In practice, the pitch is equated with the frequency (number of vibrations per time span) of an audible tone, more precisely: with the basic frequency , i.e. the frequency of the lowest partial tone in the relevant sound (see e.g. mood (music) , interval (music)) , Concert pitch ). In addition to the tone duration , loudness and timbre , the pitch is an important property of musical tones and the vowels of spoken language .
The American National Standards Institute defines pitch as a property of auditory sensation "according to which sounds can be classified on a musical scale (ANSI S1.1)". In this case, pitches are perceived as higher or lower in the sense of a musical melody, which, however, requires that the audible sound is stable enough in terms of frequency and clarity to distinguish it from a noise. With artificially generated pure tones ( sinus tone , monofrequency sound), the pitch correlates with the frequency of the tone. Usually the pitch is simply understood as the fundamental frequency of a periodic sound; But especially in music, harmonic and melodic relationships also influence perception.
Auditory sound to which the human ear can assign a pitch sensation is called tonal. Sound signals in which the time structure repeats periodically (e.g. sound of vibrating strings) have a tonal character. However, non-periodic sound signals also have a tonal character in which narrowly defined frequency ranges are emphasized (e.g. howling wind or the sound of kettledrums ).
Although the pitch can be characterized by a frequency, it is not only an objective physical property but also has a psychoacoustic component. This has been and is a central problem and the subject of ongoing research into speech synthesis and its perception through the ear. For psychoacoustics, it is interesting how high or low tones of a certain frequency are perceived. For this purpose, a separate pitch scale is built up, the perceived pitch . The perceived pitch is also called tonality referred.
Origin of the use of the term
In many languages, tones are referred to as “higher” or “lower” in comparison, and melodies (i.e. sequences of tones) are perceived and referred to as “rising” or “falling”.
These “spatial” designations are probably based on the statistical occurrence of tones and noises occurring in nature, which are perceived spatially and identified as “from above” or “from below”. The numerically larger (high) or smaller (low) frequency of a tone fits this designation. But it cannot be the cause, because the knowledge that sounds are based on vibrations is much more recent than languages.
In music , the pitch is a measure ( parameter ) that can be described separately from other measures or properties. The term contains a linear and a helical (helical) component. The linear pitch perception, which is accompanied by an approximately geometric change in the underlying vibration frequencies, is often coupled to the impression of a linear change in brightness or height localization in one's own body (chest to head). The helical component is expressed in the fact that the tones that sound an octave higher or lower - when the frequency is doubled or halved - are perceived as similar or the same. Tones that are one or more octaves apart are therefore grouped together in a tone class with the same pitch class and denoted by the same name (possibly with an addition to identify the octave space ).
Absolute and relative pitch
For musical purposes, notes that follow one another or that sound together should " sound good ". However, this is only the case if these tones adhere to certain frequency relationships, namely those of musical intervals . The frequency relationships that are useful for musical purposes are summarized in scales . The designation of the scale tone is then used to designate the (relative) musical pitch .
If the frequency of a reference tone is also given, an absolute pitch can be assigned to each musical tone. Today's musical notation usually reflects absolute pitches; The decisive factor is the definition of the a 1 pitch as a so-called concert pitch at 440 Hz, which was agreed by the 1939 International Voice Tone Conference in London. Several tone symbol systems are used for the written notation of pitch .
However, the character of a melody or a chord is essentially independent of the absolute pitch. Melodies or chords can e.g. B. be shifted as a whole by intervals ( transposing ). The absolute pitch with which a piece of music is actually performed is based on the decision of the musician , the vocal possibilities of the singers and, if applicable, the properties of the instruments used:
- With unaccompanied singing ( a cappella ), the vocal ranges of the singers determine the pitch ranges used. For example, the choir director uses a tuning fork to get in the right mood .
- Instruments that cannot be easily retuned, such as the organ , piano, or accordion, determine the absolute pitches used. Wind and string instruments, on the other hand, can be adjusted in their tuning to a limited extent to the instruments mentioned.
Absolute, relative and intonation hearing
A few people have a so-called perfect pitch (also pitch memory ). You are able to name a tone without any tools and to sing it correctly according to a given tone name.
A distinction must be made between absolute hearing and relative hearing , which enables us to name the interval between two consecutive tones and to sing correctly when given abstractly ( from the sight ). Both relative and absolute hearing can be specifically trained .
