Mean free path: Difference between revisions

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If the beat rate is less than the lowest frequency,beats are distinct, and the interval sounds like a "wahwah" instead of a true sound pair.

If humans could hear to the mean free path limit, this would limit our perception range to <math>\frac{5\cdot10^9 \ln{2}}{16}</math> or about '''216 ~~million~~-EDO'''. This corresponds to a step size of about 5.5 x 10<sup>-6</sup> cents, which is roughly the size of the [[Unnoticeable comma|unnoticeable]] rascal comma, [-7470 2791 1312⟩. Playing in a temperament which makes a distinction for intervals this small is physically impossible without beating interference on all notes.

If humans could hear to the mean free path limit, this would limit our perception range to <math>\frac{5\cdot10^9 \ln{2}}{16}</math> or about '''216,608,494-EDO'''. This corresponds to a step size of about 5.5 x 10<sup>-6</sup> cents, which is roughly the size of the [[Unnoticeable comma|unnoticeable]] rascal comma, [-7470 2791 1312⟩. Playing in a temperament which makes a distinction for intervals this small is physically impossible without beating interference on all notes.

However, higher-pitched sounds will get heavily attenuated the closer their wavelength gets to free path. When the sounds attain levels of just several MHz, some estimate they will fail to travel through the air longer than a few centimeters.

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 If the beat rate is less than the lowest frequency,beats are distinct, and the interval sounds like a "wahwah" instead of a true sound pair.
-If humans could hear to the mean free path limit, this would limit our perception range to <math>\frac{5\cdot10^9 \ln{2}}{16}</math> or about '''216 million-EDO'''. This corresponds to a step size of about 5.5 x 10<sup>-6</sup> cents, which is roughly the size of the [[Unnoticeable comma|unnoticeable]] rascal comma, [-7470 2791 1312⟩. Playing in a temperament which makes a distinction for intervals this small is physically impossible without beating interference on all notes.
+If humans could hear to the mean free path limit, this would limit our perception range to <math>\frac{5\cdot10^9 \ln{2}}{16}</math> or about '''216,608,494-EDO'''. This corresponds to a step size of about 5.5 x 10<sup>-6</sup> cents, which is roughly the size of the [[Unnoticeable comma|unnoticeable]] rascal comma, [-7470 2791 1312⟩. Playing in a temperament which makes a distinction for intervals this small is physically impossible without beating interference on all notes.
 However, higher-pitched sounds will get heavily attenuated the closer their wavelength gets to free path. When the sounds attain levels of just several MHz, some estimate they will fail to travel through the air longer than a few centimeters.