George Secor

George Secor (November 8, 1943 – March 2, 2020^[1]) was an American musician, composer and music-theorist from Chicago.^[2] He was the discoverer of miracle temperament and eponym of the secor.

As an inventor, Secor and Hermann Pedtke's Motorola Scalatron (1974) is an example of a Bosanquet

A YouTube channel with some of George's performances on Moschino Accordions illustrates his abilities on their unique keyboard, which allows for chromatic runs and open chords with the left-hand buttons, a Free-bass system, rather than the more common Stradella bass system, which has fewer bass notes, plus preset chord buttons.

George was interviewed in 2018 about the origin and organization of the Moschino accordion system here.

The Moschino Accordion System Explained

The system is explained in a video Additionally, a written discussion of the organization of the system, including Georges own explanations and diagrams is included on accordionists.info.

Secor interval

In music, a secor is the interval of 116.7 cents ( ( 18 / 5 )^1 / 19 ) Play^ⓘ 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.^[4]

It is approximated in 31 Play^ⓘ, 41 Play^ⓘ, and 72 equal temperament Play^ⓘ.^[4] For tuning purposes, a secor of seven steps of 72 equal temperament is often used.

Two secors (233.4 cents Play^ⓘ) approximate an 8:7 interval (231.17 cents), a septimal whole tone. Three of these 8:7 intervals (693.51 cents), or 6 secors (700.2 cents Play^ⓘ), approximate a fifth (701.96 cents). A neutral third of  11 / 9 (347.41 cents) is approximated by 3 secors (350.1 cents Play^ⓘ).

Miracle temperament

In music, miracle temperament is a

${\displaystyle \left({\tfrac {15}{14}}\div {\tfrac {16}{15}}={\tfrac {225}{224}}\right)}$ is tempered out, and two secors give an 8:7 interval, a

${\displaystyle \left({\tfrac {3}{2}}\div \left({\tfrac {8}{7}}\right)^{3}={\tfrac {1029}{1024}}\right)}$

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 (Play

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

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

>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