Another aspect of musical hearing is the ability to recognize imperfections in intonation - i.e. small deviations in pitch from a musically planned value. It is called the intonation hearing. This ability has its physiological limit in the frequency discrimination of the hearing. However, this limit can also be shifted through training. Experiments have shown that eight hours of training are enough to get trained musicians to be able to differentiate between frequencies. In musical practice, however, the hearing of intonation requires much more than a trained frequency distinction. In this case it is necessary to compare presented pitches with realized ones. An average deviation of three cents (3/100 semitones) has been measured in experienced singers . Measurements at the Düsseldorf Institute of Stringed Instruments Guitar & Lute showed that the pitch is perceived as correct if the intonation is within a range of around 1 cent.
Both the objective measurement and the subjective perception of pitches are subject to a certain inaccuracy (“blurring”), which is based partly on physical and partly on auditory-physiological conditions.
Physically caused blurring
Frequency and time are linked (conjugated) quantities and thus obey an "uncertainty relation", as is also clear from the Fourier transformation and its applications. The uncertainty relation has the effect that the frequency cannot be averaged more or less precisely for a precise moment, but only for a certain duration. For example, the frequency of a periodic sound event can only be measured with absolute precision if its duration is completely indefinite, i.e. infinite. Conversely, its pitch becomes more indeterminate the shorter the duration. This results in the useful knowledge for music-making practice that intonation accuracy is much more important (because it is more audible) in slow passages (long notes) than in fast passages (short notes). Strings often say - to the surprise of amateurs - that it is by no means easier to play slow pieces.
Hearing physiological blurring
After frequency analysis and conversion to nerve impulses in the inner ear , transmission takes place in frequency-specific nerve pathways, which are also multiplied in several parallel strands of the auditory pathway . Further processing takes place on several levels in the brain. This process is much more complex than a simple technical spectral analysis. How the decoding of periodicity during hearing from the stream of nerve impulses in the auditory midbrain ( colliculi inferiores ) works has not been sufficiently clarified; one hypothesis describes the function according to the principle of the coincidence detector. It has been proven that several signal periods are required so that a periodicity - and thus the basic information for the subsequent representation of pitch in the cerebrum - can be registered. Interestingly, the pitch of a natural tone of 100 Hz, with overtones , is perceived more than four times as fast as a sinus tone of the same frequency, since the brain also uses the currents of nerve impulses that are triggered by overtones.
A sinusoidal sound signal that z. B. only lasts half a period, is not perceived by the ear as a tone, but as a cracking noise with an indefinite pitch. The minimum time to trigger a discrete pitch sensation depends on the frequency. “For a sinusoidal signal of 1000 Hz , this time value is around 12 ms ; It therefore takes about 12 periods for a sinusoidal signal with the frequency f = 1000 Hz to be recorded by the ear as the pitch. 3 to 4 periods are necessary for a signal of 200 Hz, about 250 for a signal of 10 kHz. "
Perceived pitch (pitch)
In psychoacoustics, the tonality is a perception quantity with the unit of measurement Mel , which can be used to classify sound events in terms of their perceived pitch. The picture on the right shows how the relationship between the frequency of a sinusoidal tone and the perceived pitch is established based on listening tests . For complex "tones" (strictly speaking: sounds in the sense of partial tone complexes ) as they occur in reality ( vibrating systems ), these perception variables of psychoacoustics do not apply directly, and the deviation from the frequency scale is up to 5 kHz within that of the ear imperceptible boundaries.
The perception of pitch is closely related to the physiology of the inner ear and the auditory brain. The inner ear performs a frequency analysis of the signal it hears. Different frequencies lead to excitation of nerve cells in different places in the inner ear . The place at which nerve cells are increasingly stimulated can be used to determine the pitch. The exact details of the function are still the subject of research and there are several models of this.
