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Western tonality is a consequence of the biology of human hearing combined with the physics of common Western instruments. The ear converts sound to the frequen

by mrob 9y ago

Western tonality is a consequence of the biology of human hearing combined with the physics of common Western instruments. The ear converts sound to the frequency domain. If peaks in that spectrum are close together, they're perceived as a single beating sound. If they're far apart, they're perceived as separate sounds. But if they are of intermediate distance, they are perceived as a dissonant noise. Plomp and Levelt investigated this with pairs of sine tones[0], and Sethares generalized it to arbitrary sounds[1]. If you sum the dissonances on the Plomp-Levelt curve of every pair of harmonics from multiple sounds played at once, weighted by the amplitude of those harmonics, you get a good approximation of perceived dissonance. String and wind instruments make sounds with harmonics at (approximately) integer multiples of the fundamental. If you graph the calculated dissonance of frequency intervals of such sounds, the minima will match the intervals of the traditional Western scale. Other instruments, such as tuned percussion, can have prominent harmonics at non-integer multiples of the fundamental. This requires different tuning for maximum consonance. Indonesian classical music, with its extensive use of tuned percussion, is well known for this. You can of course ignore this, but most people like their music to be mostly consonant, and if you arbitrarily change tuning you're very likely to end up with something that's mostly dissonant. [0] http://www.mpi.nl/world/materials/publications/levelt/Plomp_Levelt_Tonal_1965.pdf http://www.mpi.nl/world/materials/publications/levelt/Plomp_... [1] http://sethares.engr.wisc.edu/paperspdf/consonance.pdf http://sethares.engr.wisc.edu/paperspdf/consonance.pdf (less formal summary: http://sethares.engr.wisc.edu/consemi.html http://sethares.engr.wisc.edu/consemi.html )

jdietrich 9y ago
Just intonation is far more mathematically accurate than equal temperament, but it often sounds badly out of tune to listeners who are acculturated to the latter. 12-TET is a convenient fudge, but it isn't optimal. We have become deeply accustomed to a fairly arbitrary approximation of a somewhat arbitrary set of subdivisions. To complicate matters further, pianos deviate substantially from equal temperament at the extremes of their range. A piano sounds more in tune if the bass notes are tuned slightly flat and the treble notes are tuned slightly sharp, to accommodate for the natural inharmonicity of the strings.

by mrob 9y ago

jdietrich 9y ago

Just intonation is far more mathematically accurate than equal temperament, but it often sounds badly out of tune to listeners who are acculturated to the latter. 12-TET is a convenient fudge, but it isn't optimal. We have become deeply accustomed to a fairly arbitrary approximation of a somewhat arbitrary set of subdivisions. To complicate matters further, pianos deviate substantially from equal temperament at the extremes of their range. A piano sounds more in tune if the bass notes are tuned slightly flat and the treble notes are tuned slightly sharp, to accommodate for the natural inharmonicity of the strings.