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just intonation | A Wisdom Archive on just intonation | | just intonation A selection of articles related to just intonation | |
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just intonation
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| ARTICLES RELATED TO just intonation | | | |  just intonation: Encyclopedia II - Barbershop music - Typical Barbershop SongsSPEBSQSA "Polecats" — songs which all SPEBSQSA members are encouraged to learn as a shared repertoire — all famous, traditional examples of the genre:
"Down Our Way"
"Down by the Old Mill Stream"
"Honey/Li'l Lize Medley"
"Let Me Call You Sweetheart"
"My Wild Irish Rose"
"Shine on Me"
"The Story of the Rose" ("Heart of My Heart")
"Sweet Adeline"
"Sweet and Lovely"
"Sweet Roses of Morn"
"Wait 'Til the Sun Shines, Nellie"< ...
See also:Barbershop music, Barbershop music - Ringing chords, Barbershop music - Historical origins, Barbershop music - Female Barbershop music and Beautyshop quartets, Barbershop music - Organization, Barbershop music - Notable artists, Barbershop music - Quartets, Barbershop music - Choruses, Barbershop music - Typical Barbershop Songs Read more here: » Barbershop music: Encyclopedia II - Barbershop music - Typical Barbershop Songs |
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| | | | | | just intonation: 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. Many of these intervals describe small discrepancies between notes tuned according to the tuning systems used. Most of the following intervals may be described as microtones.
A Pythagorean comma is the difference between twelve justly tuned perfect fifths and seven octaves. It is expressed by the frequency ratio 531441:524288, and is equal to 23.46 cents.
A syntonic comma ...
See also:Interval music, Interval music - Frequency ratios, Interval music - Interval number and quality, Interval music - Shorthand notation, Interval music - Enharmonic intervals, Interval music - Steps and skips, Interval music - Pitch class intervals, Interval music - Ordered and unordered pitch and pitch class intervals, Interval music - Generic and specific intervals, Interval music - Cents, Interval music - Comparison of different interval naming systems, Interval music - Consonant and dissonant intervals, Interval music - Inversion, Interval music - Interval roots, Interval music - Interval cycles, Interval music - Other intervals, Interval music - Sources Read more here: » Interval music: Encyclopedia II - Interval music - Other intervals |
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| | | | | just intonation: 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 will still be periodic with a short period, and the combination will sound consonant. For instance, a note vibrating at 200 Hz and a note vibrating at 300 Hz (a perfect fifth, or 3/2 ratio, above 200 Hz) will add together to make a wave that repeats at 100 Hz: every 1/100 of a second, the 300 Hz wave will repeat thrice and the 200 Hz wave will repeat twice. Note that the total wave repeats at 100 Hz, but there is not ac ...
See also:Musical acoustics, Musical acoustics - Methods and fields of study, Musical acoustics - Sound waves, Musical acoustics - Harmonics partials and overtones, Musical acoustics - Harmonics and non-linearities, Musical acoustics - Harmony, Musical acoustics - The natural scale, Musical acoustics - The equal tempered scale, Musical acoustics - Cent values of equal temperament Read more here: » Musical acoustics: Encyclopedia II - Musical acoustics - Harmony |
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| | | | | just intonation: 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 the experience called "sound". Most sound that people recognize as "musical" is dominated by periodic or regular vibrations rather than non-periodic ones (called a definite pitch), and we refer to the transmission mechanism as a "sound wave". In a very simple case, the sound of a sine wave, which is considered to be the most basic model of a sound waveform, causes the air pressure to increase and decrease ...
See also:Musical acoustics, Musical acoustics - Methods and fields of study, Musical acoustics - Sound waves, Musical acoustics - Harmonics partials and overtones, Musical acoustics - Harmonics and non-linearities, Musical acoustics - Harmony, Musical acoustics - The natural scale, Musical acoustics - Evolution of the natural scale, Musical acoustics - The equal tempered scale, Musical acoustics - Cent values of equal temperament Read more here: » Musical acoustics: Encyclopedia II - Musical acoustics - Sound waves |
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| | | | | just intonation: 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 can be inverted and phase shifted and be exactly the same. If the wave has any even harmonics (0f, 2f, 4f, 6f, ...), it will be asymmetrical; the top half will not be a mirror image of the bottom.
The opposite is also true. A system which changes the shape of the wave (beyond simple scaling or shifting) creates additional harmonics (harmonic distortion). This is called a non-linear system< ...
See also:Musical acoustics, Musical acoustics - Methods and fields of study, Musical acoustics - Sound waves, Musical acoustics - Harmonics partials and overtones, Musical acoustics - Harmonics and non-linearities, Musical acoustics - Harmony, Musical acoustics - The natural scale, Musical acoustics - Evolution of the natural scale, Musical acoustics - The equal tempered scale, Musical acoustics - Cent values of equal temperament Read more here: » Musical acoustics: Encyclopedia II - Musical acoustics - Harmonics and non-linearities |
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| | | | | just intonation: 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 above the fundamental. All of the frequency components that make up the total waveform, including the fundamental and the overtones, are called partials.
