Note: I misunderstood the question, and responded to mediant keys instead of mediant pitches. However, in such cases the ^7 is a non-chord tone decorative in natural rather than a functional scale degree. It could be pointed out that the raised ^7 could be used in a melodic passage over the iv or i chords or perhaps other cases where the chord involved is not a dominant. The main point of the outline above is the mediant in minor is not an augmented chord and the raised ^7 is an alteration used to form dominant chords of the minor tonic. this chord has a strong tendency to move to the relative major key in which case it is a dominant but of the mediant III rather than i.it's not a dominant (relative to the tonic i) so the ^7 is not raised.in the case that the ^7 is not raise the quality is minor where a common use would not be root position but inverted as in a descending progression i v6 iv6 V.in the case of a functional dominant the quality is major.to make a proper, functional dominant we must raise ^7.functionally this chord is weak, not normally used in minor except when modulating to the mediant (relative major) in which case it really becomes the 'tonic'.it is not a dominant so the raised ^7 is not used.Let's review these root position chord: III the ^7 degree is raised to create a dominant chord.the diatonic scale is used for the scale degrees.I thought it would be good to add some additional explanation regarding minor harmony, the raised ^7 scale degree, and the root position chords of the ^3, ^5, and ^7 scale degrees. While there isn't a distinction for the degree names, there is on for solfege syllables. So the third scale degree in major is called "mi" but in minor it can be called "ma" or "me." You question seemed to be searching for a major/minor distinction in scale degree names. While you did not ask specifically you may be interested to know that the solfege syllables do have variations for major/minor. The natural minor has a subtonic as its seventh degree. So, in minor, the harmonic and melodic minor scales have a leading tone as their seventh scale degree. The leading tone will always be a half-step below the tonic. The scale degree names are the same between major and minor.
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