Using Musical Intervals To Greatly Improve Tuning And Intonation

How to use musical intervals to achieve much greater accuracy when tuning or setting intonation.

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This method of tuning requires a basic grasp of music theory and a fairly well developed ear. Absolute beginners may need a little more experience before attempting to tune guitars using this method. Most of us are familiar with the 5th fret (4th fret in the case of the G string) method for tuning a guitar by ear. This technique uses unisons (two notes of exactly the same pitch or frequency) to tune a guitar. This method is okay if you want to get two neighbouring strings in tune with each other but it may not be particularly accurate for getting the 1st string in tune with the 5th string or the 4th string in tune with the 2nd string, and so on. Using fourths, fifths and octaves, it is possible to achieve a high degree of accuracy for any string in relation to any other.

Terminology

  • Beat rate: When tuning one string to another, you hear a "wah wah wah" sound. This slows as you approach the point where the two frequencies coincide (vibrate at exactly the same frequency). The rapidity of the wah wah wah is known as the Beat Rate.
  • Smooth: When the two frequencies coincide the "wah wah" sound stops. This is known as being Smooth. Unisons and octaves are Smooth.
  • Narrow and Wide: Fifths are Narrow. Fourths are Wide. The wah wah sound can not only be heard when tuning a unison, but can also be heard when tuning intervals, e.g. thirds, fourths, fifths and octaves. For instance, if you were to tune the 6th string (E) to the 5th string (A), you will have tuned a fourth. Assuming that your 5th string (A) is up to pitch (110Hz) and your 6th string (E) is below pitch. As you raise the pitch of the E, the Beat Rate will begin to slow (provided the E string was somewhere near pitch to begin with). You should stop raising the pitch of the E string just before it becomes Smooth. This will mean that the interval is Wide. If you were to continue raising the pitch past the Smooth point, the Beat Rate would begin to speed up again and the interval would become Narrow. Fourths are tuned slightly Wide. Imagine the A note as a point in space and the E note as another point some distance beneath the A. As you raise the pitch of the E it gets closer and closer to the A. Now imagine an interval of a fourth as being the perfect distance between these two points. If the E and the A were at this perfect distance and you raised the E, the distance between them would become narrower. If you lowered the E, the distance would become wider. Musical intervals are thought of as distances in pitch.

    Coincidental Harmonics

    Why is it possible to tune two different notes to each other, e.g. E and A? This is possible because of coincidental harmonics. When you pluck an open string on a guitar, not only do you get the note produced by the open string as it vibrates along it's whole length, but also a series of upper partials. These are known as the Harmonic Series. You don't hear these upper partials because the open string, vibrating along it's entire length, displaces much more air than the upper partials and therefore is much louder. The volume of the open string drowns out the quieter upper partials. It is possible to tune an E to an A because both notes have a coincidental harmonic in their series of upper partials. That is to say, they both have an upper partial that vibrates at exactly the same frequency. If you rest your finger on the A string over the 12th fret and pluck the string, you get a harmonic that is an octave above the A produced by the open string. This harmonic is known as the first upper partial or the second harmonic (the first harmonic being the A produced by the open A string, also known as the fundamental). By resting your finger on the string at the 12th fret, you are stopping the whole of the string from vibrating and allowing the string to vibrate either side of your finger. This silences the fundamental and allows the first upper partial (second harmonic) to be heard. If you repeat this procedure at the 7th fret you will silence the first and second harmonics and hear the third harmonic. This harmonic sounds an E, which is an octave and a fifth above the fundamental A. By resting your finger above the 5th fret of the E string you hear the fourth harmonic of the E string, which is an E at exactly the same pitch as the one on the 7th fret of the A string. It is the beat rate between these coincidental harmonics that can be heard when tuning an E to A fourth. You do not need to pick out these harmonics to hear the beat rate. The beat rate can be heard just by playing the two open strings together. The upper partials themselves may be drowned out by the volume of the fundamentals but the beat rate between the two coincidental harmonics can be heard.

