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Pythagorean tuning, the Glossary

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2.^[1]

73 relations: Augmented second, Augmented unison, Bartolomé Ramos de Pareja, Boethius, Bragod, Cent (music), Christopher Page, Comma (music), Consonance and dissonance, Crwth, Daniel Leech-Wilkinson, Diatonic scale, Diesis, Diminished fourth, Diminished second, Diminished sixth, Ditone, Enharmonic equivalence, Enharmonic scale, Equal temperament, Eratosthenes, Five-limit tuning, Frequency, Gioseffo Zarlino, Gothic Voices, Harmonic series (music), Harmony, Interval (music), Interval ratio, John Bergamo, John Schneider (guitarist), Just intonation, Key (music), List of meantone intervals, List of pitch intervals, Lou Harrison, Lyre, Major scale, Major second, Major seventh, Major sixth, Major third, Meantone temperament, Minor seventh, Minor sixth, Minor third, Music of ancient Greece, Musical keyboard, Musical temperament, Musical tuning, ... Expand index (23 more) »
3-limit tuning and intervals
Pythagoras

Augmented second

In classical music from Western culture, an augmented second is an interval that, in 12-tone equal temperament, is sonically equivalent to a minor third, spanning three semitones, and is created by widening a major second by a chromatic semitone.

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Augmented unison

In modern Western tonal music theory an augmented unison or augmented prime is the interval between two notes on the same staff position, or denoted by the same note letter, whose alterations cause them, in ordinary equal temperament, to be one semitone apart.

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Bartolomé Ramos de Pareja

Bartolomé Ramos de Pareja (ca. 1440 – 1522) was a Spanish mathematician, music theorist, and composer.

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Boethius

Anicius Manlius Severinus Boethius, commonly known simply as Boethius (Latin: Boetius; 480–524 AD), was a Roman senator, consul, magister officiorum, polymath, historian, and philosopher of the Early Middle Ages.

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Bragod

Bragod is a duo giving historically informed performances of mediaeval Welsh music.

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Cent (music)

The cent is a logarithmic unit of measure used for musical intervals.

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Christopher Page

Christopher Howard Page (born 8 April 1952) is an English expert on medieval music, instruments and performance practice, together with the social and musical history of the guitar in England from the sixteenth century to the nineteenth.

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Comma (music)

In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways.

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Consonance and dissonance

In music, consonance and dissonance are categorizations of simultaneous or successive sounds.

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Crwth

The crwth, also called a crowd or rote or crotta, is a bowed lyre, a type of stringed instrument, associated particularly with Welsh music, now archaic but once widely played in Europe.

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Daniel Leech-Wilkinson

Daniel Leech-Wilkinson is a musicologist, who is Emeritus Professor of Music at King's College London.

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Diatonic scale

In music theory, a diatonic scale is any heptatonic scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, depending on their position in the scale.

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Diesis

In classical music from Western culture, a diesis (or enharmonic diesis, plural dieses (or "difference"; Greek: "leak" or "escape" is either an accidental (see sharp), or a very small musical interval, usually defined as the difference between an octave (in the ratio 2:1) and three justly tuned major thirds (tuned in the ratio 5:4), equal to 128:125 or about 41.06 cents.

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Diminished fourth

In classical music from Western culture, a diminished fourth is an interval produced by narrowing a perfect fourth by a chromatic semitone.

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Diminished second

In modern Western tonal music theory, a diminished second is the interval produced by narrowing a minor second by one chromatic semitone.

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Diminished sixth

In classical music from Western culture, a diminished sixth is an interval produced by narrowing a minor sixth by a chromatic semitone.

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Ditone

In music, a ditone (from, "of two tones") is the interval of a major third. Pythagorean tuning and ditone are 3-limit tuning and intervals.

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Enharmonic equivalence

In music, two written notes have enharmonic equivalence if they produce the same pitch but are notated differently.

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Enharmonic scale

In music theory, an enharmonic scale is a very ancient Greek musical scale which contains four notes tuned to approximately quarter tone pitches, bracketed (as pairs) between four fixed pitches.

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Equal temperament

An equal temperament is a musical temperament or tuning system that approximates just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequencies of any adjacent pair of notes is the same.

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Eratosthenes

Eratosthenes of Cyrene (Ἐρατοσθένης; –) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist.

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Five-limit tuning

Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given reference note (the base note) by products of integer powers of 2, 3, or 5 (prime numbers limited to 5 or lower), such as.

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Frequency

Frequency (symbol f), most often measured in hertz (symbol: Hz), is the number of occurrences of a repeating event per unit of time.

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Gioseffo Zarlino

Gioseffo Zarlino (31 January or 22 March 1517 – 4 February 1590) was an Italian music theorist and composer of the Renaissance.

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Gothic Voices

Gothic Voices is a United Kingdom-based vocal ensemble specialising in repertoire from the 11th to the 15th century but also performing contemporary music, particularly pieces with medieval associations.

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Harmonic series (music)

A harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a fundamental frequency.

