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Hertz to Cents (Page 1)
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Hertz to Cents (Page 1)
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| This topic is 2 pages long: 1 2 This topic was originally posted in this forum: Pedal Steel |
| Author | Topic: Hertz to Cents |
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Mike Kowalik Member Posts: 645 |
posted 04 March 2001 08:49 PM
Can anyone tell me how many cents equal one hertz? |
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basilh Member Posts: 3417 |
posted 04 March 2001 09:41 PM
Hi Mike, There must be a formla , but I don't know it. Cents (100th part of a semitone) remain constant but the number of Hz for each Cent. varies with the frequency. ------------------
quote: http://homepage.tinet.ie/~basilhenriques/ |
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Dave Burton Member Posts: 213 |
posted 04 March 2001 10:27 PM
Hi Mike, I believe it to be 4.Can anyone confirm. 442=+8 441=+4 439.5=-2 so on. Dave |
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johnnyb Member Posts: 116 |
posted 04 March 2001 10:35 PM
I think you'd have to first know what intervals you want to compare ( in hertz ) and then do the math. The distance,in hertz, between notes grows as the pitch gets higher. But a semitone is always 100 cents, one cent being the difference in the pitch of a half tone divided by 100. johnnyb |
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Bobby Lee Sysop Posts: 14849 |
posted 05 March 2001 12:03 AM
On tuning meters, -3.94 cents = 439 Hz. |
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basilh Member Posts: 3417 |
posted 06 March 2001 06:00 PM
Therefore 878Hz (The OCTAVE of A 440 - 1 Hz ) = - 7.88 cents ....It VARIES with Frequency Baz |
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Bobby Lee Sysop Posts: 14849 |
posted 06 March 2001 07:16 PM
No, the octave of 439 Hz is still -3.94 cents from equal temperament, but the frequency is 2 Hz lower. 880 Hz is an A in tune with A=440 Hz. 878 Hz is 3.94 cents flat of that. The Hz scale is for calibration of your A note. The cents scale tells you how far away from equal temperament you are, given the current calibration. [This message was edited by Bobby Lee on 06 March 2001 at 07:17 PM.] |
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Moon in Alaska Member Posts: 1155 |
posted 06 March 2001 08:55 PM
Yes, B0b !! Some times we get the actual frequency of a note mixed up in the thinking !! I know you know the following,B0b, but maybe some of the new guys might benefit !! When looking at a tuner, the real frequency of any note played is totally unknown. Only the reference to a 440 A, and how far above or below ET you are. In actual frequency, Basil is correct, the amount of HZs in a whole tone varies with the frequency !! I think we struggle with this concept quite a bit.  ------------------ [This message was edited by Moon in Alaska on 06 March 2001 at 08:59 PM.] |
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Rick Aiello Member Posts: 3155 |
posted 07 March 2001 08:04 AM
There are always 100 cents between 2 notes one semitone apart. G#(4) has a frequency of about 415 Hz and G#(5) has a frequency of about 830 Hz and [This message was edited by Rick Aiello on 07 March 2001 at 08:12 AM.] [This message was edited by Rick Aiello on 07 March 2001 at 02:03 PM.] |
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Steve Feldman Member Posts: 2983 |
posted 07 March 2001 09:21 AM
That works for me. Thanks for the info! |
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Bobby Lee Sysop Posts: 14849 |
posted 07 March 2001 11:38 AM
Those approximations will get you in the ball park, Rick, but the actual math is not that straightforward. There are more cents between 415 Hz and 416 Hz than there are between 439 Hz and 440 Hz. To raise a pitch by 1 cent, you multiply it's frequency (Hz) by 21/1200 (about l.00057779). The lower the frequency, the more cents there are in one Hz. [This message was edited by Bobby Lee on 07 March 2001 at 11:39 AM.] |
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Rick Aiello Member Posts: 3155 |
posted 07 March 2001 02:17 PM
Thanks Bob. I am aware of the linear relationship of cents and the logarithmic relationship of frequency and the mathematical problems that arise when comparing the two. My post was meant to give a basic explaination to the original question. I didn't think that 1 cent @ 415 being 0.2397826 Hz and 1 cent @ 439 being 0.2536496 Hz was worth doing the extra math. |
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Steve Feldman Member Posts: 2983 |
posted 07 March 2001 03:31 PM
OK, Nevermind.... |
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Danny Bates Member Posts: 167 |
posted 07 March 2001 03:42 PM
One cent is 1% A = 440 hertz 4.4 = 1 cent |
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Bobby Lee Sysop Posts: 14849 |
posted 07 March 2001 04:47 PM
Wrong, Danny. 1 cent is 1/100th of a semitone, not 1% of the frequency. Rick, I figured you probably knew that. Like I said, your method gets you in the ball park. I was just showing off. |
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ToneJunkie Member Posts: 245 |
posted 07 March 2001 07:53 PM
Take the frequency of the pitch of interest, e.g., A = 440Hz, multiply it by the twelfth root of 2 (the logarithmic span between adjacent semitones), e.g., 466.16Hz, compute the difference, e.g., 26.16 Hz, and divide by 100, e.g., 0.2616 Hz = 1 cent sharp at 440 Hz. ========================================== Edited - I messed up the math again, didn't I? The stuff Bobby and Rick said was right. The cents, although there are indeed 100 of them between semitones, are not in themselves each 1/100 of a semitone. Each cent is a logarithmic interval such the frequency of a cent at a given frequency is 21/12 (for the semitone) x 21/100 (for the cent) = 21/1200 times the frequency of interest. I found this table while surfing around for some more cents - Sorry for the lengthy and mundane post, but it didn't want to perpetuate any incorrect information I had posted.
