id: 05157080
dt: j
an: 2007a.00510
au: Tan, Kuo Cheang; Chua, Boon Liang
ti: The sound of music and its link with mathematics.
so: Teach. Math. Appl. 25, No. 4, 181-188 (2006).
py: 2006
pu: Oxford University Press, Oxford; Institute of Mathematics and its
Applications (IMA), Southend-on-sea, Essex
la: EN
cc: M83
ut: music; mathematical models; mathematical applications; ratio
ci:
li: doi:10.1093/teamat/hrl001
ab: Summary: This article discusses a relatively unnoticed application of
mathematics by describing its connection with an aspect of music, in
particular, the musical scales. Stemming from a problem found in a Year
9 mathematics textbook commonly used in Singapore, the article
illustrates the role of mathematics in musical scales by first
considering the frequency ratios of consecutive musical notes in the
‘just scale’ and secondly explaining how an anomaly in the ‘just
scale’ caused by the uneven frequency ratios is resolved with the
help of mathematics, thereby leading to the development of the
well-tempered scale. The article ends with an exploration of the
frequency ratios of consecutive musical notes in the well-tempered
scale. Not only does the article aim to broaden the teachers’
horizons with such an introduction to the mathematical aspect of music,
it also hopes to enrich their mathematical experiences as well.
rv: