11 Dec
2005
11 Dec
'05
5:37 p.m.
Hi
Suppose I have an A with a frequency of 440 hz. Which formula should I
use for transposing x semitones up/down? So which frequency would the Bb
a half step higher for instance have? What about cents (1/100's of half
steps)?
--
peace, love & harmony
Atte
http://www.atte.dk
11 Dec
11 Dec
6:13 p.m.
On Sun, 11 Dec 2005 22:37:05 +0100
Atte André Jensen <atte.jensen(a)gmail.com> wrote:
Hi
Suppose I have an A with a frequency of 440 hz. Which formula should I
use for transposing x semitones up/down? So which frequency would the Bb
a half step higher for instance have? What about cents (1/100's of half
steps)?
One half step in equal tempered tuning is the frequency ratio of
1:2^(1/12)
a.k.a the twelfth root of two. So, for an octave you get:
1:(2^(1/12) * 2^(1/12) * .... * 2^(1/12)) = 1:(2^(1/12))^12 = 1:2
:)
And for any interval of n semitones you get a frequency ratio of:
1:(2^(1/12))^n = 1:2^(n/12)
Sorry, i don't know about cents. It might be the 100th root of 2^(1/12)
a.k.a 1:(2^(1/12))^(1/100) = 1:2^(1/1200). So when you go 1200 cents
(1:2^(1200/1200) = 1:2) you have again the octave. No guarantee on that
though.
Regards,
Flo
--
Palimm Palimm!
http://tapas.affenbande.org
6:15 p.m.
On Sun, 2005-12-11 at 22:37 +0100, Atte André Jensen wrote:
Suppose I have an A with a frequency of 440 hz. Which
formula should I
use for transposing x semitones up/down? So which frequency would the Bb
a half step higher for instance have? What about cents (1/100's of half
steps)?
To transpose X semitones up, multiply the frequency with 2^(X/12). To
transpose down, just use a negative X. For C cents it should be
2^(C/1200).
Bb above A440 has the frequency 440 * 2^(1/12) = 466.16.
--
Lars Luthman
PGP key: http://www.d.kth.se/~d00-llu/pgp_key.php
Fingerprint: FCA7 C790 19B9 322D EB7A E1B3 4371 4650 04C7 7E2E
6:27 p.m.
Lars Luthman wrote:
To transpose X semitones up, multiply the frequency
with 2^(X/12). To
transpose down, just use a negative X. For C cents it should be
2^(C/1200).
Thanks alot guys.
Right now I just needed the formula, but I'm hoping to find time during
christmas to write a ladspa plugin that transposes using this formula.
Don't know nothing about ladspa, but as far as I ca tell this super
simple transpose-plugin should provide the easies possible way into
ladspa for me. If I can't figure this one out I can't figure nothing out...
--
peace, love & harmony
Atte
http://www.atte.dk
6:23 p.m.
Atte André Jensen wrote:
Hi
Suppose I have an A with a frequency of 440 hz. Which formula should I
use for transposing x semitones up/down? So which frequency would the
Bb a half step higher for instance have? What about cents (1/100's of
half steps)?
You know that every note has a frequency which is twice the frequency of
the same note an octave below. You have too go from the A at 440 hz to
the A at 880 hz with 12 equal steps. So, for each semitone you have to
multiply the frequency of the previous note by the twelfth root of two
(approx. 1.059463094).
See:
http://en.wikipedia.org/wiki/Twelfth_root_of_two
c
www.cesaremarilungo.com
6:24 p.m.
On 11/12/05, Atte André Jensen <atte.jensen(a)gmail.com> wrote:
Hi
Suppose I have an A with a frequency of 440 hz. Which
formula should I use for transposing x semitones up/down?
So which frequency would the Bb a half step higher for
instance have? What about cents (1/100's of half steps)?
If A is 440 then the A an octave up (call it A') is 2 x 440 = 880.
To go from A to A' in 12 equal steps (we're assuming equal
temperament), we need an interval, call it I, so that multiplying
by I will give the frequency a semitone higher, and doing that
12 times will go up one octave:
A x I x I x I x I x I x I x I x I x I x I x I x I = A',
so, rearranging:
I^12 = A' / A
but A' / A = 440/880 = 2.
So I^12 = 2.
So I is the twelfth root of 2. Multiply the frequency of a note by
that and you get the frequency a semitone higher. The twelfth
root of two is approximately 1.05946309436, or, as kcalc has
it: 1.059463094359295264523454505045663154306
( http://en.wikipedia.org/wiki/Twelfth_root_of_two )
To go up one cent, the same logic indicates you'd multiply by
the 1,200th root of two, since there are 100 cents in a semitone.
kcalc tells me it's:
1.000577789506554859250142541782224725466
( http://en.wikipedia.org/wiki/Cent_%28music%29 )
- Pete.
12 Dec
12 Dec
12:41 p.m.
On Sunday 11 December 2005 21:37, Atte André Jensen was like:
Suppose I have an A with a frequency of 440 hz. Which
formula should I
use for transposing x semitones up/down? So which frequency would the Bb
a half step higher for instance have? What about cents (1/100's of half
steps)?
It's something like:
Pitch (Hz) = log(27.5/log(2)) + chromatic_note/12
for 12Tet, but I would check this out as I'm slightly mathematically dyslexic.
--
cheers,
tim hall
http://glastonburymusic.org.uk/tim
1:59 p.m.
On Mon, 12 Dec 2005 11:40:53 -0500, tim hall
<tech(a)glastonburymusic.org.uk> wrote:
On Sunday 11 December 2005 21:37, Atte André Jensen
was like:
The fundamental multiplier is is the 12th root of 2.
--
Using Opera's revolutionary e-mail client: http://www.opera.com/mail/
Suppose I have an A with a frequency of 440 hz.
Which formula should I
use for transposing x semitones up/down? So which frequency would the Bb
a half step higher for instance have? What about cents (1/100's of half
steps)?
It's something like:
Pitch (Hz) = log(27.5/log(2)) + chromatic_note/12
for 12Tet, but I would check this out as I'm slightly mathematically
dyslexic.
6924
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7 comments
7 participants
participants (7)
-
Atte André Jensen -
Cesare Marilungo -
Florian Schmidt -
Lars Luthman -
Pete Leigh -
tim hall -
Tyler Eaves