    Using Intervals To Tune A Guitar

    In standard tuning (E, A, D, G, B, e) you'll notice that four of the neighbouring pairs of strings are made up of fourths: E and A, A and D, D and G and B and e. The 2nd and 3rd strings (G and B) are made up of a major third. Firstly, set your A string using an A pitch fork (440Hz). The pitch created by the 440 fork corresponds to the 4th harmonic of the A string (above the 5th fret). Once again, you don't need to pick out the harmonic to hear the beat rate but you can if you want to hear it really clearly. NEVER bang a pitch fork on anything hard like a table. Strike it against some firm but with a bit of give in it; like the sole of a shoe or your knee if you're not too boney. Now play the E and A together and raise the E to just short of smooth. Check the accuracy of this by fingering the A string at the 2nd fret (B) and play the E and B together. Both the E A fourth and the E B fifth should be just off smooth. If you want to be really accurate, the fifth should be slightly smoother than the fourth, but there's not a lot in it. If the E A fourth is beating too rapidly then you need to raise the E a little more. If the E B fifth is beating too rapidly then you have raised the E too much and need to flatten it. Now tune the D to the A as a fourth. Bear in mind that whilst tuning the E to the A, the E was lower in pitch than the A and so you needed to stop short of smooth in order to make the fourth slightly wide. Because the D is higher than the A, you will need to go slightly past the smooth point to make the fourth wide. It's best in this case to tune it smooth and then check the the fifth by fingering the 2nd fret of the D string to get an A E fifth. If it is beating too much raise the D a little more and check both intervals again. Repeat the procedure used for tuning the A D fourth to tune the D G fourth. Now we come to the G B major third. Major thirds have a very rapid beat rate compared to fourths and fifths, which are almost smooth. This beat rate increases as you get higher in pitch. For example, the middle C (3rd string 5th fret) and the E (2nd string 5th fret) is a major third. This beats 10.38 times a second, almost a blur. I trained as a piano tuner in my early twenties and it was the part of the course that involved tuning this interval that separated the people who were going to complete the course from those who were not. If you have trouble hearing the beat rate between the G and B; tune the B string by fretting the G string at the 4th fret and tune the unison. Now pick out the harmonic that is just before the 4th fret of the G string and the one that is at the 5th fret of the B string. These are the coincidental harmonics for the G B third. You should now be able to clearly hear the rapid beat rate. To get a fourth and fifth for the G and B string: Finger the B string at the first fret and play it together with the open G for a fourth (G C) and the 4th fret for a fifth (G D). Then you can apply the method for tuning the fourths and fifths that was described above. Once the B string is done you can use the same method to tune the final fourth B e. You can also use octaves as a further way of checking for inaccuracies. Finger the D string at the 2nd fret and play it together with the open 6th E string as an octave. Remember, octaves should be smooth. Finger the G string at the 2nd fret and play it together with the open A string as an octave. Finger the B string at the 3rd fret and play it together with the open D string as an octave. Finger the 1st e string at the 3rd fret and play it together with the open G string as an octave. In fact, anywhere on the fret board where you can play an octave or a double octave along with an open string, you should do so; e.g. open G with the G at the 8th fret of the 2nd string or open D with the D at the 7th fret of the 3rd string. You can also apply this to fourths and fifths, or extensions of fourths and fifths i.e 11ths and 12ths or even 18ths and 19ths (these should sound just as sweet as the fourths and fifths). For instance, the open A string together with the open 1st e string as a 12th or the open D string together with the A at the 5th fret of the 1st string as a 12th. It's best to stick to double octaves, 12ths and 19ths when checking further up the fret board as these are the clearest to hear. You can of course check the 5th and 4th fret unisons too. If all your unisons and octaves are smooth and your fourths, fifths, 11ths and 12ths aren't beating too wildly, then you can be sure that your chords will sound sweet wherever you play them on the fret board. You could apply this method of tuning to achieve greater accuracy when setting the intonation on an electric guitar. I'm not going to go into the method for adjusting intonation as I'm sure someone else has already done so, but you could use double octaves, 12ths and 19ths to check the accuracy of your guitar's intonation.

