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A minor third is the same distance as the tonic to the third in a natural minor scale. This is one tone followed by on semi tone, which equates to 3 semi tones. A major sixth would equate to ten semi tones.

If you are going from the sixth of a major scale, to the third of a minor scale, you would be going down by 7 semi tones. However, if you are on the sixth note of a major scale, and go down by a minor third, then you will be going down by 3 semi tones.

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