An Aeolian Dominant scale can be considered a major scale as its home chord is a major triad. 

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The intervals in this scale after the Tonic note are Major 2nd, Major 3rd, Perfect 4th, Perfect 5th, Minor 6th and Minor 7th. 

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The Swars are Sa, Re, Ga, ma, Pa, dha, ni – all Swars are Shuddh komal dha and ni.

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In a song based on A Aeolian Dominant scale, you would commonly find the triads A, Dm, G. Other triads you can play would be B-dim, C#-dim, Em, F-Aug. Songs based on Raag Charukeshi also use the same notes. Of course, popular songs will often have other chords being played to match the melody and harmony.

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This scale is also equivalent to the 5th mode of the Melodic Minor Scale. For instance, A Aeolian Dominant scale (A, B, C#, D, E, F, G) is also the 5th mode of D Melodic Minor scale (D, E, F, G, A, B, C#). In other words, songs based on both scales can have the same chords, but the home chord will be different. 

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This scale is also referred to as a Mixolydian b6 (Flat 6th) scale. If you take A as your tonic note, A Mixolydian scale will have the notes A, B, C#, D, E, F#, G. And now if you flatten the 6th interval you will get the notes A, B, C#, D, E, F, G which is the above Aeolian Dominant scale.

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Another thing to remember is that this scale is different from the Aeolian scale, which is also known as the Aeolian Mode of the Diatonic Scale or more commonly the Natural Minor Scale. The A Aeolian scale will have the notes A, B, C, D, E, F, G and its home chord will be Am. The A Aeolian Dominant scale will have the notes A, B, C#, D, E, F, G and its home chord will be A.

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Here’s a fretboard diagram showing the notes in an A Aeolian Dominant scale. If you take the 5th note of the scale, which is D, as your Tonic note, you will get the D Harmonic Minor scale (D, E, F, G, A, Bb, C#)