Interval, melody, and harmony
The lower or upper pitch of an interval may be sharp or flat, or both pitches of an interval.
If the lower pitch is sharp or the upper pitch is flat, the interval may be said to be flat given that as a whole it is too narrow; while if the lower pitch is flat or the upper pitch is sharp, the interval may be said to be sharp given that as a whole it is too wide. Intervals are conventionally measured from the bottom, as such in an interval that is too wide the upper pitch is thus sharp. Intonation exists within the context of musical temperament, of which there are several types.
However, the interval itself may be in tune, in relation to itself (i.e. both notes of the interval are in tune in relation to each other), but flat or sharp as a whole and thus both notes of the interval are out of tune.
Notes within a melody can be either sharp or flat, or in tune, in relation to the other notes in the melody or other pitches sounding at the same time.
Strings
With fretless string instruments such as violins or cellos, intonation depends on the exact places the musician's fingers press the strings against the instrument's fingerboard, as well as any pull or push the musician exerts on the string, either along the string's length or perpendicular to it.
The pleasantly "alive" sound of a large string section results from the amount by which each stringed instrument is slightly out of tune.
Fretted instrument intonation
Several factors affect fretted instrument intonation, including depth of the string slots in the nut, bridge saddle position, the position of the frets themselves, the bending stiffness of the string, and the technique of the musician.
On fretted string instruments, pushing a string against a fret—aside from raising the string's pitch because its effective length is reduced—also causes a slight secondary raise in pitch because pushing the string increases its tension. If the instrument doesn't compensate for this with a slight increase in the distance from the bridge saddle to the fret, the note sounds sharp. Playing technique has some effect on intonation but some amount of intonation variability may be uncontrollable. [1] [2]
Most electric fretted string instruments have individually adjustable bridge saddles, adjustable with a screw driver or Allen wrench. Acoustic fretted instruments typically have either a floating bridge, held in place by string tension, or a fixed bridge, such as a pin bridge on an acoustic guitar. A luthier or technician adjusts a floating bridge simply by carefully changing its position until the intonation is correct. Adjusting intonation on a fixed bridge involves carefully shaping the bridge saddle with a file to alter the string's contact point. [3]
Another cause of poor intonation on a fretted instrument is that the maker didn't cut the string slots in the nut deep enough. If the string is higher than fret height at the nut, the string deflection-caused pitch increase is progressively greater closer to the nut.
Other instruments
Like unfretted string instruments, the trombone relies on the musician precisely positioning something, in this case the trombone's slide. The slide's pitch adjustment on a single partial is approximately the interval of a tritone on a slide length of over 80 centimeters. The trombonist may use his/her ear to minutely adjust pitch on sustained notes. By coincidence, the position of the bell on most trombones provides a reference for fourth position, but this is not accessible during fast passages and is massively unreliable as intonation varies by instrument make and model. Articulation is also an important consideration when playing trombone: imprecise articulation may add unwanted glissandi to a note not requiring it. Imprecise articulation often ends up as poor intonation and tone.
Woodwinds are manufactured with holes that must be covered or uncovered to shorten or lengthen the bore to change pitch, and (except for flute) require register keys to change octaves. Most woodwind instruments comply to a regular harmonic series of pitches and require one register key to change octaves. The exception is the clarinet, which sounds only every other pitch of the harmonic series. This means that the clarinet, rather than having an octave key, has a "register key" that raises the pitch by a 12th.
Brass instruments with valves have an inherent intonation defect in that valve combinations tend to be sharp. This is because the open horn is in a pitch of (for example) B♭, so depressing the first valve lowers the pitch to A♭. Depressing the second valve in isolation lowers the pitch to A natural. But together, these two valves produce a sharp G natural, because the second valve slide, which is long enough to lengthen a B♭ horn to A natural, is slightly too short to lower the longer A♭ horn to G. Combinations using all three valves have even worse intonation, so instruments need some means to compensate. Trumpets and flugelhorns commonly have saddles or triggers on the first and/or third valve slides to allow lengthening of the valve slides, while on larger instruments like the euphonium and tuba, such devices are impractical. Instead, better-quality tubas and euphoniums are provided a fourth valve, which takes the place of the 1-3 valve combination and allows use of 2-4 in place of 1-2-3. Better manufacturers of three-valve instruments such as Sousaphones often make the third valve slide long enough to partially address this deficiency. Also, many tuba models place the first valve slide in a position where it may be manipulated by the musician with the left hand during playing, which allows tuning for the always-flat 5th partial harmonic at the C below middle C.
Another solution for euphonium or tuba is called a compensating system, and these have been made in both three- and four-valve versions. In a compensating system, the tubing from the final valve is routed back to the first valve, and each of the valves before the final one is fitted with a short valve slide in addition to the normal ones. When the third or fourth valve, as applicable, is depressed in combination with any of the other valves, the additional tubing brings the pitch into tune. This has the primary effect of making the lowest octave playable including B natural (unplayable on non-compensating horns), and a secondary effect of putting low B natural and C natural into tune. Compensating systems add weight and "stuffiness" to a horn, so they are not commonly fitted to tubas. They find principal use in euphoniums, in which virtually all professional models are compensating. Some French horns have an altogether different system: they have a complete set of slides on each valve in B♭, parallel to the F slides. Pressing a separate trigger routes the air through the B♭ slides vice the F slides, and via shorter tubing to the bell. Intonation is less of a problem in French horn, because it usually plays using higher harmonics where use of the 1-3 and 1-2-3 valve combinations is not needed.
A brass instrument is a musical instrument that produces sound by sympathetic vibration of air in a tubular resonator in sympathy with the vibration of the player's lips. Brass instruments are also called labrosones or labrophones, from Latin and Greek elements meaning 'lip' and 'sound'.
The euphonium is a medium-sized, 3 or 4-valve, often compensating, conical-bore, tenor-voiced brass instrument that derives its name from the Ancient Greek word εὔφωνος euphōnos, meaning "well-sounding" or "sweet-voiced". The euphonium is a valved instrument. Nearly all current models have piston valves, though some models with rotary valves do exist.
The guitar is a stringed musical instrument that is usually fretted and typically has six or twelve strings. It is usually held flat against the player's body and played by strumming or plucking the strings with the dominant hand, while simultaneously pressing selected strings against frets with the fingers of the opposite hand. A guitar pick may also be used to strike the strings. The sound of the guitar is projected either acoustically, by means of a resonant hollow chamber on the guitar, or amplified by an electronic pickup and an amplifier.
In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios of frequencies. An interval tuned in this way is said to be pure, and is called a just interval. Just intervals consist of tones from a single harmonic series of an implied fundamental. For example, in the diagram, if the notes G3 and C4 are tuned as members of the harmonic series of the lowest C, their frequencies will be 3 and 4 times the fundamental frequency. The interval ratio between C4 and G3 is therefore 4:3, a just fourth.
In music, there are two common meanings for tuning:
The pitch of a brass instrument corresponds to the lowest playable resonance frequency of the open instrument. The combined resonances resemble a harmonic series. The fundamental frequency of the harmonic series can be varied by adjusting the length of the tubing using the instrument's valve, slide, key or crook system, while the player's embouchure, lip tension and air flow serve to select a specific harmonic from the available series for playing. The fundamental is essentially missing from the resonances and is impractical to play on most brass instruments, but the overtones account for most pitches.
The trombone is a musical instrument in the brass family. As with all brass instruments, sound is produced when the player's vibrating lips cause the air column inside the instrument to vibrate. Nearly all trombones use a telescoping slide mechanism to alter the pitch instead of the valves used by other brass instruments. The valve trombone is an exception, using three valves similar to those on a trumpet, and the superbone has valves and a slide.
The tuba is the largest and lowest-pitched musical instrument in the brass family. As with all brass instruments, the sound is produced by lip vibration – a buzz – into a mouthpiece. It first appeared in the mid-19th century, making it one of the newer instruments in the modern orchestra and concert band, and largely replaced the ophicleide. Tuba is Latin for "trumpet".
