 The Clarinet BBoard
|
Author: Dan Shusta
Date: 2018-10-20 04:44
Attachment: Chromatic Tuner Scale.jpg (659k)
I recently bought a CA-50 Chromatic Tuner and noticed that the scale read in “cents”. I was curious as to whether any relationship existed between “cents” and “hertz or cycles per second” and found out that there is no direct relationship. I then began to wonder… “Well, if I’m 5 cents high or low, how many hertz am I off of the center tone note frequency?”
Upon further investigation, I found 2 websites that helped me understand this non-linear relationship. First of all, I had to know the piano frequencies corresponding to various notes on the clarinet and then I found a website that converted frequency ratios into cents.
So, with the use of these two websites, I wanted to determine what the tuner would read at 1 and 2 hertz low of the actual clarinet tone frequency.
Here are the two websites I used:
To find out piano frequencies: https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Piano_key_frequencies.html
To determine the non-linear relationship between “cents” and “hertz”, I found the following website to be absolutely essential: http://www.sengpielaudio.com/calculator-centsratio.htm
To determine the frequency ratio of f2 / f1, I simply divided the center frequency (f2) by the frequency which was 1, then 2 hertz lower (f1).
Utilizing the information obtained by using the above two websites, I formulated the following graph:
tone….......frequency…..meter reading in cents
……………………………….......…….1 hertz low…..2 hertz low
E3 (D3-P)…………146.832…………-11.83………………-23.74
G3 (F3-P)…………195.997……………-8.85………………-17.75
C4 (Bb3-P)..…261.626……………-6.63………………-13.29
G4 (F4-P)……….349.228……………-4.96……………..-9.94
C5 (Bb4-P)…..466.164……………-3.72……………….-7.44
G5 (F5-P)……….698.456……………-2.48……………….-4.96
C6 (Bb5-P)………932.328……………-1.86……………..-3.72
G6 (F6-P)…………1396.91……………-1.24……………..-2.48
C7 (Bb6-P)………1864.66……………-0.93……………….-1.86
Generally speaking, I’ve read where many clarinets go very flat at the extreme low end and quite sharp at the very high end. Using this generalized information, I believe it can be easily seen that a large negative reading on the low end actually equates to just a few hertz off the center tone frequency. However, a high, off center, positive reading on the high end means the actual tone frequency is quite far off from the true, center tone frequency.
Hopefully, the above graph will help to put things into perspective for you and is useful in some way.
Would somebody please tell me what the hollowed out, downward arrows represent? Nothing was said about them in the directions. Thanks.
|
|
Reply To Message
|
|
Author: Burt
Date: 2018-10-20 17:26
The tempered scale and the traditional scale differ slightly in pitches. In particular, the major and minor thirds are far off, with the major being higher and the minor being lower for the tempered scale. Tuners use the tempered scale. I believe that the left arrow is where the major third (and minor sixth) for the traditional scale should tune. Ditto for the right arrow and the minor third (and major sixth).
In practice, I would ignore those arrows.
|
|
Reply To Message
|
|
Author: Arnoldstang
Date: 2018-10-20 18:22
How does the tuner know which key you’re in? ie. How would it know you are playing the 3rd of a chord or the tonic?
Freelance woodwind performer
|
|
Reply To Message
|
|
Author: Burt
Date: 2018-10-20 23:39
The tuner doesn't know what key you're in. Since it's based on the tempered scale, it doesn't matter; the frequency ratio between half-steps is the twelfth root of 2.
When you're playing in a given key (YOU know what key you're in), you MAY want to de-tune the thirds and sixths to the traditional values of these notes. That's what I think the arrows on the tuner are for.
In the traditional scale, the major third is 1.25 times the frequency of the root, which is flatter than the tempered scale major third. The minor third is 1.5/1.25 = 1.2 times the frequency of the root, which is sharper than the tempered scale minor third.
|
|
Reply To Message
|
|
Author: Caroline Smale
Date: 2018-10-21 01:26
The more sophisticated tuners do actually have the ability to use different temperaments. Mine has I think 12 options, and no, I don't know what most of them are either.
However by far the best tuner is a good pair of ears. That after all is what music is all about.
|
|
Reply To Message
|
|
Author: Dan Shusta
Date: 2018-10-21 02:39
According to a salesperson at Sweetwater (through whom I purchased the unit from on that auction site), the left arrow is the pure minor third and is closer to zero. The right arrow represents the pure major third. Instruments tune to these "arrows" to create harmonies when playing in ensembles.
