|I have trouble with Bessel functions at this point. I'm very impressed with how far it (frequency modulation) can be extended. But very simple frequency modulation wears me down. - Paul Lansky when asked about the most unhealthy aspects of computer music.|
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Equal Tempered Musical Scale
The Western Equal Tempered scale is one of the most versatile musical scales. It is quite unique in that a musician can change keys without needing to retune instrument. Many musicians can all play together, in any key, and have the resultant music sound quite good.
The Pythagorean Comma
The Equal Tempered Scale achieves this unique property by splitting the Pythagorean Comma, or the required disharmoniousness among all the notes equal.
Note: In actuality, good piano tuners will not tune a piano to the exact Equal Tempered Scale, but instead make small adjustments to make the more common musical keys sound a little better than music in the less common keys.
The mathematical basis for the Equal Tempered scale is simply the 12th root of 2, or a number of approximately 1.05946309436. In words, each note, is at a frequency that is 1.05946309436 times the frequency of the previous note. For example, if the center note of C is 256 Hz, then C# would be at 271.22, and D at 287.35 etc.
A few enterprising businesses have created computerized systems that will modify the Equal Tempered Scale for each song. This, although useful, ends up having only limited applicability, and seems to only be noticeable to true musicians with a highly refined ear for musical intervals and harmonics.
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The information published on this web site is for entertainment purposes only and is in no way intended to dispense medical advice or opinion or to substitute for professional medical care, whether advice, diagnosis or treatment, by a medical practitioner. If you have a medical issue or feel ill, you should consult a health care professional.