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own as upper partials harmonic or otherwise a complex tone composed of two sine waves of 1000 and 1200 hz may sometimes be heard as up to three pitches two spectral pitches at 1000 and 1200 hz derived from the physical frequencies of the pure tones and the combination tone at 200 hz corresponding to the repetition rate of the waveform in a situation like this the percept at 200 hz is commonly referred to as the missing fundamental which is often the greatest common divisor of the frequencies present 10 pitch depends to a lesser degree on the sound pressure level loudness volume of the tone especially at frequencies below 1 000 hz and above 2 000 hz the pitch of lower tones gets lower as sound pressure increases for instance a tone of 200 hz that is very loud seems one semitone lower in pitch than if it is just barely audible above 2 000 hz the pitch gets higher as the sound gets louder 11 these results were obtained in the pioneering works by s stevens 12 and w snow 13 later investigations e g by a cohen have shown that in most cases the apparent pitch shifts were not significantly different from pitch matching errors when averaged the remaining shifts followed the directions of stevens s curves but were small 2 or less by frequency i e not more than a semitone 14 lower pitches have lower frequency c 3 an octave below middle c the frequency is half that of middle c 131 hz scale 1 square is equal to 1 millisecond oscillogram of middle c 262 hz pure tone higher pitches have higher frequency oscillogram of c 5 an octave above middle c the frequency is twice that of middle c 523 hz theories of pitch perception edit theories of pitch perception try to explain how the physical sound and specific physiology of the auditory system work together to yield the experience of pitch in general pitch perception theories can be divided into place coding and temporal coding place theory holds that the perception of pitch is determined by the place of maximum excitation on the basilar membrane a place code taking advantage of the tonotopy in the auditory system must be in effect for the perception of high frequencies since neurons have an upper limit on how fast they can phase lock their action potentials 5 however a purely place based theory cannot account for the accuracy of pitch perception in the low and middle frequency ranges moreover there is some evidence that some non human primates lack auditory cortex responses to pitch despite having clear tonotopic maps in auditory cortex showing that tonotopic place codes are not sufficient for pitch responses 15 temporal theories offer an alternative that appeals to the temporal structure of action potentials mostly the phase lock of action potentials to frequencies in a stimulus the precise way this temporal structure helps code for pitch at higher levels is still debated but the processing seems to be based on an autocorrelation of action potentials in the auditory nerve 16 however it has long been noted that a neural mechanism that may accomplish a delay a necessary operation of a true autocorrelation has not been found 5 at least one model shows that a temporal delay is unnecessary to produce an autocorrelation model of pitch perception appealing to phase shifts between cochlear filters 17 however earlier work has shown that certain sounds with a prominent peak in their autocorrelation function do not elicit a corresponding pitch percept 18 19 and that certain sounds without a peak in their autocorrelation function nevertheless elicit a pitch 20 21 to be a more complete model autocorrelation must therefore apply to signals that represent the output of the cochlea as via auditory nerve interspike interval histograms 19 some theories of pitch perception hold that pitch has inherent octave ambiguities and therefore is best decomposed into a pitch chroma a periodic value around the octave like the note names in western music and a pitch height which may be ambiguous that indicates the octave the pitch is in 4 just noticeable difference edit the just noticeable difference jnd is the threshold at which a change in pitch is perceived jnd varies based on the tone s frequency content below 500 hz the jnd is about 3 hz for sine waves and 1 hz for complex tones above 1000 hz jnd becomes about 0 6 for sine waves about 10 cents 22 this difference is typically tested by playing two tones in quick succession with the listener asked if there was a difference in their pitches 11 and becomes smaller if the two tones are played simultaneously as the listener is then able to discern beat frequencies the total number of perceptible pitch steps in the human hearing range is about 1 400 the total number of notes in the equal tempered scale from 16 to 16 000 hz is 120 11 aural illusions edit the relative