just intonation - Article Index

Encyclopedia - Harmonic: Encyclopedia - Harmonic
In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fund...   » Read the article

Encyclopedia - Xenharmonic: Encyclopedia - Xenharmonic
Xenharmonic music includes all tuning systems and music using those systems not using the common European twelve-tone equal temperament. ...   » Read the article

Encyclopedia - Overtone: Encyclopedia - Overtone
An overtone is a sinusoidal component of a waveform, of greater frequency than its fundamental frequency. Usually the first overtone is t...   » Read the article

Encyclopedia - Barbershop Music: Encyclopedia - Barbershop Music
Barbershop harmony is a style of unaccompanied vocal music characterized by consonant four-part chords for every melody note in a predomi...   » Read the article

Encyclopedia - Bohlen-pierce Scale: Encyclopedia - Bohlen-pierce Scale
The Bohlen-Pierce scale (BP scale) is a musical scale that offers an alternative to the 12-tone equal temperament typical in Western musi...   » Read the article

Encyclopedia - Major Second: Encyclopedia - Major Second
A major second is one of three commonly occurring musical intervals that span two diatonic scale degrees; the others being the minor seco...   » Read the article

Encyclopedia - Wendy Carlos: Encyclopedia - Wendy Carlos
Wendy Carlos (born Walter Carlos—see Personal life section below—November 14, 1939 in Pawtucket, Rhode Island) is an American compose...   » Read the article

Encyclopedia - Arnold Dreyblatt: Encyclopedia - Arnold Dreyblatt
Arnold Dreyblatt (b. New York City, 1953) is an American composer and visual artist. He studied with Pauline Oliveros, La Monte Young, an...   » Read the article

Encyclopedia - Cent Music: Encyclopedia - Cent Music
The cent is a logarithmic unit of measure used for musical intervals. Typically cents are used to measure extremely small intervals, or t...   » Read the article

Encyclopedia - Dominant: Encyclopedia - Dominant
The word dominant has several possible meanings: In music theory, the dominant or dominant note (second most important) of a key is that...   » Read the article

Encyclopedia - Terry Riley: Encyclopedia Ii - Terry Riley - Musical Style And Techniques
While his early endeavors were influenced by Stockhausen, Riley changed direction after first encountering La Monte Young, whose Theater ...   » Read the article

Encyclopedia - Pythagorean Tuning: Encyclopedia Ii - Pythagorean Tuning - Method
Pythagorean tuning is based on a stack of perfect fifths, each tuned in the ratio 3:2, the next simplest ratio after 2:1, which is the ra...   » Read the article

Encyclopedia - 53 Equal Temperament: Encyclopedia Ii - 53 Equal Temperament - Theoretical Properties
The 53-et tuning equates to the unison, or tempers out, the intervals 32805/32768, known as the schisma, and 15625/15552, known as the kl...   » Read the article

Encyclopedia - Wendy Carlos: Encyclopedia Ii - Wendy Carlos - Work
Switched-On Bach was perhaps the first album to attempt the use of synthesizers as an alternative to an orchestra. Having assisted Robert...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - The Natural Scale
Human beings distinguish sounds on the basis of their frequency. Actually what really matters is the ratio between their frequencies. The...   » Read the article

Encyclopedia - Pitch Class: Encyclopedia Ii - Pitch Class - Pitch Classes In Other Systems Of Tuning
In the case of just intonation, we may express pitches in terms of positive rational numbers p/q, expressed by reference to a 1 (often wr...   » Read the article

Encyclopedia - Barbershop Music: Encyclopedia Ii - Barbershop Music - Historical Origins
As a result of scholarship by Lynn Abbott and Dr. Jim Henry it is now generally accepted that barbershop singing originated in African-Am...   » Read the article

Encyclopedia - Accidental Music: Encyclopedia Ii - Accidental Music - Standard Use Of Accidentals
In most cases, a sharp raises the pitch of a note one semitone while a flat lowers it a semitone. A natural is used to cancel the effect ...   » Read the article

Encyclopedia - Barbershop Music: Encyclopedia Ii - Barbershop Music - Ringing Chords
The defining characteristic of the barbershop style is the ringing chord. This is a name for one specific and well-defined acoustical eff...   » Read the article

Encyclopedia - Pitch Space: Encyclopedia Ii - Pitch Space - History Of Pitch Space
The idea of pitch space goes back at least as far as the ancient Greek music theorists known as the Harmonists. To quote one of their num...   » Read the article

