document.write( "Question 1163598: An orchestra tunes to a Frequency of 440,which sounds the A above middle c.Eech octave higher double the frequency,and each of the 12 some time in the octave increases the frequency in the same ratio.
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Algebra.Com's Answer #787812 by AnlytcPhil(1810)\"\" \"About 
You can put this solution on YOUR website!
There were a few typos, so I corrected them and reposted.

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document.write( "Indeed, the frequencies of the musical scale are in GP, with first term \r\n" );
document.write( "A = a1 = 440 and the next higher A, an octave higher, is a13 = 880,\r\n" );
document.write( "which has twice the frequency.\r\n" );
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document.write( "an = a1∙rn-1\r\n" );
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document.write( "a13 = 440∙r13-1\r\n" );
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document.write( "880 = 440∙r12\r\n" );
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document.write( "2 = r12\r\n" );
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document.write( "\"root%2812%2C2%29=r\"\r\n" );
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document.write( "That's the ratio, approximately  1.059463094\r\n" );
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document.write( "So the A above middle C vibrates 400 times a second.\r\n" );
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document.write( "A-sharp (B-flat) vibrates at\r\n" );
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document.write( "\"400root%2812%2C2%29=423.78522377\"\r\n" );
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document.write( "we multiply by \r\n" );
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document.write( "\"root%2812%2C2%29=r\"\r\n" );
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document.write( "each time.\r\n" );
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document.write( "B vibrates at 448.9848192\r\n" );
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document.write( "C above middle C vibrates at 475.6828457\r\n" );
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document.write( "So middle C vibrates at half that\r\n" );
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document.write( "So middle C vibrates at 237.8414229  \r\n" );
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document.write( "C)Where on the scale is a note with a Frequency of 600?\r\n" );
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document.write( "\"matrix%282%2C1%2C%0D%0A%22%22%2C%0D%0A600=400root%2812%2C2%29%5En%29\"\r\n" );
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document.write( "\"600%2F400=%28root%2812%2C2%29%29%5En\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C3%2F2=%282%5E%281%2F12%29%29%5En%29\" \r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C3%2F2=2%5E%28n%2F12%29%29\" \r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C2%2Aexpr%283%2F2%29=2%2A2%5E%28n%2F12%29%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C3=2%5E%281%2Bn%2F12%29%29\"  \r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C3=2%5E%28%2812%2Bn%29%2F12%29%29\"  \r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Cln%283%29=ln%282%5E%28%2812%2Bn%29%2F12%29%29%29\" \r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Cln%283%29=%28%2812%2Bn%29%2F12%29ln%282%29%29\" \r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C12ln%283%29=%2812%2Bn%29ln%282%29%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C12ln%283%29%2Fln%282%29=12%2Bn%29\" \r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C12ln%283%29%2Fln%282%29-12=n%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C7.019550009=n%29\"\r\n" );
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document.write( "That's a tiny bit sharper than the 7th note of the scale\r\n" );
document.write( "starting on A-440.\r\n" );
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document.write( "A, A#, B, C, C#, D, D#, E, F, F#,  G, G#\r\n" );
document.write( "1,  2, 3, 4,  5, 6,  7, 8, 9, 10, 11, 12\r\n" );
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document.write( "So 600 is a bit sharper than D#, the same as Eb.\r\n" );
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document.write( "[# means sharp, b means flat]\r\n" );
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document.write( "Edwin
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