![]() For dissonances, like the minor second, none of the overtones line up, and severe beatings arise from the overtones, resulting in a 'rough' perceived sound. For example, for the minor third, only every fifth overtone lines up, and other overtones start to generate beatings. The situation gets even worse for the other intervals. In this case only every second overtone of the higher note lines up with an overtone of the lower note. The situation is already different for a perfect fifth. This means that any beating in the resulting sound is reduced to a minimum. The point is that if you produce a perfect octave on a musical instrument, the frequencies of all the overtones of the higher note will exactly line up with frequencies of the overtones of the lower note. The point I can add to these previous answers gives a hint, why the octave is a very special interval sounding most pure. As Pieter explained, musical instruments produce tones with many overtones of different intensities, where usually the frequency assigned to the tone is the lowest (fundamental frequency $f_0$), and the overtones are integer multiples $nf_0$ of it. The fact that we hear the octave as a pleasant pure interval is hard-wired in the human hearing system. I basically agree with the answers of Ben Crowell and of Pieter. The beats would be beats between the first harmonic of the lower note and the fundamental of the higher note. You can still tune to these notes between octaves, and the beats can still be heard if out of tune. So notes differing by an octave in pitch have waveforms that are related by the fact that their periods are in a 2 to 1 ratio. Pitch perception can be complicated in some cases, but essentially our sense of pitch is normally based on the period of the wave. How do the sound waves compare between different octaves? It seems likely that it has at least some physical basis, because periodic tones usually have their first two frequencies (fundamental and first harmonic) in the ratio of two to one.Īn octave above a note is the fourth overtone, I'm assuming That may mean that nobody has such an explanation, or just that it wasn't something that Deutsch wanted to get into in this anthology of articles. Looking through the index entries on this topic in Diana Deutsch, The psychology of music, 3rd ed., 2013, I don't see anything about any physical, neurological, or evolutionary explanation of octave equivalence. So this is really a fact about the ear-brain system (i.e., psychology and physiology) rather than physics, although it does relate to a physical property. (We know it's hard-wired because it's present without musical training and is true cross-culturally.) Notes that differ in frequency by a factor of 2 (or a power of 2) are perceptually similar, and may be mistaken for one another, even by trained musicians. It's a hard-wired thing in the human ear-brain system. And if so, I don't understand what I'm doing differently this time around to produce exactly half the velocity I found last time.The phenomenon you're asking about is known as octave equivalence. My question is, for a string or an object to create an audible noise, must the velocity of the string be greater than 344 m/s. Now, I had worked this problem earlier on a black board and my velocity I believe came out to be around 366 m/s, which seems to make much more sense to me, considering the speed of sound in the air is 344 m/s. Since we are talking about its fundamental frequency, I set n=1. I believe the first thing I need to do is calculate the velocity of the string. (a) What should be the tension in the string? String S_1 has a mass of 8.00 g and produces the note middle C (frequency 262 Hz) in its fundamental mode. You are designing a two-string instrument with metal strings 35.0 cm long.
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