moffdnb
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Semitone and Hz - Whats the correlation?
Hi,
Has anyone got the correlation between Hz and semitones? I need some info on what a semitone's range is over frequencies
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Susan G
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 02:28:59
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2.30 gigahertz Intel Core i7-3610QM; 16 GB RAMWindows 10 x64; NI Komplete Audio 6.SONAR Platinum (Lexington) x64
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Jose7822
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 02:31:55
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Infinite5ths
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 02:41:15
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There is no linear correlation. It depends on what octave you mean. (i.e. Frequency [in hertz] is a linear measurement system, tones/semitones/cents are a non-linear measurement system.) The above sites help you to convert between the two.
Think of it this way: Every time you double the frequency, you raise the pitch by an octave (12 semitones). So from A-440Hz to A-880Hz is 12 semitones. But then from A-880Hz to A-1760Hz is also 12 semitones. In one case you have a change of 440Hz spread over 12 semitones. In the other you have a change of 880Hz spread over 12 semitones. So as you go up the pitch scale, each semitone consists of a slightly larger change in frequency than the semitone below it. That is why the pitch system is non-linear. There is no set number of (change in) Hz per semitone.
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moffdnb
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 02:42:11
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WOW Cool n the gang!
Thanks guys!
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jinga8
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 02:49:09
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Celebrate Good Times, Come ON!! (Its a Celebration....(this low part is dedicated to Jose...no idea why, i just picture him with such a bassy/baritone/bellowing voice) No offense, Jose....y, por favor, regalanos con la identidad del "hombre blanco" que nos mira con los ojos tan mediocerrados y llenos de sangre.... 
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Jose7822
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 10:57:30
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ORIGINAL: Infinite5ths
There is no linear correlation. It depends on what octave you mean. (i.e. Frequency [in hertz] is a linear measurement system, tones/semitones/cents are a non-linear measurement system.) The above sites help you to convert between the two.
Think of it this way: Every time you double the frequency, you raise the pitch by an octave (12 semitones). So from A-440Hz to A-880Hz is 12 semitones. But then from A-880Hz to A-1760Hz is also 12 semitones. In one case you have a change of 440Hz spread over 12 semitones. In the other you have a change of 880Hz spread over 12 semitones. So as you go up the pitch scale, each semitone consists of a slightly larger change in frequency than the semitone below it. That is why the pitch system is non-linear. There is no set number of (change in) Hz per semitone.
To add to this, the non-linearity that Mike speaks of actually comes from the fact that we use the 12-Tone Equal Temperament Tuning System. This system is full of compromises (with the exception of the octave interval) that were purposely created in order to enable some instruments to play in all 12 keys without retuning. These compromises include having a 5th that's a little smaller than a pure 5th and a 3rd that's a little bigger than a pure 3rd, etc. The reason for the emergence of this system was because not all instruments have the capacity of adjusting their pitch on the spot. Instruments like the voice or the violin can play pure intervals without the need to retune. On the other hand, instruments like the piano obviously can't adjust tunning on the spot so they end up sounding good on some keys and out of tune in others. But the 12-Tone Equal Temperament System solved this problems, and was actually very well recieved by most (although some musicians didn't like the sound of impure perfect intervals). Take care!
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Jose7822
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 11:05:16
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ORIGINAL: jinga8
Celebrate Good Times, Come ON!! (Its a Celebration....(this low part is dedicated to Jose...no idea why, i just picture him with such a bassy/baritone/bellowing voice) No offense, Jose....y, por favor, regalanos con la identidad del "hombre blanco" que nos mira con los ojos tan mediocerrados y llenos de sangre....
( Hahaha  Thanks Jinga8, for dedicating a post to me. Although I have to correct you in that I'm actually considered a Tenor (at least when I used to sing in the college choir). Hopefully, sometime this year, I will build a website which I'll link here. I just wanna get some songs done before that though. Take care!
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s_barber
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 12:17:14
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I believe the correlation is the 12th root of 2. So...if you take the square root of 2 and the root of the result, repeating 12 times that end result is the interval between semi-tones. Supposedly you can multiply that number times the HZ of say A 440 the result will be B flat. I think the number you get has a gazillion places though. I guess science does have it's place in music. I've never tried it but that's the theory as I understand it.
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nprime
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 12:21:35
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feedback50
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 13:21:56
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ORIGINAL: s_barber
I believe the correlation is the 12th root of 2. So...if you take the square root of 2 and the root of the result, repeating 12 times that end result is the interval between semi-tones. Supposedly you can multiply that number times the HZ of say A 440 the result will be B flat. I think the number you get has a gazillion places though. I guess science does have it's place in music. I've never tried it but that's the theory as I understand it.
You recall correctly. The equal temperament scale is based on the twelfth root of two which is roughly 1.059463 … (2 raised to the 1/12 power). Assuming that A natural (in the U.S.) is 440 Hz, then B-flat (a single chromatic step) is 440 * (1.059463 raised to the first power) which comes out to 631.8883ish Hz. Continuing on, the pitch for B natural (two chromatic steps above our reference A 440) is calculated as 440 * (1.059463 raised to the second power) , or 493.883ish Hz. Each pitch is calculated by changing the exponent used with the 12th root of 2. Eventually, you come to the octave A 880, which is 12 chromatic steps from A 440. The calculation is 440 * (1.059463 raised to the 12th power) which comes out to 879.999ish Hz (not quite 880, but the error here is due to rounding the 12th root of two to 7 decimal places.
post edited by feedback50 - 2008/01/11 13:36:52
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Jose7822
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 14:02:17
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ORIGINAL: feedback50
ORIGINAL: s_barber
I believe the correlation is the 12th root of 2. So...if you take the square root of 2 and the root of the result, repeating 12 times that end result is the interval between semi-tones. Supposedly you can multiply that number times the HZ of say A 440 the result will be B flat. I think the number you get has a gazillion places though. I guess science does have it's place in music. I've never tried it but that's the theory as I understand it.
You recall correctly. The equal temperament scale is based on the twelfth root of two which is roughly 1.059463 … (2 raised to the 1/12 power). Assuming that A natural (in the U.S.) is 440 Hz, then B-flat (a single chromatic step) is 440 * (1.059463 raised to the first power) which comes out to 631.8883ish Hz. Continuing on, the pitch for B natural (two chromatic steps above our reference A 440) is calculated as 440 * (1.059463 raised to the second power) , or 493.883ish Hz. Each pitch is calculated by changing the exponent used with the 12th root of 2. Eventually, you come to the octave A 880, which is 12 chromatic steps from A 440. The calculation is 440 * (1.059463 raised to the 12th power) which comes out to 879.999ish Hz (not quite 880, but the error here is due to rounding the 12th root of two to 7 decimal places.
According to your calculations Bb is much higher in pitch then B natural.
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nprime
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 14:08:28
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It should be 466.16372 Hz.
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feedback50
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 14:17:43
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Correct (my error). Sadly at this location I am trying to use the windows calculator rather than my scientific calc at home.
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Blades
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 14:52:33
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Can't you turn your windows calc to scientific mode
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jinga8
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 17:42:12
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Can't you turn your windows calc to scientific mode What kind of doofus would want to use a COMPUTER to do SCIENCE stuff??? I mean, the pure analog error rate would skew any legitmate research into mush. Crazy, man. Crazy...
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feedback50
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RE: Semitone and Hz - Whats the correlation?
2008/01/11 18:25:58
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ORIGINAL: Blades
Can't you turn your windows calc to scientific mode
Yeah, but I can't make my fingers run in mousepad mode on my laptop (which has no numpad) if I've had more than two cups of coffee :)
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