IMO, Caroline is correct when she stated: "by far the best tuner is a good pair of ears." However, one of the items mentioned about the tuner was "ear training". So, perhaps, by tuning instruments (or voices) to these minor and major third interval arrows, one can "train the ear" as to what the harmony should sound like.
|
|
Reply To Message
|
|
Author: Arnoldstang
Date: 2018-10-21 07:18
Why are we discussing pure thirds when we are playing one note into a tuner?
Surely if I play A=440 into a tuner it will register in tune. (at that pitch standard) That is set in stone.
Perhaps that A is the third of chord, fifth, seventh or whatever. How would these arrows actually be employed and why only deal with 3rds?
Freelance woodwind performer
|
|
Reply To Message
|
|
Author: JohnP
Date: 2018-10-21 12:56
The left arrow is the major third, the right arrow the minor third. The salesperson was wrong. Imagine you are playing the the third in a B flat major chord in the orchestra, on the Bb clarinet you would be playing an E obviously, if the B flat an F are played at a pitch with the needle centred the left arrow will give you the correct pitch for your E, the major third.
You can try the following also. With your right hand play the fifth B flat and F on a keyboard while at the same time playing E on the Bb clarinet and adjusting your note downwards to get to the sweet spot where the chord sounds in tune. Now compare your note with the keyboard D, there should be a noticeable difference.
Similarly the right arrow will give you the correct pitch for the minor third in a chord. In a minor chord there is a major third between the 3rd and the 5th so as you can’t bring down the 5th you need to narrow the major 3rd interval by sharpening the third, hope that makes sense.
I’m sure most people on this forum know to bring down the major third in a chord and sharpen a minor third so I hope this post doesn’t come across as patronising but just brings clarity.
John
|
|
Reply To Message
|
|
Author: Chris P
Date: 2018-10-21 16:47
Chromatic tuner readings in a nutshell:
Needle in the centre - in tune
Needle to the left - flat
Needle to the right - sharp.
The rest is up to you;
There. End of story.
Former oboe finisher
Howarth of London
1998 - 2010
The opinions I express are my own.
|
|
Reply To Message
|
|
Author: JohnP
Date: 2018-10-22 11:54
Dan, in a major chord the third needs to be flattish for the chord to be in tune. I’ve been a professional orchestral player for over 40 years so I can say for definite this is the case from daily personal experience. It has nothing to do with how close the arrow is to the centre.
|
|
Reply To Message
|
|
Author: Luuk ★2017
Date: 2018-10-22 16:31
In just intonation (see https://en.wikipedia.org/wiki/Just_intonation) the frequency of a major third is 1.25 times the root frequency, that of the minor third is 1.2 times the root frequency. Thus:
root : major third = 1 : 1.25
root : minor third = 1 : 1.2
In equal temperament this is (see https://en.wikipedia.org/wiki/Equal_temperament
root : major third = 1 : 1.259921
root : minor third = 1 : 1.189207
Please note that just intonation thirds are beat free, due to their 'clean' ratios. An equal tempered major third appears about 1% too high (+13.69 cents), and a minor third about 1% too low (-15.64 cents) to be beat free.
-13.69 and +15.64 cents are exactly the locations of the arrows on your tuner, so they can be used to locate just intonation thirds as was explained by Burt and JohnP.
In parallel, the equal tempered minor sixth will be 13.69 cents too low and the major sixth will be 15.64 cents too high. The same arrows but swapped ...
Regards,
Luuk
Philips Symphonic Band
The Netherlands
|
|
Reply To Message
|
|
Author: Dibbs
Date: 2018-10-22 19:18
Dan Shusta wrote:
>
> I believe it can be
> easily seen that a large negative reading on the low end
> actually equates to just a few hertz off the center tone
> frequency. However, a high, off center, positive reading on the
> high end means the actual tone frequency is quite far off from
> the true, center tone frequency.
>
> Hopefully, the above graph will help to put things into
> perspective for you and is useful in some way.
>
This needs more explanation.
Our perception of pitch is logarithmic like the cents scale. i.e. an octave is always 1200 cents whereas the freequency (Hz.) doubles. In this sense cents show you how far from "true" a pitch is better than the frequency.
However, the number of beats per second perceived when you hear an out of tune unison is equal to the difference in Hz between the the two pitches. So both figures are useful.
Then there's, dynamic temperament (the thirds everyone's talking about above), the ear's sensitivity to pitch in different registers and other perceptual stuff to take into account that no meter will tell you.