Encyclopedia - Equal Temperament: Encyclopedia Ii - Equal Temperament - History
Vincenzo Galilei (father of Galileo Galilei) may have been the first person to advocate equal temperament (in a 1581 treatise). The first...   » Read the article

Encyclopedia - Well Temperament: Encyclopedia Ii - Well Temperament - Origins
"Well tempered" means that the 12 notes per octave of the standard keyboard are tuned in such a way that it is possible to play music in ...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - The Natural Scale
Human beings distinguish sounds on the basis of their frequency. Actually what really matters is the ratio between their frequencies. The...   » Read the article

Encyclopedia - Modulatory Space: Encyclopedia Ii - Modulatory Space - Five-limit Modulatory Space
Five limit just intonation has a modulatory space based on the fact that its pitch classes can be represented by 3a 5b, where a and b are...   » Read the article

Encyclopedia - Gioseffo Zarlino: Encyclopedia Ii - Gioseffo Zarlino - Life
Zarlino was born in Chioggia, near Venice. His early education was with the Franciscans, and he later joined the order himself. In 1536 h...   » Read the article

Encyclopedia - Interval Music: Encyclopedia Ii - Interval Music - Interval Number And Quality
In diatonic or tonal theory intervals are labelled according to their diatonic function and according to the number of members or degrees...   » Read the article

Encyclopedia - Meantone Temperament: Encyclopedia Ii - Meantone Temperament - Meantone Temperaments
The term meantone temperament is sometimes used to refer specifically to quarter-comma meantone. However, systems which flatten the fifth...   » Read the article

Encyclopedia - Musical Tuning: Encyclopedia Ii - Musical Tuning - Comparisons And Controversies Between Tunings
All musical tuning have advantages and disadvantages. Twelve tone equal temperament is the standard and most usual tuning system used in ...   » Read the article

Encyclopedia - Timbre: Encyclopedia Ii - Timbre - Spectra
Each note produced by a musical instrument is made of a number of distinct frequencies, measured in hertz (Hz). The lowest frequency is c...   » Read the article

Encyclopedia - Lou Harrison: Encyclopedia Ii - Lou Harrison - Biography
Harrison was born in Portland, Oregon, but moved with his family to a number of locations around the San Francisco Bay area as a child. T...   » Read the article

Encyclopedia - Playing The Violin: Encyclopedia Ii - Playing The Violin - Playing The Violin
The violin is usually held under the chin and supported by the left shoulder. The strings may be sounded by either plucking (pizzicato) w...   » Read the article

Encyclopedia - Bohlen-pierce Scale: Encyclopedia Ii - Bohlen-pierce Scale - Bohlen-pierce Temperament
Dividing the tritave into 13 equal steps tempers out, or reduces to a unison, both of the intervals 245/243 (sometimes called the minor B...   » Read the article

Encyclopedia - Mathematics Of Musical Scales: Encyclopedia Ii - Mathematics Of Musical Scales - Temperament
Western common practice music usually cannot be played in just intonation, even when it is confined to a single key. This is because the ...   » Read the article

Encyclopedia - Interval Music: Encyclopedia Ii - Interval Music - Interval Number And Quality
In diatonic or tonal theory intervals are labelled according to their diatonic function and according to the number of members or degrees...   » Read the article

Encyclopedia - Microtonal Music: Encyclopedia Ii - Microtonal Music - Microtonalism In Rock Music
The American hardcore punk band Black Flag (1976-86) made interesting vernacular use of microtonal intervals, via guitarist Greg Ginn, a ...   » Read the article

Encyclopedia - Modulatory Space: Encyclopedia Ii - Modulatory Space - Toroidal Modulatory Spaces
If we divide the octave into n parts, where n = rs is the product of two relatively prime integers r and s, we may represent every elemen...   » Read the article

Encyclopedia - Modulatory Space: Encyclopedia Ii - Modulatory Space - Cylindrical Modulatory Spaces
A temperament of rank two which is not linear has one generator which is a fraction of an octave, called the period. We may represent the...   » Read the article

Encyclopedia - Modulatory Space: Encyclopedia Ii - Modulatory Space - Seven-limit Modulatory Space
In similar fashion, we can define a modulatory space for seven-limit just intonation, by representing 3a 5b 7c in terms of a correspondin...   » Read the article

Encyclopedia - Modulatory Space: Encyclopedia Ii - Modulatory Space - Circles Of Generators
A basic and important example of a modulatory space is the circle of fifths. In equal temperament, twelve succesive fifths equate to seve...   » Read the article

