How is meantone temperament calculated?
The formula for successive equal temperament 12-notes-to-an-octave semitones (called 12tet) is a frequency ratio of one to the twelfth root of two ( 12√2 or 21/12), which approximately equals ~1:1.05946. As an example, to find the frequency of the A# semitone above A440, multiply 440 by 1.05946 to get ~466.163.
How many cents is a comma?
For instance, the Pythagorean comma (531441:524288, or about 23.5 cents) can be computed as the difference between a chromatic and a diatonic semitone, which is the opposite of a Pythagorean diminished second (524288:531441, or about −23.5 cents).
What is a syntonic comma interval?
In music theory, the syntonic comma, also known as the chromatic diesis, the Didymean comma, the Ptolemaic comma, or the diatonic comma is a small comma type interval between two musical notes, equal to the frequency ratio 81:80 (= 1.0125) (around 21.51 cents).
Is Meantone just intonation?
Meantone temperament provided an alternative to just intonation, which derived the proper tuning of all the intervals in the scale by various additions and subtractions of perfect natural fifths and thirds (in tune with the fifths and thirds found in the natural harmonic series, perceivable as faint overtones above a …
What do you think a scale in 1/4 tones means?
A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, and have 24 different pitches.
How many commas make a tone?
9 commas
The tone. A tone is formed of a chromatic semitone and a diatonic semitone. It therefore has a total of 9 commas.
What is a comma in musical tuning?
comma, in music, slight difference in frequency (and therefore pitch) occurring when a note of a scale, say E in the scale of C, is derived according to different systems of tuning. There are two commonly cited commas, the Pythagorean comma and the comma of Didymus, or syntonic comma.
What is a comma pump?
A comma pump is a harmonic sequence (or chord progression) wherein the tuning base shifts up or down by one comma.
What is the wolf fifth?
In music theory, the wolf fifth (sometimes also called Procrustean fifth, or imperfect fifth) is a particularly dissonant musical interval spanning seven semitones.
What is the difference between just intonation and equal temperament?
Equal temperament pretends you can have it both ways; Just Intonation makes a conscious choice about which intervals matter most. In meantone tuning, the thirds are kept as perfect as they can be, and the maths tries to ‘lose’ the discrepancy within the fifths by spreading the awkward ratio over more octaves.
What is quarter-comma temperament?
Quarter-comma meantone, which tempers the fifths by 1/4 comma, is the best known type of meantone temperament, and the term meantone temperament is often used to refer to it specifically.
What is the difference between meantone and meantone temperament?
While the term meantone temperament refers primarily to the tempering of 5-limit musical intervals, temperaments that approximate 5-limit intervals well, such as Quarter-comma meantone, can also approximate 7-limit intervals well, defining septimal meantone temperament.
What is the difference between a third and a quarter comma?
Quarter-comma meantone produces the “just” major third (5:4, 386 cents, a syntonic comma lower than the Pythagorean one of 408 cents). Third-comma meantone produces the “just” minor third (6:5, 316 cents, a syntonic comma higher than the Pythagorean one of 294 cents).
What is the difference between meantone and septimal meantone temperament?
While the term meantone temperament refers primarily to the tempering of 5-limit musical intervals, temperaments that approximate 5-limit intervals well, such as Quarter-comma meantone, can also approximate 7-limit intervals well, defining septimal meantone temperament. In Figure 1, the valid tuning ranges of 5-limit, 7-limit,…