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Hi, folks:

Pardon my ignorance, but what are "cents"? My tuner told me he had to raise my piano 20 cents. He acted as though I should be reported to some sort of piano abuse hotline.

I nodded knowingly and withdrew... any enlightenment would be great!

Thanks,
Nina

There are 1200 cents in an octave (regardless of the type of temperament a piano is tuned to). If equal temperament is used (the most common among modern pianos), each semitone is equal to 100 cents. 20 cents mean the note is 1/5 of a semitone off.

Eric

More simply put, there are 100 cents between half steps. If one takes the note Middle C and lowers it 100 cents it becomes B. If a G is 60 cents flat, then its pitch is closer to G flat than G. If your piano was 20 cents flat it is not too bad. Going from high humidity in summer to low humidity in winter can do it. That is why you should have your piano tuned twice a year. The word "cents" is mostly piano tuner talk and do not be alarmed by not being familiar with the terminology. Hope this helps, Thammer

Thanks, this is helpful to know. I was actually pleased that my piano had kept its tune fairly well from late summer - midwinter. It's new (2nd in-home tuning) and has been performing to my ear much better than I had hoped.

Glad to know that 20 cents isn't horrific!

Nina

It should be tuned 4 times the first year you have it and twice each year afterward. Buy Larry Fines book "The Piano Book."Great reading for tuners and owners.

My new piano arrived tuned 2 cents sharp, A-442. My tech said he would wait and see how it settled rather than lowering it to A-440 right away. The manufacturer concurred.

I ran into a lot of talk about cents when dealing with non-western, such as Hindustani, music that makes tonal gradations much finer than our western half-steps. It will bend your mind when you first start listening to it, but once you get it you'll love it.

T2- If your piano is at A 442, it is about 7 cents sharp, not 2 cents. It is 2 Hz sharp, but Hz and cents are not the same unit of measurement. I'm not trying to nitpick, just wanted you to be sure of the difference....Sam

Oh, okay. Thanks. I stand corrected.

T2

I'm totally amateur when it comes to tuning, but one thing I've noticed when I accompany my kids when they practice other instruments, especially stringed instruments like violin and guitar.

When tuning their instruments to the keyboard before starting, I listen for beats, or overtones as I approach the same pitch. lets say I'm tuning the G string (no jokes please) of a violin, which is G below middle C on piano. Am I right in assuming that the two are properly in tune when I can no longer hear beats, or should there be beats for a certain pitch? Also is there a relationship between "cents" and the frequency of the beats you hear for a certain off pitch? Say the tuning is a bit flat, and I'm hearing an overtone of about two beats per second. What would the relationship of that frequency be to "cents".

Jamie

Jamie,

Beat frequency is defined as the difference between two frequencies, so the two notes will be vibrating at the same frequency when you can no longer hear the beats between them. In your example, assuming the G on the piano is in tune, then when you can no longer hear the beats between the G on the piano and the G on the violin, the violin will be tuned to the G on the piano.

I don't know .02 cents about the "cents" though.

Mike

I had thought my piano was out of tune, but I guess it wasn't --- after playing for my tuner, he said I had no musical cents at all!


-Brad

I don't know whether I can explain this to your satisfaction without getting too technical or mathematical. But here it goes:

Beats are pulsations of sound that one perceives when two sound waves that do not vibrate at the same frequency OR whose frequencies are not INTEGRAL multiple of each other interact in successive constructive and destructive interferences. Theoretically, one should hear no beats when two notes are in tune (i.e., when they are vibrating at the same frequency), or when they are octaves (i.e., when the frequency of the higher note is an integral multiple of the lower note).

As far as frequency and cents are concerned, there is a relationship between the two, but this relationship is not linear. This nonlinearity arises because cents follow a linear progession, but frequencies follow a geometrical progession. For instance, the DIFFERENCE in cents between any two semitones is a constant and is equal to 100, but the DIFFERENCE in frequencies between the same two semitones is NOT a constant. The constant is in the RATIO of their frequencies (it is equal to 1.059463094 for an equal tempered scale).

As an example, consider the theoretical frequencies for C and C# in three octaves as given below:

Middle C - 261.626 Hz, Middle C# - 277.183 Hz
C an octave higher - 523.251 Hz, C# an octave higher - 554.365 Hz
C two octaves higher - 1046.502 Hz, C# two octaves higher - 1108.731 Hz.

Note that regardless of which pairs of semitones we are looking at, if we take the RATIO of the frequency for C# to that of C, we will always get 1.05946... However, if we take the DIFFERENCE of the frequencies for C# and C, we will get 15.557 Hz, 31.114 Hz, and 62.229 Hz, respectively for the three octaves. Note that the difference 'expands by a factor of two' for every octave going up (or 'contracts by a factor of 1/2' for every octave going down). This expansion or contraction is NOT reflected in the difference in cents. There are 100 cents between C and C# (and all other semitones) regardless of which octaves we are looking at. As a result, from middle C to middle C#, each cent represents a frequency difference of 15.557/100=0.15557 Hz. One octave higher, each cent represents a frequency difference of 31.114/100=0.31114 Hz. And two octaves higher, each cent represents 62.229/100=0.62229 Hz. Because of this nonlinear relationship, one needs to specify which two notes on the scale one is looking at before a valid relationship between cents and frequency can be established.

Eric

"Cents" is mostly piano tuner talk. It divides each half step into 100 equal parts. It serves us well, but I think musicians and scientists probably better understand "Vibrations per second." If one string in a unison is tuned to A440 and another in the same unison is tuned to A441 one will hear 1 beat(or vibration) per second when the two strings are struck simultaneously,which is the difference between the two pitches. Most string players are not real crazy about pianos because pianos cannot be tuned by the musician and pianos are frequently out of tune.Hope this helps, Thammer

Eric,

Thanks for that - believe it or not, I think I actually followed it, and can understand the basic concept of what you are trying to say. I guess my next question is, would the change in ratios of the semitone difference over the octaves you described in your example have more to do with the physics (mechanical properties) of the strings at different diameters over these ranges than any actual acoustic properties? Just curious.

Jamie

All pianos begin to go out of tune when the tuner puts away his tools.It is just a matter of degree according to the quality of the instrument, tuner, conditions and perception of the owner.

Jamie: Theoretically, if a string is strong and long enough, it can be tuned to any frequency just by changing its tension. In reality, this can not be done because of limits placed on the string's strength and length. When the diameter of a string is increased, its flexibility will decrease, and inharmonicity will set in as a result. Inharmonicity refers to the 'errors' in frequencies of the higher partials in relation to the fundamental frequency. When a string vibrates, not only do we hear its fundamental frequency (i.e., first partial), we also hear many higher partials (i.e., harmonics) created by the vibrating string. The relative strength (or intensity) of the fundamental frequency and its partials form what is referred to as a frequency spectrum. It is this spectrum that defines the timber of a musical instrument, or if we confine ourselves to just pianos, this spectrum defines the characteristic tone of the particular piano. Believe it or not, inharmonicity actually makes things sound 'right' to our ears, may be because we are used to hearing sound with inharmonicity.

The frequencies in the example I gave in an earlier post referred only to the fundamental frequencies, and so the effect of inharmonicity was NOT considered. Because string diameter affects inharmonicity and not the fundamental frequency, string diameter has therefore nothing to do with the relationship between (fundamental) frequency and cents that I was trying to elucidate in that earlier post.

Inharmonicity (and hence string diameter) does affect beats. This is because beats are calculated as the difference between two closest frequencies of two vibrating strings considering ALL partials.

Hope this explains rather than confuses the issue.

Eric

[ March 08, 2002: Message edited by: EricL ]