Resources tagged with: Music

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There are 8 results

Broad Topics > Cross-curricular Contexts > Music

Tuning and Ratio

Age 16 to 18 Challenge Level:

Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?

Euclid's Algorithm and Musical Intervals

Age 16 to 18 Challenge Level:

Use Euclid's algorithm to get a rational approximation to the number of major thirds in an octave.

Ding Dong Bell

Age 11 to 18

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.


Age 16 to 18 Challenge Level:

Show that it is rare for a ratio of ratios to be rational.

Pythagoras’ Comma

Age 14 to 16 Challenge Level:

Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.

Six Notes All Nice Ratios

Age 14 to 16 Challenge Level:

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.

Equal Temperament

Age 14 to 16 Challenge Level:

The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.

Dancing with Maths

Age 7 to 16

An article for students and teachers on symmetry and square dancing. What do the symmetries of the square have to do with a dos-e-dos or a swing? Find out more?