When referring to stringed instruments, the scale length (often simply called the "scale") is the maximum vibrating length of the strings that produce sound, and determines the range of tones that string can produce at a given tension. It's also called string length. On instruments in which strings are not "stopped" or divided in length (typically by frets, the player's fingers, or other mechanism), such as the piano, it is the actual length of string between the nut and the bridge.
String instruments produce sound through the vibration of their strings. The range of tones these strings can produce is determined by three primary factors: the mass of the string (related to its thickness as well as other aspects of its construction: density of the metal/alloy etc.), the tension placed upon it, and the instrument's scale length.
On many, but not all, instruments, the strings are at least roughly the same length, so the instrument's scale can be expressed as a single length measurement, as for example in the case of the violin or guitar. On other instruments, the strings are of different lengths according to their pitch, as for example in the case of the harp or piano.
On most modern fretted instruments, the actual string length is a bit longer than the scale length, to provide some compensation for the "sharp" effect caused by the string being slightly stretched when it is pressed against the fingerboard. This causes the pitch of the note to go slightly sharp (higher in pitch). Another factor in modern instrument design is that, at the same tension, thicker strings are more sensitive to this effect, which is why saddles on acoustic (and often electric) guitars are set on a slight diagonal. This gives the thicker strings slightly more length.
All other things being equal, increasing the scale length of an instrument requires an increase in string tension for a given pitch.
A musical string may be divided by the twelfth root of two , approximately 1.059463094 and the result taken as the string-length position at which the next semitone pitch (fret position) should be placed from the previous fret (or, in case this is the first calculation, the nut or zero fret) of the instrument. This quotient is then divided again by itself to locate the next semitone higher, and so on.
Alternatively, the string may be divided by , approximately 17.817154, and the quotient taken as the location of the next semitone pitch from the nut of the instrument. The remainder is again divided by 17.817154 to locate the next semitone pitch higher, and so on. For centuries the divisor 18 was used instead; this "Eighteen Rule" produced a sort of rough compensation. Actual fret spacing on the fretboard was often done by trial and error method (testing) over the ages. Since the nineteenth century, however, luthiers generally use precision measuring instruments to lay out frets with mathematical accuracy.
In many instruments, for example the violin, the scale of a full-sized instrument is strictly standardised. Smaller scale instruments exist for:
Larger than standard scale instruments are rare, but may be used by experimental and avant-garde players, or specially made for soloists with particularly extended reach. In other instruments, for example the viola and the electric guitar, the scale of a full-sized instrument varies a great deal.
The two most famous violin makers, Antonio Stradivari (1644-1737) and Giuseppe Guarneri del Gesù (1698-1744), both used an open string length of 12.8 in (327 mm) for their violins, which had already been established a generation before by Jacob Stainer (c. 1617-1683). Later makers have been unwilling to deviate from this.
Smaller scale instruments are used extensively to teach younger players. The size of these is described by a "conventional" fraction that has no mathematical significance. For example, a 7/8 violin has a scale of about 317 mm, a 3/4-size instrument a scale of 307 mm, a half-size one 287 mm, and a quarter-size one 267 mm. 1/8, 1/10, 1/16 and 1/32 and even 1/64 violins also exist, becoming progressively smaller, but again in no proportional relationship. (A full-size instrument is described as 4/4.)
Cellos exist in a smaller range of sizes than violins, with 4/4, 3/4, 1/2, 1/4, 1/8, and 1/10 being reasonably common. As with the violin, the Stradivarius scale is regarded as standard for orchestral work; This is about 27.4 in (695 mm).
Violas are commonly described in terms of their body length rather than--as with other violin-family instruments--by a fraction. There are two reasons for this. First, unlike that of the violin and the cello, the viola scale length has not standardised, but rather advanced player use whatever scale length best suits them. Secondly, student sizes are not as often required, as most viola players who start learning at a young age start on the violin. Common sizes include 17 in (43 cm), 16.5 in (42 cm), 16 in (41 cm), 15.5 in (39 cm), 15 in (38 cm), 14 in (36 cm), and less commonly 12 in (30 cm), smaller than a standard violin; These measurements are nominal and approximate. At least one of the surviving Stradivarius violas has a scale length of 14.25 in (362 mm).
There is some variation in the scale length of an orchestral double bass, generally in the range 41.3 - 43.3 inches (105 - 110 cm). There are also smaller versions of this "full scale" double bass with the same scale length but with a smaller sound box, intended for other musical idioms. Smaller scale instruments are also quite commonly used by full-sized players in jazz, folk music and similar ensembles.
