One of the most often neglected detail about a guitar is the scale length. It's often presumed that it doesn't play any major role in the sound of the guitar. However it's quite the opposite case, the scale length of a guitar is what makes it sound and feel in one particular fashion.
Not many people are generally aware of what scale length is. Scale length is the length of the string from the bridge saddle to the nut; the two points of contact that define the portion of the string that vibrates to produce the sound.
However simple this sounds the actual mathematics behind this is not so simple. The length of the scale affects not only the playing but also the sound in a couple of ways:
To discuss more about this let's take an example of two of the most popular guitar types, ie the Stratocaster and Les Paul. The scale length of a Stratocaster is 25.5" while the scale of a Les Paul is 24 3/4". To visualize the difference you can take a stratocaster and put a capo at the first fret. The new shorter effective length of the string from fret to the saddle is roughly equal to that of a Les Paul. However, this change also increases the pitch of the strings by a half-step. Now to get back into standard tuning at the first fret, you'll have to detune all the strings by a half step. It's now pretty obvious that the shorter scale length results in decrease of the tension on the strings.
This essentially translates to the conclusion that, for a given string to be tuned to a particular pitch, a longer scale length will require more string tension while a shorter scale length will require less. To simplify it further, this means that the same string, if put on a Staratocaster and a Les Paul, will be easier to bend on a Les Paul.
Now people who like to bend it pretty often will ask, why don't they go even shorter as to decrease the tension even more. To discuss this, let's go on to our next section.
In the first section we learned that shorter scales have lower string tension and are easier to bend. However, low string tension is not such a good thing after-all. As the gauge of the strings increase from 1st (higher e, in case of standard tuning) to 6th (lower E) or 7th (lower B, in case of seven string guitars) the string travel also increases. This means that while vibrating, the lower string travels more than the higher tuned string. So as we drop the tension the travel increases. This means that not just the strings have a lot more tendency of fret buzz, but they also feel mushy. Sound wise, higher the tension, brighter the tone of a string, lower the tension, warmer the strings. This can be clearly observed in the same example of a Les Paul and Stratocaster. A Les Paul sounds much more rounded and has a very warm tone to it while a stratocaster sounds brighter, clearer and have a bell like texture to it. Though pickups, woods and necks are also responsible for this sound difference but stings play a major role too, and are often overlooked all the same.
We already learned that lower strings need more tension to sound clearer, so it's not hard to imagine that a 7 or 8 string guitar or a 5 or 6 string bass guitar will face difficulty to reproduce clear low ends. So generally speaking the lower you go, more the problems you face. It's easy to imagine now what an eight string bassist have to go through. Most of 4 string basses have a scale length of 34" while many 5 and 6 strings have a 35" scale length to give the lower strings more tension and hence more definition.
A couple of 7 and 8 string guitars also have longer scale lengths. 26.5" and 27" for 7 string guitars and 28" for 8 string guitars. This longer scale enables the low end strings to sound clear with required definition.
Now such long scales make the top end sound very bright and harsh. To solve this purpose fanned fret or multi scale instruments came into picture. these instruments don't have parallel frets, bridge and nut. Instead the fret layout is like a Chinese fan.
Now it's pretty clear from the image that a in a fanned instrument top end has a shorter scale hence less tension and bottom end has a long scale hence more tension. These guitars are not very common but they are very effective in solving the problems faced by a long scale guitar.
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