The perceived pitch of tones is essentially determined by frequency. This does not mean, however, that pitch is entirely independent of other parameters of sound such as intensity, spectral composition, and superposition of additional sound, cf.  p. 329-340. When the pitch of a tone of constant frequency changes appreciably due to a change of intensity or on superposition of another sound, this is called a pitch shift. When the pitch of a tone turns out to deviate from a value which according to some smart thinking was expected, this is called a pitch deviation.
An example of pitch deviation is the interaural pitch difference (IPD, binaural diplacusis ). When one and the same tone is alternately presented to the right and left ear alone, there is a good chance that a slight but, for a fixed frequency systematic, difference between the pitch from the right ear and that from the left can be noticed.
Another example of pitch deviation is the difference in pitch between a pure tone and a harmonic complex tone with identical (fundamental) frequencies and about the same loudness. In many cases, the pitch of the harmonic complex tone turns out to be slightly lower than that of the pure tone ( p. 353-356; though, for a certain combination of SPLs of test stimuli, Platt & Racine 1985a found the opposite tendency). In more general terms this implies that the precise pitch of "one and the same" tone depends on the tone's spectral envelope, i.e., timbre. For example, the precise pitch of a tone played on a clarinet is not necessarily identical to that of a tone that with exactly the same fundamental frequency is played on an oboe.
The amount of pitch shifts and pitch deviations which may occur in normal-hearing persons is between 0 and plus/minus a few percent (in terms of equivalent frequency departure). It was found that individual persons differ systematically in their amount (although not the direction) of pitch shift/deviation for any given stimulus ( p. 343).
So, keeping in mind that the amount of pitch shift/deviation may differ from one individual to another, one can say that the pitch of a tone with constant frequency in general is basically dependent on
These influences superimpose quasi-linearly. That is, a pitch shift induced by, e.g., a change in intensity may be either enhanced or compensated for by superposition of another sound of suitable type and intensity. Likewise, an interaural pitch difference between identical tones may be either enhanced or compensated for by suitably changing the intensity (cf. van den Brink 1965a) or spectral envelope of one of the tones; and so on.
Measurement of pitch shift/deviation is efficiently accomplished by presenting the two tones to be compared in alternate succession, with tone durations between 0.2 and 1 s, and silent intervals between tones of 0 to 0.5 s. As auditory short -term memory for pitch is very accurate through silent intervals up to several seconds these parameters are not critical. When the listener is advised to adjust the frequency of one of the tones such that no difference in pitch can be heard, the resulting difference between the two tone frequencies is a measure for the pitch deviation that would exist when the frequencies were equal.
Generally it can be noted that the influence of intensity and of superimposed noise on the pitch of a tone is less pronounced for the tones of real life, i.e., complex tones, than it is for sine tones (Walliser1969c, Stoll 1985a). Where the case of superimposed noise is concerned, the pitch-shifting effect of the noise ordinarily is associated with, and dependent on, partial masking of the tone by the noise. This also applies to nonsimultaneous presentation of the tone and noise. When the noise precedes the tone within a time interval of less than about 200 ms, an if the noise's intensity is high enough, both partial masking and pitch shift of the tone may be obtained (Rakowski & Hirsh 1980a). However, monaural sine tones have been shown to be shifted in pitch by simultaneous presentation of another tone or random noise at the opposite ear with an intensity that by far is insufficient to produce any amount of masking by acoustic spread to the ear to which the tone is presented . Though this latter case is not of much relevance to hearing in real life, it may be significant for the understanding of binaural cooperation.
Obviously, the existence of pitch shifts/deviations affects the perception of music, and therefore, the performance of music, such as in the following respects.
1. When one and the same musical note is played on different instruments individually such that the perceived pitch is (within natural limits) identical, the fundamental frequencies may significantly differ. As a consequence, there will occur undesirable beats when those instruments switch to playing simultaneously. To remove those beats, fundamental frequencies would have to be made equal. So, optimal intonation (i.e., choice of fundamental frequency) does depend not only on the type of instrument (with its particular timbre) but also on whether tones are played successively or simultaneously.
2. When two individuals listen to one and the same melodic performance (e.g., on a violin), they may well differ in their evaluation of correctness of fine intonation. An intonation which for one individual sounds correct may for another appear slightly "out of tune". It is apparent that in such a case a person whose pitch shifts/departures are systematically small has an advantage. Those who do not have that advantage could improve their judgment if they knew what kind of ears they were born with (i.e., whether they have small, medium or large deviations). That applies in particular to the decision for playing a particular instrument. A person (eventhough highly musically talented) who was born with large pitch deviations should not envisage a professional career as a soloist on the violin or any other instrument on which intonation is crucially dependent on auditory control - including the singing voice.
3. When to a particular listener a melodic performance sounds slightly out of tune, he can only to a limited extent evaluate whether this is the player's or his own ears' fault. This probably is the reason why the human cognitive auditory system proves to be fairly tolerant about the intonation of musical performance, at least where pitch (as opposed to audible beats) is concerned. That kind of pitch-uncertainty" moreover provides an argument for the usefulness of frequency vibrato in music.
4. As a consequence of considerable theoretical significance, the pitch-shift effect can be said to be the ultimate source of the general tendency in music to stretch the intonation of the musical tone scale, a phenomenon that essentially can be inferred from the phenomenon of octave stretch. The explanation of octave stretch is included in the explanation of octave equivalence.
Author: Ernst Terhardt email@example.com - Mar 10 2000