Why is the guitar tuned like that?

Wuchak

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I found this explanation and thought it was worth sharing.

Richard Lloyd - Matters: Studies: The Pentatonic Scale Part 2

Why Is The Guitar Tuned Like That?
Why is the guitar tuned in such an unusual way? It seems that almost all guitarists have asked that question; but not be able to find a satisfactory answer, the question fades away, only returning from time to time to nag at the guitarist while he wonders why one pair of strings is tuned differently from the rest. In order to get an answer to this question, we will first have to talk about the Cycle of Fifths/Fourths, because for the most part, the guitar is tuned in Fourths. What does this mean? We will discuss that first, before we try to figure out why the tuning relationship between the second and third strings (the G and B strings) is a Major Third rather than a Fourth. If you remember, the twelve notes which make up the chromatic (all color) scale can be developed by dividing a vibrating string by two-thirds, and then dividing that two-thirds by another two-thirds etc. This method of creating the notes which we use in music and the order in which they are created in after we number them vertically along a major scale (by using the formula whole, whole, half, whole, whole, whole, half, or W-WH-W-W-WH), is called the Cycle of Fifths. The Cycle of Fifths is very much like the DNA of music, forming a spiral which weaves through the vertical scale. It is also a magic skeleton key of music. There are very few things which one needs to know in order to understand everything about music, and the Cycle of Fifths is definitely one of them. Since the Cycle of Fifths is the method through which the architecture of much of the world's music is developed (in fact, the Western scale is developed in another way -- by ratio, but that makes no difference for our purposes -- the Cycle of Fifths is still the skeleton key)! It stands to reason that anyone who knows about the Cycle of Fifths can re-create everything there is about music from it.

Another thing to realize about the Cycle of Fifths is that the Fifth is the most powerfully consonant interval in relationship to the tonic. It is so important and powerful and consonant that it has been called the Dominant. The other side of this coin is that because the Cycle of Fifths is a cycle, you can move in both directions along the cycle, either up or down the staircase of fifths. If you count the eight numbers from octave to octave you will see what I mean: 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- 1. If you count up five numbers from the 1 you get the five, but if you count down five numbers from the octave you get the four, like this. 1 -- 7 -- 6 -- 5 -- 4 -- 3 -- 2 -- 1. So five up from the one is the five and five down from the one is the four. Confused yet?

The Cycle of Fifths is really better called the Cycle of Fifths/Fourths, because it goes in either direction. The fifth and the fourth notes in a major scale are both the same distance from the tonic. The Fifth is five notes up and four notes down and the Fourth is the opposite -- four notes up and five notes down from the tonic. Because the Fourth sits lower in the Major scale than the Fifth it gets the named the Subdominant.

Now, one can ponder this sort of thing for a long time without getting to the bottom of it. It is very much like looking at the night sky or an image of a galaxy -- impenetrable, awe inspiring and magnificent. This is because the mechanics of the Cycle of Fifths/Fourths IS identical to the spiral of a galaxy or sea shell or the workings of atomic particles or movements of the planets. It is a look at the handiwork of the creator. I will say again that the Cycle of Fifths is NOT the work of some clever musician. It is a direct view into the genetic code of music.

But let us get back to the subject at hand, from which we hope to absorb some understanding. How would you tune a musical instrument if you were to invent one? First of all, forget the piano, which has a separate string for every chromatic pitch stop. We are only talking about instruments which have multiple strings which might be fretted or played with the hand. There we really have a simple solution -- we will try to tune our instruments in fifths first because that interval is the most powerful and harmonic interval that exists. The violin is tuned to fifths. The cello is tuned to fifths. The violin in particular, really lends itself nicely to this tuning because of its small size. Any ordinarily sized hand can be reasonably expected to reach the fourth scale note with the pinkie while holding down the tonic with the index finger. So the next string ought to be the Fifth. That is also going to give us a consonant and harmonically balanced instrument. We certainly aren't going to tune an instrument in whole steps or in flatted sixths or so on unless we want it to sound discordant and weird (alternative "chordal" tunings aside). But the guitar is a larger scaled instrument which is played sitting in one's lap. Even though the cello is a larger instrument than the violin, it is played with the neck vertically, which allows the hand to have a little bit easier time reaching for notes. With the guitar sitting in the lap and the neck diagonal to the player, the bend in the wrist starts to make it more difficult to spread out the fingers. So our next best choice for tuning any larger scaled multistringed instrument is going to be to tune in Fourths, which are a little closer together. On a guitar a person with a normal sized hand can reasonably be expected to sound the Major Third with the pinkie finger while holding down the tonic with the index finger. So it makes sense that the next string should be the Fourth. So far, so good. You follow?

