Cosmic Harmonics
Cosmic Harmonics
Cosmic Harmonics
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Notes on a Scale<br />
Our “tempered” scale is multiplicative<br />
Frequency (Hz)<br />
1000<br />
500<br />
300<br />
100<br />
♪<br />
♪<br />
♪<br />
1000 600 200 Hz<br />
3520<br />
×2<br />
1760<br />
×2<br />
880<br />
×2<br />
440<br />
×2<br />
220<br />
110<br />
×2<br />
×2<br />
55<br />
27.5<br />
×2<br />
7 octaves on A<br />
Notes within the Octave<br />
• 12 semitones make an octave: f 13 /f 1 = 2.00<br />
A A # B C C # D D # E F F # G G #<br />
B ь D ь E ь G ь A ь<br />
• From one to the next is the same frequency ratio<br />
f 2 /f 1 = f 3 /f 2 = f 4 /f 3 ……… f 12 /f 11 = q<br />
•Now, f 2 /f 1 ×f 3 /f 2 ×f 4 /f 3 ……… × f 13 /f 12 = f 13 /f 1 = 2<br />
so q 12 = 2 q = 2 1/12 = 1.0569…<br />
and f n = f 1 ×q n/12 = f 1 × (1.0569…) n<br />
8
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