Musician: Cents Sharp/Flat?

Question

The other day in my wind ensemble, we had an intonation quiz. This consists of the entire band playing and holding a chord. Then the director points to one of us and cuts the rest of the band off. The person he points to, has to continue the pitch and keep it in tune. Well, I ended up being 2 cents flat when it was my turn. I never learned about cents in tuning. So what does being 2 cents flat mean and how does it read on a tuner?

Answer 1

"Cents" in regard to musical tuning is basically "percentage of a semitone"



The difference in Hz between notes gets greater and great as you go higher and higher. For example, middle C is roughly 261Hz. The C# above that is roughly 277Hz. A difference of 16Hz. An octave higher, the difference between those two pitches is roughly 31Hz.



So obviously we can't tell people "Oh, you were 2Hz flat" or something. Our ears just don't work that way. So we use "cents". 10 cents sharp would be 10% of the way up towards the next pitch; 10 cents flat would be 10% of the way down to the next pitch.



2 cents is nothing... hardly noticeable. Even the shallowest of vibratos changes the pitch by 10-15 cents.

Answer 2

Bottom Line - You were slightly off. If you play into a tuner, the needle will be slightly to the left. If the needle's not dead on in the middle, your pitch is off. After a while, you'll be able to hear when your pitch is dead on, relative to an ensemble.



BTW - Most tuners have a scale which indicates how many cents off you are.

Answer 3

just a comment: that's an interesting exercise, and if you were off by only 2 cents you probably have a great sense of pitch and good control over your intonation. Its hard not to follow the ensemble if the rest of them are off...whatever you're doing, keep it up.

Answer 4

Cents

Musical intervals are often expressed in cents, a unit of pitch based upon the equal tempered octave such that one equal tempered semitone is equal to 100 cents. An octave is then 1200¢ and the other equal tempered intervals can be obtained by adding semitones:







If f1 = Hz and f2 = Hz then the interval is cents.





Advantages of cents Mathematical expressions Just noticeable difference in pitch

Index



Temperament and musical scales

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Calculating Cents

The fact that one octave is equal to 1200 cents leads one to the power of 2 relationship:





This is convenient for calculating the frequency corresponding to a certain number of cents. To calculate the number of cents for any two frequencies, the above relationship must be reversed. Taking the log of both sides gives:







If f1 = Hz and f2 = Hz then the interval is cents.





Advantages of cents

f1 = Hz and f2 = Hz then the interval is cents.





Just noticeable difference in cents























Just Noticeable Difference in Pitch

The just noticeable difference in pitch must be expressed as a ratio or musical interval since the human ear tends to respond equally to equal ratios of frequencies. It is convenient to express the just noticeable difference in cents since that notation was developed to express musical intervals. Although research reveals variations, a reasonable estimate of the JND is about five cents. One of the advantages of the cents notation is that it expresses the same musical interval, regardless of the frequency range.



You can hear about

a nickel's worth of difference





Cents

Musical intervals are often expressed in cents, a unit of pitch based upon the equal tempered octave such that one equal tempered semitone is equal to 100 cents. An octave is then 1200¢ and the other equal tempered intervals can be obtained by adding semitones:







If f1 = Hz and f2 = Hz then the interval is cents.





Advantages of cents Mathematical expressions Just noticeable difference in pitch

Index



Temperament and musical scales

HyperPhysics***** Sound R Nave

Go Back

















Calculating Cents

The fact that one octave is equal to 1200 cents leads one to the power of 2 relationship:





This is convenient for calculating the frequency corresponding to a certain number of cents. To calculate the number of cents for any two frequencies, the above relationship must be reversed. Taking the log of both sides gives:







If f1 = Hz and f2 = Hz then the interval is cents.





Advantages of cents

Index



Temperament and musical scales

HyperPhysics***** Sound R Nave

Go Back











Advantages of Cents Notation

Examining the semitone A to B-flat at different points in the range of the piano will illustrate the fact that if expressed in cents, every equal tempered semitone is the same. Expressed in Hz difference, every semitone is different. The interval value in cents expresses the ratio of the frequencies, which is the same for every equal tempered semitone.





Included with the semitone intervals above is an evaluation of the deviation in Hz needed to equal 5¢, the nominal just-noticeable difference for these pitches. Note that the range represented by 5¢ increases from less than a tenth of a Hz at the low end of the piano to about 10 Hz at the top end of the piano.





If f1 = Hz and f2 = Hz then the interval is cents.





Noticeable Difference in Pitch

The just noticeable difference in pitch must be expressed as a ratio or musical interval since the human ear tends to respond equally to equal ratios of frequencies. It is convenient to express the just noticeable difference in cents since that notation was developed to express musical intervals. Although research reveals variations, a reasonable estimate of the JND is about five cents. One of the advantages of the cents notation is that it expresses the same musical interval, regardless of the frequency range.