how to calc. the cents?

Hi,

how do you convert the 1/4 note to cents? I know that the 1/4= 50
cents? Is there any formula to do that?

--- In tuning@yahoogroups.com, "karim8411" <karim8411@y...> wrote:
> Hi,
>
> how do you convert the 1/4 note to cents? I know that the 1/4= 50
> cents? Is there any formula to do that?

One tone = 200 cents, so 1/4 tone = 50 cents.

Karim,

Here are a couple of C functions for you...

/*
coverts frequency to cents
ref is the reference pitch (ie A440)
hertz is the desire pitch
returns the cent value for hertz relative to ref
*/
double hertzToCents(double ref, double hertz) {
return log10(hertz / ref) / log10(pow(2.0, 1.0 / 1200.0));
}

/*
converts cents to frequency
ref is the reference pitch
cents is the desired value
returns the hertz (frequency) for cents relative to ref
*/
double centsToHertz(double ref, double cents) {
return ref * pow(2.0, cents / 1200.0);
}

for example, to find cents from a pitch:

my_cents = hertzToCents(220, 233.082);

my_cents should now be 100

the reverse would be:

my_hertz = centsToHertz(220, 100);

my_hertz should be 233.082

This will also work with cent values that are negative, this will return a frequency that is lower than the reference.

Hope this helps,

Mike

karim8411 wrote:
> Hi,
> > how do you convert the 1/4 note to cents? I know that the 1/4= 50 > cents? Is there any formula to do that?
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Thanks for the quick reply. One more question. I found someting that
talks about having 1 2 3 4 5 6 7 8 9 10 11 12 = one tone
According to your answer, 6 will be 1/5 step!! is that correct?
I am trying to find the notes for the Byzantine scale which is = 72
notes per scale. This is for church music that Greeks and Arabs are
still using in the worship.

I have this : 12 8 10 12 12 8 10 = 72 notes (Diatonic scale). I am
still trying to find the notes in the scale. For example, 12 is
perfect tone which is 200 Cents. However, I am not sure about it.Let
us find 8, if I divided 8/12 = 133 cents and so forth. Does it make
since to you?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "karim8411" <karim8411@y...> wrote:
> > Hi,
> >
> > how do you convert the 1/4 note to cents? I know that the 1/4= 50
> > cents? Is there any formula to do that?
>
> One tone = 200 cents, so 1/4 tone = 50 cents.

--- In tuning@yahoogroups.com, "karim8411" <karim8411@y...> wrote:

> Thanks for the quick reply. One more question. I found someting that
> talks about having 1 2 3 4 5 6 7 8 9 10 11 12 = one tone
> According to your answer, 6 will be 1/5 step!! is that correct?

In terms of the 12-equal system, 0,1,2,3,...12 *semitones* (which are
half-tones, not full tones) corresponds to 0, 100, 200, 300, ... 1200
cents. An octave in this system is 1200 cents, and any fraction of the
octave is that fraction of 1200 cents. What you describe is the
72-equal system, where 6 would be 6/72 = 1/12 of an octave, or
1/12 * 1200 = 100 cents.

> I am trying to find the notes for the Byzantine scale which is = 72
> notes per scale. This is for church music that Greeks and Arabs are
> still using in the worship.
>
> I have this : 12 8 10 12 12 8 10 = 72 notes (Diatonic scale). I am
> still trying to find the notes in the scale. For example, 12 is
> perfect tone which is 200 Cents.

12 I presume means 12 steps out of 72; the fraction of the octave we
are talking about therefore is 12/72 = 1/6 octave = 1/6 * 1200 =
200 cents.

However, I am not sure about it.Let
> us find 8, if I divided 8/12 = 133 cents and so forth. Does it make
> since to you?

8/72 = 1/9, so we are talking about 1/9 * 1200 cents = 133.333...
cents, so I think you've got the idea.

> From: "Gene Ward Smith" <gwsmith@svpal.org>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, May 18, 2003 6:32 PM
> Subject: [tuning] Re: how to calc. the cents?
>
>
> --- In tuning@yahoogroups.com, "karim8411" <karim8411@y...> wrote:
>
> > Thanks for the quick reply. One more question. I found someting that
> > talks about having 1 2 3 4 5 6 7 8 9 10 11 12 = one tone
> > According to your answer, 6 will be 1/5 step!! is that correct?
>
> In terms of the 12-equal system, 0,1,2,3,...12 *semitones* (which are
> half-tones, not full tones) corresponds to 0, 100, 200, 300, ... 1200
> cents. An octave in this system is 1200 cents, and any fraction of the
> octave is that fraction of 1200 cents. What you describe is the
> 72-equal system, where 6 would be 6/72 = 1/12 of an octave, or
> 1/12 * 1200 = 100 cents.
>
> > I am trying to find the notes for the Byzantine scale which is = 72
> > notes per scale. This is for church music that Greeks and Arabs are
> > still using in the worship.
> >
> > I have this : 12 8 10 12 12 8 10 = 72 notes (Diatonic scale). I am
> > still trying to find the notes in the scale. For example, 12 is
> > perfect tone which is 200 Cents.
>
> 12 I presume means 12 steps out of 72; the fraction of the octave we
> are talking about therefore is 12/72 = 1/6 octave = 1/6 * 1200 =
> 200 cents.
>
> However, I am not sure about it.Let
> > us find 8, if I divided 8/12 = 133 cents and so forth. Does it make
> > since to you?
>
> 8/72 = 1/9, so we are talking about 1/9 * 1200 cents = 133.333...
> cents, so I think you've got the idea.

one step of 72edo is precisely 1200/72 = exactly 16 & 2/3 cents.
so 8/72 of an octave is exactly 133 & 1/3 cents. Gene gave a
typical approximate notation with 133.333... cents.

nothing beyond 1/10 of a cent is audible, so generally it's
not necessary to specify precision in cents beyond two or
three decimal places. but when an equal-temperament *does*
provide exact fractional values of cents, i prefer to use them
simply because they are precise values.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> one step of 72edo is precisely 1200/72 = exactly 16 & 2/3 cents.
> so 8/72 of an octave is exactly 133 & 1/3 cents. Gene gave a
> typical approximate notation with 133.333... cents.

That's not an approximate notation, but an exact one; the ellipsis
means that the decimal expansion is to be carried out to infinity. To
give an approximation, one merely says for example 133 cents, or
133.333 cents.