In the end you've just got to trust your lugs.
|
|
Reply To Message
|
|
Author: gatto
Date: 2018-10-22 19:42
Maybe I do not understand your question, but why don't you use a tuner app on the Laptop or Smartphone?
I use, on Linux, the app FMIT --- Free Music Instrument Tuner
https://gillesdegottex.github.io/fmit/
(also available for Windows).
You set the basic pitch for A4 you aim at, the key of the instrument (or the corresponding transposition in order to see the note you finger [1]). Then every information is given:
The aimed frequency, the actual frequency you play, the fingered note, and the deviation given in cents and a needle indicator. It is very easy.
Footnote [1]: For the B-flat clarinet I even set C4 --> D1, in order to see the fingered note in a notation (european??) I prefer; for the A clarinet it would be C4 --> Eb1.
Post Edited (2018-10-22 19:44)
|
|
Reply To Message
|
|
Author: gatto
Date: 2018-10-23 00:40
By the way, if you are interested in understanding the link between Hz and Cents (that is, mathematical formulae), then Aunt Wikipedia is helping you:
https://en.wikipedia.org/wiki/Cent_(music)
But in a nutshell: Hz (frequency) is absolute, cents is relative. More precisely: the "difference" between a tone and the tone an octave higher is always 1200 cents (constant), but the frequency doubles (2x), and in particular its value (in Hz) depends on the note itself. Therefore the logarithm (base 2) enters the game...
Post Edited (2018-10-23 00:43)
|
|
Reply To Message
|
|
Author: Dan Shusta
Date: 2018-10-23 01:49
Dibbs,
You stated that my comment:
> I believe it can be
> easily seen that a large negative reading on the low end
> actually equates to just a few hertz off the center tone
> frequency. However, a high, off center, positive reading on the
> high end means the actual tone frequency is quite far off from
> the true, center tone frequency.
>
> Hopefully, the above graph will help to put things into
> perspective for you and is useful in some way.
>
"This needs more explanation."
According to the formula found at http://www.sengpielaudio.com/calculator-centsratio.htm, a +20 cent deviation corresponds to an f2/f1 frequency ratio of 1.011619.
If f1 represents our known pitch or frequency, rearranging the formula of f2/f1=1.011619 yields f2=1.011619 x f1.
For a clarinet E3, the center frequency (f1) is 146.832 Hz. (Piano D3)
Therefore, f2=1.011619 x 146.832 = 148.538 Hz.
The +20 cent offset for clarinet E3 is the difference in the two frequencies or 148.538 - 146.832 = 1.7 Hz.
For a clarinet C7, the center frequency (f1) is 1864.66 Hz. (Piano Bb6)
Therefore, f2 = 1.011619 x 1864.66 = 1886.325 Hz.
The +20 cent offset for clarinet C7, again, is the difference in the two frequencies or 1886.325 - 1864.66 = 21.67 Hz.
To help clarify this non-linearity, the following represents a +5 cent reading from E3 to C7 in a non-chromatic fashion:
For a constant +5 reading, here’s how far off pitch (in hertz) the following clarinet notes are:
E3=0.372 Hz
F3=0.475 Hz
G3=0.503 Hz
A3=0.565 Hz
B3=0.634 Hz
C4=0.672 Hz
D4=0.754 Hz
E4=0.847 Hz
F4=0.897 Hz
G4=1.010 Hz
A4=1.134 Hz
B4=1.272 Hz
C5=1.348 Hz
D5=1.513 Hz
E5=1.698 Hz
F5=1.799 Hz
G5=2.019 Hz
A5=2.267 Hz
B5=2.545 Hz
C6=2.696 Hz
D6=3.026 Hz
E6=3.397 Hz
F6=3.599 Hz
G6=4.040 Hz
A6=4.535 Hz
B6=5.090 Hz
C7=5.393 Hz
Doing this mathematical exercise concerning the relationship of cents to hertz has been quite illuminating for me.
I hope this helps others.
|
|
Reply To Message
|
|
Author: Dibbs
Date: 2018-10-24 16:02
Dan, I attempted to clarify the situation in my post above by explaining when cents are more useful and when frequency is more useful.
|
|
Reply To Message
|
|
Author: gatto
Date: 2018-10-24 17:44
I don't see that there is still a problem. The equation f2=1.011619 x f1 in Dan's last post says it. The value of the difference between f2 and f1, that is, f2-f1, depends of course on the value of f1. Although the factor corresponding to +20 cents is constant.