Encyclopedia - Meantone Temperament: Encyclopedia Ii - Meantone Temperament - Wolf Intervals And Extended Meantones
A whole number of just perfect fifths will never add up to a whole number of octaves, because they are incommensurable (see Fundamental t...   » Read the article

Encyclopedia - Playing The Violin: Encyclopedia Ii - Playing The Violin - Tuning
Violins are tuned by turning the pegs in the pegbox under the scroll, or by winding the fine tuner screws at the tailpiece. A violin alwa...   » Read the article

Encyclopedia - Barbershop Music: Encyclopedia Ii - Barbershop Music - Typical Barbershop Songs
SPEBSQSA "Polecats" — songs which all SPEBSQSA members are encouraged to learn as a shared repertoire — all famous, traditional examp...   » Read the article

Encyclopedia - Playing The Violin: Encyclopedia Ii - Playing The Violin - Mute
Attaching a small metal or rubber device called a "mute" to the bridge of the violin alters the tone by adding mass to the bridge and so ...   » Read the article

Encyclopedia - Interval Music: Encyclopedia Ii - Interval Music - Other Intervals
There are also a number of intervals not found in the chromatic scale or labeled with a diatonic function which have names of their own. ...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Harmony
If two notes are simultaneously played, with frequency ratios that are simple fractions (e.g. 2/1, 3/2 or 5/4), then the composite wave w...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Sound Waves
Variations in air pressure against the ear drum, and the subsequent physical and neurological processing and interpretation, give rise to...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Harmonics And Non-linearities
When a periodic wave is composed of a fundamental and only odd harmonics (f, 3f, 5f, 7f, ...), the summed wave is half-wave symmetric; it...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Harmonics Partials And Overtones
The fundamental is the frequency at which the entire wave vibrates. Overtones are other sinusoidal components present at frequencies abov...   » Read the article

Encyclopedia - Equal Temperament: Encyclopedia Ii - Equal Temperament - Explanation
The distance between each step and the next is aurally the same for any two adjacent steps; though, because steps form a geometric sequen...   » Read the article

Encyclopedia - Equal Temperament: Encyclopedia Ii - Equal Temperament - Twelve-tone Equal Temperament
The ratio between two adjacent semitones can be found with a few steps: 1. Let an be the frequency of a tone n, with a12 an octave above...   » Read the article

Encyclopedia - Equal Temperament: Encyclopedia Ii - Equal Temperament - Non-12 Tet
Five and seven tone equal temperament, with 240 and 171 cent steps relatively, seem the most common outside of 12-tET. A Thai xylophone m...   » Read the article

Encyclopedia - Barbershop Music: Encyclopedia Ii - Barbershop Music - Typical Barbershop Songs
SPEBSQSA "Polecats" — songs which all SPEBSQSA members are encouraged to learn as a shared repertoire; these are all famous, traditiona...   » Read the article

Encyclopedia - Pitch Space: Encyclopedia Ii - Pitch Space - Fibered Pitch Space
In analogy with mathematical usage, we might call a modulatory space the base space, and another space over each point of it, giving the ...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Harmonics And Non-linearities
When a periodic wave is composed of a fundamental and only odd harmonics (f, 3f, 5f, 7f, ...), the summed wave is symmetrical; it can be ...   » Read the article

Encyclopedia - Barbershop Music: Encyclopedia Ii - Barbershop Music - Notable Artists
Barbershop music - Quartets. Acoustix, 1990 international quartet champions Bluegrass Student Union, 1978 international quartet champi...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Harmony
If two notes are simultaneously played, with frequency ratios that are simple fractions (e.g. 2/1, 3/2 or 5/4), then the composite wave w...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - The Equal Tempered Scale
In the natural scale the ratio of the frequencies of two notes which differ for one tone is not always the same. Consequently a certain m...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Harmonics Partials And Overtones
The fundamental is the frequency at which the entire wave vibrates. Overtones are other sinusoidal components present at frequencies abov...   » Read the article

Encyclopedia - Barbershop Music: Encyclopedia Ii - Barbershop Music - Organization
Singing a cappella music in the barbershop style is a hobby enjoyed by men and women worldwide. The hobby is practiced mostly within one ...   » Read the article

Encyclopedia - Wendy Carlos: Encyclopedia Ii - Wendy Carlos - Personal Life
Carlos' musical education began when she started playing the piano at the age of six. Her formal education included Brown University wher...   » Read the article

