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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.

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    See also: Interval Perception.
    – Aaron
    Commented May 1, 2022 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
    Commented May 1, 2022 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
    Commented May 1, 2022 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
    Commented May 1, 2022 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
    Commented May 1, 2022 at 21:30

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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.

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