Help me understand "cents" re: intonation

Is the common reference that a given note is 00 cents off frequency a way of saying 00% or what? Just wondering...

It's one hundredth of a semitone, if I understand it. A semitone is 1/12th of an octave or one step of a note as we understand notes (versus the half tones of African music, for example.) So as you go up the chromatic scale (all the sharps and flats) you have semitones. A cent is 1/100th of that.

It's a little bit of a moving target.

Let's take A=440 for example 440 means 440 Hertz

Let's say you're a hair sharp at 441 Hertz

That 1 hertz difference equals almost 4 cent difference

Now let's move up the scale to two C's above that A440

That C is around 1047 hertz

Now let's say you're a hair sharp at 1048 hertz

that 1 hertz difference is now equals a 1.65 cent difference

Now here's the problem. Most tuners you buy in the music store aren't accurate. They are typically off by around +/- 3 cents.

So if one string is sharp by 3 cents, another string is flat by 3 cents but your tuner is showing all strings in tune. But when you play a chord it still doesn't sound quite right.

If your uke has been properly setup and the intonation is correct and things still don't sound right, it's probably because your tuner's lack of accuracy is working against you. Time to invest a few extra dollars in a strobe tuner. Super accurate tuning accurate to within +/- .1 cent

Gwynedd said:

It's one hundredth of a semitone, if I understand it. A semitone is 1/12th of an octave or one step of a note as we understand notes (versus the half tones of African music, for example.) So as you go up the chromatic scale (all the sharps and flats) you have semitones. A cent is 1/100th of that.

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So there are 200 cents between C and D? 2 semi-tones... or am I wrong about that?

itsscottwilder said:

So if one string is sharp by 3 cents, another string is flat by 3 cents but your tuner is showing all strings in tune. But when you play a chord it still doesn't sound quite right.

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I can see how that spread can work against you and essentially double the inaccuracy.

Cents are a measure of frequency designated to make everybody but piano tuners over-think.

stevepetergal said:

Cents are a measure of frequency designated to make everybody but piano tuners over-think.

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LOL - Nice!!!

stevepetergal said:

Cents are a measure of frequency designated to make everybody but piano tuners over-think.

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Very well put, thank you.

And I tuned pianos for 25 years.

stevepetergal said:

Cents are a measure of frequency designated to make everybody but piano tuners over-think.

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Steve, I've never tuned a piano in my life. So exactly how does your observation apply to those of us who tune our ukuleles with inexpensive tuners ? Thanks, Bill

With the number of posts I've seen about intonation etc. it seems to me that we are obsessing a little. I've read that in reality stringed instruments by their nature never play perfectly in tune. Just close enough so that our ear and brain don't recognize it. That's the goal. Steve is right about over thinking this.

mr roper said:

With the number of posts I've seen about intonation etc. it seems to me that we are obsessing a little. I've read that in reality stringed instruments by their nature are never play perfectly in tune. Just close enough so that our ear and brain don't recognize it. That's the goal. Steve is right about over thinking this.

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Then instead of the ubiquitous "the intonation is spot on", a description I always view with doubt, it ought to be "the intonation is 'almost' spot on."

I also play fretless bass... I think intonation is highly overrated

mr roper said:

With the number of posts I've seen about intonation etc. it seems to me that we are obsessing a little. I've read that in reality stringed instruments by their nature are never play perfectly in tune. Just close enough so that our ear and brain don't recognize it. That's the goal. Steve is right about over thinking this.

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I agree completely. After all, ukuleles have a fixed nut, frets, and saddle. How much can one affect intonation when you can't change anything but the string action at the nut and saddle? Very little, if any, is the answer. You have to have the capability to change string length to materially affect intonation on any stringed instrument. Lowering the string action at either the nut or saddle does not materially affect the string length. I know I'll get an argument from some folks out of this but if you understand trigonometry, geometry, and string dynamics...enough said. By the way, Buzz Feiten developed a pretty good system for tuning guitars that employs an adjustable nut. I haven't seen anything like that being sold for ukuleles.

In response to BillMc's question, as an experienced piano tuner (though retired) tuning with a cheap electronic tuner will give more than 99% of us everything we will ever need out of our ukuleles. I've responded to intonation questions on several threads and believe perhaps we should have an on-line clinic some time.

The long and short of it is this. There is no such thing as perfect intonation in any fretted or keyboard instrument. When tuning a piano, we use a tempered scale. Tempering a scale is, in reality, compromising. We compromise for the inability of the instrument to play in perfect tune in every key. The fact is that the laws of physics as they pertain to sound don't permit it. Each key should technically be tuned to the overtone series of the root note. This causes great problems with a piano having 88 fixed notes because, just for example, a G in the key of C major is different than a G in the key of Eb. And that G is different from the G in the key of G or Ab or any other key. All those Gs are minutely different from each other. That's the way every note is in every key. It could boggle the mind. But, in tempering the scale, we attempt to get the instrument to sound equally in tune (and equally out of tune) in each key. The simplest hope is that it will sound good to the ear, no matter what you're playing.

This is the short version. If you want it complicated, read about J.S. Bach's Well Tempered Klavier. It is a set of pieces written for keyboard and the instrument is intended to be tuned differently in EACH KEY! (My understanding even those tunings are imperfect in their intended keys.)

Now pianos are like ukuleles in that they are limited in what is actually attainable and that the bigger the instrument and the higher the quality of the scale design (and the execution of the manufacturing) the better your chances of attaining a good result.

The ukulele has four strings. Yes, the best players in the world can bend and adjust to improve octaves and unisons as they go. But, we are all confined to the limitations of the laws of nature.

What I always recommend is tune to the cheap tuner, and start having fun!!!!

Maybe one day you'll hear an adjustment that can be made for your ear, maybe you won't. But, if you want to go down the road of perfect intonation, beware that it is a long road indeed. In fact, there is no end.

It's all in the ear of the beholder.

Some people can hear the benefits of using a strobe tuner. Others cannot.

If you can't, consider yourself blessed and be happy with results a regular cheapo tuner gives you.

Half a cent? I wouldn't care either. When it gets into double digits, then I care.

Thanks for your clear explanation Steve.

Sorry... still confused.

Is "10 cents" 10% out of tune or 5% out of tune, or doesn't it translate to that.

In other words, if a B is judged to be 10 cents flat does that mean it is 10% of the way to Bb?

I guess I just don't understand where the term "cents" comes from other than there are 100 cents in a dollar. And why the degree out of tune is expressed in cents rather than a percentage.