    Strings

    Strings can affect tuning and intonation. I find that about one out of every four or five packs of strings has a faulty one in there. I think it has something to do with the winding. Finally, if you find your guitar drifts out of tune often, (if you train your ears to hear interval beat rates you'll know about it alright) then it may be because you haven't set the string after a re-stringing.

    String Setting

    After stringing your guitar and tuning it up to pitch. Be sure to set the strings by pulling them away from the fret board. Rounabout where the fret board meets the sound hole or pick up, take hold of the string with your first two fingers and with your thumb pressing against the front of your guitar, pull it away from the guitar. You'll find the pitch has dropped a lot because you are taking out the excess slack. retune and repeat several times until it no longer drops. You should feel the string becoming much more tense as you reapeat this proceedure. Be fairly gentle with the 1st ans 2nd strings. You should now find that your guitar stays in tune for much longer. If you don't know how to string a guitar the way they do in a guitar workshop then check around the internet or read a guitar maintainece handbook. Basically, it involves wrapping the string back under itself so that as you tighten it up it traps itself.
  • 51 comments sorted by best / new / date

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      isaac_bandits
      The notes in those songs can be musically notated, but not with the twelve tone scale. There are half flats which lower the note 1 quarter tone, and look like a backwards flat. Flat and a halfs look like a flat with a mirror image that is joined at its stem and lower the pitch 3 quarter tones. Half sharps raise pitch 1 quarter tone, and look like half a sharp sign, with one line going up, and two across it. Sharp and a halfs raise the pitch 3 quartertones, and look like a sharp with three vertical lines. So A (sharp and a hlaf) is equal to B (half flat). Notating a song like this would be a bitch, unless you were to put half flats etc in the key signature
      mattyp90
      So, to the people discussing Fb and E and Ebb notes and the like, when I hear a song that is between frets (a quarter step up/down), for example "No Surprises" by Radiohead, it's actually musically legitimate and could be written out perfectly in standard notation using these strange notes? I've always wondered about it because it really annoys me when I have to tune my guitar such a miniscule degree differently in order to play a song.
      tweekus420ccc
      the article was cool and everything but what is wrong with using a regular old tuner? is it not as accurate as i thought it was? ps. wanna hear som crazy jimi hendrix out of tune shit then listen to his woodstock cd.
      barking boris
      Some more information about the A# Bb thing, it's all about the key you're playing in. I play the guitar and piano, but also the trombone, and for trombone playing you have to have a good ear to correctly place the slide in an in-tune position. For instance, the note D on a trombone is normally played at 4th position. If I was playing a D in a D major scale, I would play it at normal 4th position, but if I was playing D in an Eb Major scale(where it would be the leading note)I would sharpen it slightly otherwise it would sound out of tune. Hope this makes a bit of sense. And you were right when you said pianos can't tell which key you are playing in, so none of this is relevant if you were playing the piano.
      rik231
      chris, theory is great but you sound a little sad (very talented by the sounds of it) but sad! shame:-
      ohmerrymayhem
      chris flatley wrote: tuning the harmonic at the 5th fret of the E string perfectly smooth with the harmonic at the 7th fret of the A string isn't accuate I'm afraid. I used to think so too but know I have a diploma that says it ain't. Once again I really don't mean to sound like a smart arse. When I referred to fourths and fifths I was talking about intervals and not fret numbers
      So anything behind a diploma is inesacapably true? That's not a good way to think. Plenty of people with a diploma (or multiple diplomas) are wrong on a daily basis. Base your theory on something other than just something you read out of a book or somethin another guy told you. I can tune my guitar, using the harmonic method, to pitch, by ear and checked with a tuner. Tell that to your diploma.
      ohmerrymayhem
      Oh, and just for the record, without me being mean spirited - you do sound like a smart ass.. You're not meaning to, I'm sure. Just letting you know.
      niguitars.com
