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In musical tuning, a temperament is a system of tuning which slightly compromises the pure intervals of just intonation in order to meet other requirements of the system. In music, there are two common meanings for tuning: Tuning practice The act of tuning an instrument or voice. ...
In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by whole number ratios; that is, by positive rational numbers. ...
In just intonation, every interval between two pitches corresponds to a whole number ratio between their frequencies. Such just intervals have a stability, or purity to their sound. If one of those pitches is adjusted slightly, that stability decreases, and slow changes in the timbre of the interval's sound begin to appear: an effect known as beating. As the adjustment becomes more severe, the beating becomes faster. To intentionally chose an interval with beating as a substitute for a just interval is the act of tempering that interval. These adjustments can make different musical possibilities available to the musician that would be impractical in just intonation. The actual measure of these adjustments are usually called commas. In music theory, an interval is the relationship between two notes or pitches, the lower and higher members of the interval. ...
The whole numbers are the nonnegative integers (0, 1, 2, 3, ...) The set of all whole numbers is represented by the symbol = {0, 1, 2, 3, ...} Algebraically, the elements of form a commutative monoid under addition (with identity element zero), and under multiplication (with identity element one). ...
In number and more generally in algebra, a ratio is the linear relationship between two quantities of the same unit. ...
Sine waves of various frequencies; the lower waves have higher frequencies than those above. ...
In music, timbre, also timber (French, IPA /tæmbər/ as in the first two syllables of tambourine), is the quality of a musical note or sound which distinguishes different types of sound production or musical instruments. ...
In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies. ...
In music theory, a comma is a small or very small interval between two enharmonic notes tuned in different ways. ...
Meantone temperament -
Before Meantone temperament became widely used in the Renaissance, the most commonly used tuning system was Pythagorean tuning. Pythagorean tuning was a system of just intonation which tuned every note in a scale from a progression of pure perfect fifths. This was quite suitable for much of the harmonic practice until then (See: Quartal harmony), but in the Renaissance, musicians wished to make much more use of Tertian harmony. The major third of Pythagorean tuning differed from a just major third by an amount known as Syntonic comma, which musicians of the time found annoyingly impure. Meantone temperament is a system of musical tuning. ...
Renaissance music is European classical music written during the Renaissance, approximately 1400 to 1600. ...
Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. ...
The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ...
Quartal harmonies and quintal harmonies are harmonies based on fourths and fifths rather than the traditional harmonies based on thirds. ...
In music or music theory, tertian is the quality of a chord constructed from thirds, and other things constructed from thirds such as counterpoint. ...
A major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ...
The syntonic comma, also known as the comma of Didymus or Ptolemaic comma, is a small interval between two musical notes, equal to the frequency ratio 81:80, or around 21. ...
Their solution, laid out by Pietro Aron in the early 16th century, was to temper the interval of a perfect fifth slightly narrower than in just intonation, and then proceed much like Pythagorean tuning, but using this tempered fifth instead of the just one. With the correct amount of tempering, the Syntonic comma is removed from its major thirds, making them just. This compromise, however, leaves all fifths in this tuning system with a slight beating. However, because a sequence of four fifths makes up one third, this beating effect on the fifths is only one quarter as strong as the beating effect on the thirds of Pythagorean tuning, which is why it was considered a very acceptable compromise by Renaissance musicians. Pietro Aron (also Pietro Aaron), c. ...
The syntonic comma, also known as the comma of Didymus or Ptolemaic comma, is a small interval between two musical notes, equal to the frequency ratio 81:80, or around 21. ...
Pythagorean tuning also had a second problem, which Meantone temperament does not solve, which is the problem of modulation (see below), which is restricted because both have a broken circle of fifths. A series of 12 just fifths as in Pythagorean tuning does not return to the original pitch, but rather differs by a Pythagorean comma, which makes that tonal area of the system more or less unuseable. In meantone temperament, this effect is even more pronounced (the fifth over the break in the circle is known as the Wolf interval, as its intense beating was likened to a "howling".) 53 equal temperament provides a solution for the Pythagorean tuning, and 31 equal temperament for the Meantone. In music, modulation is most commonly the act or process of changing from one key (tonic, or tonal center) to another. ...
In music theory, the circle of fifths is a geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale. ...
When one ascends by a cycle of justly tuned perfect fifths (ratio 3:2), leapfrogging 12 times, one eventually reaches a note around seven octaves above the note one started on, which, when lowered to the same octave as the starting point, is 23. ...
When the twelve notes within the octave are tuned using meantone temperament, one of the fifths will be much sharper than the rest. ...
In music, 53 equal temperament, called 53-tet, 53-edo, or 53-et, is the scale derived by dividing the octave into fifty-three equally large steps. ...
In music, 31 equal temperament, called 31-tet, 31-edo, or 31-et, is the scale derived by dividing the octave into 31 equally large steps. ...
Well temperament and Equal temperament -
Just intonation has the problem that it cannot modulate to a different key (a very common means of expression throughout the Common practice period of music) without discarding many of the tones used in the previous key, thus for every key the musician wishes to modulate to, his instrument must provide a few more strings, frets, or holes for him to use. When building an instrument, this can be very impractical. Well temperament (or circular temperament) is a type of tuning described in 20th-century music theory. ...
Equal temperament is a scheme of musical tuning in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ...
In music, modulation is most commonly the act or process of changing from one key (tonic, or tonal center) to another. ...
In music theory, the key identifies the tonic triad, the chord, major or minor, which represents the final point of rest for a piece, or the focal point of a section. ...
In music the common practice period is a long period in western musical history spanning from before the classical era proper to today, dated, on the outside, as 1600-1900. ...
Look up String in Wiktionary, the free dictionary. ...
The neck of a guitar showing the first four frets. ...
Well temperament is the name given to a variety of different systems of temperament that were employed to solve this problem. 12 tone equal temperament (12-TET) is the modern standard version of it, and it can be seen as another modification of Pythagorean tuning. Unlinke Meantone temperament, which alters the fifth to temper out the Syntonic comma, 12-TET tempers out the Pythagorean comma, thus creating a cycle of fifths that repeats itself exactly after 12 steps. This allowed the intervals of Tertian harmony, thirds and fifths, to be fairly close to their just counterpoints (the fifths almost imperceptibly beating, the thirds a little milder than the Syntonic beating of Pythagorean tuning), while permitting the freedom to modulate to any key and by various means (e.g. common-tone and enharmonic modulation, see modulation). This freedom of modulation also allowed substantial use of more distant harmonic relationships, such as the Neapolitan chord, which became very important to Romantic composers in the 19th century. Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. ...
Meantone temperament is a system of musical tuning. ...
When one ascends by a cycle of justly tuned perfect fifths (ratio 3:2), leapfrogging 12 times, one eventually reaches a note around seven octaves above the note one started on, which, when lowered to the same octave as the starting point, is 23. ...
In music or music theory, tertian is the quality of a chord constructed from thirds, and other things constructed from thirds such as counterpoint. ...
In music, modulation is most commonly the act or process of changing from one key (tonic, or tonal center) to another. ...
In music theory, a Neapolitan chord is a major chord built on the lowered second (supertonic) scale degree. ...
The era of Romantic music is defined as the period of European classical music that runs roughly from the early 1800s to the first decade of the 20th century, as well as music written according to the norms and styles of that period. ...
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