| Author |
Topic: Hertz to Cents Conversion? |
Bob Snelgrove
From:
san jose, ca
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Posted 8 Sep 2008 5:15 pm |
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I know it's not that simple but I'm trying to use Newmans' tuning chart with the BIAB tuner set to fine adjust at "442.5" (Reference for E's)
I'd like to know how many cents flat of that are all the other notes:
441.5, 439,438.5, 435.5 etc?
Otherwise, I have to change the fine adjust for each note rather than look at the numeric pitch (-cents) continuous readout.
thx
bob |
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Ken Mizell
From:
Lakeland, Florida, 33809, USA
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Posted 8 Sep 2008 6:52 pm
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Basically, it's approximately - 1hz = 4 cents.
_________________
Steeless. |
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Jeff Valentine
From:
Colorado Springs, USA
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Posted 8 Sep 2008 8:21 pm
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A cent is 1/100 of a semitone, so it's different depending on what note you're talking about. This link might help you if you check it out. You'll find various equations that will give you what you need.
-Jeff |
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Bob Snelgrove
From:
san jose, ca
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Posted 8 Sep 2008 9:41 pm
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Link?
thx
bob
| Jeff Valentine wrote: |
A cent is 1/100 of a semitone, so it's different depending on what note you're talking about. This link might help you if you check it out. You'll find various equations that will give you what you need.
-Jeff |
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chas smith R.I.P.
From:
Encino, CA, USA
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Posted 8 Sep 2008 10:27 pm
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| Quote: |
| Basically, it's approximately - 1hz = 4 cents. |
No, cents is the distance between notes. To rephrase what Jeff said, there are 100 cents between each semi-tone (half step) in the tempered 12-tone octave, regardless of what the frequencies are.
There are 100 cents between A-440 and Bb-466, there are 100 cents between A-55 and Bb-58, there are 100 cents between A-1760 and Bb-1864.
To find the cents difference between 2 notes (hz) like: 440hz and 435.5hz you take log(440) - log (435.5) divided by log( 1200 root of 2)
log(440) = 2.643
log(435.5) = 2.638
the 1200th root of 2 (one cent) is 1.000578
the log of that is = .000251
2.643 - 2.638 = .004465/ .000251 = 17.79 cents |
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Olli Haavisto
From:
Jarvenpaa,Finland
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Posted 9 Sep 2008 1:05 am
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For this specific practical purpose ie converting hertz readings to cents on a tuner or a chart based on hertz readings for A (440) 1hz= app. 4 cents works fine IMO.
_________________
Olli Haavisto
Finland |
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Jeff Valentine
From:
Colorado Springs, USA
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Posted 9 Sep 2008 4:55 am
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Like I said, a cent is 1/100 of a semitone, which IS a distance between two notes..... It is different depending on the note you're talking about because the number of herz between each semitone is different. Here's the link.
http://www.sengpielaudio.com/calculator-centsratio.htm
-Jeff |
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Steve Alcott
From:
New York, New York, USA
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Posted 9 Sep 2008 6:22 am
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| You might want to try this; it seems kinda backwards, but it works for me. Tune your Es and Bs to 440, 442, or whatever you use. Tune the rest of the open strings by ear. When you're satisfied, check them with whatever tuner you use, make a note of the offset, and you're set. |
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C Dixon
From:
Duluth, GA USA
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Posted 9 Sep 2008 6:29 am
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Bob Snellgrove wrote:
| Quote: |
I know it's not that simple but I'm trying to use Newmans' tuning chart with the BIAB tuner set to fine adjust at "442.5" (Reference for E's)
I'd like to know how many cents flat of that are all the other notes:
441.5, 439,438.5, 435.5 etc? |
I know of no better way than the following:
1. Please click on the following link:
http://www.precisionstrobe.com/
2. Scroll down and download the "Operation manual and specifications"
3. Scroll down to page 14 and study "Appendex E".
Note the following:
1. A 440 referenced to 0.0 "cents".
2. Then note the cents difference for frequencies above and below 440.
For example: an A note tuned to 441 is 3.9 cents sharp.
3. These same numbers apply to any of the 12 notes in our 12 note "western" form of music.
For example: and E note that is tuned to 442.5 (A440 reference) is 9.8 "cents" sharp.
A C# note that is tuned to 438.5 is 5.9 "cents" flat.
etc. etc.
So "4 cents" for each HZ shift (up or down) is more than adaquate for all practical purposes. More suuccinctly put: throw out all the math and the charts and simply USE 4 "cents" per HZ, and you will be fine dear person.
c.
