Cosmic Harmonics
Cosmic Harmonics
Cosmic Harmonics
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Perfectly Harmonic Notes<br />
• Many musical instruments have simple harmonic sequences<br />
e.g. strings & air columns: f n = n × f 1<br />
An integral number of waves fit between the two ends<br />
1 2 3<br />
4<br />
5 6<br />
7<br />
8<br />
9 10 11 12 13 14 15 16 17 18 19<br />
Flute<br />
• We “hear” the pitch of f 1 while the relative strength of all<br />
the harmonics gives the “quality” or “color”<br />
Inharmonic Notes<br />
• Some instruments have more complex modes of vibration<br />
e.g. drums, bells, bars:<br />
• Sometimes, hear a “ghost strike tone” – not actually present<br />
some partials are harmonically related (f = nf s)<br />
We hear f s even if f s isn’t itself present<br />
• What is the primordial sound?<br />
It is basically harmonic, but 1 st and 2 nd are inharmonic<br />
A ghost strike tone defined by the higher partials<br />
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