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#### Resources tagged with Music similar to Euclid's Algorithm and Musical Intervals:

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### There are 9 results

Broad Topics > Applications > Music

### Euclid's Algorithm and Musical Intervals

##### Stage: 5 Challenge Level:

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

### Equal Temperament

##### Stage: 4 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.

### Tuning and Ratio

##### Stage: 5 Challenge Level:

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

### Rarity

##### Stage: 5 Challenge Level:

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

### Dancing with Maths

##### Stage: 2, 3 and 4

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?

### Ding Dong Bell Interactive

##### Stage: 5 Challenge Level:

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'.

### Six Notes All Nice Ratios

##### Stage: 4 Challenge Level:

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

### Ding Dong Bell

##### Stage: 3, 4 and 5

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.

### Pythagoras’ Comma

##### Stage: 4 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.