Overtones which are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic, but not exact, it is sometimes called a harmonic partial, although they are often referred to simply as harmonics. Sometimes overtones are created that are not anywhere ...
See also:Musical acoustics, Musical acoustics - Methods and fields of study, Musical acoustics - Sound waves, Musical acoustics - Harmonics partials and overtones, Musical acoustics - Harmonics and non-linearities, Musical acoustics - Harmony, Musical acoustics - The natural scale, Musical acoustics - The equal tempered scale, Musical acoustics - Cent values of equal temperament Read more here: » Musical acoustics: Encyclopedia II - Musical acoustics - Harmonics partials and overtones |
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| | | | | just intonation: 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 sequence, the difference in frequency increases from one to the next. A linear sequence of one frequency difference would create ever smaller intervals (ratios), such as the harmonic series. See also logarithmic scale.
Equal temperaments allow the use of integer notation; a single integer can be used to represent the pitch. The pitch classes can then be expressed in terms of modular arithmetic modulo the number of divisions of the octave, and this expedites mathematic ...
See also:Equal temperament, Equal temperament - Explanation, Equal temperament - History, Equal temperament - Twelve-tone equal temperament, Equal temperament - Cent values of equal temperament, Equal temperament - Non-12 TET, Equal temperament - Sources Read more here: » Equal temperament: Encyclopedia II - Equal temperament - Explanation |
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| | | | | | just intonation: 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 measured by Morton (1974) "varied only plus or minus 5 cents," from 7-tET. A Ugandan Chop xylophone measured by Haddon (1952) also tuned to 171 cent steps. Gamelans are tuned to 5-tET according to Kunst (1949), but according to Hood (1966) and McPhee (1966) their tuning varies widely and according to Tenzer (2000) contain stretched octaves. It is now well-accepted that of the two primary tuning systems in Ga ...
See also:Equal temperament, Equal temperament - Explanation, Equal temperament - History, Equal temperament - Twelve-tone equal temperament, Equal temperament - Cent values of equal temperament, Equal temperament - Non-12 TET, Equal temperament - Sources Read more here: » Equal temperament: Encyclopedia II - Equal temperament - Non-12 TET |
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| | | | | | just intonation: 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 register, a fiber. This gives what might be called a fibered picture of pitch space.
Less well known is the fact that a fibered picture of pitch space can also be obtained where the base space is a chordal space. For instance, suppose 2^a 3^b 5^c is a five-limit interval. If the base space is a chordal space of triads, and if each fiber consists of the integers, we may represent the five-limit interv ...
See also:Pitch space, Pitch space - History of pitch space, Pitch space - Fibered pitch space, Pitch space - External link Read more here: » Pitch space: Encyclopedia II - Pitch space - Fibered pitch space |
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| | | | | just intonation: 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 inverted and phase shifted and be exactly the same. If the wave has any even harmonics (0f, 2f, 4f, 6f, ...), it will be asymmetrical; the top half will not be a mirror image of the bottom.
The opposite is also true. A system which changes the shape of the wave (beyond simple scaling or shifting) creates additional harmonics. This is called a non-linear system. If it affects the wave symmetrically, the harmonics produced will only be odd, if asymmetrically, a ...
See also:Musical acoustics, Musical acoustics - Methods and fields of study, Musical acoustics - Sound waves, Musical acoustics - Harmonics partials and overtones, Musical acoustics - Harmonics and non-linearities, Musical acoustics - Harmony, Musical acoustics - The natural scale, Musical acoustics - The equal tempered scale, Musical acoustics - Cent values of equal temperament Read more here: » Musical acoustics: Encyclopedia II - Musical acoustics - Harmonics and non-linearities |
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| | | | | just intonation: Encyclopedia II - Barbershop music - Notable artists
Barbershop music - Quartets.
Acoustix, 1990 international quartet champions
Bluegrass Student Union, 1978 international quartet champions
The Buffalo Bills, 1950 international champions, appeared in stage and screen productions of The Music Man, frequently appeared on Arthur Godfrey's radio show
The Chordettes, women's quartet, recorded a number of mainstream popular hits during the 1950s, notably Mr. Sandman
The Dapper Dans of Disney, who regularly sing to visitor ...
See also:Barbershop music, Barbershop music - Ringing chords, Barbershop music - Historical origins, Barbershop music - Female Barbershop music and Beautyshop quartets, Barbershop music - Organization, Barbershop music - Notable artists, Barbershop music - Quartets, Barbershop music - Choruses, Barbershop music - Typical Barbershop Songs Read more here: » Barbershop music: Encyclopedia II - Barbershop music - Notable artists |
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| | | | | just intonation: 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 will still be periodic with a short period, and the combination will sound consonant. For instance, a note vibrating at 200 Hz and a note vibrating at 300 Hz (a perfect fifth, or 3/2 ratio, above 200 Hz) will add together to make a wave that repeats at 100 Hz: every 1/100 of a second, the 300 Hz wave will repeat thrice and the 200 Hz wave will repeat twice. Note that the total wave repeats at 100 Hz, but there is not ac ...
