Mean free path: Difference between revisions

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== Analysis with respect to equal-step tunings ==

If ~~there~~ is a ~~species which can hear this high~~ of a sound~~, the maximum edo which~~ can be ~~applied will be defined~~ by the ~~species'~~ lowest frequency~~, or the place where the difference between rhythm and pitch occurs~~.

There exists a point in frequency which marks the transition between rhythm and pitch. The beat rate of an interval is their frequency difference. If the beat rate is lower than the the said lowest frequency, beats are distinct, and the interval sounds like a "wahwah" instead of a true sound pair. It can be argued, by such criteria, that the smallest interval useful as a pitch material has the same beat rate as the lowest frequency.

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 an interval whose base frequency is played at the mean free path limit, and beats at the lowest frequency, given as 16 Hz for human beings{{citation needed}}, the interval would have a size of about 5.5 × 10<sup>-6</sup> cents, corresponding to a step of about 200-million-edo. Playing in a tuning system 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 '''200 million-EDO,''' to within error'''.'''. 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{{citation needed}}.

~~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~~.

In small-atom solids such as dense metals, the sound can travel at much higher frequencies due to both higher sound speed and the periodicity and strength of the lattice (→ [[Wikipedia: Speed of sound]]). Theoretically, an alien civilization with their "ears" fit for hearing through solids rather than gases would be able to make music with these higher frequencies, and perceive intervals as distinct instead of "wahwah".

In small-atom solids such as dense metals, the sound can travel at much higher frequencies due to both higher sound speed and the periodicity and strength of the lattice. Theoretically, an alien civilization with their "ears" designed to hear through solids rather than gases would be able to make music with these higher frequencies, and perceive intervals as distinct instead of "wahwah".

[[Category:Psychoacoustics]]

[[Category:Limiting cases]]

[[Category:~~Extreme~~]]

@@ Line 25: / Line 25: @@
 == Analysis with respect to equal-step tunings ==
-If there is a species which can hear this high of a sound, the maximum edo which can be applied will be defined by the species' lowest frequency, or the place where the difference between rhythm and pitch occurs.
+There exists a point in frequency which marks the transition between rhythm and pitch. The beat rate of an interval is their frequency difference. If the beat rate is lower than the the said lowest frequency, beats are distinct, and the interval sounds like a "wahwah" instead of a true sound pair. It can be argued, by such criteria, that the smallest interval useful as a pitch material has the same beat rate as the lowest frequency.
-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 an interval whose base frequency is played at the mean free path limit, and beats at the lowest frequency, given as 16 Hz for human beings{{citation needed}}, the interval would have a size of about 5.5 × 10<sup>-6</sup> cents, corresponding to a step of about 200-million-edo. Playing in a tuning system 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 '''200 million-EDO,''' to within error'''.'''. 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{{citation needed}}.
-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.
+In small-atom solids such as dense metals, the sound can travel at much higher frequencies due to both higher sound speed and the periodicity and strength of the lattice (→ [[Wikipedia: Speed of sound]]). Theoretically, an alien civilization with their "ears" fit for hearing through solids rather than gases would be able to make music with these higher frequencies, and perceive intervals as distinct instead of "wahwah".
-In small-atom solids such as dense metals, the sound can travel at much higher frequencies due to both higher sound speed and the periodicity and strength of the lattice. Theoretically, an alien civilization with their "ears" designed to hear through solids rather than gases would be able to make music with these higher frequencies, and perceive intervals as distinct instead of "wahwah".
+[[Category:Psychoacoustics]]
+[[Category:Limiting cases]]
-[[Category:Extreme]]