George Secor

(Redirected from Miracle temperament)

George Secor (born November 8, 1943), a composer from Chicago,[1] is the discoverer of miracle temperament and eponym of the secor.

Secor and Hermann Pedtke's Motorola Scalatron (1974) is a Bosanquet generalized keyboard featuring a multicolored arrangement of 240 tunable oval keys, about which Secor said: "There is not much point in using this alternative keyboard for systems below 31 tones in the octave."[2] However, "even if it were completely impractical musically, it would make a wonderful prop for a futuristic movie."[2] Though its synthesizer capacities may not reach performance level, according to Easley Blackwood, "It has rock-steady tuning capabilities; you can always count on it to be right."[2]

Secor

7-limit 8:7 septimal whole tone .

In music, a secor is the interval of 116.7 cents ((18/5)(1/19))   named after George Secor. Secor devised it to allow a close approximation, generated from a single interval, to Harry Partch's 43 tone just intonation scale. All 11-limit consonances are approximated to within 3.32 cents.[3]

It is approximated in 31  , 41  , and 72 equal temperament  .[3] For tuning purposes, a secor of seven steps of 72 equal temperament is often used.

Two secors (233.4  ) approximate an 8:7 interval (231.17), a septimal whole tone. Three of these 8:7 intervals (693.51), or six secors (700.2  ), approximate a fifth (701.96). A neutral third of 11:9 (347.41) is approximated by three secors (350.1  ).

Miracle temperament

In music, miracle temperament is a regular temperament discovered by George Secor in 1974 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 ${\displaystyle \left({\tfrac {15}{14}}\div {\tfrac {16}{15}}={\tfrac {225}{224}}\right)}$ 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 ${\displaystyle \left({\tfrac {3}{2}}\div \left({\tfrac {8}{7}}\right)^{3}={\tfrac {1029}{1024}}\right)}$ is also tempered out. This gives the seven-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 ${\displaystyle \left({\tfrac {8}{7}}\times {\tfrac {6}{5}}={\tfrac {48}{35}}\right)}$ and the 11th harmonic (an 11:8 ratio), 385:384 ${\displaystyle \left({\tfrac {11}{8}}\div {\tfrac {48}{35}}={\tfrac {385}{384}}\right)}$., 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 ten note Miracle scale ( ) and the distributionally even scale known as Blackjack ( ). The twenty-one note Blackjack scale is derived from twenty successive secors and has been used by several composers, including New York composer Joseph Pehrson.[4]

s is a secor, q is the difference between 10 secors and 1 octave, and r is the difference between s and q. If the Miracle scale is
0    1    2    3    4    5    6    7    8    9       0'
s    s    s    s    s    s    s    s    s    s    +q
q +r q +r q +r q +r q +r q +r q +r q +r q +r q +r +q

then the Blackjack scale is
0 >0 1 >1 2 >2 3 >3 4 >4 5 >5 6 >6 7 >7 8 >8 9 >9 <0 0'
q  r q  r q  r q  r q  r q  r q  r q  r q  r q  r  q


this may also be viewed as a chain of 20 secors:

>0 >1 >2 >3 >4 >5 >6 >7 >8 >9 0 1 2 3 4 5 6 7 8 9 <0
s  s  s  s  s  s  s  s  s  s s s s s s s s s s s


References

1. ^ Barbieri, Patrizio (2008). Enharmonic: Instruments and Music 1470-1900; revised and translated studies, p.96. Il Levante Libreria Editrice. ISBN 9788895203140.
2. ^ a b c Vail, Mark (2000). 9780879306038, p.101. Backbeat Books. ISBN 9780879306038.
3. ^ a b "Secor", TonalSoft.com. Accessed: July 2013
4. ^ "Miracle Temperaments", Xenharmony.