An overtone is any resonant frequency above the fundamental frequency of a sound. In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental is the lowest pitch. While the fundamental is usually heard most prominently, overtones are actually present in any pitch except a true sine wave. The relative volume or amplitude of various overtone partials is one of the key identifying features of timbre, or the individual characteristic of a sound.
A transposing instrument is a musical instrument for which music notation is not written at concert pitch. For example, playing a written middle C on a transposing instrument produces a pitch other than middle C; that sounding pitch identifies the interval of transposition when describing the instrument. Playing a written C on clarinet or soprano saxophone produces a concert B♭, so these are referred to as B♭ instruments. Providing transposed music for these instruments is a convention of musical notation. The instruments do not transpose the music; rather, their music is written at a transposed pitch. Where chords are indicated for improvisation they are also written in the appropriate transposed form.
A fret is any of the thin strips of material, usually metal wire, inserted laterally at specific positions along the neck or fretboard of a stringed instrument. Frets usually extend across the full width of the neck. On some historical instruments and non-European instruments, frets are made of pieces of string tied around the neck.
In music, inharmonicity is the degree to which the frequencies of overtones depart from whole multiples of the fundamental frequency.
The fingerboard is an important component of most stringed instruments. It is a thin, long strip of material, usually wood, that is laminated to the front of the neck of an instrument. The strings run over the fingerboard, between the nut and bridge. To play the instrument, a musician presses strings down to the fingerboard to change the vibrating length, changing the pitch. This is called stopping the strings. Depending on the instrument and the style of music, the musician may pluck, strum or bow one or more strings with the hand that is not fretting the notes. On some instruments, notes can be sounded by the fretting hand alone, such as with hammer ons, an electric guitar technique.
A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, and have 24 different pitches.
In music, a guitar chord is a set of notes played on a guitar. A chord's notes are often played simultaneously, but they can be played sequentially in an arpeggio. The implementation of guitar chords depends on the guitar tuning. Most guitars used in popular music have six strings with the "standard" tuning of the Spanish classical guitar, namely E–A–D–G–B–E' ; in standard tuning, the intervals present among adjacent strings are perfect fourths except for the major third (G,B). Standard tuning requires four chord-shapes for the major triads.
Guitar tunings are the assignment of pitches to the open strings of guitars, including classical guitars, acoustic guitars, and electric guitars. Tunings are described by the particular pitches that are made by notes in Western music. By convention, the notes are ordered and arranged from the lowest-pitched string to the highest-pitched string, or the thickest string to thinnest, or the lowest frequency to the highest. This sometimes confuses beginner guitarists, since the highest-pitched string is referred to as the 1st string, and the lowest-pitched is the 6th string.
A nut, on a stringed musical instrument, is a small piece of hard material that supports the strings at the end closest to the headstock or scroll. The nut marks one end of the vibrating length of each open string, sets the spacing of the strings across the neck, and usually holds the strings at the proper height from the fingerboard. Along with the bridge, the nut defines the scale lengths of the open strings.
The harmonic seventh interval, also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio (about 969 cents). This is somewhat narrower than and is, "particularly sweet", "sweeter in quality" than an "ordinary" just minor seventh, which has an intonation ratio of 9:5 (about 1018 cents).
In music, 41 equal temperament, abbreviated 41-TET, 41-EDO, or 41-ET, is the tempered scale derived by dividing the octave into 41 equally sized steps. Each step represents a frequency ratio of 21/41, or 29.27 cents, an interval close in size to the septimal comma. 41-ET can be seen as a tuning of the schismatic, magic and miracle temperaments. It is the second smallest equal temperament, after 29-ET, whose perfect fifth is closer to just intonation than that of 12-ET. In other words, is a better approximation to the ratio than either or .
Among alternative tunings for the guitar, an overtones tuning selects its open-string notes from the overtone sequence of a fundamental note. An example is the open tuning constituted by the first six overtones of the fundamental note C, namely C2-C3-G3-C4-E4-G4.