Encyclopedia - Lou Harrison: Encyclopedia Ii - Lou Harrison - Harrison's Music
Many of Harrison's early works are for percussion instruments, often made out of what would usually be regarded as junk such as garbage c...   » Read the article

Encyclopedia - Interval Music: Encyclopedia Ii - Interval Music - Other Intervals
There are also a number of intervals not found in the chromatic scale or labeled with a diatonic function which have names of their own. ...   » Read the article

Encyclopedia - Barbershop Music: Encyclopedia Ii - Barbershop Music - Notable Artists
Barbershop music - Quartets. Acoustix, 1990 international quartet champions Bluegrass Student Union, 1978 international quartet champi...   » Read the article

Encyclopedia - Timbre: Encyclopedia Ii - Timbre - Envelope
The timbre of a sound is also greatly effected by the following factors: attack or Interonset interval, decay, sustain, release, and tran...   » Read the article

Encyclopedia - Barbershop Music: Encyclopedia Ii - Barbershop Music - Organizations
Singing a cappella music in the barbershop style is a hobby enjoyed by men and women worldwide. The hobby is practiced mostly within one ...   » Read the article

Encyclopedia - Barbershop Music: Encyclopedia Ii - Barbershop Music - Female Barbershop Music And Beautyshop Quartets
Traditionally, the word "barbershop" has been used to encompass both men's and women's quartets singing in the barbershop style. Harmony,...   » Read the article

Encyclopedia - Mathematics Of Musical Scales: Encyclopedia Ii - Mathematics Of Musical Scales - Just Intonation
If we take the ratios constituting a scale in just intonation, there will be a largest prime number to be found among their prime factori...   » Read the article

Encyclopedia - Timbre: Encyclopedia Ii - Timbre - In Music
Timbre is often cited as one of the fundamental aspects of music. Formally, timbre and other factors are usually secondary to pitch. "To ...   » Read the article

Encyclopedia - Terry Riley: Encyclopedia Ii - Terry Riley - Life
Born in Colfax, California, Riley studied at Shasta College, San Francisco State University, and the San Francisco Conservatory before ea...   » Read the article

Encyclopedia - Accidental Music: Encyclopedia Ii - Accidental Music - Microtonal Notation
Composers of microtonal music have developed a number of notations for indicating the various pitches outside of standard notation. One s...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Sound Waves
Variations in air pressure against the ear drum, and the subsequent physical and neurological processing and interpretation, give rise to...   » Read the article

Encyclopedia - Barbershop Music: Encyclopedia Ii - Barbershop Music - Historical Origins
As a result of scholarship by Lynn Abbott and Dr. Jim Henry it is now generally accepted that barbershop singing originated in African-Am...   » Read the article

Encyclopedia - Barbershop Music: Encyclopedia Ii - Barbershop Music - Female Barbershop Music And Beautyshop Quartets
Traditionally, the word "barbershop" has been used to encompass both men's and women's quartets singing in the barbershop style. Harmony,...   » Read the article

Encyclopedia - Accidental Music: Encyclopedia Ii - Accidental Music - Courtesy Accidentals
Although a barline is always understood to cancel the effect of an accidental (except for a tied note), often publishers will use a court...   » Read the article

Encyclopedia - Interval Music: Encyclopedia Ii - Interval Music - Pitch Class Intervals
Post-tonal or atonal theory, originally developed for equal tempered European classical music written using the twelve tone technique or ...   » Read the article

Encyclopedia - Interval Music: Encyclopedia Ii - Interval Music - Inversion
An interval may be inverted, by raising the lower pitch an octave, or lowering the upper pitch an octave (though it is less usual to spea...   » Read the article

Encyclopedia - Interval Music: Encyclopedia Ii - Interval Music - Consonant And Dissonant Intervals
Consonance and dissonance are relative terms referring to the stability, or state of repose, of particular musical effects. Dissonant int...   » Read the article

Encyclopedia - Interval Music: Encyclopedia Ii - Interval Music - Comparison Of Different Interval Naming Systems
It is possible to construct just intervals which are closer to the equal-tempered equivalents, but most of the ones listed above have bee...   » Read the article

Encyclopedia - 53 Equal Temperament: Encyclopedia Ii - 53 Equal Temperament - Chords Of 53 Equal Temperament
Standard musical notation can be used to denote 53 equal temperament; however, since it is a Pythagorean system, with nearly pure fifths,...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - The Equal Tempered Scale
In the natural scale the ratio of the frequencies of two notes which differ for one tone is not always the same. Consequently a certain m...   » Read the article