The above analysis is sufficient to explain the perception of consonance and dissonance of pure and complex tones. However, it raises an interesting question about complex tones. To create a complex tone, we start with a pure tone at the pitch that we want, as Hz.
We then add harmonics to change the tone quality of the note — this can make the note "richer" or "brighter" or more "mellow", any of the qualities we associate with a musical tone. The question is: why does the adding of harmonics not change our perception of the pitch of the note — only the tone quality?
What Fourier realized was that if you add a harmonic to a fundamental, the resulting wave always has the same period as the fundamental, no matter how many harmonics you add!
Thus, the resultant wave always seems to have the same pitch as the fundamental, even though is can sound quite different.
Although if you looked at 2f alone, you would say it has a shorter period than 1f. However, 2f does repeat after a time equal to the period of the fundamental. It happens to repeat twice in that time, but it is still repeating.
The same is true of 3f and all higher harmonics. Although their basic period gets shorter and shorter, all of these waves do repeat at the period of the fundamental. Thus, when you add them all together, the resulting wave also repeats with a period equal to the fundamental.
Actually, Fourier analysis is the reverse: given a complex but repeating wave, what combination of fundamental and harmonics will produce this wave? A very interesting observation follows from this discussion. Because all of the harmonics repeat with the fundamental period, the fundamental frequency does not need to be the loudest to preserve the pitch of the note.
In fact, the fundamental need not be present at all! Even if the fundamental is removed from a note, the note still seems to have the same pitch. Even though the fundamental was not added to the total wave, only 2f and 3f, the period of the total wave is still equal to that of the fundamental. Of course, if you played 2f alone, it would sound an octave higher than the fundamental.
It is as though our brains calculate the difference in Hertz from one harmonic to the next to decide what the real "pitch" of the tone is. This is called a "difference tone". If you like, you can try making a spectrogram of the sound yourself with Praat to confirm the harmonic structure of the tones. Additionally, when you hear two pure tones, even when they do not have the same harmonic structure, the ear and brain again subtract one frequency from the other, and you "hear" a lower-pitched tone with a frequency equivalent to this difference.
For example, if you've ever played with a two-tone whistle e. This is called a Tartini tone or combination tone. If the difference between the two pitches is about 70 Hz or less, you usually hear a pitch that is an average of the frequencies of the two tones, with a "beat". The rate of the beat will be determined by how big the difference in frequencies is.
The second harmonic can sometimes be detected in the timbre of an instrument such as the flute, where the same fingering can be used to produce tones D1 and D2, for example from the first and the second octave range simultaneously using the so-called overblowing technique. The third harmonic sounds just a perfect fifth from the second harmonic, although the difference between the two tones measured in Hz remains the same.
The difference in frequency between the successive harmonics is always the same. Ear, therefore, perceives the pitch differences logarithmically: the interval between Hz and Hz is perceived to be the same as the interval between Hz and Hz.
In both cases, the difference constitutes an octave. The 4th, 5th and 6th harmonics form the tones of the so-called pure major triad. The 7th harmonic is noticeably low and shows the most severe departure from any equally tempered system, while the 8th harmonic is exactly two octaves above the perceived pitch of the sound. A natural harmonic series corresponding with the theoretical harmonic series can be produced using many acoustic instruments.
When produced using stringed instruments they are called flageolet tones , while players of wind instruments speak of overblowing using the same fingering to produce tones belonging to a natural harmonic series. A natural harmonic series, however, consists of tones, not just pure tones. Clarinets and other wind instruments with a so-called cylindrical bore produce an octave and a fifth when overblown. Instruments using a conical bore or two open ends such as the flute, the oboe, the saxophone and the brass winds produce an octave and all of its natural overtones when overblown.
The timbre that is characteristic of the clarinet is a result of its very weak even 4th, 6th, 8th, Early synthesizers and electronic organs produced a timbre resembling a clarinet synthetically using only the odd harmonics.
0コメント