4 ms·

It's a discredit to the arxiv that this paper is still up, and I have to assume it's because there are just many fewer 'music theory nuts' out there than 'quant

It's a discredit to the arxiv that this paper is still up, and I have to assume it's because there are just many fewer 'music theory nuts' out there than 'quantum physics nuts.'

gardano 10y ago
I'd love to read a paper that modernises pythagorean music theory with modern mathematics. However, medieval music theory would balk at modern piano tuning -- much less 2nd Viennese School compositions -- so at first blush, I can't see how that could be done.
- mrob 10y ago
  The Pythagorean theory (simple ratios are consonant) is a consequence of the design of most Western musical instruments. They're typically built around either a string or a column of air, which is constrained at both ends. The overtones are unavoidably integer multiples of the fundamental because of this constraint. If they were not then at least one end of the string would be oscillating, which is not possible because it is clamped in place. Perception of consonance of a sound can be approximated by decomposing it into sine waves and calculating the sum of the values on the Plomp and Levelt curve (which is empirically measured and a consequence of human biology) for the intervals of all pairs of sine waves, weighted by amplitude. For instruments based around the harmonic series this results in standard Western harmony. There is nothing mystical about it, and the human brain does not have any ratio detector hardware. It's purely an artefact of a simpler underlying rule. Other instruments, eg. tuned percussion, do not have this constraint. If you clamp a bar at one end and strike it you can get all kinds of inharmonic overtones. This means cultures with music based around these types of instruments (eg. Indonesian classical music) need completely different harmonic theory. See http://sethares.engr.wisc.edu/paperspdf/consonance.pdf http://sethares.engr.wisc.edu/paperspdf/consonance.pdf This generalizes all existing theories of musical harmony, and explains things like stretched tuning in pianos (a consequence of non-ideal strings).
drauh 10y ago
I don't think it's a discredit. arXiv is a preprint database, which means nothing is refereed. It's under "Computer Science", but that's just the author's own classification. I don't think there's a way for the admins of arXiv to remove a paper. Once a paper is in the arXiv, it's there permanently: even the authors themselves can only update.[0] E.g. this bit of quackery "Electromagnetic Signals from Bacterial DNA"[1] [0] https://arxiv.org/help/withdraw https://arxiv.org/help/withdraw [1] https://arxiv.org/abs/1104.3113v1 https://arxiv.org/abs/1104.3113v1
- GFK_of_xmaspast 10y ago
  Crackpot stuff gets disappeared tho?
  - drauh 10y ago
    I don't think so. The link [1] I posted is crackpot. See also: * https://motls.blogspot.com/2006/05/crackpot-papers-on-arxiv.html https://motls.blogspot.com/2006/05/crackpot-papers-on-arxiv.... * https://arxiv.org/abs/gr-qc/0605023 https://arxiv.org/abs/gr-qc/0605023 (dated 2006)

It's a discredit to the arxiv that this paper is still up, and I have to assume it's because there are just many fewer 'music theory nuts' out there than 'quantum physics nuts.'

gardano 10y ago

I'd love to read a paper that modernises pythagorean music theory with modern mathematics. However, medieval music theory would balk at modern piano tuning -- much less 2nd Viennese School compositions -- so at first blush, I can't see how that could be done.

mrob 10y ago
The Pythagorean theory (simple ratios are consonant) is a consequence of the design of most Western musical instruments. They're typically built around either a string or a column of air, which is constrained at both ends. The overtones are unavoidably integer multiples of the fundamental because of this constraint. If they were not then at least one end of the string would be oscillating, which is not possible because it is clamped in place. Perception of consonance of a sound can be approximated by decomposing it into sine waves and calculating the sum of the values on the Plomp and Levelt curve (which is empirically measured and a consequence of human biology) for the intervals of all pairs of sine waves, weighted by amplitude. For instruments based around the harmonic series this results in standard Western harmony. There is nothing mystical about it, and the human brain does not have any ratio detector hardware. It's purely an artefact of a simpler underlying rule. Other instruments, eg. tuned percussion, do not have this constraint. If you clamp a bar at one end and strike it you can get all kinds of inharmonic overtones. This means cultures with music based around these types of instruments (eg. Indonesian classical music) need completely different harmonic theory. See http://sethares.engr.wisc.edu/paperspdf/consonance.pdf http://sethares.engr.wisc.edu/paperspdf/consonance.pdf This generalizes all existing theories of musical harmony, and explains things like stretched tuning in pianos (a consequence of non-ideal strings).

drauh 10y ago

I don't think it's a discredit. arXiv is a preprint database, which means nothing is refereed. It's under "Computer Science", but that's just the author's own classification. I don't think there's a way for the admins of arXiv to remove a paper. Once a paper is in the arXiv, it's there permanently: even the authors themselves can only update.[0] E.g. this bit of quackery "Electromagnetic Signals from Bacterial DNA"[1] [0] https://arxiv.org/help/withdraw https://arxiv.org/help/withdraw [1] https://arxiv.org/abs/1104.3113v1 https://arxiv.org/abs/1104.3113v1

GFK_of_xmaspast 10y ago
Crackpot stuff gets disappeared tho?
- drauh 10y ago
  I don't think so. The link [1] I posted is crackpot. See also: * https://motls.blogspot.com/2006/05/crackpot-papers-on-arxiv.html https://motls.blogspot.com/2006/05/crackpot-papers-on-arxiv.... * https://arxiv.org/abs/gr-qc/0605023 https://arxiv.org/abs/gr-qc/0605023 (dated 2006)