Does anyone know the relationship between hertz and cents ?
If i recalibrate the A from 440 to 441 how much sharper in cents does this make the A
http://home.tiscali.be/johan.broekaert3/Tuning_English.html
http://www.mcgee-flutes.com/cents_to_hertz_calculator.htm
http://www.geocities.com/CapeCanaveral/Lab/8779/chc3.html
http://www.harmonics.com/lucy/lsd/chap2.html
http://www.tunesmithy.netfirms.com/fts_help/faq_scales.htm
Hertz = cycles per second - refers to air vibrations. A=440Hz means the tone you hear is the air vibrating 440 cycles per second.
Cent = 1/100 - simply tells how many more or less per cent (%) you are above or below an intended point.
You would have to know the vibration rate for each note, e.g. A and Ab, subtract to get the difference, and then divide by 100 to get the percentage.
djm
This is the magic number. Study it closely.
1.059463094
This is the twelfth root of two. If you multiply it together twelve times, you get two. Wonderful, I hear you cry. So what? Well, if you multiply a particular pitch value (say 440) by this whimsical number, you get the ptich one semitone higher (and if you divide, you get a semitone lower. Maths is wondrous). So:
440 * 1.059463094
= 466.1637614
which is the pitch of Bb. So the difference is:
466.1637614 - 440
= 26.1637614
So here, one cent is about:
26.1637614 / 100
= 0.261637614Hz
It should be obvious that a one cent change in pitch is not always a set change in Hz, but in the range 440 - 880, it varies from a quarter Hz to a half Hz.
For those who are still reading, the formula for pitch change relative to Hz is
P = p * ( 1.00057779 ) ^ c
where P is the pitch you want to know, p is the starting pitch, and c is the number of cents you wish to raise the pitch by. ^ means exponent, or multiply 1.00057779 by itself c times.
Cheers,
Calum “the mathematician”
PS Cents isn’t a strictly linear (ie percentage) based relationship but it is a close enough approximation for any non-pedants out there 
Great stuff but… 
(and I’m a math-invoking architect)
Keep in mind that all those decimal places in the above post are for even tempered tuning and are teriffic for pianos and the like. Cents and Hz kind of go out the window when you are playing pipes because they are usually better tuned accoustically than mathematically. This means that if all is going well with your chanter, your F# should be well in tune and resonating nicley when it is somewhat below (flat) what a tuner that measures even tempered tuning will show. This is because of a harmonic resonance that creates an artificial “beat” that actually vibrates two octaves below the root (D in the drones). Even tempered tuning shortens this harmonic wave cycle making it sharp of the true double 8vb. Only by lowering the major third, F#, will it come into that “locked” solid harmony. 
If you were playing in F# (never recommended) though you would of course want the true pitch.
Cheers
Scott McCallister
It’s based on two facts:
- when you take two sounds separated by one octave (bottom D and back D for instance), th frequency of the sharper sound is twice the frequency of the lower;
- when you take a half-tone from a tempered scale, you divide it in 100 cents; for frequencies aren’t additive, cents are logarithmic: to go from a note to the note just a half-tone (tempered) above, you have to calculate:
f’ = f * a^100 (a is the value for a cent)
An octave consists of 12 tempered half-tones, each of them counts 100 cents. On the other hand, an octave doubles the frequency of a sound.
So you can write both following (for D and back D for instance):
f(back D) = 2f(bottom D)
f(back D) = f(bottom D) * a^1200
So a^1200 = 2
and (take the calculator) a= 2 ^(1/1200)
a= 1,00057779 - as Calum said
Well, it’s a math forum!
Philippe
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