Musical acoustics
Musical acoustics or music acoustics is a multidisciplinary field that combines knowledge from
The pioneer of music acoustics was Hermann von Helmholtz, a German polymath of the 19th century who was an influential physician, physicist, physiologist, musician, mathematician and philosopher. His book On the Sensations of Tone as a Physiological Basis for the Theory of Music[7] is a revolutionary compendium of several studies and approaches that provided a complete new perspective to music theory, musical performance, music psychology and the physical behaviour of musical instruments.
Methods and fields of study
- The musical instruments
- Frequency range of music
- Fourier analysis
- Computer analysis of musical structure
- Synthesisof musical sounds
- Music cognition, based on physics (also known as psychoacoustics)
Physical aspects
Whenever two different pitches are played at the same time, their sound waves interact with each other – the highs and lows in the air pressure reinforce each other to produce a different sound wave. Any repeating sound wave that is not a sine wave can be modeled by many different sine waves of the appropriate frequencies and amplitudes (a
) can usually isolate these tones and hear them distinctly. When two or more tones are played at once, a variation of air pressure at the ear "contains" the pitches of each, and the ear and/or brain isolate and decode them into distinct tones.When the original sound sources are perfectly periodic, the
Subjective aspects
Variations in
Pitch ranges of musical instruments
*This chart only displays down to C0, though some pipe organs, such as the Boardwalk Hall Auditorium Organ, extend down to C−1 (one octave below C0). Also, the fundamental frequency of the subcontrabass tuba is B♭−1.
Harmonics, partials, and overtones
The fundamental is the frequency at which the entire wave vibrates. Overtones are other sinusoidal components present at frequencies above the fundamental. All of the frequency components that make up the total waveform, including the fundamental and the overtones, are called partials. Together they form the harmonic series.
Overtones that are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic, but not exact, it is sometimes called a harmonic partial, although they are often referred to simply as harmonics. Sometimes overtones are created that are not anywhere near a harmonic, and are just called partials or inharmonic overtones.
The fundamental frequency is considered the first harmonic and the first partial. The numbering of the partials and harmonics is then usually the same; the second partial is the second harmonic, etc. But if there are inharmonic partials, the numbering no longer coincides. Overtones are numbered as they appear above the fundamental. So strictly speaking, the first overtone is the second partial (and usually the second harmonic). As this can result in confusion, only harmonics are usually referred to by their numbers, and overtones and partials are described by their relationships to those harmonics.
Harmonics and non-linearities
When a periodic wave is composed of a fundamental and only odd harmonics (f, 3 f, 5 f, 7 f, ...), the summed wave is half-wave
Conversely, a system that changes the shape of the wave (beyond simple scaling or shifting) creates additional harmonics (
Harmony
If two notes are simultaneously played, with frequency
Additionally, the two notes from acoustical instruments will have overtone partials that will include many that share the same frequency. For instance, a note with the frequency of its fundamental harmonic at 200
Although the mechanism of human hearing that accomplishes it is still incompletely understood, practical musical observations for nearly 2000 years[10] The combination of composite waves with short fundamental frequencies and shared or closely related partials is what causes the sensation of harmony: When two frequencies are near to a simple fraction, but not exact, the composite wave cycles slowly enough to hear the cancellation of the waves as a steady pulsing instead of a tone. This is called beating, and is considered unpleasant, or dissonant.
The frequency of beating is calculated as the difference between the frequencies of the two notes. When two notes are close in pitch they beat slowly enough that a human can measure the frequency difference by ear, with a
- For the example above, | 200 Hz− 300 Hz | = 100 Hz .
- As another example from modulation theory, a combination of 3425 Hz and 3426 Hz would beat once per second, since | 3425 Hz − 3426 Hz | = 1 Hz .
The difference between consonance and dissonance is not clearly defined, but the higher the beat frequency, the more likely the interval is dissonant. Helmholtz proposed that maximum dissonance would arise between two pure tones when the beat rate is roughly 35 Hz.[11]
Scales
The material of a musical composition is usually taken from a collection of pitches known as a
The
The following table shows the ratios between the frequencies of all the notes of the just major scale and the fixed frequency of the first note of the scale.
C | D | E | F | G | A | B | C |
---|---|---|---|---|---|---|---|
1 | 9/8 | 5/4 | 4/3 | 3/2 | 5/3 | 15/8 | 2 |
There are other scales available through just intonation, for example the minor scale. Scales that do not adhere to just intonation, and instead have their intervals adjusted to meet other needs are called temperaments, of which equal temperament is the most used. Temperaments, though they obscure the acoustical purity of just intervals, often have desirable properties, such as a closed circle of fifths.
See also
- Acoustic resonance
- Cymatics
- Mathematics of musical scales
- String resonance
- Vibrating string
- 3rd bridge (harmonic resonance based on equal string divisions)
- Basic physics of the violin
References
- ISBN 9780486264844.
- ISBN 9780387983745.
- ISBN 9780191591679.
- ISBN 9780387094700.
- ISBN 9789723109870.
- ISBN 9780810863590.)
{{cite book}}
: CS1 maint: multiple names: authors list (link - ^ )
- ISBN 9780226425498.
- ISBN 978-1884365089.
- Harmonikon Ἁρμονικόν[Harmonics]. year c. 180 CE.
- ^ "Roughness". music-cog.ohio-state.edu (course notes). Music 829B. Ohio State University.
External links
- Music acoustics - sound files, animations and illustrations - University of New South Wales
- Acoustics collection - descriptions, photos, and video clips of the apparatus for research in musical acoustics by Prof. Dayton Miller
- The Technical Committee on Musical Acoustics (TCMU) of the Acoustical Society of America (ASA)
- The Musical Acoustics Research Library (MARL)
- Acoustics Group/Acoustics and Music Technology courses - University of Edinburgh
- Acoustics Research Group - Open University
- The music acoustics group at Speech, Music and Hearing KTH
- The physics of harpsichord sound
- Visual music
- Savart Journal - The open access online journal of science and technology of stringed musical instruments
- Interference and Consonance from Physclips
- Curso de Acústica Musical (Spanish)