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Harmony

In music, harmony is the concept of combining different sounds together in order to create new, distinct musical ideas.

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Interval (music)

In music theory, an interval is a difference in pitch between two sounds.

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Interval ratio

In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval.

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John Bergamo

John Bergamo (May 28, 1940 – October 19, 2013) was an American percussionist and composer known for his film soundtrack contributions and his work with numerous other notable performers.

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John Schneider (guitarist)

John Schneider (born 1950) is a Grammy® Award winning and 4-time Grammy® nominated American classical guitarist.

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Just intonation

In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios (such as 3:2 or 4:3) of frequencies.

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Key (music)

In music theory, the key of a piece is the group of pitches, or scale, that forms the basis of a musical composition in Western classical music, art music, and pop music.

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List of meantone intervals

The following is a list of intervals of extended meantone temperament.

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List of pitch intervals

Below is a list of intervals expressible in terms of a prime limit (see Terminology), completed by a choice of intervals in various equal subdivisions of the octave or of other intervals.

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Lou Harrison

Lou Silver Harrison (May 14, 1917 – February 2, 2003) was an American composer, music critic, music theorist, painter, and creator of unique musical instruments.

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Lyre

The lyre is a stringed musical instrument that is classified by Hornbostel–Sachs as a member of the lute family of instruments.

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Major scale

The major scale (or Ionian mode) is one of the most commonly used musical scales, especially in Western music.

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Major second

In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones.

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Major seventh

In music from Western culture, a seventh is a musical interval encompassing seven staff positions (see Interval number for more details), and the major seventh is one of two commonly occurring sevenths.

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Major sixth

In music from Western culture, a sixth is a musical interval encompassing six note letter names or staff positions (see Interval number for more details), and the major sixth is one of two commonly occurring sixths.

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Major third

In classical music, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third is a third spanning four half steps or two whole steps. Along with the minor third, the major third is one of two commonly occurring thirds.

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Meantone temperament

Meantone temperaments are musical temperaments, that is a variety of tuning systems, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them narrower than a perfect fifth), in order to push the thirds closer to pure.

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Minor seventh

In music theory, a minor seventh is one of two musical intervals that span seven staff positions.

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Minor sixth

In Western classical music, a minor sixth is a musical interval encompassing six staff positions (see Interval number for more details), and is one of two commonly occurring sixths (the other one being the major sixth).

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Minor third

In music theory, a minor third is a musical interval that encompasses three half steps, or semitones.

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Music of ancient Greece

Music was almost universally present in ancient Greek society, from marriages, funerals, and religious ceremonies to theatre, folk music, and the ballad-like reciting of epic poetry.

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Musical keyboard

A musical keyboard is the set of adjacent depressible levers or keys on a musical instrument.

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Musical temperament

In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements.

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Musical tuning

In music, there are two common meanings for tuning.

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Novalis

Georg Philipp Friedrich Freiherr von Hardenberg (2 May 1772 – 25 March 1801), pen name Novalis, was a German aristocrat and polymath, who was a poet, novelist, philosopher and mystic.

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Octave

In music, an octave (octavus: eighth) or perfect octave (sometimes called the '''diapason''') is a series of eight notes occupying the interval between (and including) two notes, one having twice the frequency of vibration of the other.

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Perfect fifth

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so. Pythagorean tuning and perfect fifth are 3-limit tuning and intervals.

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Perfect fourth

A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth is the fourth spanning five semitones (half steps, or half tones). Pythagorean tuning and perfect fourth are 3-limit tuning and intervals.

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Ptolemy

Claudius Ptolemy (Πτολεμαῖος,; Claudius Ptolemaeus; AD) was an Alexandrian mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine, Islamic, and Western European science.

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Pythagoras

Pythagoras of Samos (Πυθαγόρας; BC) was an ancient Ionian Greek philosopher, polymath and the eponymous founder of Pythagoreanism.

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Pythagorean comma

In musical tuning, the Pythagorean comma (or ditonic comma), named after the ancient mathematician and philosopher Pythagoras, is the small interval (or comma) existing in Pythagorean tuning between two enharmonically equivalent notes such as C and B, or D and C. It is equal to the frequency ratio. Pythagorean tuning and Pythagorean comma are 3-limit tuning and intervals.

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References

[1] https://en.wikipedia.org/wiki/Pythagorean_tuning

Also known as 3-limit, Pythagorean intonation, Pythagorean scale, Pythagorean temperament, Pythagorean tuning system, Three-limit tuning.

, Novalis, Octave, Perfect fifth, Perfect fourth, Ptolemy, Pythagoras, Pythagorean comma, Quarter-comma meantone, Regular temperament, Scale (music), Semitone, Shi'er lü, Superparticular ratio, Syntonic comma, Tetrachord, Timaeus (dialogue), Tritone, Unison, Violin family, Well temperament, Whole-tone scale, Wolf interval, 53 equal temperament.

Pythagorean tuning, the Glossary

Table of Contents

See also

3-limit tuning and intervals

Pythagoras

References