4 ms·

How did they transform the original music to A=432Hz? If they did it in the naïve way, it would result in a decrease in tempo by almost 2%.

rob74 5y ago
Good question, but nowadays all video players and platforms are able to increase/decrease the speed of a video without affecting the audio's pitch, so I guess the reverse is also widespread...
- cannam 5y ago
  It is, but I'm sure the audible artifacts introduced by a pitch shifter would outweigh any perceptual effects due to the change in tuning. It has to be one of the two - either the lower-frequency music is fractionally slower or it has been modified in a non-transparent way - I don't think the article tells us which. There seem to be other things the article doesn't tell us, such as how the authors verified that the music they used had been tuned to A=440 in the first place (since it's far from universal) or why, given an infinite number of possible tuning frequencies, a great many of which have been chosen by musicians at some point, and given no obvious physical basis for this specific choice, they went for A=432 instead of any other value below 440. [edit: removed warranted but uncivil snark]
  - insickness 5y ago
    You can transparently slow music without changing the pitch or pitch music without changing the tempo far more than 2%, which was what was done here. This technology has been in use by DJs spinning CDs since the 90s and is also used in music production. Depending on the source material, you can actually double the pitch or tempo with no artifacts.
    - cannam 5y ago
      I agree with you that you can often do this in a way that is still pleasant to listen to. But timestretching/pitch shifting is very far from being transparent in the way that a decent resampler is. Even a small shift will introduce some audible artifacts in most music. Will they be more or less apparent to the listener than the difference between recordings tuned to A=440 or 432 would be? I don't know. Depends on the music and the listener, I imagine. That would (be one of the many, many unstated things that would) matter to a paper like this. (For what it's worth, I wrote and maintain a widely-used timestretcher library. Possibly this means I am more aware of the limitations than the strengths of such technology)
    - marcan_42 5y ago
      There is no way to do this with no artifacts; it's just fundamental to how audio works. We have pretty good algorithms for it, but in the end you're doing psychoacoustics to try to make it sound good. There's no mathematical model for doing this "perfectly" like there is for resampling. It's not hard to hear the artifacts in DJ tempo stretch algorithms if you listen closely, especially when they are applied to a full mix (as opposed to single instruments). Of course they're small these days, but when you're trying to measure a subtle effect, they're too much of a confounding variable.
dt2m 5y ago
i'm also guessing they didn't test different temperament tunings either, which is a shame given that the whole argument for 432Hz has to do with mathematical symmetry
- mandmandam 5y ago
  Nice to see this argument referred to on here. A 432 A makes the math behind music so much nicer to work with (ignoring legacy baggage).
  - acadapter 5y ago
    Why? The length of the second is arbitrary.
    - tripa 5y ago
      The length of the second is irrelevant. 432 makes the math easier by virtue of being more easily factorable, with no incidence as to what's heard.
      - arbitrage 5y ago
        You are just wrong. Musicians can absolutely tell the difference between 432Hz and 440Hz. Audience typically can too, although they might not be able to put into words what is different. Personally, I prefer a brighter concert-A, 444 or higher.
        Sporktacular 5y ago
        Doubtful the audiences can, unless maybe they just heard another piece in 440 for comparison. Maybe those with good pitch memory would notice something before they readjusted. Maybe.
        OscarCunningham 5y ago
        The pieces they used were John Williams movie soundtracks, so I can image that they were very familiar to some of the audience.
Cthulhu_ 5y ago
In modern music editing software you can finetune the frequencies corresponding to each tone, then just replay the same patterns. More involved would be to re-tune a piano and play the same song twice.

rob74 5y ago

Good question, but nowadays all video players and platforms are able to increase/decrease the speed of a video without affecting the audio's pitch, so I guess the reverse is also widespread...

cannam 5y ago
It is, but I'm sure the audible artifacts introduced by a pitch shifter would outweigh any perceptual effects due to the change in tuning. It has to be one of the two - either the lower-frequency music is fractionally slower or it has been modified in a non-transparent way - I don't think the article tells us which. There seem to be other things the article doesn't tell us, such as how the authors verified that the music they used had been tuned to A=440 in the first place (since it's far from universal) or why, given an infinite number of possible tuning frequencies, a great many of which have been chosen by musicians at some point, and given no obvious physical basis for this specific choice, they went for A=432 instead of any other value below 440. [edit: removed warranted but uncivil snark]
- insickness 5y ago
  You can transparently slow music without changing the pitch or pitch music without changing the tempo far more than 2%, which was what was done here. This technology has been in use by DJs spinning CDs since the 90s and is also used in music production. Depending on the source material, you can actually double the pitch or tempo with no artifacts.
  - cannam 5y ago
    I agree with you that you can often do this in a way that is still pleasant to listen to. But timestretching/pitch shifting is very far from being transparent in the way that a decent resampler is. Even a small shift will introduce some audible artifacts in most music. Will they be more or less apparent to the listener than the difference between recordings tuned to A=440 or 432 would be? I don't know. Depends on the music and the listener, I imagine. That would (be one of the many, many unstated things that would) matter to a paper like this. (For what it's worth, I wrote and maintain a widely-used timestretcher library. Possibly this means I am more aware of the limitations than the strengths of such technology)
  - marcan_42 5y ago
    There is no way to do this with no artifacts; it's just fundamental to how audio works. We have pretty good algorithms for it, but in the end you're doing psychoacoustics to try to make it sound good. There's no mathematical model for doing this "perfectly" like there is for resampling. It's not hard to hear the artifacts in DJ tempo stretch algorithms if you listen closely, especially when they are applied to a full mix (as opposed to single instruments). Of course they're small these days, but when you're trying to measure a subtle effect, they're too much of a confounding variable.

dt2m 5y ago

i'm also guessing they didn't test different temperament tunings either, which is a shame given that the whole argument for 432Hz has to do with mathematical symmetry

mandmandam 5y ago
Nice to see this argument referred to on here. A 432 A makes the math behind music so much nicer to work with (ignoring legacy baggage).
- acadapter 5y ago
  Why? The length of the second is arbitrary.
  - tripa 5y ago
    The length of the second is irrelevant. 432 makes the math easier by virtue of being more easily factorable, with no incidence as to what's heard.
    - arbitrage 5y ago
      You are just wrong. Musicians can absolutely tell the difference between 432Hz and 440Hz. Audience typically can too, although they might not be able to put into words what is different. Personally, I prefer a brighter concert-A, 444 or higher.
      - Sporktacular 5y ago
        Doubtful the audiences can, unless maybe they just heard another piece in 440 for comparison. Maybe those with good pitch memory would notice something before they readjusted. Maybe.
        OscarCunningham 5y ago
        The pieces they used were John Williams movie soundtracks, so I can image that they were very familiar to some of the audience.

Cthulhu_ 5y ago

In modern music editing software you can finetune the frequencies corresponding to each tone, then just replay the same patterns. More involved would be to re-tune a piano and play the same song twice.