Difference between Cents and Frequency

Can some one tell me what the conceptual difference
actually is between the term 'cents' and 'frequency' ?

I understand that cents is a logarithmic measure of
some kind and that frequency is simply a rate of
vibratory speed over time.

I understand there is a relation between the two and
they can be converted into each other, but they do not
seem to be the exact same thing. How are they
different?

What is the logarithmic cents actually a measure of,
some sort of position?

If frequency is a measure of how fast a sound is, and
cents a measure of its position some how, is there
some sort of measure that describes sequence or
placement of a given note that is different from cents
or frequency - is this what is called key signature?

Thanks or any insights you can provide!

Dan Amateur

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Hi Dan,

> Can some one tell me what the conceptual difference
> actually is between the term 'cents' and 'frequency' ?
>
> I understand that cents is a logarithmic measure of
> some kind and that frequency is simply a rate of
> vibratory speed over time.
>
> I understand there is a relation between the two and
> they can be converted into each other, but they do not
> seem to be the exact same thing. How are they
> different?

Units of frequency are usually cycles per second (aka
Hertz), abbreviated cps or Hz. Cents are units of
logarithmic frequency. A cent is equal in size to one
step of 1200-tone equal temperament. That is, it is
1/100th of a "semitone" on a guitar or piano. Its value
is the 1200th root of 2, or 2^(1/1200).

Pitch perception is logarithmic with respect to frequency.
That is, two tones with frequencies standing in a 2:1
ratio sound like an octave no matter what pitch you play
them at, ie. 100 Hz. & 200 Hz., 400 Hz. & 800 Hz., etc.

> What is the logarithmic cents actually a measure of,
> some sort of position?

A musical interval is a distance between two pitches.
Sometimes pitches are named after the interval they form
with a fixed reference pitch, like A=440 or the tonic
of a piece of music. Saying "the third", for example,
means E in the key of C. Cents may be used in this
fashion, though I think that's pretty rare. It's more
common with just intonation frequency ratios. For
example, pitches are called things like 3/2, 5/3, etc.

-Carl

Although Carl did an excellent job in answering your questions, Dan, let me
dare to reply to the last paragraph.

There are several units of intervallic measurement that can explain how far
away a certain note is from a "tone of reference". Cents, as proposed by
Alexander Ellis, which corresponds to 1/100th of an "equal semitone", is by
far the most famous one. Before that, people used Savarts, I believe, the
corrected version of which equals exactly 4 cents.

But these units are meaningless if you are playing a guitar which is
designed specifically to accomodate twelve-tone equal temperament, where the
smallest unit is ordinarily 1 equally tempered semitone.

So, using this unit of measurement, you can see that the note G4 in
reference to C4 (~260 Hz) is 7 units up (hence, 700 cents). This means, that
in the key of C, G occupies the 7th position in the chromatic scale.

You can assign numbers from 1 to 12 in this fashion to the twelve notes,
with 0 denoting the tone (i.e. note) of reference in any particular key you
might wish to sound.

Thus, in the key of C,

0=C
1
2=D
3
4=E
5=F
6
7=G
8
9=A
10
11=B
12=c

Cordially,
Oz.

----- Original Message -----
From: "Dan Amateur" <xamateur_dan@yahoo.ca>
To: <tuning@yahoogroups.com>
Sent: 02 Ekim 2006 Pazartesi 3:37
Subject: [tuning] Difference between Cents and Frequency

>
> Can some one tell me what the conceptual difference
> actually is between the term 'cents' and 'frequency' ?
>
> I understand that cents is a logarithmic measure of
> some kind and that frequency is simply a rate of
> vibratory speed over time.
>
> I understand there is a relation between the two and
> they can be converted into each other, but they do not
> seem to be the exact same thing. How are they
> different?
>
> What is the logarithmic cents actually a measure of,
> some sort of position?
>
> If frequency is a measure of how fast a sound is, and
> cents a measure of its position some how, is there
> some sort of measure that describes sequence or
> placement of a given note that is different from cents
> or frequency - is this what is called key signature?
>
> Thanks or any insights you can provide!
>
> Dan Amateur
>
>
>

--- In tuning@yahoogroups.com, Dan Amateur <xamateur_dan@...> wrote:
>
>
> Can some one tell me what the conceptual difference
> actually is between the term 'cents' and 'frequency' ?

There are two: one is that cents measures relative pitch and frequency
absolute pitch, and the other is that cents is logarithmic.

If f1 and f2 are two frequencies (say, in Hertz) then

cents(f2/f1) = 1200 log2(f2/g1)

where log2 is log base 2. Cents is actually log base 2^(1/1200) of the
frequency ratio.