Fact Check - 5. Music, Temperament, and Social Concord
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Query: 5. Music, Temperament, and Social Concord
Fact Check
Quoted text:
Setting the intervals by fifths (3:2 ratios) produced one mathematical-tonal series, doing so by thirds (5:4 or 6:5 for the major and minor third respectively) another.
Calendar-makers solved this problem by setting a year-end “time out of time.” After all, they hardly could take an average of 360 days and lengthen each day. The sun rose and set 365 1/4 times each calendrical year as measured by the sun, and there was nothing to do but add some extra days.
But musicians found a different solution available—indeed, dictated. They hardly could add an “extra note” to the gamut of octaves. (If they had, there would be two separate keys for G♯ and A♭ in one of the higher octaves.) Musical tuners did what calendar-makers could not do: Having drawn an analogy comparing musical tones and octaves to the days and months of the year, they then adjusted each tone slightly, so as to temper each tone by just enough so that there would be no “large” disparities developing among the “later generations” of tones such as G♯/A♭. At least, this was the “equal temperament” system developed thousands of years before Bach took the great step toward re-establishing the tendency with his Well-Tempered Clavier in 1722.Can a music expert check that this makes sense?
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