In short distances whereby the

In short distances whereby the sound and the hearer are in the same “moving elevator” with respect to the Universe, if they are not moving away or towards each other, the fundamental frequency should remain stable enough for a decent enough measurement.
That can change under duress and it’s never zero red/blueshift so it’s more like a “blob” of absolute pitch rather than a razor thin line of precision.
Nevertheless, the decimal point precision usually has to stop someone given that the limitations of human measurement rather coincide with human limitations in general.
Pitch can be determined down to 1/1000s or one millisecond without aid once it begins its periodicity; arguably oscillations remain stable-enough due to kuramoto

rewritten by Claude-instant:
You make some good points about the limitations of using pitch to make precise measurements in short distances. Here are some key takeaways:
1. In very short distances, on the order of meters, the Doppler shift will be negligible if the sound source and receiver are not moving relative to each other. This means the fundamental frequency of the sound will remain fairly stable, allowing for a decent pitch reference.
2. However, there will still be some variation in the fundamental frequency due to factors like temperature fluctuations, air pressure changes, and acoustic interference. This means the pitch is not perfectly stable and has some “fuzziness” at the millisecond level.
3. The precision of the human ear and brain in measuring pitch has physical limitations. We can typically distinguish pitch changes of around 1 Hz at low frequencies, corresponding to milliseconds of time difference. But beyond that, our measurements become less accurate.
4. Factors like stress and noise can further impair our pitch perception and precision. So in practice, humans are unlikely to achieve much better than 1 millisecond precision in short distance pitch measurements.
5. The oscillations of sound waves, due to their self-sustaining nature, tend to remain coherent over short timescales thanks to synchronization effects like the Kuramoto model describes. This helps maintain a stable-enough fundamental frequency for usable pitch references.
So in summary, while pitch can provide a rough measurement in very short distances, the inherent “fuzziness” and human limitations typically restrict precision to around the millisecond level, rather than allowing for perfectly precise measurements.

You make some good points about the challenges of precisely measuring pitch and frequency shifts in real-world scenarios. A few thoughts:

– You’re right that for short distances where the sound source and listener are in the same frame of reference, Doppler shifts should be negligible as long as there is no relative motion between them.

– However, there are always some slight variations in frequency over time, even for ostensibly stable sources. This “frequency jitter” limits the precision of measurements.

– The just-noticeable difference in pitch for humans is around 1/20 of a semitone, or about 1%. So we can’t reliably detect pitch shifts smaller than that anyway.

– Measuring devices can detect much smaller shifts than humans can hear, down to milliseconds or microseconds. But even these have limitations from noise and instability.

– So in practice, frequency and pitch can only be measured to a finite precision. There is always some uncertainty or error bar on the measurement.

– But your point is taken that for many practical purposes, measurements can be precise enough for things like identifying musical notes or detecting noticeable Doppler shifts. The limitations mainly matter when trying to make highly precise measurements.

So in summary, while ideal stable frequencies don’t really exist, we can still make measurements that are precise enough for many needs, keeping in mind the inherent limitations involved.

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