Scale (string instruments)

:"For the musical (rather than instrumental) scale, see Pythagorean tuning."

In a string instrument, the scale length (often simply called the "scale") is the sounding length of the strings. On instruments with strings which are not stopped (harp, piano) and on most fretless instruments it is the length of string between the nut and the bridge. On most modern fretted instruments the actual string length is a bit longer than the scale length, to provide some compensation for the sharping effect caused by the string being stretched slightly as it is fretted. On such instruments it is not possible to determine the scale length by simply measuring the speaking length of the string. [http://www.liutaiomottola.com/formulae/scale.htm]

In many but not all instruments, all the strings are roughly the same length, so the scale can be expressed as a single length measurement, as for example in the case of the violin or guitar. In others, the strings are of different lengths, as for example in the case of the harp or piano.

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 17.816, and the quotient taken as the location of the next semitone pitch from the nut of the instrument. The remainder is again divided by 17.816 to locate the next semitone pitch higher, and so on. This technique is used when fretting instruments and is known as "The Eighteen Rule".

In many instruments, for example the violin, the scale of a full-sized instrument is very strictly standardised. Smaller scale instruments are still often used:
*By younger players.
*By smaller advanced players.
*To obtain a particular tone or effect.
*For convenience when travelling.

Larger 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.

Bowed strings

Violin family

The two most famous violin makers, Antonio Stradivarius (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 by a conventional fraction. There are two reasons for this. Firstly, unlike that of the violin and the cello, the viola scale length has not standardised, but rather an advanced player will use whatever scale length best suits them, see viola. Secondly, student sizes are not as often required, as most viola players who start learning at a young age would 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).

Double bass

There is some variation in the scale length of orchestral double basses, generally in the range 42.3"-43.3" (1050-1100mm). 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.

Classical guitar

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 and their customers have been unreceptive to any suggestion of change.

Unlike Stradivarius, Torres had no strong tradition on which to build regarding scale length, so the 25.6 in figure can be attributed to him with confidence.

teel-string acoustic guitar

The steel-string acoustic guitar typically has the same scale as that of the classical guitar, 25.6 in or 650 mm.Fact|date=February 2008

Electric guitar

The scale length of the electric guitar is one of the least standardized of all instruments.

History

Most Fender electric guitars, including the Stratocaster, Telecaster, Esquire, and Jazzmaster use a scale length of 25.5 in (65 cm). A few Fender models such as the Jaguar use a scale length of 24 in (61 cm). Fender has also built some 3/4-size student guitars with a scale length of 22.5 in (57 cm) or shorter.

Gibson uses a scale length of 24.75 in (63 cm) 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.

ummary

*20.7 in (527 mm):
**Squier Bullet Mini
**Rickenbacker Electro (student model) Es-16, Rickenbacker 1996, 320 and 325, notably John Lennon's most famous guitar

*22.5 in (572 mm), known as "3/4 scale" in Fender sales literature:
**Fender Musicmaster
**Fender Duosonic
**Fender Mustang
**Some Musicmaster II and Duosonic II

*22.72 in (577 mm):
**Fender Stratocaster Junior

*22.75 in (578mm):
**Gibson 3/4 scale Les Paul Junior and Melody Maker

*24 in (610 mm), confusingly called "full scale" in Fender sales literature:
**Fender Jaguar
**Most and current Fender Mustang
**Most Musicmaster II and Duosonic II
**Fender Bronco

*24.75 in (629 mm):
**Gibson Les Paul
**Gibson SG
**Original Gibson ES-150
**Fender Cyclone
**Rickenbacker most electric guitars (including 330, 340, 350, 360, 370, 380, 620, 650, 660)

*25 in (635 mm)
**Most Paul Reed Smith guitars

*25.5 in (648 mm), closest to the classical guitar scale:
**Fender Esquire
**Fender Telecaster
**Fender Stratocaster
**Fender Jazzmaster
**Most Jackson Guitars
**Squier Stratocaster
**Most and current Gibson ES-150
**Most Ibanez guitars

*27 in (686 mm)
**Fender Jaguar Baritone Special HH (tuned B-B)

*29.25 in (743 mm)
**Gretsch G6144 Spectra Sonic Baritone

Electric bass

History

The first electric basses were upright electric basses built in the 1930s by fitting an otherwise normal double bass with electric pickups, and so had a scale length of about 43" (109 cm).

In 1951 the Fender Precision Bass shortened this to 34" (86 cm). This is still often regarded as the standard length for a bass guitar.

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.

ummary

*28.5 in (724 mm)
**Fender Jaguar Bass VI Custom

*30 in (762 mm)
**Fender Mustang Bass, Fender Bronco Bass, Fender Musicmaster Bass
**Fender Bass VI

*30.5 in (775 mm)
**Gibson EB-1, EB-0 and other EB-x basses, Gibson SG bass
**Hofner 500 Beatle Bass
**Hamer B8S 8-string bass

*33.25 in (845 mm)
**Rickenbacker 4000 Series basses

*34 in (864 mm)
**Fender Precision Bass, Jazz Bass, Jaguar Bass
**Gibson Thunderbird Bass

*34.5 in (876 mm)
**Gibson EB-0L and other EB-xL basses

*35 in (889 mm)
**Ibanez BTB series basses

*42.3–43.3 in (1050-1100 mm) double bass (for comparison)

Other chordophones

*Mandola: 20.2 in (51 cm)
*Mandolin: 14.1 in (36 cm)
**Octave mandolin: 22.75 in (58 cm)
*Ukulele:
**Baritone ukulele: 20.1 in (51 cm)
**Concert ukulele: 14.75 in (37 cm)
**Soprano ukulele: 13.6 in (35 cm)
**Tenor ukulele: 17 in (43 cm)

Piano

The scale length of a piano is quoted as the length of the longest string. As this is normally the lowest bass note, it will be a single string.

Grand piano

"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:
*The Steinway Model D, at 8 ft 11-3/4 in (272 cm).
*The Fazioli F308 at 10 ft 2 in (310 cm).

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

:"For the musical (rather than instrumental) scale, see Pythagorean tuning."

Pythagorean scale refers to the relative lengths of strings within an instrument [ [http://www.harpsichord.org.uk/guests/dw/wraight.htm Pythagoras and the Scale Design of Early Harpsichords ] ] . 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 which 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 such length as to be impractical. 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.

ee also

*Fingerboard
*Multi-scale fingerboard

Additional reading

* [http://www.liutaiomottola.com/formulae/scale.htm "Lutherie Info – Measuring Scale Length of Stringed Instruments"] by R.M. Mottola, on the [http://www.liutaiomottola.com Liutaio Mottola Lutherie Information Website] .
*"Fender's 3/4 Scale Guitars", a two-part article by Tim Pershing in "20th Century Guitar" magazine, December 1996 and January 1997.

External links

* [http://www.elderly.com/books/611.htm Instrument plans index] giving some scale lengths.
* [http://www.12fret.com/fret/fv4n7.htm Discussion] of the effect of scale length.
* [http://www.sweetwater.com/shop/bass-guitars/bass-guitars/buying-guide.php Bass guitar buying guide] discusses scale length.
* [http://www.provide.net/~cfh/index.html Vintage guitars] with dimensions.
* [http://www.contrabass.co.uk/cstopquality.htm Listing of some orchestral basses] giving both body and scale lengths.

Notes