- In the perception of the pitch, the composition of the tone from the fundamental and overtones plays an important role. Since the period of the tone is important for the pitch perception, determine z. B. If the fundamental tone is inaudible, the perceptible or audible components of the overtones are the perceived pitch. This is related to the residual sound that the human ear forms from a frequency mixture . The period of a tone is only retained if the greatest common divisor of the overtone frequencies reproduces the fundamental tone. Although this rarely happens in a natural environment, it is basically possible. Is there e.g. If, for example, a tone is made up of the fundamental and its first two overtones and the fundamental and first overtone then become inaudible, the tone appears an octave and a fifth higher. That can be calculated with the greatest common factor (GCF). Is the keynote z. B. 100 Hz, the first two overtones are at 200 Hz and 300 Hz. The GCF of 100, 200, 300 is then 100. If the fundamental is missing, the fundamental is calculated from 200 and 300, which is still 100. But if the first overtone is also missing, it is clear that the GCF of 100 and 300 is 100. This effect can occur if z. B. an instrument is filtered or is superimposed by other sounds in such a way that certain frequencies are masked or assigned to other sounds. The knowledge, memory and expectations of the listener also play a role in the perception of the pitch. So you would z. B. always interpret octaves as one tone, since the GCD or the period in such a frequency mixture would always result in the lowest fundamental tone. The brain can assess this on the basis of the timbre - i.e. the weighting, composition and change of the overtones. The more trained or conditioned the listener is to a certain sound, the more likely they are to perceive several pitches. This is also related to the recognition and perception of chords, since the timbre of the GCF in chords rarely occurs in monotonous sound events, since very many of the first overtones would be missing and the period would be very long. Because of this, in these cases the brain interprets several sounds instead of one very deep note. It should be noted that the brain does not determine mathematically exactly; it also has its tolerances. The GCF is just a mathematical tool to approximate how long the period of several frequencies will be.
- Mel (unit of measure for perceived pitch)
- Universals of music perception
- Ernst Terhardt: On the pitch perception of sounds :
- Psychoacoustic basics . In: Acustica. International Journal on Acoustics , 26: 173-186 (1972), ISSN 0001-7884 .
- A functional scheme . In: Acustica. International Journal on Acoustics , 26, 187-199 (1972), ISSN 0001-7884
- Ernst Terhardt, Gerhard Stoll, Manfred Seewann: Algorithm for extraction of pitch and pitch salience from complex tonal signals . In: Journal of the Acoustical Society of America , Vol. 71 (1982), No. 3, pp. 679-688, ISSN 0001-4966
- Ernst Terhardt: Calculating Virtual Pitch . In: Hearing Research. An international Journal , Vol. 1 (1979), pp. 155-182, ISSN 0378-5955
- Ernst Terhardt: acoustic communication. Basics with audio examples . Springer Verlag, Berlin 1998, ISBN 3-540-63408-8 (+ 1 CD-ROM).
- Eberhard Zwicker , Hugo Fastl: Psychoacoustics. Facts and Models (Springer series in information sciences; 22). 2nd edition Springer Verlag, Berlin 1999, ISBN 3-540-65063-6 .
- William M. Hartmann: Signals, Sound, and Sensation . Springer, New York 1998, ISBN 1-56396-283-7 .
- Christopher J. Plack, Andrew J. Oxenham, Richard R. Fay, Arthur N. Popper: Pitch. Neural Coding and Perception (Springer Handbook of Auditory Research; 24). Springer, New York 2005, ISBN 0-387-23472-1 .
- Lynne A. Werner, Richard R. Fay, Arthur N. Popper: Human Auditory Development . 2012, ISBN 1-4614-1421-0 (English, limited preview in Google Book Search).
- Carryl L. Baldwin: Auditory Cognition and Human Performance: Research and Applications . 2012, ISBN 0-415-32594-3 (English, limited preview in Google Book Search).
- JA Simmons, A. Megela Simmons: Bats and frogs and animals in between: evidence for a common central timing mechanism to extract periodicity pitch. In: Journal of comparative physiology. A, Neuroethology, sensory, neural, and behavioral physiology. Volume 197, number 5, May 2011, ISSN 1432-1351 , pp. 585-594, doi : 10.1007 / s00359-010-0607-4 , PMID 21072522 , PMC 3257830 (free full text) (review).
- Change of pitch depending on the sound level (PDF; 46 kB)
- Frequency table - all playable musical notes and their frequency (PDF; 163 kB)
- ^ Roy D. Patterson, Etienne Gaudrain, Thomas C. Walters: Music Perception - The Perception of Family and Register in Musical Tones . 2010, ISBN 978-1-4419-6113-6 , pp. 38 (English, online in Google Book Search).
