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Thread: Intonation

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    Default Intonation

    Is intonation on the A string, around C and C# a common issue on Mandolins? I have three mandolins, one a fine hand made instruments, and a mandola, and it is the same on all of them. If I tune the A to an electric tuner, the C always sounds slightly flat.

    I’m aware of the concept of equal temperament and how stringed instruments have to have tuning adjusted. Thoughts, anyone?

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    Default Re: Intonation

    That raises interesting questions. As equal temperament tuning is centred round C (true?), that's one note you'd expect to be dead on in every octave. Few of us start tuning from C - orchestras (and violinists/fiddlers) tune to A, guitarists often start with an E, and mando books I have suggest starting with G (wouldn't it be more logical to start somewhere in the middle and tune up and down?). However I assume electronic tuners take account of equal temperament, so if you initially tuned your mandolin to say the open A string, by the time you get to C at the 3rd fret you shouldn't be far off. Have you checked it with a tuner you know is accurate (eg a strobotuner), or does it sound off pitch to you? I believe relative pitch can sound different to the ear depending on the harmonics an instrument makes.

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    Default Re: Intonation

    Can't say I've noticed that, if anything I tend to find that to be true of the wound strings ( mostly the G) and generally above the 7th fret , but really only on mandolins, my mandolas don't seem to do that so much.

    Is it possible the course pairs don't match tuning exactly?

    The open string should match the 12th fret ( if not move the bridge, but loosen the strings before you do that), and I like to use the harmonics

    harmonic 7th on the G = harmonic 12th on the D
    harmonic 7th on the D = harmonic 12th on the A
    harmonic 7th on the A = harmonic 12th on the E

    I tend to start on the D tuning - then move to A, then to G and then E but that is in no way a strict pattern.

    on the mandola and mandocello you do tune to open C, but I rarely start on the bottom course
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    Default Re: Intonation

    Quote Originally Posted by dprestidge View Post
    If I tune the A to an electric tuner, the C always sounds slightly flat.
    You can't draw definite conclusions with testing each fret with a strobe tuner for best results. Peterson sells a app for smartphones for $9.
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    Default Re: Intonation

    I have a Peterson strobe tuner. You can adjust the 'sweetening'on it, i.e. the extent to which each note is tempered. A number of Celtic musicians, especially fiddlers, play off natural rather than tempered scales, unless there's a tempered instrument like a piano or accordion in the band. I set a 'Celtic' tempering to play a natural scale on C and progressively get more 'out of temper' as you play keys and modes with more sharps and flats. In theory that means the tempering can be biased towards C on the circle of 5ths, and the keys nearest to it (the 'folk' keys of C to A one way and C to Bb the other). If more Celtic and English folk style musicians listened to their tuning more, this might make a difference. As it is, I think I wasted my time

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    Registered User sunburst's Avatar
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    Default Re: Intonation

    A few things:
    -Yes, equal temperament exists and can be considered a compromise. When we use frets we are almost completely bound by it.
    -Even accurately placed frets are not perfect because of string gauge and tension differences. It may not even be possible to have perfect intonation at all frets with only one string, and it is definitely impossible (with normal frets) with more than one string.
    -Ideally, the 12th fret note will be an exact octave of the open string, but there is nothing magical about that. If you play the 7th fret (for example) more than the 12th fret, why not set the intonation so it is correct at the 7th fret and allow a slight error at the 12th rather than the other way around?
    -Electronic tuners don't care what note you start with if you use the tuner for all strings. If, like I do, you tune one string (I use a tuning fork) and then tune the rest of the strings to that, there may end up being slight differences depending on what string you start with, but any differences will be very slight is they exist at all.
    -Tuning is and will always be a compromise. The best we can do is reduce errors to a minimum through string gauge choices, good fret work, and adjustments at the bridge and nut, and then accept the inevitable errors. We can move errors to more suitable areas of the fingerboard so that we can play more 'in tune', and we can tune the instrument specifically for certain songs or tunes to improve intonation.

    One of my favorite guitarists that I've have heard play live is Martin Simpson. He plays in various different tunings in the course of a show, and changing tunings is something that throws all of our careful bridge and nut 'compensating' out the window. As he would talk to the audience between tunes he would re-tune his guitar by ear, often repeatedly playing a figure and adjusting the tuning. During the next tune or song, especially when he would sustain a chord or a note or two, the guitar would ring out so exactly in tune that it made a definite impression on me. He did that by tuning the guitar so that errors fell somewhere other than the frets where he needed the intonation to be good for that song, all the while speaking to the audience to spin a web and draw them into the song. A masterful entertainer for sure, but a big part of that was his technical ability to tune his guitar.

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    Default Re: Intonation

    Quote Originally Posted by maxr View Post
    That raises interesting questions. As equal temperament tuning is centred round C (true?), that's one note you'd expect to be dead on in every octave. Few of us start tuning from C - orchestras (and violinists/fiddlers) tune to A, guitarists often start with an E, and mando books I have suggest starting with G (wouldn't it be more logical to start somewhere in the middle and tune up and down?). However I assume electronic tuners take account of equal temperament, so if you initially tuned your mandolin to say the open A string, by the time you get to C at the 3rd fret you shouldn't be far off. Have you checked it with a tuner you know is accurate (eg a strobotuner), or does it sound off pitch to you? I believe relative pitch can sound different to the ear depending on the harmonics an instrument makes.
    Equal temperament is NOT centered around C. It is the opposite: just temperaments are centered around a particular key (usually C), but equal temperament did away with that.

