Theory. Cambridge: Cambridge University Press. ISBN 0521616972. Centaur a 7 limit tuning shows Centaur tuning plus other related 7 tone tunings by others...

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...

intonation, their harmonic limit may be ambiguous. 3-limit (Pythagorean) tuning Five-limit tuning 7-limit tuning Numerary nexus Otonality and Utonality Tonality...

Pythagorean tuning is a broken circle of fifths. This creates two distinct semitones, but because Pythagorean tuning is also a form of 3-limit just intonation...

Pipe organs were the last fixed-tuning instrument to adopt equal temperament. With the transition of organ tuning from meantone to equal-temperament...

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths which are...

distinguish the 5:4 ratio from major thirds created using other tuning methods. 7 limit and higher systems use higher prime number partials in the overtone...

point for comparison, in three-limit tuning the Pythagorean major third is an 81/64 ratio, which is 407.8 cents. A tuning is a choice of pitches in a scale...

thirds of 6/5 plus a septimal minor third of 7/6 and an octave (2/1). This comma is important to certain tuning systems, such as septimal meantone temperament...

extend tuning beyond common-practice, extending music to the 7-limit, including the 7/6 septimal minor third, the 7/5 septimal tritone and the 8/7 septimal...

narrow 7:6 subminor third...The seventh harmonic...was problematic in all Western tuning systems. The interval it forms with the sixth harmonic [7:6 subminor...

F, B♭ (ratios 4:6:7:8:9:12 Play), adding C and E♭ to the magic chord when combined as the magic opening chord (Play). The Well-Tuned Piano is based on...

tempered out by a number of equally tempered tuning systems, including 19-ET, 24-ET and 29-ET; these tunings do not distinguish between the septimal whole...

take a specific alternative name in Pythagorean tuning, five-limit tuning, or meantone temperament tuning systems such as quarter-comma meantone. All the...

with respect to Pythagorean tuning, which can be considered a 3-limit just intonation tuning. Namely, while Pythagorean tuning determines only 2 wolf intervals...

or about 48.77 cents wide. The name derives from the interval being the 7-limit approximation of a quarter tone. The septimal quarter tone can be viewed...

meantone will give four septimal thirds among the twelve major thirds of the tuning; this entails that three septimal major triads appear along with one chord...

possible in 5-limit tuning. 7-limit tuning allows for the justest possible ratios (ratios with the smallest numerator and denominator), namely 7:5 for the...

interval in its own right, or as a comma; if it is tempered out in a given tuning system, the distinction between these two intervals is lost. The septimal...

meanings for tuning: Tuning practice, the act of tuning an instrument or voice. Tuning systems, the various systems of pitches used to tune an instrument...

second play is the musical interval exactly or approximately equal to an 8/7 ratio of frequencies. It is about 231 cents wide in just intonation. 24 equal...

interval 7:5, about 582.51 cents Septimal whole tone, the musical interval exactly or approximately equal to an 8/7 ratio of frequencies 7-limit tuning, musical...

He also describes 7-limit "soft" diatonics and an 11-limit "even" diatonic. This tuning was declared by Zarlino to be the only tuning that could be reasonably...

In musical tuning, a lattice "is a way of modeling the tuning relationships of a just intonation system. It is an array of points in a periodic multidimensional...

In music and tuning, the ragisma is an interval with the ratio of 4375:4374, ≈0.396 cents (a superparticular ratio). It is usually defined as the difference...

ratios most commonly of 250/243 in 5-limit tuning, or of 36/25 in 7-limit tuning. The 5-limit just intonation schisma (ratio 32 805 / 32 768) is a micro-coincidence...

fourth, respectively. The 7:5 interval (diminished fifth) is equal to a 6:5 minor third plus a 7:6 subminor third. The 10:7 interval (augmented fourth)...

S2, S3, S4 are semitones as defined in five-limit tuning#Size of intervals. Notice that for 5-limit tuning, 1⁄6-, 1⁄5-, 1⁄4-, and 1⁄3-comma meantone, the...

v t e Intervals Twelve- semitone (post-Bach Western) Other tuning systems Other intervals List of pitch intervals...

interval of approximately 7.7 cents. Factoring it into primes gives 2−5 32 52 7−1, which can be rewritten 2−1 (5/4)2 (9/7). That says that it is the...