------------------ [This message was edited by ToneJunkie on 07 March 2001 at 07:56 PM.] [Because his math skills need work] [This message was edited by ToneJunkie on 07 March 2001 at 07:59 PM.] [This message was edited by ToneJunkie on 17 March 2001 at 07:01 PM.] [This message was edited by ToneJunkie on 17 March 2001 at 07:04 PM.] [This message was edited by ToneJunkie on 17 March 2001 at 07:05 PM.] |
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Rick Aiello Member Posts: 3155 |
posted 08 March 2001 05:57 AM
What you are doing is computing the average "size" of a cent between A(4)and Bb(4). This is what I was doing in my original post. The log relationship of a semitone is 2 raised to the 1/12 power. The log relationship of a cent(as Bob has stated) is 2 raised to the 1/1200 power. The correct value of 1 cent sharp at 440 is 0.2542274 Hz.The average size of the 100 cents that seperate A(4) from Bb(4) is 0.2616 Hz. [This message was edited by Rick Aiello on 08 March 2001 at 06:10 AM.] [This message was edited by Rick Aiello on 08 March 2001 at 06:12 AM.] |
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Steve Feldman Member Posts: 2983 |
posted 08 March 2001 06:38 AM
I am making a 'Citizen's Proclamation' and willing this thread over to the Humor section.... |
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ToneJunkie Member Posts: 245 |
posted 08 March 2001 04:05 PM
Oh I don't know Steve, I think we can get another 10 or 12 posts outta this... Cheers ------------------ |
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Bobby Lee Sysop Posts: 14849 |
posted 08 March 2001 05:55 PM
That'll get you in the ballpark, ToneJunkie, but the actual number is 11 x 21/12.  |
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ToneJunkie Member Posts: 245 |
posted 08 March 2001 06:11 PM
Ha! |
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Bill Crook Member Posts: 1820 |
posted 12 March 2001 01:22 AM
quote:
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Rick Aiello Member Posts: 3155 |
posted 12 March 2001 08:01 AM
The original question inquired about the relationship between cents and Hz. I gave a brief and reasonable explaination with examples. It was only after replies to my post that a more detailed mathematical discussion ensued. Not all theoretical topics have "real life" applications but I for one enjoy them. |
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Bobby Lee Sysop Posts: 14849 |
posted 12 March 2001 08:59 AM
1 Hz on the 440 Hz tuning meter is about 4 cents. I know I can hear that. In the bass register, 1 Hz difference on an A note (55 Hz) is nearly 1/3 of a semitone! A 1 Hz difference means that you hear 1 beat per second. I agree that most of us should be able to live with that. But when you add up those 1 Hz variances in 3 and 4 note chords, the accumulated beats can get pretty distracting. ------------------ |
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Tom Olson Member Posts: 1410 |
posted 14 March 2001 06:20 PM
If one cent = 1/100 of a semi-tone, then isn't the comparison of cents to HZ kind of like comparing apples to oranges? That is, the frequency (HZ), as a function of tone, varies with some sort of logrithmic or geometric function, while the value of a cent depends on the particular pair of notes that it lies between. In other words, it's sort of (loosely) like asking how many decibels equal a watt. It depends on how loud you're playing at the time. |
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Rick Aiello Member Posts: 3155 |
posted 14 March 2001 08:46 PM
You got it Tom. Frequency is an "absolute" logarithmic scale and cents is a "relative" linear scale. Physics and chemistry are loaded with these types of relationships. Calculus is usually required to resolve issues encountered when linking two related scales such as these. [This message was edited by Rick Aiello on 15 March 2001 at 06:44 AM.] |
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Brad Sarno Member Posts: 2398 |
posted 15 March 2001 10:27 AM
Great discussion. Bobby you got it nailed. My personal opinion is that we should ALL stop using the "440Hz" and "438.5Hz" numbers as tuning references. The true and accurate numbers that are of practical use to PSG are the cents and not hertz. On our tuners the center "440" only refers to true 440 Hz A when and if we tune to that particular A note. For all other notes we are referring to how sharp or flat of the "equal tempered" note we are shooting for. When I tune my F# for example, my tuner will center on "440" or "0" when my F# is exactly in tune with the "equal tempered" F#. But since none of us are likely to tune to the equal tempered F#, we use the tuner to show us how many cents sharp or flat of that note we are. My F# will never be any where near 440Hz or 436Hz, etc. The needle on my tuner may point to the A tuning scale that shows these numbers but they dont actually refer to the F# I'm going for, by a long shot. Rant rant rant! Brad Sarno |
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Bobby Lee Sysop Posts: 14849 |
posted 15 March 2001 11:06 AM
I agree 100% with your rant, Brad. |
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Jeff Lampert Member Posts: 2636 |
posted 15 March 2001 11:16 AM
quote: I think I hear that extra .00057779. Or I have dirt in my ear. Whatever. |
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B Cole unregistered Posts: 2636 |