perception of pitch can be fooled resulting in aural illusions there are several of these such as the tritone paradox but most notably the shepard scale where a continuous or discrete sequence of specially formed tones can be made to sound as if the sequence continues ascending or descending forever definite and indefinite pitch edit not all musical instruments make notes with a clear pitch the unpitched percussion instruments a class of percussion instruments do not produce particular pitches a sound or note of definite pitch is one where a listener can possibly or relatively easily discern the pitch sounds with definite pitch have harmonic frequency spectra or close to harmonic spectra 11 a sound generated on any instrument produces many modes of vibration that occur simultaneously a listener hears numerous frequencies at once the vibration with the lowest frequency is called the fundamental frequency the other frequencies are overtones 23 harmonics are an important class of overtones with frequencies that are integer multiples of the fundamental whether or not the higher frequencies are integer multiples they are collectively called the partials referring to the different parts that make up the total spectrum a sound or note of indefinite pitch is one that a listener finds impossible or relatively difficult to identify as to pitch sounds with indefinite pitch do not have harmonic spectra or have altered harmonic spectra a characteristic known as inharmonicity it is still possible for two sounds of indefinite pitch to clearly be higher or lower than one another for instance a snare drum sounds higher pitched than a bass drum though both have indefinite pitch because its sound contains higher frequencies in other words it is possible and often easy to roughly discern the relative pitches of two sounds of indefinite pitch but sounds of indefinite pitch do not neatly correspond to any specific pitch pitch standards and standard pitch edit main article concert pitch a pitch standard is the conventional pitch reference that musical instruments in a group are tuned to for a performance this may vary from ensemble to ensemble and has varied widely over musical history 440 hz problems playing this file see media help since 1939 the a above middle c is usually set at 440 hz often written as a440 or sometimes a 440 hz although other frequencies such as 442 hz are also often used as variants another standard the so called baroque pitch is now set at a 415 hz a semitone lower than a440 so that period and modern instruments can be used together by transposing classical pitch for fortepianos and other instruments for music of the classical period can be tuned to either 427 hz about halfway between a415 and a440 or 430 hz also between a415 and a440 but slightly sharper than the quarter tone and ensembles specializing in authentic performance of repertoire from the romantic era set the a above middle c to 432 hz or the french standard until the 1930s of 435 hz transposing instruments conventionally have their parts transposed and written in different keys from voices and non transposing instruments and indeed from different transposing instruments as a result musicians speak of concert pitch to avoid ambiguity when talking to each other for example the most common type of clarinet or trumpet when playing a note written in their part as c sounds a pitch that is called b on a non transposing instrument like a violin which indicates that at one time these wind instruments played at a standard pitch a tone lower than violin pitch to refer to that pitch unambiguously a musician calls it concert b meaning the pitch that someone playing a non transposing instrument like a violin calls b labeling pitches edit this section needs more citations please help improve this section by adding citations to reliable sources unsourced material may be challenged and removed december 2024 learn how and when to remove this message see also musical note distinguishing pitches of a scale for a comprehensive list of frequencies of musical notes see scientific pitch notation and frequencies of notes note frequencies four octave c major diatonic scale starting with c 1 pitches are labeled using letters as in helmholtz pitch notation 24 25 a combination of letters and numbers as in scientific pitch notation where notes are labelled upwards from c 0 the 16 hz c numbers that represent the frequency in hertz hz the number of cycles per second for example one might refer to the a above middle c as a a 4 or 440 hz in standard western equal temperament the notion of pitch is insensitive to spelling the description g 4 double sharp refers to the same pitch as a 4 in other temperaments these may be distinct pitches human perception of musical intervals is approximately logarithmic with respect to fundamental frequency