Tone
Every sound has its own color, tone. Every sound is built up by adding many partials. Each partial is a sine-wave and they all make the final sound that you hear.
Musical sound, note, has a pitch and a color. If one can not define the pitch of the sound, it is called noise (that has its color like many percussion instruments).
Definition of the Sound in Wikipedia
Musical sound, note, has a pitch and a color. If one can not define the pitch of the sound, it is called noise (that has its color like many percussion instruments).
Definition of the Sound in Wikipedia
Combining partials, building the wave form
In the following figure, the first six partials have been added up, with the amplitude of each partial being in inverse proportion to its ordinal number. The resulting wave approaches a sawtooth wave.
The adjacent animation shows the evolution of a sawtooth wave when it is built up by adding partials.
See also Wikipedia
See also Wikipedia
Have a look more on Wikipedia
Partials, overtones
These are the16 first partials (or in another way basic frequency + 15 overtones), that sound together with the pitch C2. Note that overtones are not equally tempered, so the pitches shown here are indicative only.
When the fundamental frequency f is the frequency of the pitch C2, then half its wavelength sounds an octave higher at C3 and its frequency is 2f (2 times f).
The third partial has a frequency of 3f, sounding at G3. The fourth partial has a frequency of 4f, sounding at C4. The fifth partial has a frequency of 5f, sounding at E4, etc.
The figure shows the pitches on a music staff and their partial number, which is at the same also the multiplicator of the fundamental frequency f of the pitch C2. One can also see the frequency ratios of the partials. Ex. octave ratio is 2:1, perfect fift is 3:2. Chords can be expressed as multiple ratios. Major chord is 4:5:6. Minor is 10:12:15. Just for information that minor chord's wave lenght (λ) ratios are 6:5:4!
One can find from the overtones many interesting facts and resemblances with the western music history and theory.
When the fundamental frequency f is the frequency of the pitch C2, then half its wavelength sounds an octave higher at C3 and its frequency is 2f (2 times f).
The third partial has a frequency of 3f, sounding at G3. The fourth partial has a frequency of 4f, sounding at C4. The fifth partial has a frequency of 5f, sounding at E4, etc.
The figure shows the pitches on a music staff and their partial number, which is at the same also the multiplicator of the fundamental frequency f of the pitch C2. One can also see the frequency ratios of the partials. Ex. octave ratio is 2:1, perfect fift is 3:2. Chords can be expressed as multiple ratios. Major chord is 4:5:6. Minor is 10:12:15. Just for information that minor chord's wave lenght (λ) ratios are 6:5:4!
One can find from the overtones many interesting facts and resemblances with the western music history and theory.
Sound of an instrument in a space
When an instrument produces a sound, this is what happens (it’s complicated and you do not need to memorise this):
- vibration is initiated by inputting energy into the vibrating element (by plectrum, bowing, blowing, striking, etc.)
- the energy makes the vibrating element to vibrate, producing vibrations according to its physical capabilities and thus having its own spectrum
- the vibrating element is connected to the structure of the instrument (tube, body, etc.), which begins to resonate
- the resonator has its own fixed spectrum or formant (e.g. the vowel A will sound like an vowel A regardless of which pitch it is sung at)
- the sound of the instrument results from the spectrum of the vibrating element interacting with the spectrum of the resonator
- this combined vibration radiates into the space, which has its own resonance (listen to "I Am Sitting In A Room" by Alvin Lucier, where he 'plays' the room)
One way of visualize the sound
The partials of a sound can be analysed using Fourier transformation. This generates the spectrum of the sound, which shows which partial frequencies are present and what their amplitudes are.
The figure shows the spectrum of a violin note. It clearly shows the principal harmonic partials but also shows quieter noises that are included, which comes from the rasp of the bow and other extraneous noises.
Viulun spektriä = the spectrum of the violin
Taajuus (kHz) = frequency in kHz
Voimakkuus (dB) = amplitude (dB)
The figure shows the spectrum of a violin note. It clearly shows the principal harmonic partials but also shows quieter noises that are included, which comes from the rasp of the bow and other extraneous noises.
Viulun spektriä = the spectrum of the violin
Taajuus (kHz) = frequency in kHz
Voimakkuus (dB) = amplitude (dB)
The adjacent simplified spectra shows that the spectra of instrument sounds are not mathematically ideal, i.e. their partials do not line up exactly with the integer multiples of the fundamental frequency.
The image shows that on a violin, pizzicato and a down bow will produce spectras that slightly differ from the theoretical model for a violin string.
It is also useful to remember that the spectrum, or overtone structure, of an instrument is not static; it varies somewhat over the duration of a tone. This is why we feel that notes played on traditional instruments are ‘alive’. Sounds produced on electronic instruments are generally static and do not undergo minor random internal variation.
Teoreettinen kieli = string in theory
Pizzicato: parittomat alavireisiä -> epäharmoninen = Pizzicato: uneven overtones are under tuned -> non-harmonic
Arco: kaikki alavireisiä, mutta harmonisesti = Down bow: all under tuned but hamonically
The image shows that on a violin, pizzicato and a down bow will produce spectras that slightly differ from the theoretical model for a violin string.
It is also useful to remember that the spectrum, or overtone structure, of an instrument is not static; it varies somewhat over the duration of a tone. This is why we feel that notes played on traditional instruments are ‘alive’. Sounds produced on electronic instruments are generally static and do not undergo minor random internal variation.
Teoreettinen kieli = string in theory
Pizzicato: parittomat alavireisiä -> epäharmoninen = Pizzicato: uneven overtones are under tuned -> non-harmonic
Arco: kaikki alavireisiä, mutta harmonisesti = Down bow: all under tuned but hamonically
Finally, here is a crescendo on a trombone illustrated in two ways: spectras taken at the beginning and end of the tone, and a sonogram showing how the partials increase in amplitude (more red) over time.
Facts:
- A sound is built up of sine wave partials at various frequencies which are at or close to integer multiples of the fundamental
- An instrument consists of a vibrating element (e.g. a string) and a resonator (e.g. a body) that both contribute to the color of the final sound
- An instrument is also always in an acoustic space whose properties further affect the sound
version 29.6.2022