Miracle temperament
Encyclopedia
In music
, miracle temperament is a regular
temperament discovered by George Secor which has as a generator an interval, called the secor
, that serves as both the 15:14 and 16:15 semitones. Because 15:14 and 16:15 are equated, their ratio 225:224
is tempered out, and two secors give an 8:7 interval, a septimal whole tone
. Three of these 8:7 intervals, or six secors, make up a fifth, so that 1029:1024
is also tempered out. This gives the 7-limit
version of miracle.
A septimal whole tone of 8:7 as we have seen is approximated by two secors, and a neutral third of 11:9 by three secors. In miracle, a minor third plus a septimal whole tone is also equated with the 11th harmonic
. This means that the gap between a minor third plus a septimal whole tone
and the 11th harmonic (an 11:8 ratio), 385:384 
., is also tempered out. Miracle, therefore, is the temperament tempering out 225:224, 1029:1024 and 385:384 at the same time.
For tuning purposes, a secor of seven steps of 72 equal temperament
can be used. While this also tempers out 4375:4374 (the ragisma
), doing this is not regarded as a part of the definition of miracle temperament.
Miracle temperament, particularly in the distributionally even scale known as Blackjack, a scale of twenty-one notes derived from twenty successive secors, has been used by several composers, including New York composer Joseph Pehrson
.
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
, miracle temperament is a regular
Regular temperament
Regular temperament is any tempered system of musical tuning such that each frequency ratio is obtainable as a product of powers of a finite number of generators, or generating frequency ratios...
temperament discovered by George Secor which has as a generator an interval, called the secor
Secor (interval)
In music, a secor is the interval of 116.7 cents named after George Secor, discoverer of miracle temperament.It is approximated in 31 , 41 , and 72 equal temperament . For tuning purposes, a secor of seven steps of 72 equal temperament is often used....
, that serves as both the 15:14 and 16:15 semitones. Because 15:14 and 16:15 are equated, their ratio 225:224
is tempered out, and two secors give an 8:7 interval, a septimal whole toneSeptimal whole tone
In music, the septimal whole tone, septimal major second, or supermajor second is the musical interval exactly or approximately equal to a 8/7 ratio of frequencies. It is about 231 cents wide in just intonation. Although 24 equal temperament does not match this interval particularly well, its...
. Three of these 8:7 intervals, or six secors, make up a fifth, so that 1029:1024
is also tempered out. This gives the 7-limitLimit (music)
In music theory, limit or harmonic limit is a way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale. The term was introduced by Harry Partch, who used it to give an upper bound on the complexity of harmony; hence the name...
version of miracle.
A septimal whole tone of 8:7 as we have seen is approximated by two secors, and a neutral third of 11:9 by three secors. In miracle, a minor third plus a septimal whole tone is also equated with the 11th harmonic
Harmonic
A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...
. This means that the gap between a minor third plus a septimal whole tone
and the 11th harmonic (an 11:8 ratio), 385:384 ., is also tempered out. Miracle, therefore, is the temperament tempering out 225:224, 1029:1024 and 385:384 at the same time.For tuning purposes, a secor of seven steps of 72 equal temperament
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
can be used. While this also tempers out 4375:4374 (the ragisma
Ragisma
In music and tuning, the ragisma is an interval with the ratio of 4375:4374, ≈0.396 cents. It is usually defined as the difference between the septimal minor third and two Bohlen-Pierce small semitones . It is also the difference between minor Bohlen-Pierce diesis and septimal semicomma ....
), doing this is not regarded as a part of the definition of miracle temperament.
Miracle temperament, particularly in the distributionally even scale known as Blackjack, a scale of twenty-one notes derived from twenty successive secors, has been used by several composers, including New York composer Joseph Pehrson
Joseph Pehrson
- Life :Pehrson comes from Detroit, Michigan. He studied at the University of Michigan and Eastman School of Music. . His teachers include Leslie Bassett, Joseph Schwantner, Otto Luening and Elie Siegmeister. From 1992 to 1993 he was composer-in-residence at the University of Akron. Since 1983 he...
.