See also:Musical acoustics, Musical acoustics - Methods and fields of study, Musical acoustics - Sound waves, Musical acoustics - Harmonics partials and overtones, Musical acoustics - Harmonics and non-linearities, Musical acoustics - Harmony, Musical acoustics - The natural scale, Musical acoustics - Evolution of the natural scale, Musical acoustics - The equal tempered scale, Musical acoustics - Cent values of equal temperament Read more here: » Musical acoustics: Encyclopedia II - Musical acoustics - Harmony |
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| | | | | just intonation: 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 melody cannot be played starting from a random note of the scale. For instance, a melody starting with the two notes C and D (ratio 9/8) cannot be transposed one tone higher, since the ratio of the frequencies of E and of D is very near ((5/4)/(9/8) = 10/9), but not equal to 9/8.
To obviate this inconveniency, we today use the so-called Equal Temperament, which constitutes the compromise adopted in moder ...
See also:Musical acoustics, Musical acoustics - Methods and fields of study, Musical acoustics - Sound waves, Musical acoustics - Harmonics partials and overtones, Musical acoustics - Harmonics and non-linearities, Musical acoustics - Harmony, Musical acoustics - The natural scale, Musical acoustics - Evolution of the natural scale, Musical acoustics - The equal tempered scale, Musical acoustics - Cent values of equal temperament Read more here: » Musical acoustics: Encyclopedia II - Musical acoustics - The equal tempered scale |
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| | | | | just intonation: 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 above the fundamental. All of the frequency components that make up the total waveform, including the fundamental and the overtones, are called partials.
Overtones which are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic, but not exact, it is sometimes called a harmonic partial, although they are often referred to simply as harmonics. Sometimes overtones are created that are not anywhere ...
See also:Musical acoustics, Musical acoustics - Methods and fields of study, Musical acoustics - Sound waves, Musical acoustics - Harmonics partials and overtones, Musical acoustics - Harmonics and non-linearities, Musical acoustics - Harmony, Musical acoustics - The natural scale, Musical acoustics - Evolution of the natural scale, Musical acoustics - The equal tempered scale, Musical acoustics - Cent values of equal temperament Read more here: » Musical acoustics: Encyclopedia II - Musical acoustics - Harmonics partials and overtones |
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| | | | | just intonation: 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 of the three main barbershop associations, which have a combined membership in the neighborhood of eighty thousand.
The primary men's organization in the US and Canada is the Barbershop Harmony Society. also known as the Society for the Preservation and Encouragement of Barber Shop Quartet Singing in America (SPEBSQSA). Women have two organizations in North America, Swee ...
See also:Barbershop music, Barbershop music - Ringing chords, Barbershop music - Historical origins, Barbershop music - Female Barbershop music and Beautyshop quartets, Barbershop music - Organization, Barbershop music - Notable artists, Barbershop music - Quartets, Barbershop music - Choruses, Barbershop music - Typical Barbershop Songs Read more here: » Barbershop music: Encyclopedia II - Barbershop music - Organization |
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| | | | | | | just intonation: 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. Many of these intervals describe small discrepancies between notes tuned according to the tuning systems used. Most of the following intervals may be described as microtones.
A Pythagorean comma is the difference between twelve justly tuned perfect fifths and seven octaves. It is expressed by the frequency ratio 531441:524288, and is equal to 23.46 cents
A syntonic comma ...
See also:Interval music, Interval music - Frequency ratios, Interval music - Interval number and quality, Interval music - Shorthand notation, Interval music - Enharmonic intervals, Interval music - Steps and skips, Interval music - Pitch class intervals, Interval music - Ordered and unordered pitch and pitch class intervals, Interval music - Generic and specific intervals, Interval music - Cents, Interval music - Comparison of different interval naming systems, Interval music - Consonant and dissonant intervals, Interval music - Inversion, Interval music - Interval roots, Interval music - Interval cycles, Interval music - Other intervals, Interval music - Sources Read more here: » Interval music: Encyclopedia II - Interval music - Other intervals |
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| | | | | just intonation: Encyclopedia II - Barbershop music - Notable artists
Barbershop music - Quartets.
Acoustix, 1990 international quartet champions
Bluegrass Student Union, 1978 international quartet champions
The Buffalo Bills, 1950 international champions, appeared in stage and screen productions of The Music Man, frequently appeared on Arthur Godfrey's radio show
The Chordettes, women's quartet, recorded a number of mainstream popular hits during the 1950s, notably Mr. Sandman
The Dapper Dans of Disney, who regularly sing to visitor ...
See also:Barbershop music, Barbershop music - Historical origins, Barbershop music - Female Barbershop music and Beautyshop quartets, Barbershop music - Organizations, Barbershop music - Notable artists, Barbershop music - Quartets, Barbershop music - Choruses, Barbershop music - Typical Barbershop Songs Read more here: » Barbershop music: Encyclopedia II - Barbershop music - Notable artists |
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