      yeah chris the tu2 i think is more accurate than most peoples ears id rateher be a cent out than anal about my a's being exactly 440 i think youd be better suited in pure music theory forum than ug alot of people here are big fans of hendrix and even me with my crappy industry standard tuner can hear he was often a good bit out
      CLaSH88
      Checked... always wanted to say that... did not understand any of it... i think i'm tone deaf
      shwilly
      When you pluck an open string on a guitar, not only do you get the note produced by the open string as it vibrates along it's whole length, but also a series of upper partials. These are known as the Harmonic series. You dont hear these upper partials because the open string, vibrating along it's entire length, displaces much more air than the upper partials and therefore is much louder. The volume of the open string drowns out the quieter upper partials.
      okay, so are these the harmonics I hear when singing certain notes right into the soundhole of my acoustic guitar? For example: when I hit a high b, the b-string will produce a very loud harmonic-like sound (which isn't there when I do the same with a low b), or were you referring to a whole different type of harmonics? Sweet article, by the way!
      David Fyfield
      Hi Zhille: From David Fyfield I hope its OK in Serbia? It must be a pain with tremolos. Just give up a little and play very slightly out of tune. After all the average tuner who has a lot of experience can tune to about 2 htz. Getting to zero as you said just depends upon the correct intonation as well as your ear.Life is too short if you do not have a guitar set up perfectly. I play an acoustic Fylde guitar. Check out Roger Bucknells Fylde guitar site in UK. He made the one I have rather well. It is a great idear to give beginners a chance to have their guitar intonation checked by someone who can re-set up the guitar. Even so called cheap guitars can be improved way beyond the makers capabilities by a geezer who knows what he is doing and can get the best out of what was a poorly made instrument.
      PerfectCrime
      thanks for this chris, this is really great - tis way better than using a tuner. I actually found the 3rd intervals easiest to do althougth i gound the first a-e one the hardest - proably because i've a bit of fret buzz; but i'll sort that out sometime and proably try out this technique for setting the intonation. Thanks for the great article, and sorry for ever thinking that an elctric tuner could do the same as a professional piano tuner!
      ades
      One of the best articles I've read. However, I do have one question for you: can the GB strings not be tuned using the 2nd 3rd of 4th harmonics?
      BOYERxBREAKDOWN
      maggot555 wrote: nice article. definitly gives good affirmation to those who have already learned and teaches something to people who are new. and to clear up jk and your discussion Bb and A# are the same note sonically which in otherwords are called "enharmonic" of each other. they really are the same note though and are given different names only to aid the writer or reader of the music in certain situations. As for Fb i dont think ive seen a notation like that before and the enharmonic of "Fb" would be "E#" and i havnt seen that before either. I'm not certain but i beleive that is because there isnt a black key between E and F on a piano and its just a halfstep between them. someone correct me if im wrong. The twelve notes possible on any instrument are as follows (note that the slashes represent enharmonic notes): a, a#/Bb , b , c , C#/Db, D, D#/Eb, E , F, F#/Gb,G, G#/Ab if i made mistakes or anything, please someone correct me.
      E# is F, man.
      zhille
      I agree with David about the article, and about Sympathetic..., for example, when my guitar is in "Sympathetic Tune" I find myself playing chordal acoustic music for hours...and find myself amazed by the sound and in love with the music. One thing I would like to point out is CORRECT INTONATION! I don't know the english expression, but in Serbia we call it something like "Coting" You can tune your guitar perfect, only if it's perfectly intonated! All the effort is meaningless when even one string goes out of intonation.(for begginers: by that I mean when your, for example, E on the 12th fret of the E string sounds off tune and your open E is right in tune.) The thing I hate the most in my life is changing strings on guitars with Floyd Rose type locking tremolos. Every time new strings go out of intonation and you need awful lot of time to correct the intonation, and it's a pain in the ass process. But without that you can never tune a guitar to sound right! So, guitar and bass playesr, before you tune, or start "barking" at a man who tries to contribute and share knowledge, check your intonation!
      David Fyfield