- ↑ http://www.ansi.org/
- ↑ “The pitch is defined as the property of a hearing sensation according to which sounds can be arranged on a musical scale (ANSI S1.1), i.e. on a continuum from 'low' to 'high'. In the case of sine tones, it is closely related to the frequency of the tone. ”Stefan Weinzierl: Handbuch der Audiotechnik . 2008, ISBN 3-540-34300-8 , pp. 65 ( limited preview in Google Book search).
- ↑ “ For the purposes of this book we decided to take a conservative approach, and to focus on the relationship between pitch and musical melodies. Following the earlier ASA definition, we define pitch as 'that attribute of sensation whose variation is associated with musical melodies.' Although some might find this too restrictive, an advantage of this definition is that it provides a clear procedure for testing whether or not a stimulus evokes a pitch, and a clear limitation on the range of stimuli that we need to consider in our discussions. "Christopher J., Andrew J. Oxenham, Richard R. Fay: Pitch: Neural Coding and Perception . 2005, ISBN 0-387-23472-1 , pp. 2 (English, limited preview in Google Book Search).
- ^ “ Melody: In the most general case, a coherent succession of pitches. Here pitch means a stretch of sound whose frequency is clear and stable enough to be heard as not noise; succession means that several pitches occur; and coherent means that the succession of pitches is accepted as belonging together. Randel, Don Michael: The Harvard Dictionary of Music . 2003, ISBN 978-0-674-01163-2 , pp. 499 (English, online in Google Book Search).
- ↑ “The pitch is determined by the frequency of the sound, not primarily by its wavelength. […] In air and water you perceive the same sound, although the wavelengths are very different at the same frequency. ”Hartmut Zabel: Kurzlehrbuch Physik . 2010, ISBN 3-13-162521-X , pp. 150 ( limited preview in Google Book search).
- ^ " Pitch is an important quality of sound, the focus of intense inquiry and investigation since antiquity. Pitch is basic to two forms of behavior specific to humans: speech and music. Pitch is usually understood as a one-dementional precept determined by the period of the stimulus (or its inverse, F0), and insensitive to changes along other stimulus dimensions. However, its complex role within music involves harmonic and melodic effects that go beyond this simple one-dementional model. There is still debate as to where, and how, pitch is extracted within the auditory system. ”Christopher J. Plack, David R. Moore: Hearing Olp Series Oxford Handbooks Oxford library of psychology Volume 3 of The Oxford Handbook of Auditory Science, Christopher J. Plack . 2010, ISBN 0-19-923355-1 , pp. 95 (English, limited preview in Google Book Search).
- ↑ Frequencies audible to humans encompass a range from 16 to 20,000 Hz, and musically useful frequencies can be found between 30 and 5000 Hz. Clemens Kühn : Musiklehre. Laaber-Verlag, Laaber 1980, p. 43.
- ↑ a b Hartmann, William Morris: Signals, Sound, and Sensation . 1997, ISBN 1-56396-283-7 , pp. 145, 284, 287 (English, limited preview in Google Book search).
- ↑ Cesare V. Parisea, Catherine Knorre, Marc O. Ernsta: Natural auditory scene statistics shapes human spatial hearing. PNAS , Volume 111, No. 16 (2014), pp. 6104-6108.
- ^ " Pure [Sinus] tones produce a clear, unambiguous pitch, and we are very sensitive to changes in their frequency. For instance, well-trained listeners can distinguish between two tones with frequencies of 1000 and 1002 Hz - a difference of only 0.2% (Moore, 1973). A semitone, the smallest step in the Western scale system, is a difference of about 6%, or about a factor of 30 greater then the JND of frequency for pure [Sinus] tones. Perhaps not surprisingly, musicians are generally better then nonmusicans at discriminating small changes in frequency; what is more surpising is that it does not take much practice for people with no musical training to 'catch up' with musicians in terms of their performance. In a recent study, […] it took only between 4 and 8 hours of practice […] of the untrained listeners to match those of the trained musicians, […] ”Diana Deutsch: The Psychology of Music . 2012, ISBN 0-12-381461-8 , pp. 9, 10 ( limited preview in Google Book search).