The system of conventional fractions is taken to its logical conclusion with string bass sizes, in that a full-size (4/4) bass is uncommon. Most basses are 3/4 or 7/8, and younger players can use 1/2 or even 1/4 size instruments.
Like that of the violin, the scale of the classical guitar was standardized by the work of its most famous maker. Antonio De Torres (1817-1892) used a scale length of 25.6 in (650 mm), and later makers have followed suit. However, from the mid- 20th Century luthiers seeking increased volume have moved to a 26 in (660mm) scale, which is now the standard for such leading makers as Ramirez.
The steel-string acoustic guitar typically has a scale slightly shorter than the classical instrument, the most common scales ranging between short scale : 24 inches (610 mm) and long scale: 25.5 inches (648 mm). Small travel guitars and guitars specifically designed for children can have even shorter scales. For example, a 3/4 size steel string guitar might have a scale length of 23 inches (580 mm).
The scale length of an electric guitar affects both its playability and its tone. Regarding playability, a shorter scale length allows more compact fingering and favors shorter fingers and hand-span. A longer scale allows more expanded finger and favors longer fingers and hand-span. With regard to tone, a longer scale (e.g. Fender Telecasters with 25.5 inch (648 mm) scale length) favors "brightness" or cleaner overtones and more separated harmonics versus a shorter scale (e.g., Gibson Les Paul with 24.75 in (628 mm) scale length), which favors "warmth" or more muddy overtones. According to Dave Hunter's Tone Manual (2011), each scale length has its characteristic sound and tone, which is individual from other sounds in the tone chain: strings, pickups, pedals, amplifiers, speakers, and cabinets.
Most Fender electric guitars, including the Stratocaster, Telecaster, Esquire, and Jazzmaster use a scale length of 25.5 in (648 mm). A few Fender models such as the Jaguar use a scale length of 24 in (610 mm). Fender has also built some 3/4-size student guitars with a scale length of 22.5 in (572 mm) or shorter.
Gibson uses a scale length of 24.75 in (628 mm) on many of its electric guitars, including the Les Paul, Flying V, Explorer, SG, and ES-335. Gibson has used other scale lengths on various models through the years. Gibson's nominal "24.75" in scale length has itself varied, sometimes measuring 24 5/8" or 24 9/16" depending on the production equipment used. As Gibson necks are not often interchangeable, this usually goes unnoticed in practice.
On a modern bass guitar, 30" (76 cm) or less is considered short scale, standard (also called long) scale is 34" (86 cm) for a 4-string and 35" (89 cm) for a B-E-A-D-G 5-string, and extra-long scale basses of 36" (91 cm) also exist.
Quite an uncommon scale construction using the Novax Fanned-Fret system that "fan outward" for the ability to play in tune with the unequal scale lengths of each string that is used to find the optimal equal tonal response and equal string tension from string-to-string for easier playing is represented by Dingwall Basses, who uses a 37" to 34" span on their Prima, Z1, Z2, and Afterburner original designs and a shorter 34.25" to 32" span for their "Super J" Jazz Bass design.
Helios R-Evolution 7 strings bass Heliosguitars
Helios ANTARES 6 strings bass Heliosguitars
The scale length of a piano is the length of the longest string. As this is normally the lowest bass note, it is a single string.
Concert grand pianos range in scale from about 7 ft 6 in (229 cm) to 9 ft (274 cm) or occasionally more. Notable concert grands include:
Smaller grand pianos vary in naming. The larger models, about 6 ft (183 cm) or more in scale length, may have the full grand piano action, and are used in smaller concert spaces. Others are intended for larger homes, and may have a simplified action lacking the repeat lever that is only useful for advanced players.
Baby grand pianos are the smallest, intended for homes, restaurants and similar applications where the grand style of piano is desired even at the expense of the longer scale and better sound that an upright format would permit in the available space.
Pythagorean scale refers to the relative lengths of strings within an instrument. This kind of scaling dictates that the ratio of string lengths should be equal to the harmonic ratio of their pitches. It is a logarithmic scale that doubles at each octave. This type of scaling was offered under the assumption that by keeping all other factors consistent (esp. string thickness and tension) and changing only length, the sound of the instrument would be homogeneous across its full range.
Because the length of strings increases so quickly in the bass register, it often would produce an instrument of impractical length. If pythagorean scaling were applied to the stringed instruments, the double bass would be extremely cumbersome. In pianos and harpsichords, generally less tension or thicker strings are used in the lower register to avoid the need for such large dimensions as demanded by a Pythagorean scale.