      David Fyfield, Hi Chris, Fantastic article, Man has known about harmonics since 500 BC when pythagorus's mates wrote about 1/2 string and 1/3 rd a string etc.The problem about any explanation to create understanding is that the best approach is to assume a variety of (in your case) readers have the full spectrum of background knowledge from nil to your level.This will enable you to pass the information on in many different ways and so catch each type of learner.Its hard being perfect. When a guitar is in tune and starts ringing with sympathetic harmonics its the most wonderfull sound. Often this is not captured on recorded music and is the extra enjoyment a listener and performer gets from a live performance in a small quiet venue. When a guitarist achieves this it is perfect. Its best to love what you play and to love the listener. Thanks
      LeftyDave
      There are many ways in which to tune a guitar, but there is one that works very well, and is nearly flawless in design and application. Tune the high E using a quality tuner, and make sure it is dead on, neither flat nor sharp. Now begin to tune the rest of the strings to that note. Work your way down to low E. Fret the B string at 5th fret for E, listen to the "wah, wah's" and tune to match. Now the G string at the 9th fret to the hi E. Next is the D string at the 14th fret to hi E. Then is the A string at 7th fret, which will be an octave below hi E. Lastly is low E, which you will do the harmonic on 5th fret.
      LeftyDave
      Now cross check that tuning with the following: Low E harmonic at 12th fret to fretted A string at 7th fret. A harmonic at 12th fret to D fretted at 7th fret. D harmonic at 12th to G fretted at 7th. G harmonic at 12th to B fretted at 8th fret. And lastly B harmonic at 12th to hi E fretted at 7th. By tuning both ways you will find that the guitar is very very well tuned, and can even help with some poorly adjusted guitars, or those with minor intonation issues. Give it a try.
      LeftyDave
      In the first of these 3 posts, tuning all the strings to the high E string will eliminate small errors on one string affecting the others. By cross checking with the harmonics, you are basically doing what Chris wrote, but just in a simplified way, with out all the jargon. The "kiss" rule applies to guitars too. Keep It Simple Sucka.
      LeftyDave
      Chris, the "kiss" bit was not meant out of disrespect, but rather for newbies, beginners, intermediates to guitaring that don't really need to know, or don't care to know about what causes what and why this does that in relation to tuning. It is dummied down, but with good reason. In today's rush rush, fast paced world, many people just don't have the time to read and learn vast amounts of information, unless they wish to. This method, practiced a few times and used regularly, is basic, easy and fast, just as yours is once you get right down to it. I do understand your point of view tho in that your trying to describe something in text without the help of visual aids, and also I did enjoy the article. Your very knowledgable about music theory, but many are not, thus my post(s).
      Mattson
      yeah, that was just annoying me a little. and neat trick there^ id noticed how it was off when i use that harmonic to tune, but id never known why. could you go through how a few other intervals should sound, like minor 3rds and 7ths?
      Mattson
      wow, i really didnt find it too confusing. the theory behind it is pretty basic. i found it helpful, good job. just one question though: you said octaves should be smooth but major 3rds, 4ths, and 5ths, should have a beat rate, right? then do anyone know why, in general, we use major chords with a root, 3rd, 5th and octave? shouldnt it sound way out of tune with all the different beat rates going on at once, or at least a little muddy?
      DaveGilmour1189
      i think what your discussing is "beats." it a phenomina caused when two noises are played only slightly out of tune. I think you threw everyone off at the "wah wah" refernce. Its more of a phase type thing. THe various frequencies interact with each other causing regions of higher amplitude(loudness) to both waves. You get this pulsing sound of the sounds going in and out of phase. But in order to do this you need the sounds almost identical, only 5 or 6 cents off.
      jazkel24
      oh yeah. it was confusing. but helpful. Now i just need to find enough time to go back through the article and put it into tuning my guitar. thanks a lot.
      PLOP
      Very helpful, detailed and generally excellent albeit slightly complex and confusing.
      andrewb610
      tuning to the fifth and seventh harmonics is more accurate. if you get the 5th harmonic on the lower pitched string and the 7th harmonic on the higher pitched string you tune the higher string until there is the least amount of fluctuation between the strings
      SethMegadefan
