Pythagorean Tuning
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online.Pythagorean tuning is based on a stack of perfect fifths, each tuned in the ratio 3:2, the next simplest ratio after 2:1, which is the ratio of an octave. Starting from D for example, the A is tuned such that the frequency ratio of A and D is 3:2 if D is tuned to 288 Hz, then the A is tuned to 432 Hz. The E above A is also tuned in the ratio 3:2 with the A at 432 Hz, this puts the E at 648 Hz, 9:4 above the original D. When describing tunings, it is usual to speak of a...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online.Pythagorean tuning is based on a stack of perfect fifths, each tuned in the ratio 3:2, the next simplest ratio after 2:1, which is the ratio of an octave. Starting from D for example, the A is tuned such that the frequency ratio of A and D is 3:2 if D is tuned to 288 Hz, then the A is tuned to 432 Hz. The E above A is also tuned in the ratio 3:2 with the A at 432 Hz, this puts the E at 648 Hz, 9:4 above the original D. When describing tunings, it is usual to speak of all notes as being within an octave of each other, and as this E is over an octave above the original D, it is usual to halve its frequency to move it down an octave. Therefore, the E is tuned to 324 Hz, a 9:8 above the D. The B at 3:2 above that E is tuned to the ratio 27:16 and so on. Starting from the same point working the other way, also from D to G is tuned as 3:2. With D at 288 Hz, this arrives at G at 192 Hz, or, brought into the same octave, to 384 Hz.
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