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The frequency of the A440 or Stuttgart pitch is 440 Hz. I wonder to what extent people are able to differentiate between the correct pitch height and increasingly further deviations from this standard. I'm looking for academic studies that lay out to what extent people can tell the difference between, say, 440 Hz and 440.1 Hz, 441 Hz or 442 Hz.

It would be great if the academic studies would go into:

  1. Professional musicians, hobby musicians and people who haven't played any musical instruments in their life. To what extent do their musical abilities affect their ability to detect (subtle) deviations to the pitch of the notes?
  2. To what extent the speed at which the notes are played sequentially affects peoples' abilities to detect these deviations.
  3. Whether or not there are major differences between people that are used to the classical Western note scales and people who are used to different scales.
  4. If the ability to detect deviations also depends on the frequency of the note itself? Are people better at detecting deviations from an A440 Hz note, or a C2093 note? Why?

Moreover, I'd be interested in graphs that depict what proportion of a large population is able to detect a frequency deviation of, say, 0.01%, 0.1%, 1% and 10% of frequency of a given note.

Max Muller
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    See also: Interval Perception. – Aaron May 01 '22 at 19:47
  • Just curious, why does it matter? Suppose you knew exactly your answer, what could you do with such "knowledge"? Clearly ear training will only improve ones ability and generally speaking someone that works with musical pitch regularly will be more perceptive such things. It's well known that most people can detect differences, in isolation, of around 5-10 cents. 25 cents is a quarter tone and generally in direct comparison that is relatively easy to detect. Generally speaking even a few cents though, in context, can alter the musical color. But knowing such things does what? – Gupta May 01 '22 at 19:58
  • @Gupta I have an idea for an application in mind that alters the musical notes of any song slightly and randomly, to give listeners the impression (perhaps subconsciously) that the song is slightly different and therefore "new" in a sense to them, making it more interesting to them to listen to the same song multiple times – Max Muller May 01 '22 at 20:41
  • I don't expect the difference to be in percent (which is at least a relative scale) or even in Hertz. As Gupta comments, cent is the scale to search for. – guidot May 01 '22 at 20:44
  • The composer Bela Bartok was renowned for his acute differentiating of notes, even quartertones and smaller differentiating increments. I would research him to see exactly what increments he was capable of differentiating. – Wyvern123 May 01 '22 at 21:30
  • Hmm, I don't think that is really that easy as you think. You can't just alter things randomly and you basically need to know the harmonic and melodic structure of the music. E.g., you can't shift a pitch up or down x cents and it mean the same thing in all scenarios. It depends on how it is functioning. If you use randomization it is more likely, unless you keep it very subtle, to produce bad results. While it could be done I think ultimately you have to predetermine the changes to make sure they produce good effects. Microtones can really alter the music when used correctly. – Gupta May 02 '22 at 04:47
  • For example, One can play with microtonal shifts of major and minor thirds to produce quite drastic shifts of mood(relatively speaking) but it depends to some degree on absolute relationships. That is, Say the reference is at 0 cents and you shift it down 4 cents and it can sound unpleasing but then at 5 cents it sound darker then at 6 cents it sounds harsh again. Somehow at around 5 cents it locks in with the rest of the music(Probably related to Just intonation). I don't know how to describe the effects but when one plays on a variable pitch instrument such as a violin one gets used to these – Gupta May 02 '22 at 04:51
  • subtle effects(generally they are bad but at least in isolated conditions with awareness one can learn to hear the finer colors that exist. Good players do this naturally by slightly altering pitches to fit the mood but in general it's not worth it(since it has a lot to do with context and even the acoustics). There are probably better ways to achieve more interest that is more natural such as having different parts have variations(this might be drastic but one can think of it as a remix). Ultimately all you can do is try and experiment. – Gupta May 02 '22 at 04:52
  • back when the majority of the audio equipment was not digital and the reproduced pitch varied with the tape speed, it was quite normal for the speed to be less than ideally stable. quick variations were quite noticeable, but like half a tone drift (5% of the speed) over the song duration was almost acceptable – fraxinus May 02 '22 at 15:11
  • Max, your comment changes the question a lot: distinguishing two pitches playing consecutively is very different from distinguishing two pitches played at the same time – the latter is much easier thanks to (or due to) beating. You might be interested in studying about non-equal temperaments, which may yield more predictable and and more pleasant results in your application than random shifts. – user1079505 May 02 '22 at 23:16

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From the Encyclopedia Brittanica, In the section Dynamic Range of the Ear of the entry Hearing:

"The audio frequency range encompasses nearly nine octaves. Over most of this range, the minimum change in the frequency of a sinusoidal tone that can be detected by the ear, called the frequency just noticeable difference, is about 0.5 percent of the frequency of the tone, or about one-tenth of a musical half-step. The ear is less sensitive near the upper and lower ends of the audible spectrum, so that the just noticeable difference becomes somewhat larger."

A brief research suggests that there are indeed some studies about the matter. I found the slides of one of the lectures in the Musical Acoustics by Carlos Bertulani, member of the Department of Physics and Astronomy of the Texas A&M University which suggest that the course deals with the matter in more detail.

Felipe Martins
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