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Author: alanporter
Date: 2008-07-20 23:57
I have often seen on the forum references to intonation being so many cents off. Excuse my ignorance, but what is a "cent" ? Thanks.
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Author: Koo Young Chung
Date: 2008-07-21 02:09
1 cent = 2^(1/1200) , which is 0.0577789 %
100 cents= 1 semi tone
major third= 400 cents, perfect fifth= 700 cents etc
Post Edited (2008-07-21 02:15)
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Author: ww.player
Date: 2008-07-21 03:46
Another way to think about it is that a cent is one percent, or 1/100th, of the distance from one note to the adjacent chromatic note. So, if your D is 10 cents sharp, it is 10% of the way to being a D#.
Also, here is some other useful information regarding cents and tuning. The human ear (mind) is not as sensitive as a tuner. Tests have shown that the average person can only hear a note as out of tune when it is at least two cents flat or four cents sharp (not surprisingly, some people can hear tuning better than others). This means that the average person is twice as sensitive to a note being flat as being sharp.
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Author: clarnibass
Date: 2008-07-21 05:14
>> Tests have shown that the average person can only hear a
>> note as out of tune when it is at least two cents flat or four
>> cents sharp (not surprisingly, some people can hear tuning
>> better than others). This means that the average person is
>> twice as sensitive to a note being flat as being sharp.
It is important to add how exactly those tests were done, because in different situation and in different pitches people can hear more or less tuning difference.
The tests I know were done by playing two notes, one after the other. This showed that the very close to the G above the staff is where people hear the most intonation difference and with the notes one after the other they can hear as little as 5 cents. Above and below gradullay more difference is needed to be able to hear the difference. For example in the area of middle C people can only hear in this way a difference of 8 cents.
It was also found that although this is average, actually there are very few differences between most people and not many can hear better or worse than this. Those who hear better or worse it is usually only very slightly better or worse.
Without specifying exactly how the test you descrtibed above was done it actually is more likely to mislead people to think usually people can just hear let's say a 2 cents flat note almost all situations, which is actually not true at all.
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Author: NorbertTheParrot
Date: 2008-07-21 14:02
Experimental results on whether people can hear the difference between consecutive notes are all very well, and of interest to physiologists, but in musical terms they mean very little.
There are two main reasons for this. One is simple, the other is more subtle.
The simple reason is that our ability to hear out-of-tuneness is much greater when notes are played concurrently than when they are played consecutively. If you play A=440 and A=441 at the same time, you will hear a beat once a second, and in a long note this will be quite obvious to almost any listener. But this is only about 4 cents.
The subtle reason is that in-tuneness is not just a matter of being in tune with a tuner. It is a matter of being in tune with other instruments. Playing with a piano is one thing, playing with strings or voice is a different matter. If a piano plays a C major scale, then the interval ratio from C to D and the interval ratio from D to E will be exactly the same, two equal-temperament semitones or 200 cents.
But when an unaccompanied string player or singer performs the same scale, they will (or should) make the C-to-D interval wider than the D-to-E. C-D should be 204 cents, D-to-E only 182 cents. If the C is in tune with the piano, the D will be 4 cents sharp and the E will be 14 cents flat.
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Author: mrn
Date: 2008-07-21 15:31
The concept of "cents" is related to "equal temperament" tuning. What we perceive as an "interval" between two notes is the *ratio* of the frequencies of the two notes. For pure octaves, this ratio is 2. (i.e., one octave up from A=440 Hz is 880 Hz).
In equal temperament tuning, the scale is built using a rigid definition of a "semitone," so that any two notes a semitone apart will have the same ratio between their frequencies and the ratio between any two notes an octave apart will still be 2.
To do this, equal temperament tuning defines the frequency interval for a semitone as
12 ______
\/ 2
or alternatively stated, 2^(1/12) [two to the one-twelfth power]
This number comes out to about 1.05946309436 on a calculator (it's an irrational number, so you can never write down all the digits).
So in equal temperament, if you start with A=440 Hz, going up a semitone gives you 440*2^(1/12) or about 466.163 Hz. Likewise, a semitone up from 880 Hz is 880*2^(1/12) or about 932.33 Hz.
It's called equal temperament because the frequency ratio between any two notes depends only on the number of semitones difference between the notes (e.g., all thirds, for instance, have the same frequency ratio no matter what note the third starts on)
If you take this semitone frequency ratio and multiply it by itself 11 times (i.e., take the 12th power of the ratio), you get 2 (an octave). If you don't believe me, try it on a calculator and you'll get something very close to 2.
A cent is also an "equal temperament" interval, but it's much smaller than a semitone. There are 100 cents in a semitone or 12*100=1200 cents in an octave. The ratio of two frequencies one cent apart is always 2^(1/1200) or the "twelve-hundredth root of 2." This is about 1.00057778951 on a calculator. If you multiplied this number by itself 1,199 times (take it to the 1,200th power), you'd get 2. If you can imagine a piano keyboard with 1,200 keys for every octave, you'll get the picture.
As to beat frequencies, the beat frequencies you hear when one note is "out of tune" with another are not due to the *ratio* between the two frequencies, but rather, to the *difference* in frequencies. That is why you hear one beat per second if you play 440 Hz together with 441 Hz. The beat frequency is 441-440 = 1 Hz.
What this means is that the beat frequency between two notes one cent apart will be different depending on the frequency of the notes themselves. A four cent difference at 1000 Hz, for example, would generate about a 2.3 Hz beat tone (about two beats per second), while the same four cent difference at 100 Hz would generate a 0.23 Hz beat tone (or a beat about every 4.3 seconds). This also helps explain why high notes are often so difficult to tune on any instrument. A given high note on your instrument might be only a cent or two off from the theoretical perfect intonation (so you sound very well in tune by yourself), but even a very slight deviation at that high a frequency could generate noticable beat tones when you're trying to play in unison with someone else.
Post Edited (2008-07-21 15:48)
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Author: alanporter
Date: 2008-07-21 15:59
Thank you for your explanations, fellow forumites. I wish I had paid more attention to physics classes when I was in school ! Now I can put my tuner to even better use.
Alan
tiaroa@shaw.ca
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Author: William
Date: 2008-07-21 16:09
LOL--ask what time it is (cent) and you get how to build the clock. Simply, a cent is how far off pitch your are sounding compared to a specific accepted frequency--ex. A=440 on your tuner. The cent(s) are usually defined on the face on the dial--ex. 2, 10, etc....meaning 2 cents flat/sharp, 10 cents f/s, etc.
OK, not so scientific an explanation but to me, an average musician tuning up my instrument, thats all I need to know......and my "two cents worth"
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