- ↑ “ The average JND for the octave was 16 cents, and JNDs for other intervals of the chromatic scale ranged from 13 to 26 cents. […] For Example, Hagerman and Sundberg (1980) reported that the average intonation accuracy in a sample of expert barbershop songs was less then 3 cents. ”Diana Deutsch: The Psychology of Music . 2012, ISBN 0-12-381461-8 , pp. 124, 125 ( limited preview in Google Book search).
- ^ Karl Sandvoss: Constructive basic rules for the construction of intonation-safe acoustic guitars and the string problem. New research and developments, Part 2. (Report from the Institute of Stringed Instruments Guitar & Lute ISIGL Düsseldorf) In: Guitar & Laute 7, 1985, Issue 1, pp. 52–57; here: p. 52.
- ↑ "The fact that a measurement has an inevitable blurring is not a specialty of quantum mechanics, but basically applies to all wave-like phenomena - from music to the alpha decay of atomic nuclei." Norbert Treitz: From false tones to the uncertainty relation, the principle of uncertainty . 2013 ( online [PDF]).
- ↑ “Their cause is the wave property of the sound and the resulting uncertainty of the frequency with short signals. The term 'frequency', as it is commonly used, implies a signal that is repeated exactly and periodically for all times. In a time-varying signal, the validity of the term depends on the duration of observation or on the rate of change; there is only such a thing as fuzzy 'momentary frequencies'. An extremely short signal 'has' no more frequency (if you shorten a harmonic oscillation step by step, the sound gradually turns into a noise). ”Thomas Görne: Sound engineering . 2nd Edition. Carl Hanser Verlag, Munich 2008, ISBN 978-3-446-41591-1 , p. 148 ff . ( online in Google Book Search)
- ^ A b “ Effects of Peripheral Tuning on the Auditory Nerve's Representation of Speech Envelope and Temporal Fine Structure Cues. "Enrique A. Lopez-Poveda, A. Alan R. Palmer, Ray Meddis: The Neurophysiological Bases of Auditory Perception . 2010, ISBN 1-4419-5686-7 (English, online in the Google book search).
- ^ " The mechanism by which neurons process the coding of signals is not well understood. Here, we propose that coincidence detection, […] ”Yueling Chen, Hui Zhang, Hengtong Wang, Lianchun Yu, Yong Chen: The Role of Coincidence Detector Neurons in the Reliability and Precision of Subthreshold Signal Detection in Noise . 2013 (English, online [PDF]).
- ↑ “ The principles that govern the relationship between natural sound ensembles and observed responses in neurophysiological studies remain unclear. "Michael A. Carlin, Mounya Elhilal: Sustained Firing of Model Central Auditory Neurons Yields a Discriminative Spectro-temporal Representation for Natural Sounds . 2013 (English, online ).
- ↑ JA Simmons, A. Megela Simmons: Bats and frogs and animals in between: evidence for a common central timing mechanism to extract periodicity pitch. In: Journal of comparative physiology. A, Neuroethology, sensory, neural, and behavioral physiology. Volume 197, number 5, May 2011, ISSN 1432-1351 , pp. 585-594, doi : 10.1007 / s00359-010-0607-4 , PMID 21072522 , PMC 3257830 (free full text) (review).
- ↑ “ The 100 Hz pitch associated with the fundamental is acquired in under 20 ms, whereas that of 100 Hz sinusoid takes in excess 80 ms. "Roy D. Patterson, Robert W. Peters, Robert Milroy: Threshold duration for melodic pitch. In: Rainer Klinke , Rainer Hartmann: Hearing, physiological bases and psychophysics. Proceedings of the 6th International Symposium on Hearing, Bad Nauheim, Germany, April 5–9, 1983. Springer, Berlin / Heidelberg / New York / Tokyo 1983, ISBN 3-540-12618-X , pp. 321–326 ( PDF ) .
- ↑ Werner Kaegi : What is electronic music . Orell Füssli, Zurich 1967, p. 63 .
- ^ " There is some psychoacostical evidence for both place and temporal codes. One piece of evidence in favor of a temporal code is that pitch discrimination abilities deteriorate at frequencies above 4 to 5 kHz - the same frequency range above which listeners' ability to recognize familiar melodies (Oxenham, Micheyl, Keebler, Loper, & Santurette, 2011 ), degrades. […] ”Diana Deutsch: The Psychology of Music . 2012, ISBN 0-12-381461-8 , pp. 11 (English, limited preview in Google Book Search).