Musical notation and mathematics

[Chronos]

I am curious if musical notation could be considered a branch of applied mathematics. For example, could spectral lines be represented in musical notation? Would they reveal harmonic relationships with other elements similar to the periodic table?

[ophecleide]

That's a really interesting question, the kind that will probably keep me up at night (I'm serious, these things do). I imagine you could write spectral lines in in musical notation, but the only problem I see is in the way that light waves are fundamentally quantized as compared to the way in which we have quantized sound waves, artificially to produce music. The problem is that one octave in music would cover pretty much the entire visible spectrum, but our (western) musical system would only allow for 12 different wavelengths, or frequencies as would probably be more appropriate when using music as a model. Obviously, there are far more than 12 different possible wavelengths between 4e-7m and 8e-7m (just to pick rough values for the bounds on visible light). At the moment, I can think of two "solutions" to this problem. First of all, the number of 'notes' per octave could be increased to more closely match the actual quantization of light. This model would hardly resemble music in many fasions, but it would still model music in the most basic sense. Second, a relatively unmodified musical model may still be useful even with this (relatively) huge frequency gap between 'notes'. The number of spectal lines observed with the visible spectrum is pretty limited in many cases for a limited sample. Anyway, that's my gut reaction. Thanks for bringing it up, even if it does cause loss of sleep.

[Chronos]

I was thinking about using logarithmic scales.

[Chrono]

I was thinking about using logarithmic scales.

I was thinking that it used that, too.

I may ask my old band director. He had to take a music theory class so I'm sure he knows something about it.

[Chronos]

We are thinking in similar terms. An octave represents one order of magnitude [OOM]. Perhaps a scale factor could be derived based on emission line frequency relationships - say, hydrogen, helium and carbon, or something along those lines. The thing that fascinates me about musical notation is its precision and deep relational orders. What got me thinking about this is that sea mammals [e.g. whales] have apparently developed tonal based language skills. Furthermore, it appears whales and dolphins can communicate. Cross species communication? Apparently there are some mutually understood conventions in a language so based [should we notify SETI?]. I found this article chilling:
http://www.cnn.com/EARTH/9704/10/whale.talk/