posted 15 March 2001 11:34 AM
WOW enough aready I'm going back to the tuning fork. Now Steve I can see very well you understand all of this. But to be honest I don't really think it matters as long as you are playing a Fessenden guitar with Lawrence pickups 2 pickups that is |
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B Cole unregistered Posts: 2636 |
posted 15 March 2001 11:39 AM
Steve not to but I aint broke a G# string in 5 weeks playing every day must be the strings I use or it could be the guitar. Now maybe some one can figure out some formula to tell how long these strings will last I will change strings when that string breaks |
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ToneJunkie Member Posts: 245 |
posted 15 March 2001 03:58 PM
b0b, You called it... 11 x 21/12 more posts. Cheers ------------------ |
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SmallCap Member Posts: 70 |
posted 17 March 2001 04:53 AM
I think to practice that whole stuff it would be helpful to convert all the notes of a score into hertz values - and maybe use a cents value relative to first note of every bar ....
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Sage Member Posts: 525 |
posted 17 March 2001 07:31 AM
Brad's post above is good, but now I'm confused. Is the labeling of the tuner "440" refering to HZ something that is only correct when you are playing an A? It is actually displaying cents, relative to ET pitches in a full range- right? So why are tuners labeled in HZ when they actually display cents? |
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Joe Delaronde Member Posts: 901 |
posted 17 March 2001 08:05 AM
This doesn't make "sense" to me. Joe |
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Bobby Lee Sysop Posts: 14849 |
posted 17 March 2001 08:22 AM
The A note is the standard reference for tuning an orchestra. The Hz marking shows you the frequency of the A, and is used to calibrate the tuner so that everyone will tune to the same A. Tuner manufacturers assume that everyone wants to tune equal temperament. Nobody without an engineering degree cares what the actual Hz of all the notes are. Musicians only care about is how close the notes are to the standard that everyone is tuning to. That measurement is made in cents. There are 100 cents in a musical semitone. The Hz scale is for calibration of the A note. The cents scale is for tuning. Seems simple enough to me. ------------------ |
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ToneJunkie Member Posts: 245 |
posted 17 March 2001 07:07 PM
I've installed some errata and a Cents-to-Hertz link in a previous post here. Cheers ------------------ |
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Bobby Lee Sysop Posts: 14849 |
posted 18 March 2001 12:42 PM
That chart at www.pianosupply.com/cents-hz is very accurate, but it's useless to a musician. Maybe if you were using a frequency counter instead of a musical instrument tuner, you could look up the frequency of each note on that chart and tune to that. But why not just use a musical instrument tuner instead? When you use cents, you are measuring the frequency on a musical scale. Hz is the "cycles per second" measurement of frequency. A Hz measurement in the audio range does measure pitch, technically speaking, but it doesn't give you the pitch as it relates to a musical system. That's why the cents system was invented. Hz and cents measure the same thing, but Hz is a linear measurement starting at 0, while cents is a musical measurement starting at a known reference point (typically A=440 Hz). ------------------ |
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ToneJunkie Member Posts: 245 |
posted 18 March 2001 01:20 PM
Hi Bobby,
quote: While I agree with your assertion about the utility of the chart to the typical musician, I think it does help to graphically illustrate our collective responses to the original post. If not, no harm done. I for one use a tuner to get my Es and that's about it. The rest of it is where the ears come in handy, and at that point, none of this really matters, does it? Cheers ------------------ |
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Rick Aiello Member Posts: 3155 |
posted 18 March 2001 05:11 PM
quote: Sorry Bob, but although frequency is usually discussed as whole numbers (1,2,3...440...) this does not make it a linear scale. If you plot the frequencies (Hz) of an octave starting at A-440 and ending at A-880 on the Y axis of a graph and the chromatic scale on the x axis (using 100 cents per semitone) you get a CURVE not a straight line. Frequency applied to a musical octave is logarithmic not linear. If you find the slope of a tangent line anywhere on the curve you get the relationship of hertz to cents at that frequency and/or cent. This is the answer to the original question but as I stated in an earlier post it requires a bit of calculus and the extra math really isn't worth it. Most players are only interested in using cents to tune their instruments but cents are useful in many ways - not just in tuning. Comparing vibratos comes to mind. A typical concert violinist's vibrato has a vibrato rate of 6 Hz and a vibrato extent (maxima to minima) of 30 cents (15 cents sharp of the note and 15 cents flat of the note. I promise ya'll - this will be my last post. |
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