the reader be warned, 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.”
Instead of reading music off an orchestral score, the performance will be generated by a 3D lattice grid of notation options, designed by Dr Ryan.
A trained pianist, Dr Ryan has uploaded examples of the new notation system in action on the SoundCloud web platform. To the untrained ear, his synthesised versions of Stevie Wonder’s You Are The Sunshine Of My Life and Bach’s Prelude in C Major sound like the “chiptune” music of early 80s arcade games.
There may be resistance to the junking of centuries of Western musical notation. “The music sounds different. Some people might say my pieces sound out of tune but these are pure harmonies and they are more interesting,” Dr Ryan told the Independent. “Bagpipes are tuned using JI and they aren’t out of tune, they just sound different.”
Dr Ryan, who works at R&D tax credits company Jump Start, is awaiting peer review of his paper, which he has published online. His research expands upon the work of Harry Partch, the US composer who built custom-made instruments to perform his own music which used Just Intonation scales. “I hope someone will design for new instruments to capture these different computer-generated sounds,” Dr Ryan said.
Music notation timeline
2000 BC: The earliest form of musical notation was found in a cuneiform tablet at Nippur, in Sumer (Iraq). The tablet fragments contain instructions for performing music, composed in harmonies of thirds, which was written using a diatonic, seven note scale. The diatonic scale is also the foundation for the ancient Chinese and Indian music.
530 BC: Pythagoras found the relation of musical intervals with ratios of integers, by using the interval of the fifth to create further intervals.
800 Neumes – inflexive marks in the form of freeform wavy lines, allow the melodic recitation of Gregorian plainchants, previously transmitted orally.
1025: Italian Benedictine monk Guido d'Arezzo creates a notation system using a 4-line staff which evolves into the system denoting pitch used today. Guido’s note names were mapped to parts of the human hand.
13th century: Five-line staves appeared in Italy, fixed note lengths are recorded from the 14th century.
16th century: Modern tonal harmony in Western music develops and the use of regular measures (bars) becomes commonplace by the end of the 17th century.
1800: The piano becomes the predominant keyboard instrument during the Classical era and the basic instrumental composition for an orchestra becomes standardised, regulating the execution of a performance.
20th century: US composer Harry Partch rejects conventional notation and creates works using scales of unequal intervals allowing for more tones of smaller intervals.
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