the perceived interval between the pitches a220 and a440 is the same as the perceived interval between the pitches a440 and a880 motivated by this logarithmic perception music theorists sometimes represent pitches using a numerical scale based on the logarithm of fundamental frequency for example one can adopt the widely used midi standard to map fundamental frequency f to a real number p as follows p 69 12 log 2 f 440 hz displaystyle p 69 12 times log _ 2 left frac f 440 mbox hz right this creates a linear pitch space in which octaves have size 12 semitones the distance between adjacent keys on the piano keyboard have size 1 and a440 is assigned the number 69 see frequencies of notes distance in this space corresponds to musical intervals as understood by musicians an equal tempered semitone is subdivided into 100 cents the system is flexible enough to include microtones not found on standard piano keyboards for example the pitch halfway between c 60 and c 61 can be labeled 60 5 the following table shows frequencies in hertz for notes in various octaves named according to the german method of octave nomenclature note sub contra contra great small one lined two lined three lined four lined five lined b c 16 35 32 7 65 4 130 81 261 63 523 25 1046 5 2093 4186 c d 17 3125 34 625 69 3 138 59 277 18 554 37 1108 75 2217 5 4435 d 18 35 36 71 73 42 146 83 293 6 587 3 1174 65 2349 3 4698 6 d e 19 45 38 89 77 7 155 5625 311 125 622 25 1244 5 2489 4978 e f 20 6 41 2 82 41 164 81 329 625 659 25 1318 5 2637 5274 e f 21 83 43 65 87 31 174 61 349 23 698 45 1396 9 2793 8 5587 6 f g 23 125 46 25 92 5 185 370 740 1480 2960 5920 g 24 5 49 98 196 392 784 1568 3136 6272 g a 25 96 51 91 103 83 207 65 415 3 830 6 1661 2 3322 4 6644 8 a 27 5 55 110 220 440 880 1760 3520 7040 a b 29 125 58 25 116 5 233 466 16 932 3 1864 6 3729 3125 7458 625 b c 30 87 61 75 123 47 246 9375 493 875 987 75 1975 5 3951 0625 7902 125 scales edit the relative pitches of individual notes in a scale may be determined by one of a number of tuning systems in the west the twelve note chromatic scale is the most common method of organization with equal temperament now the most widely used method of tuning that scale in it the pitch ratio between any two successive notes of the scale is exactly the twelfth root of two or about 1 05946 in well tempered systems as used in the time of johann sebastian bach for example different methods of musical tuning were used in almost all of these systems interval of the octave doubles the frequency of a note for example an octave above a440 is 880 hz if however the first overtone is sharp due to inharmonicity as in the extremes of the piano tuners resort to octave stretching other musical meanings of pitch edit in atonal twelve tone or musical set theory a pitch is a specific frequency while a pitch class is all the octaves of a frequency in many analytic discussions of atonal and post tonal music pitches are named with integers because of octave and enharmonic equivalency for example in a serial system c and d are considered the same pitch while c 4 and c 5 are functionally the same one octave apart discrete pitches rather than continuously variable pitches are virtually universal with exceptions including tumbling strains 26 and indeterminate pitch chants 27 gliding pitches are used in most cultures but are related to the discrete pitches they reference or embellish 28 see also edit 3rd bridge harmonic resonance based on equal string divisions absolute pitch diplacusis eight foot pitch harmonic pitch class profiles just intonation meantone temperament music and mathematics piano key frequencies pitch circularity pitch class pitch detection algorithm pitch of brass instruments pitch shifter pitch pipe relative pitch scale of vowels vocal and instrumental pitch ranges references edit anssi klapuri introduction to music transcription in signal processing methods for music transcription edited by anssi klapuri and manuel davy 1 20 new york springer 2006 p 8 isbn 978 0 387 30667 4 plack christopher j andrew j oxenham richard r fay eds 2005 pitch neural coding and perception new york springer isbn 978 0 387 23472 4 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 roy d patterson etienne gaudrain thomas c walters 2010 the perception of family and register in musical tones in mari riess jones richard r fay arthur n popper eds music perception springer pp 37 38 isbn 978 1 4419 6113 6 1 2 3 hartmann william morris 1997 signals sound and sensation springer pp 145 284 287 isbn 978 1 56396 283 7 1 2 3 plack christopher j andrew j oxenham richard r fay eds 2005 pitch neural coding and perception springer isbn 978 0 387 23472 4 robert a dobie susan b van hemel 2005 hearing loss determining eligibility for social security benefits national academies press pp 50 51 isbn 978 0 309 09296 8 1...