Sheer Melody

Tuning a guitar is a tough job. For two reasons, it’s tough to have perfect ears, and most of the time the ears respond to aural clues not coming from the guitar too; and secondly because of equal temperament. I have wanted to write this article for several years now, because every day in my musical journey, I am fascinated by the trap of the tempered third.

The easiest way to tune the guitar is by using an electronic tuner. You turn the pegs until the tuner clicks and tells you that your string is tuned perfectly. Easy, simple and takes the least amount of time. But of course, if you are the perfectionist, this mechanism is rarely going to satisfy you.

The problem is compounded if you are going to play with a fixed pitch instrument (Which is not an electronic keyboard). There is a small chance that there is a conflict between what your tuner says and what the instrument says. In such conditions, it’s always best to tune your guitar to the fixed-pitch instrument, which will enhance your performance and the purists will have lesser areas to frown upon. Ideally, of course, all fixed-pitch instruments should be tuned to concert pitch, but they are sometimes way off, sometimes clearly lying between two notes on the electronic tuner, and that’s where the guitarist’s problems are compounded.

There was an informal jam session I participated in, in which there were five of us, and another guitarist who was new. He was not new to the guitar, he was new to us. So everything was fine, until he decided to join in. So he takes out his guitar, his electronic tuner, tunes his guitar and joins in. The jam session was wrecked. He was on concert pitch, but none of us were, and he was unaware that he was way off – possibly, because he was hard of hearing, or partially tone-deaf. I had contemplated telling him to switch to another guitar, or tune his guitar for him, but as one is painfully aware, the social dynamics of tuning another guitarist’s guitar for him is a non-trivial matter.

The best way, and something that has been supporting me lately in my exploits with the guitar is the D tuning. Tune the D (4th string) to the concert pitch, or what all of you in your informal jam session agree to as the concert pitch D. Using this D, tune the other strings using the open 4th string as a reference. The reason I ask you to do this, is because in this case, you won’t be basing your references on thirds or fifths to tune, but all your tuning would be based on the pure interval – which is the octave.

The problem is created now by the major third interval (that is the F# note on the key of D). This is important in most of all the music that you hear and most of rock, folk, country music anyways, that you would want it to sound good. Play your D chord now; and you will notice that it doesn’t sound good. Do you want to tweak the strings which play the F# so that it sounds good? You would be tempted, as I am all the time. But I guess that’s the peril of equal temperament, something that was experimented with for years, and ultimately resulted in a fret-board in which one perfect chord leads to other imperfect chords. The human ear which would always be more satisfied by the just temperament simply fails to agree with the guitar which wants to be tuned to equal temperament, with the result that most guitarists are moody people who are rarely happy.

So what is this equal temperament thingy which musicians have been so worried about over the years?

The scale is divided into equally-spaced semitones, and each semitone is around a hundred (100) cents away from each other. So a cent is 1/100 of a semitone. Simple concept.
Before we had equal temperament, all musical instruments were tuned according to the overtone series – which is the sequence of harmonics which we hear when a particular note is sung, plucked or blown upon. And that resulted in what is known as just temperament, something that nature designed every individual scale to be.

But that was not easy for the piano, which cannot be tuned in between a performance which shifts from one key to another. Thus arose equal temperament, which was first experimented with by Bach, who wrote his famous The well-tempered clavier, with a series of fugues and preludes in both major and minor keys to illustrate that with all it’s failures, equal temperament is the way to go, because it makes all your thirds slightly off, but not so far off as to actually sound discordant when played as a part of a musical performance.

So what’s the problem with equal temperament? Taking heed from the hundred cents which separate each semitone from its next (or previous), if we investigate the equally tempered scale, we find that the third (the major third) is 14 cents sharper than what the actual major third is supposed to be. So the actual major third on your equally-tempered piano is 14/100 times sharper than the actual third which occurs on that scale using the overtone series. The octave however, in equal temperament, is perfect, it’s exactly double the frequency of the lower note in the same key. Which implies that it’s always best to tune using octaves, something which I mentioned in the very beginning of this article. Tempered fourths and fifths are not very far off from their actual sounds in the equally tempered scale, in that the fourth is 2 cents sharper than the actual, and the tempered fifth is 2 cents flatter than the actual. The minor third, incidentally is a bigger problem than the major third, in that it is around 16 cents flatter than the actual minor third which is a part of the scale as per the overtone series.

This concept is academic in the case of fixed-pitch instruments, like the flute, the oboe, or the recorder, which can only change their ranges slightly but the pitches which these instruments can play are fixed in the mechanism of the instrument. The violin and stringed instruments, on the other hand, are more tunable, because of the pegs which are provided with the instrument, and that is what you notice concert fiddlers doing in the middle of performances. They change their pitches ever so slightly to adjust with the new key which the next concert piece is going to be played on. Guitars are stringed instruments but they should not be regularly tuned to the key because the frets are a limiting factor, making the instrument prominently like the piano as far as equal temperament is concerned.

So what is the trap of the major third as I mentioned in the beginning?

Let me illustrate with the simplest G – open chord. The 2nd string in the G open chord is also open, and it plays a B, which as we all know – is the major third in the G major chord. Now let us say, using the electronic tuner which we recently purchased, we tuned the guitar perfectly as per instructions and played the G chord. Well, to most ears, it will sound right – but to ears which were born fussy and inconclusive, the G will not sound good, the 2nd string sounds distinctly off. Wouldn’t it be nice, if I tuned it down a little, turned that peg just a little bit, and make the G chord sound like the most beautiful thing in the world? Well, that’s what I used to do when I first played the guitar; and that was a big trap. I always used to get a world-class G chord, but when I decided to play the next song on the scale of E, I sounded terrible. I spent days trying to understand what I was doing wrong, until I decided to ask someone who knew more than me, and that’s how I learnt all this. What was happening was that in my urge to get the perfect third in the G major chord, I was tuning the B open string (2nd string) to the perfect B, which is actually 14 cents lower than what it should actually be as per the equally tempered scale. On the E scale, however, the B is the fifth of the scale, which even in the equally tempered scale should never be more than two cents off, but because of my efforts, was actually 14 cents off, and hence my E chord always sounded horrible.

This is incidentally, one of the reasons why it will never be possible under realistic scenarios to play Carnatic classical music on the piano.