Musical transposition calculator in circular slide-rule format

Musical transposition calculator in circular slide-rule format, plus key, in velvet-lined fishskin case, unsigned, United Kingdom, 1840-1880

The first is by J Wilson and is dated 1820. The second is not signed and dates from the mid 19th century. Because all the notes in a scale have a fixed frequency ratio, music can be ‘transposed’ up or down the various keys. These little devices are like circular adding machines; moving the tonic, or fundamental note, a certain number of tones up or down moves all the notes in the scale by the same interval, so music can be rewritten in a different key. The second calculator has the tonic at the top and reveals the notes in the appropriate major scale.