When the guitar was developed as an instrument it sometimes had different numbers of strings, called courses. Four string guitars, six string guitars. With the development of the six string guitar course something unpleasant happened. The two outer strings came into a very discordant interval by following the tuning in fourths across all six strings. If you take an ordinary modern guitar and follow the alphabetical pitch names of each string as they would be if they were tuned all the way across in fourths, you end up with: E, A, D, G, C, F. Well, E and F are a semitone or a minor second from one another. This is a god awful interval, and threatens to sour the whole thing. So what are we going to do? Since the F is a half step above the E, it's pretty easy to lower it down a half step so that matches the E on the other side (only two octaves up in pitch). Now the outside to strings of the course sound identical in character, but somewhere in the middle we now have a mess -- with an extra semitone that we have to get rid of. What are we going to do?

Now let's take a look at the Cycle of Fifths as a diagram. We will put the numbers for the seven major scale tones on the outside of it in Roman numerals, and we will also put the alphabetical pitch names inside of it using C as our one. Why is C rather than A is another matter, but we can take that up another time? For now we will just go with it. Here's the way it looks:



You will notice that the One has the Fourth and Fifth on either side of it. On the cycle, the One is surrounded by the two most consonant intervals. We are getting pretty close to being able to understand why the guitar has such an unusual tuning. What I am about to explain requires a slight twist in your thinking, something like studying a Mobius strip or that peculiar branch of mathematics called topology which studies shapes like doughnuts. So here we go: now we have the pitch of E on both sides of the instrument. This makes E the total center of the instrument, because the E now becomes predominant. (There are twice as many E's as any other note, and E is the first note you hear when strummed from either direction) Technically however, the guitar is an instrument which is considered to be in the key of C. This is only because all of its named open strings are in the key of C -- no any sharps or flats in them. But the real tonal center of the guitar now becomes E. Because of that, the pitch of E becomes the One, displacing C in our circle. Let's leave the alphabet where it is, but move the Roman numerals so that E equals 1:



Now you can see that the E is surrounded by its Fourth and Fifth, represented by the pitches A (fourth) and B (fifth). And because E is our instrument's total center, and because we want to always follow the Cycle of Fifths/Fourths as much as we can, we want to have the notes adjacent to E be one or another of these. Due to the fact that both pitches of E are on the outside edges of the instrument, the fourth or fifth will have to be next to it on the inside. This is the part that requires that "donut" thinking. That makes the second string B (strings are counted from the highest pitch down) and the fifth string A. Whew! Almost there. Finally, since we have already decided to tune our instrument in Fourths, we will run Fourths from the bottom E as far as we can. This gives us E, A, D, G, before we run into the B which we have placed there to improve the consonance of the instrument. Now we can examine the relationship between the G and the B strings. With the removal of the half step at the top which brought our original pitch of F down to an E, the removal of the half step which we have moved to between the second and third string now turns out to be a Major Third. That's a hell of a lot sweeter than the original interval of a minor second which we had to deal with. Voila!

Even though it has never stopped people from trying to improve the guitar by trying to eliminate the little tuning hitch in it, it is very unlikely to happen, because if you understand how this peculiar tuning came about, and how it follows the deepest laws of musical harmony, you are sure to grow in appreciation of the charming and graceful six course guitar.
 




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