_________________
A broken heart + † = a new heart. |
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Craig A Davidson
From:
Wisconsin Rapids, Wisconsin USA
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Posted 9 Sep 2008 6:38 am
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| So for instance 435 would be -20 Right? 435 is 5 less than 440, and 5x4=20. Am I on the right track? |
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David Doggett
From:
Bawl'mer, MD (formerly of MS, Nawluns, Gnashville, Knocksville, Lost Angeles, Bahsten. and Philly)
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Posted 9 Sep 2008 7:09 am
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Yes, Craig, you have it.
I agree with Ken, Olli and Carl. When you are talking about Hz near 440, the 1 Hz = 4 cents is plenty accurate enough. In Chas' example, that would give a difference of 18 cents, as opposed to 17.79 cents with his more complicated calculation. Nobody can hear that 0.21 cent difference between the two methods. In fact it is difficult to hear differences less than 2 cents or so. All those charts with decimal places after the Hz or cents are a bit silly.
But Chas is correct that if the Hz you are talking about are not near 440, you have to use his formula. |
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chas smith R.I.P.
From:
Encino, CA, USA
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Posted 9 Sep 2008 1:05 pm
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| Next time, I'll just keep it to myself. |
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Olli Haavisto
From:
Jarvenpaa,Finland
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Posted 10 Sep 2008 11:11 pm
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Chas, no offence intended !
_________________
Olli Haavisto
Finland |
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Bob Snelgrove
From:
san jose, ca
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Posted 11 Sep 2008 6:31 am
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Thanks, Carl
I printed that chart out 
bob
| C Dixon wrote: |
Bob Snellgrove wrote:
| Quote: |
I know it's not that simple but I'm trying to use Newmans' tuning chart with the BIAB tuner set to fine adjust at "442.5" (Reference for E's)
I'd like to know how many cents flat of that are all the other notes:
441.5, 439,438.5, 435.5 etc? |
I know of no better way than the following:
1. Please click on the following link:
http://www.precisionstrobe.com/
2. Scroll down and download the "Operation manual and specifications"
3. Scroll down to page 14 and study "Appendex E".
Note the following:
1. A 440 referenced to 0.0 "cents".
2. Then note the cents difference for frequencies above and below 440.
For example: an A note tuned to 441 is 3.9 cents sharp.
3. These same numbers apply to any of the 12 notes in our 12 note "western" form of music.
For example: and E note that is tuned to 442.5 (A440 reference) is 9.8 "cents" sharp.
A C# note that is tuned to 438.5 is 5.9 "cents" flat.
etc. etc.
So "4 cents" for each HZ shift (up or down) is more than adaquate for all practical purposes. More suuccinctly put: throw out all the math and the charts and simply USE 4 "cents" per HZ, and you will be fine dear person.
c. |
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C Dixon
From:
Duluth, GA USA
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Posted 11 Sep 2008 6:46 am
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You're welcome dear friend, may it be a blessing to you,
c.
_________________
A broken heart + † = a new heart. |
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Earnest Bovine
From:
Los Angeles CA USA
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Posted 11 Sep 2008 7:31 am
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| Which is more: add, multiply, or percent? |
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C Dixon
From:
Duluth, GA USA
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Posted 11 Sep 2008 7:46 am
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depends
_________________
A broken heart + † = a new heart. |
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Ray Minich
From:
Bradford, Pa. Frozen Tundra
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Posted 11 Sep 2008 9:51 am
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| I just know that my Fluke frequency counter that reads to 1 hz resolution is useless in this instance... |
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chas smith R.I.P.
From:
Encino, CA, USA
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Posted 11 Sep 2008 11:55 am
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| Quote: |
| Chas, no offence intended ! |
Olli, simply put, music has been the focus of my life, and because of that, I want to know as much as I can about every aspect of it, from various kinds of composition to the "nuts and bolts" of what are sounds and notes and scales made of.
Now granted, I'm not intimately familiar with the wants and needs of the Dear People and perhaps they really do need to be protected from "all the math and charts". I'm not going to deny that sometimes an easy Q&D is all that is needed, but to summarily dismiss the math of "Hertz to Cents Conversion", which is the topic of the thread, is in fact promoting ignorance. |
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Ray Minich
From:
Bradford, Pa. Frozen Tundra
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Posted 11 Sep 2008 12:59 pm
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Check out this link,
http://www.apronus.com/music/lessons/unit01.htm
A 'cent" is one/one-hundredth of the distance between two adjacent semitones.