If I want to see how good (or bad) my intonation is, over the entire range of the instrument, then clearly I am only interested in cents, NOT Hz, since the cents describe my failure much better, and independent of the value of the note itself. For instance, I could say, that I am happy that my intonation over the entire range lies between -2 and +5 cents. I could not express a similar statement in terms of frequencies.
|
|
Reply To Message
|
|
Author: Dan Shusta
Date: 2018-10-24 22:01
Dibbs and gatto, I agree with both of you. I've been in electronics all of my life and dealt with Hz on a daily basis. So, for me, Hz has more meaning. However, I can understand where a "cents" reading is certainly easier to deal with for a musician.
By the way, according to the following article by D'Addario, there are two types of tuners...a "sweep" tuner and a "strobe" tuner. Succinctly stated, the basic Korg is a sweep tuner and takes longer to stabilize at a reading because a lot of "math" is going on inside the unit. "Strobe" tuners are instantaneous and are more accurate. http://www.daddario.com/upload/MNED_PM_laird_picking_tuners_17168.pdf
Concerning meter accuracy, Korg has an advertised "tone accuracy" of +/- 1.5 cents https://www.korg.com/us/products/tuners/ca_1/page_1.php whereas the Peterson Strobe Tuner has a tone accuracy of +/- 0.1 cent accuracy. https://www.petersontuners.com/ (See ad for StroboClip HD, center of page on the left side.)
"In tune" or "out of tune"...that appears to depend upon the individual listener's hearing capability. For a discussion on this, I recommend reading: https://forum.saxontheweb.net/archive/index.php/t-52400.html
|
|
Reply To Message
|
|
Author: Mojo
Date: 2018-10-25 17:13
tone….......frequency…..meter reading in cents
……………………………….......…….1 hertz low…..2 hertz low
E3 (D3-P)…………146.832…………-11.83………………-23.74
G3 (F3-P)…………195.997……………-8.85………………-17.75
C4 (Bb3-P)..…261.626……………-6.63………………-13.29
G4 (F4-P)……….349.228……………-4.96……………..-9.94
C5 (Bb4-P)…..466.164……………-3.72……………….-7.44
G5 (F5-P)……….698.456……………-2.48……………….-4.96
C6 (Bb5-P)………932.328……………-1.86……………..-3.72
G6 (F6-P)…………1396.91……………-1.24……………..-2.48
C7 (Bb6-P)………1864.66……………-0.93……………….-1.86
I think it is interesting that players using a tuner would probably try to get all their notes in tune within say 5-7 cents or so. Due to the non-linear scale they would favor tuning the low notes at the expense of the high notes.
MojoMP.com
Mojo Mouthpiece Work LLC
MojoMouthpieceWork@yahoo.com
|
|
Reply To Message
|
|
Author: gatto
Date: 2018-10-25 17:52
>>Due to the non-linear scale they would favor tuning the low notes at the expense of the high notes.
I don't understand that statement.
|
|
Reply To Message
|
|
Author: Burt
Date: 2018-10-26 01:27
When two notes are not quite in tune, you hear beats, and that sounds terrible, musically. The beat rate is half the difference in frequency between the two notes. For a 1-second note (whole note in a cut-time march), at C7 (using Dan's table), you would have to be within 2 cents to prevent a beat. At a more realistic note, C6, that's a bit less than 4 cents. But at E3, that's about 27 cents off.
That's a good reason not to put 2 high-pitch instruments in unison on a long note.
But to minimize the problem, I would want the instruments in tune as well as possible on the HIGH notes.
|
|
Reply To Message
|
|
Author: Mojo
Date: 2018-10-26 16:46
“I don't understand that statement.”
If you are off by 5 cents on a high note, you can be off pitch by 4-5 Hz. Whereas 5 cents off on a low note is only ~0.5 Hz.
But both are similar percentages of their frequencies. So maybe this is OK.
MojoMP.com
Mojo Mouthpiece Work LLC
MojoMouthpieceWork@yahoo.com
|
|
Reply To Message
|
|
Author: Arnoldstang
Date: 2018-10-27 17:54
I agree with Chris P but with one slight alteration.
“Chromatic tuner readings in a nutshell:
Needle in the centre - in tune
Needle to the left - flat
Needle to the right - sharp.
The rest is up to you;
There. End of story.”
I would change “End of story” to “Beginning of story”.
Freelance woodwind performer
|
|
Reply To Message
|
|
The Clarinet Pages
|
 |
.jpg){kind=small}
.jpg){kind=small}
.jpg){kind=small}
.jpg){kind=small}
.jpg){kind=small}
.jpg){kind=small}