      Wow, great stuff. A bit difficult to fully wrap my head around (although I'm no sound genius or anything), but I still learned quite a few things I didn't know (or even think of) before. Thanks a bunch for writing this; it's really very awesome stuff.
      SethMegadefan
      Glen'sHeroicAct wrote: dont double post!
      You've just won the most ironic post ever award. Congratulations. It is confusing, I'll admit, but I have to say that if I'd known this stuff when I was first starting guitar I would've found it really useful. It's really a very well-written article, and I guess I'm just lucky that I understood most of it. I guess it's just not the article for everyone.
      RockerPseudonym
      This is the kind of thing I need to learn for music. Physical techniques are "easy" to learn, just takes time. Plus...doesn't really matter how good you are if your Low E is tuned to Fb and your high E is tuned to C# ...Actually...I'm gonna go try that out and get back to you...
      singurel
      it`s been a long time since my guitar sounded this good.... man, your lesson`s great, after i tuned my low 5 a 5th down from A i got the hang of it....this really did greatly improve my tuning...(saw people tune without fretting, but didn`t try it before...also, i usually used 8th to check my tunig) this helped a lot, thank you
      jk919
      Yes.... Theoretically if i played lets say a DM scale i'll play D-E-F#-G-A-B-C#-D, but when i play a AbM i'll play Ab-Bb-C-Db-Eb-F-G-Ab. Obviously... The theory, and what i was trying to explain... is that, even though C# and Db are "enharmonically the same" if i was playing it correctly.. my C# would play a few degrees higher than my Db.. It's kinda hard to get, i understand this.... but think about it like this.... If i'm playing that same DM scale mentally, (and without prior know ledge of a piano!) i almost want C# to be higher than Db and the same goes if i'm playing the AbM scale I want the Db to be lower so that it flows and correlates with the sound.... i'm gonna look for my book or try and find something online to help you out.... Til then, let me know if this helped at all.
      minichibi
      Thanks... difficult to understand but im gonna look into it more and come back.
      maggot555
      oh i didnt know that jk. thanks for the new info. you learn something new everyday.
      rik231
      beats! you mean the strings are oscillating at the same frequency.....also why do you need to tune this way other than to improve your ear (of which there are many better ways to do it).
      jk919
      alright maggot you're mostly correct.... on a piano Bb and A# are considered the same note because they are so similar that creating to keys for the couple of hz would be dumb and make it much more difficult to learn the piano..... but in reality there is an actual difference in the sound wave between the two that can really only be achieved on an instument that can easily and greatly bend sound aka a stringed instrument... (note a guitar w/frets cannot achieve this unless you pull the string). But not many people would know this unless they were looking for it. (And yes, it is possible to hear the difference) Now as for the Fb point... In classical music you do occasionally run into Fb or even double flats (Ebb) but for the most part they are related to playing in very strange and sometimes theoretical keys) But in response to the specific Fb scenario Fb does equal E not E# because if you think about it G does not equal E (which would be the case if you took both Fb and E and dropped them a half-step). And not that it really matters but the only time you would see Fb is if you were playing a song in Cb-M(ab-m) or a theoretical key. I hope this makes sense... let me know.
      mrFood
      hippyguitardude wrote: i didn't read this but wanted the first comment... foo's
      Congratulations, you're an *****. :]
      jk919
      Actually Chris... Fb IS lower than an E.... just like Bb is lower than A#....technically... but great article anyway...
      maggot555
      nice article. definitly gives good affirmation to those who have already learned and teaches something to people who are new. and to clear up jk and your discussion Bb and A# are the same note sonically which in otherwords are called "enharmonic" of each other. they really are the same note though and are given different names only to aid the writer or reader of the music in certain situations. As for Fb i dont think ive seen a notation like that before and the enharmonic of "Fb" would be "E#" and i havnt seen that before either. I'm not certain but i beleive that is because there isnt a black key between E and F on a piano and its just a halfstep between them. someone correct me if im wrong. The twelve notes possible on any instrument are as follows (note that the slashes represent enharmonic notes): a, a#/Bb , b , c , C#/Db, D, D#/Eb, E , F, F#/Gb,G, G#/Ab if i made mistakes or anything, please someone correct me.