Musical notation and mathematics

In summary, the conversation discusses the potential for musical notation to be considered a branch of applied mathematics, specifically in regards to representing spectral lines and revealing harmonic relationships with other elements. The conversation also touches on the use of logarithmic scales and the precision and relational nature of musical notation. The possibility of cross-species communication through tonal-based language is also mentioned, referencing a chilling article about whales and dolphins.
  • #1
Chronos
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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?
 
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  • #2
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.
 
  • #3
I was thinking about using logarithmic scales.
 
  • #4
Chronos said:
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.
 
  • #5
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/
 
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1. What is the relationship between musical notation and mathematics?

The relationship between musical notation and mathematics is that musical notation is essentially a system of symbols used to represent musical sounds and rhythms, much like how mathematical symbols are used to represent numbers and equations. Both systems rely on a set of rules and symbols to convey meaning and communicate complex ideas.

2. How does mathematics play a role in creating and interpreting musical notation?

Mathematics plays a crucial role in creating and interpreting musical notation. For example, the concept of time signature, which indicates the number of beats per measure, is based on mathematical principles. Additionally, the placement of notes and rests on a musical staff is determined by their mathematical duration, with whole notes being held for four beats and half notes for two beats.

3. What is the significance of mathematical ratios in musical notation?

Mathematical ratios are used in musical notation to determine the intervals between notes and the construction of scales. For instance, the ratio of 2:1 corresponds to an octave, and the ratio of 3:2 corresponds to a perfect fifth. These ratios are essential in creating harmonious and pleasing sounds in music.

4. How does musical notation use geometric shapes and patterns?

Musical notation often uses geometric shapes and patterns to convey information about the pitch and duration of notes. For example, the shape of a notehead and the position of a note on the staff can indicate its pitch, while the use of flags and beams can show the duration of a note. These geometric representations help musicians quickly read and interpret musical notation.

5. Are there any connections between musical notation and other mathematical concepts?

Yes, there are several connections between musical notation and other mathematical concepts. For example, the use of fractions in music, such as dividing a whole note into four quarter notes, is similar to how fractions are used in mathematics. Additionally, concepts like symmetry and patterns are also present in both music and mathematics.

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