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    Default Re: Intonation

    So, David L, are you saying that equal temperament means that the note C is also adjusted to be 'averagely out of tune' like all the others?

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    Default Re: Intonation

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    Default Re: Intonation

    Tuning is based upon a standard. A440 is widely used as concert pitch.
    In equal temperament, only octaves are in tune.

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    Default Re: Intonation

    Quote Originally Posted by Jacob View Post
    Tuning is based upon a standard. A440 is widely used as concert pitch.
    In equal temperament, only octaves are in tune.
    Thanks Jacob. So, in equal temperament, C is a tempered note and only A is mathematically 'in tune'? Ditto (in theory at least) for electronic tuners that don't have adjustable temperament?

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    Default Re: Intonation

    Quote Originally Posted by maxr View Post
    Thanks Jacob. So, in equal temperament, C is a tempered note and only A is mathematically 'in tune'? Ditto (in theory at least) for electronic tuners that don't have adjustable temperament?
    It doesn't mean anything to say A is in tune, as it has to agree usefully with all other notes. You could as well tune the C to a standard and then ensure the others agree usefully.

    If there were no higher harmonics present, a one-beat-per-second drift would be unnoticeable in practice. The short scale makes the higher harmonics a bit non-linear, skewed sharp, I think. This is why it is hard to find a sweet tuning with everything otherwise perfectly laid out.

    I recommend everyone try a strobe on their low frets. My current favorite mandolin played correctly at fret 1 but audibly sharp on 2 and up, with the error consistent. This suggested that shortening the fingerboard would solve the problem. Because the first fret, next to the nut, will be prone to playing sharp I trusted it would work out. I get beautiful chords in any key now, up past fret 12.

    I don't believe people hear a Steinway out of tune when it renders a Beethoven sonata. For me most interest in special tuning schemes is a failure of good fret work

    To be fair, I have shortened the distance to first fret on four out five mandolins I own. I think I have an explanation why standard layout needs this fix. Consider the string angle in the nut. It is tilted up, so the first fret asks the string to bend at a greater angle down than subsequent frets. The angle change between two fretted notes is trivial by comparison.

    In my case I shortened fingerboards by roughly .010". I understand Taylor does this, and Sunburst here. I love my results, which made a solo acoustic recording a pleasure. And I have those pleasing results across five courses and no string by string compensation anywhere, just a slanted bridge saddle.

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    Default Re: Intonation

    Quote Originally Posted by maxr View Post
    So, David L, are you saying that equal temperament means that the note C is also adjusted to be 'averagely out of tune' like all the others?
    Equal temperament has to do with the relationship between all of the notes. "Averagely out of tune" is in relation to other notes. There is no one note that is "in tune", and conversely, any note can be considered "in tune".

    We do use A=440 as a standard, which is a different issue all together. But the A is no more "in tune" than any other note.

    The notes aren't tempered, the distances between the notes are tempered.

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    Default Re: Intonation

    Quote Originally Posted by Tom Wright View Post
    ...I think I have an explanation why standard layout needs this fix...
    You are correct that I normally shorten the distance from the nut to the first fret, and your explanation is close, and could even be considered the same as this explanation:
    Imagine a string stretched between two supports in space. If you push on the string at it's center you can deflect it with very little pressure. Now apply the same pressure near the end of the string and deflection will be considerably less with the same pressure.
    The stretched string is stiffer near it's ends. That means that we must press an instrument string harder to deflect it to the first fret than to deflect it on higher frets, so the string stretches more when fretted near it's ends and thus the first 3 or so frets are commonly sharp. Adjusting the distance at the nut helps that problem.

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    Default Re: Intonation

    Quote Originally Posted by Tom Wright View Post
    I don't believe people hear a Steinway out of tune when it renders a Beethoven sonata.
    I think it depends what you're used to hearing. I played for several years in a pipe band, and also played fiddle at UK folk sessions where, like bagpipes, a number of the instruments sometimes play off natural scales. Scottish fiddlers will often play a minor 7th flat at natural scale pitch, and sometimes flatten the 3rd and 5th a little, like Highland bagpipes. I joined a Scottish dance band with a pianist, and I had to alter my fiddle fingering slightly to get in tune with that. There's also the psychology of tuning displayed in the old orchestral string player statement that 'there's no need to play out of tune when you can play sharp'.

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    Default Re: Intonation

    Quote Originally Posted by sunburst View Post
    You are correct that I normally shorten the distance from the nut to the first fret, and your explanation is close, and could even be considered the same as this explanation:
    Imagine a string stretched between two supports in space. If you push on the string at it's center you can deflect it with very little pressure. Now apply the same pressure near the end of the string and deflection will be considerably less with the same pressure.
    The stretched string is stiffer near it's ends. That means that we must press an instrument string harder to deflect it to the first fret than to deflect it on higher frets, so the string stretches more when fretted near it's ends and thus the first 3 or so frets are commonly sharp. Adjusting the distance at the nut helps that problem.
    This effect adds to it but is reduced arbitrarily to zero with an extremely low nut. I tested that by lowering strings to barely useful height, and still got sharp readinngs.

    A shortening offers the freedom to have a generously high clearance, which has its value for tone and finger feel. I would like to see a survey to find out if many have actually tested their frets at high precision.
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