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.
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?
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?
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.
The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.
Try ringing hand bells for yourself with interactive versions of Diagram 2 (Plain Hunt Minimus) and Diagram 3 described in the article 'Ding Dong Bell'.
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
How many different rhythms can you make by putting two drums on the wheel?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Investigate the different sounds you can make by putting the owls and donkeys on the wheel.
This article, written by Nicky Goulder and Samantha Lodge, reveals how maths and marimbas can go hand-in-hand! Why not try out some of the musical maths activities in your own classroom?
Show that it is rare for a ratio of ratios to be rational.
Use Euclid's algorithm to get a rational approximation to the number of major thirds in an octave.
Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
Suppose you are a bellringer. Can you find the changes so that, starting and ending with a round, all the 24 possible permutations are rung once each and only once?
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.