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How are the Aeolian and Ionian modes related to modern minor and major scales?

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The Aeolian and Ionian modes are directly related to modern scales because their pitch series are identical to the natural minor and major scales, respectively.123

In 1547, the Swiss humanist Henricus Glareanus introduced these two modes in his treatise Dodecachordon to better account for the evolving importance of harmony in Western music. By identifying the Aeolian mode (based on A) and the Ionian mode (based on C), Glareanus provided the first formal recognition of the diatonic structures that underpin the modern major scale and minor scale systems.123

While the natural minor scale corresponds exactly to the Aeolian mode, it is frequently subject to chromatic alterations—such as raising the seventh degree—to create the harmonic or melodic minor forms necessary for functional diatonic harmony.3