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# Secor (interval)

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 Title: Secor (interval) Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Secor (interval)

George Secor is the discoverer of miracle temperament and eponym of the secor.

## 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 $\left\left(\tfrac\left\{15\right\}\left\{14\right\}\div\tfrac\left\{16\right\}\left\{15\right\} = \tfrac\left\{225\right\}\left\{224\right\}\right\right)$ 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 $\left\left(\tfrac\left\{3\right\}\left\{2\right\}\div\left\left(\tfrac\left\{8\right\}\left\{7\right\}\right\right)^3 = \tfrac\left\{1029\right\}\left\{1024\right\}\right\right)$ 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 $\left\left(\tfrac\left\{8\right\}\left\{7\right\} \times \tfrac\left\{6\right\}\left\{5\right\} = \tfrac\left\{48\right\}\left\{35\right\}\right\right)$ and the 11th harmonic (an 11:8 ratio), 385:384 $\left\left(\tfrac\left\{11\right\}\left\{8\right\}\div\tfrac\left\{48\right\}\left\{35\right\} = \tfrac\left\{385\right\}\left\{384\right\}\right\right)$., 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 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.

## Secor

In ) named after George Secor.

It is approximated in equal temperament is often used.

Two secors (233.4 )).

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.