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So many schemes of intonation with a goal of getting beyond equal temperament end up hitting a giant rock: the number 12, or a diatonic 7. There is NO reason for a set of pitches used in music to be twelve in number.

With the low and high RE, the FI, and the TE, a very simple diatonic set of pitches contains 10 notes, with which much music from the Renaissance to the Rock and Roll can be put into sound. Not 7!!! See “Ein Feste Burg” below, where the RE of the first two systems should be tuned low and the RE of the final system should be tuned high. The third system could easily use a FI (F#) in end of the first bar, many transcriptions do.