Perfect fifth in the context of "Octave"

The violin, sometimes referred to as a fiddle, is a wooden chordophone, and is the smallest, and thus highest-pitched instrument (soprano) in regular use in the violin family. Smaller violin-type instruments exist, including the violino piccolo and the pochette, but these are virtually unused. Most violins have a hollow wooden body, and commonly have four strings (sometimes five), usually tuned in perfect fifths with notes G3, D4, A4, E5, and are most commonly played by drawing a bow across the strings. The violin can also be played by plucking the strings with the fingers (pizzicato) and, in specialized cases, by striking the strings with the wooden side of the bow (col legno).

Violins are important instruments in a wide variety of musical genres. They are most prominent in the Western classical tradition, both in ensembles (from chamber music to orchestras) and as solo instruments. Violins are also important in many varieties of folk music, including country music, bluegrass music, and in jazz. Electric violins with solid bodies and piezoelectric pickups are used in some forms of rock music and jazz fusion, with the pickups plugged into instrument amplifiers and speakers to produce sound. The violin has come to be incorporated in many non-Western music cultures, including Indian music and Iranian music. The name fiddle is often used regardless of the type of music played on it.

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths which are "pure" or perfect, with ratio ${\displaystyle 3:2}$. This is chosen because it is the next harmonic of a vibrating string, after the octave (which is the ratio ${\displaystyle 2:1}$), and hence is the next most consonant "pure" interval, and the easiest to tune by ear. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is ≈ 702 cents wide.

The system dates back to Ancient Mesopotamia;. (See Music of Mesopotamia § Music theory.) It is named, and has been widely misattributed, to Ancient Greeks, notably Pythagoras (sixth century BC) by modern authors of music theory. Ptolemy, and later Boethius, ascribed the division of the tetrachord by only two intervals, called "semitonium" and "tonus" in Latin (256:243 × 9:8 × 9:8), to Eratosthenes. The so-called "Pythagorean tuning" was used by musicians up to the beginning of the 16th century. "The Pythagorean system would appear to be ideal because of the purity of the fifths, but some consider other intervals, particularly the major third, to be so badly out of tune that major chords [may be considered] a dissonance."

In music, monophony is the simplest of musical textures, consisting of a melody (or "tune"), typically sung by a single singer or played by a single instrument player (e.g., a flute player) without accompanying harmony or chords. Many folk songs and traditional songs are monophonic. A melody is also considered to be monophonic if a group of singers (e.g., a choir) sings the same melody together at the unison (exactly the same pitch) or with the same melody notes duplicated at the octave (such as when men and women sing together). If an entire melody is played by two or more instruments or sung by a choir with a fixed interval, such as a perfect fifth, it is also said to be monophony (or "monophonic"). The musical texture of a song or musical piece is determined by assessing whether varying components are used, such as an accompaniment part or polyphonic melody lines (two or more independent lines).

In the Early Middle Ages, the earliest Christian songs, called plainchant (a well-known example is Gregorian chant), were monophonic. Even into the twenty-first century, songwriters still often write songs that intersperse sections using monophony, heterophony (two singers or instrumentalists doing varied versions of the same melody together), polyphony (two or more singers or instrumentalists playing independent melodic lines at the same time), homophony (a melody accompanied by chords), or monody (a single melodic line with instrumental accompaniment) elements throughout the melody to create different atmospheres and styles. Monophony may not have underlying rhythmic textures, and must consist of only a single melodic line.

Organum (/ˈɔːrɡənəm/) is, in general, a plainchant melody with at least one added voice to enhance the harmony, developed in the Middle Ages. Depending on the mode and form of the chant, a supporting bass line (or bourdon) may be sung on the same text, the melody may be followed in parallel motion (parallel organum), or a combination of both of these techniques may be employed. As no real independent second voice exists, this is a form of heterophony. In its earliest stages, organum involved two musical voices: a Gregorian chant melody, and the same melody transposed by a consonant interval, usually a perfect fifth or fourth. In these cases the composition often began and ended on a unison, the added voice keeping to the initial tone until the first part has reached a fifth or fourth, from where both voices proceeded in parallel harmony, with the reverse process at the end. Organum was originally improvised; while one singer performed a notated melody (the vox principalis), another singer—singing "by ear"—provided the unnotated second melody (the vox organalis). Over time, composers began to write added parts that were not just simple transpositions, thus creating true polyphony.

In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth (for example C to G) is 3:2 (Play), 1.5, and may be approximated by an equal tempered perfect fifth (Play) which is 2 (about 1.498). If the A above middle C is 440 Hz, the perfect fifth above it would be E, at (440*1.5=) 660 Hz, while the equal tempered E5 is 659.255 Hz.

Ratios, rather than direct frequency measurements, allow musicians to work with relative pitch measurements applicable to many instruments in an intuitive manner, whereas one rarely has the frequencies of fixed pitched instruments memorized and rarely has the capabilities to measure the changes of adjustable pitch instruments (electronic tuner). Ratios have an inverse relationship to string length, for example stopping a string at two-thirds (2:3) its length produces a pitch one and one-half (3:2) that of the open string (not to be confused with inversion).

In music theory, a major chord is a chord that has a root, a major third, and a perfect fifth. When a chord comprises only these three notes, it is called a major triad. For example, the major triad built on C, called a C major triad, has pitches C–E–G:

In harmonic analysis and on lead sheets, a C major chord can be notated as C, CM, CΔ, or Cmaj. A major triad is represented by the integer notation {0, 4, 7}.

The violoncello (/ˌvaɪələnˈtʃɛloʊ/ VY-ə-lən-CHEL-oh, Italian pronunciation: [vjolonˈtʃɛllo]), commonly abbreviated as cello (/ˈtʃɛloʊ/ CHEL-oh), is a medium-low pitched bowed (sometimes plucked and occasionally hit) string instrument of the violin family. Its four strings are usually tuned in perfect fifths: from low to high, C₂, G₂, D₃ and A₃. The viola's four strings are each an octave higher. Music for the cello is generally written in the bass clef; the tenor clef and treble clef are used for higher-range passages.

Played by a cellist or violoncellist, it enjoys a large solo repertoire with and without accompaniment, as well as numerous concerti. As a solo instrument, the cello uses its whole range, from bass to soprano, and in chamber music, such as string quartets and the orchestra's string section, it often plays the bass part, where it may be reinforced an octave lower by the double basses. Figured bass music of the Baroque era typically assumes a cello, viola da gamba or bassoon as part of the basso continuo group alongside chordal instruments such as organ, harpsichord, lute, or theorbo. Cellos are found in many other ensembles, from modern Chinese orchestras to cello rock bands.

The viola (/viˈoʊlə/ vee-OH-lə, () Italian: [ˈvjɔːla, viˈɔːla]) is a string instrument of the violin family, and is usually bowed when played. Violas are slightly larger than violins, and have a lower sound. Since the 18th century, it has been the middle or alto voice of the violin family, between the violin (which is tuned a perfect fifth higher) and the cello (which is tuned an octave lower). The strings from low to high are typically tuned to C₃, G₃, D₄, and A₄.

In the past, the viola varied in size and style, as did its names. The word viola originates from the Italian language. The Italians often used the term viola da braccio, meaning, literally, 'of the arm'. "Brazzo" was another Italian word for the viola, which the Germans adopted as Bratsche. The French had their own names: cinquiesme was a small viola, haute contre was a large viola, and taile was a tenor. Today, the French use the term alto, a reference to its range.