Mathematics and Music

Posted: August 27th, 2021

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Mathematics and Music

            A close relationship exists between music and mathematics as exhibited in various aspects. Some of the notable areas of music such as rhythm, tone scales, pitch and patterns as well as intervals, harmonies and symbols, among others embrace mathematical connotations. Additionally, the composers’ sounds and notions developed by musicians are interrelated to mathematics. In advancing the concept of mathematical – music relationship, Pythagoreans and Archytas were the first people to document this relationship (Pfordresher et al., 42). Their focus was mainly on music scales and correlation to mathematics. Subsequently, ancient Egyptians, Chinese and Indians studied on mathematical principles in relation to music. Accordingly, Pythagoreans studied the humming of musical strings as a geometrical concept of mathematics (Pfordresher et al., 45). Furthermore, Pythagoras is the early known researcher investigating the musical scales to numerical ratios and small integers’ values. Therefore, this paper will analyze the Pythagorean tuning on exploring the correlation between mathematics with music.

           The studies by Pythagoras’ concepts about basic mathematical relationship that exists between the harmony and vibrating strings were digitized as well, enjoyed in the music world. The Pythagorean tuning basis its principles on perfect consonances, fifth, fourth, octave, and the major third known as ditone, meaning two tones. Therefore, the music’s strings are exactly half the length of a pitch, which is exactly an octave higher when plucked and when the string is into thirds, it raises the pitch to an octave and fifth (Pfordresher et al., 50). The ditone is given by the ratio of 9:8 squared, implying 81:64, which is above the harmonic and independent 5:4 ratio equivalent to 80:64. The whole tone, which forms the second interval is obtained from the three to two (3:2) squared that are the two perfect fifths, equivalent to nine to eight ratio (9:8) (Pfordresher et al., 50). The five to four ratio (5:4) is forms the perfect major third while six to five ratio (6:5) the perfect minor third. Equally, a synthetic comma equivalent to eighty-one to eighty (81:80) with the exception of their equivalent Pythagorean of eighty-one to sixty-four (81:64) ratio and thirty-two to twenty-seven (32:27) respectively (Pfordresher et al., 51). Therefore, the dependent third obey the Pythagorean Theorem with the independent third and harmonic tuning intervals. Thus, the perfect third pitch should be set to 81:64 and the perfect fifth at the ratio 3:2 to raise the music pitch.

Works Cited

Pfordresher, Peter Q., and Steven Brown. “Vocal mistuning reveals the origin of musical scales.” Journal of Cognitive Psychology 29.1 (2017): 35-52.