The study of musical sound

Usage examples of harmonics.

For example, a musical note at 200Hz will have harmonics at 400Hz and 600Hz, and the ratio between these is 2:3, which corresponds to the harmonic interval that would exist between two notes with fundamental frequencies of 400Hz and 600Hz.

The harmonics are clearly visible in the vowel portions of the syllables.

The basic trick in constructing these tones is that the only harmonics are those with frequencies which are multiples of the fundamental frequency by powers of 2, i.

And we know that these are the same ratios that occur between frequencies of harmonics of individual sounds, for certain types of sounds.

It requires calibrations to be made against higher harmonics of very low frequency sounds, where the higher harmonics are in the range of the intervals that you are calibrating against.

This suggests that the brain does not bother to use higher harmonics for the purpose of calibrating comparisons of interval sizes.

The main reason to doubt that this type of arithmetic plays a significant role in the calibration of interval perception is the same as the second reason given above for supposing that higher harmonics are not involved in this calibration: complex fractions are not observed to be significant in music perception.

The flows shown by dashed arrows represent raw information about individual harmonics and processed information about timbre being included in the inputs to cortical maps that process melody.

But there are two ways to measure the rise in pitch: either we estimate each pitch value first, from the observed values of all the harmonics, and then calculate the ratio between the pitch value estimates, or, we calculate the corresponding ratio between each pair of corresponding harmonic frequencies, and then average these ratios to get our estimate of the change in pitch.

X and sound Y can be performed by comparing all the harmonics of sound X and all the harmonics of sound Y .