In \'just intonation\' a note and a note which is a third above it will sound ha

Question

In 'just intonation' a note and a note which is a third above it will sound harmonically pure, and the two notes have a 4:5 ratio. If you start with with a 100 Hz, sound, what frequency would you get for the third above it? Alternatively, what frequency would you find if you tuned by 'equal temperament', subdividing an octave into 12 equally proportioned parts? (Hint: a third is 4 half-steps from the base note.) In 'just intonation' a note and a note which is a third above it will sound harmonically pure, and the two notes have a 4:5 ratio. If you start with with a 100 Hz, sound, what frequency would you get for the third above it? Alternatively, what frequency would you find if you tuned by 'equal temperament', subdividing an octave into 12 equally proportioned parts? (Hint: a third is 4 half-steps from the base note.)

Explanation / Answer

we get 125Hz frequency third above it.

100/125Hz ratio equals to 4/5.

which is 4 half steps from the base note

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