George Secor

George Secor, a composer from Chicago, 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." However, "even if it were completely impractical musically, it would make a wonderful prop for a futuristic movie." 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."

Secor

7-limit 8:7 septimal whole tone <phonos file="Septimal major second on C.mid">Play 8:7</phonos> <phonos file="Two secors on C.mid">Play two secors</phonos>.

In music, a secor is the interval of 116.7 cents ((18/5)^(1/19)) <phonos file="Secor on C.mid">Play</phonos> 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.

It is approximated in 31 <phonos file="3 steps in 31-et on C.mid">Play</phonos>, 41 <phonos file="4 steps in 41-et on C.mid">Play</phonos>, and 72 equal temperament <phonos file="7 steps in 72-et on C.mid">Play</phonos>. For tuning purposes, a secor of seven steps of 72 equal temperament is often used.

Two secors (233.4 <phonos file="Two secors on C.mid">Play</phonos>) approximate an 8:7 interval (231.17), a septimal whole tone. Three of these 8:7 intervals (693.51), or six secors (700.2 <phonos file="Six secors on C.mid">Play</phonos>), approximate a fifth (701.96). A neutral third of 11:9 (347.41) is approximated by three secors (350.1 <phonos file="Three secors on C.mid">Play</phonos>).

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 $\left(\tfrac{15}{14}\div\tfrac{16}{15} = \tfrac{225}{224}\right)$ 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 $\left(\tfrac{3}{2}\div\left(\tfrac{8}{7}\right)^3 = \tfrac{1029}{1024}\right)$ 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 $\left(\tfrac{8}{7} \times \tfrac{6}{5} = \tfrac{48}{35}\right)$ and the 11th harmonic (an 11:8 ratio), 385:384 $\left(\tfrac{11}{8}\div\tfrac{48}{35} = \tfrac{385}{384}\right)$., 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 (<phonos file="Miracle scale.mid">Play</phonos>) and the distributionally even scale known as Blackjack (<phonos file="Blackjack scale.mid">Play</phonos>). 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.

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

Further reading

• Secor, George (1975). "A New Look at the Partch Monophonic Fabric" Xenharmonikon 3. Frog Peak, N.H. Located at Selected papers of George Secor.

External links

• "George+Secor", Xenharmonic.Wikispaces.com.
• "Miracle Temperaments", Graham's Website: Intonation Information. Accessed: July 2013
• " The Motorola Scalatron ", The Motorola Scalatron on "120 years Of Electronic Music"