One cent is less than 1 hz wide. I'm now even more amazed at the guts of a chromatic guitar tuner. |
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ed packard
From:
Show Low AZ
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Posted 11 Sep 2008 1:37 pm
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EB...do you walk to work, or carry your lunch?
CARL...I did not know you needed "depends"!
RAY...1 Hz resolution won't do it....but technically, one "cent" is NOT one/one hundredth of the distance between adjacent semi tones (notes), and Chas can tell you why; hint = the first cent is not the same as the second cent etc in Hz.
AND...the 1 Hz = 4 cents "rule/convenience" is only approximate at 440 Hz (the 0.011 G#4 pulled to A)...Chas can also tell you why that is so.
Something about Gnats and Camels comes to mind here. |
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Ray Minich
From:
Bradford, Pa. Frozen Tundra
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Posted 11 Sep 2008 4:58 pm
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| Ed, yes, there are a lot of ticks on log paper, but the distance between them ain't the same....Pardon me whilst I look stupid for a moment... |
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Rick Aiello
From:
Berryville, VA USA
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Posted 12 Sep 2008 2:14 pm
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Chas , at least you weren't laughed at ... 
I answered this question ... in probably my second post ever on the SGF (circa Oct 2000) ... and was really ridiculed/flamed quite abit ...
I probably didn't post again for a year ... not the warmest of welcomes (can't find that post in the archives) ...
Anyway ... back then, I had just moved and my graphing calculator was in storage ... so I graphed it all out on graph paper ... and tried to explain it with words.
But now ... 
Here's a graph of two octaves (A-220 to A-880) ...
One point per semitone ...
| Tab: |
X Y
0 220
100 233.08
200 246.94
etc...
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220 Hz to 880 Hz on the Y-axis ...
0 to 2400 cents on the X-axis ...
The resulting curve shows the logarithmic nature of pitch.
Plotting ... log(frequency) vs cents ... linearizes the curve ...
As does plotting ... log(frequency) vs log(cents)
Anyway ... as far as relating frequency to cents ...
Back up to the first graph, please ... 
The slope of the secant line (straight line passing through any two points on the curve) ... will give you the mean (average) value ... of the relationship between hertz and cents between that distance ...
Not really too useful for anything ... but it's a start ...
EX:
Slope = 880 - 830.61 / 2400 - 2300 = 0.4939 Hz/cents
Then taking the reciprocal ... 2.02 cents/Hz
Gives us a mean value of ... 1 Hz equals 2.02 cents ... over this semitone.
Meaningless, but it gives you an idea of the logarithmic nature ... when you compare it to a semitone at the beginning of the graph ...
EX:
Slope = 233.08 - 220 / 100 - 0 = 0.1308 Hz/cents
Then taking the reciprocal ... 7.65 cents/Hz
Gives us a mean value of ... 1 Hz equals 7.65 cents ... over this semitone.
Now for the good stuff ...
If you find the slope of the tangent line (straight line touching a point, but not "cutting through" the curve) ... at any point on the curve ...
It will give you the exact relationship between hertz and cents ... at that point.
I've chosen three points ...
Point A (1200,440) ...
Point B (300,261.63) ...
Point C (2300,830.61) ...
The straight line formula for the line tangent to Point A ... is ... f(x) = 0.2541522 x + 135
Therefore the slope of that tangent line = 0.2541522
Which means ... 0.2541522 Hz/cent ... and taking the reciprocal ...
1 Hz at A-440 is equal to 3.934650 cents ...
The straight line formula for the line tangent to Point B ... is ... f(x) = 0.1504709 x + 215
Therefore the slope of that tangent line = 0.1504709
Which means ... 0.1504709 Hz/cent ... and taking the reciprocal ...
1 Hz at C-261.63 is equal to 6.645803 cents ...
The straight line formula for the line tangent to Point C ... is ... f(x) = 0.4797083 x - 276
Therefore the slope of that tangent line = 0.4797083
Which means ... 0.4797083 Hz/cent ... and taking the reciprocal ...
1 Hz at Ab-830.61 is equal to 2.084600 cents ...
Enough math for y'all ... |
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Bob Snelgrove
From:
san jose, ca
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Posted 12 Sep 2008 4:49 pm
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Ken Mizell
From:
Lakeland, Florida, 33809, USA
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Posted 12 Sep 2008 6:05 pm
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_________________
Steeless. |
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