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Your Minor 251 substitution of Am is incorrect, as it should be Bdim Em Am. However if you add 7th's, then strictly speaking you then have Bm7b5 Em7 Am7, though fairly frequently this gets altered to Bm7b5 E7 Am7, because this increases the amount of tension that needs resolution.
Firstly you have the "natural minor" way of doing it with the diminished 2 and the minor 5. Which is in keeping with the harmonised chords of the key’s relative major:
ii° - v - i, or
ii° - v7 - i
Or if, as ATD says, you chose to majorize the 5 chord to make the resolution to the 1 chord more effective, which is the "harmonic minor" way and probably the most common way in classical music, it'd be:
ii° - V - i, or
ii° - V7 - i
Despite this being the most common in classical music, it doesn't have a proper name - it's typically known as "a 251 in a minor key, except with a proper dominant, you know, like it's normally done".
And of course, you can do all of the above without diminishing the ii:
For example, you can keep the 5 as a minor chord, which would effectively be playing in Dorian, in which case you'd have:
ii - v - i, or
ii - v7 - i
Or you can majorize the 5 chord as before, but without the diminished 2, which would be the "melodic minor ascending" way, which is very common in modern (and classical) music, which would be:
ii - V - i, or
ii - V7 - i
They're all 251s in a minor key.
Back to the OP; in case you want to taste the different flavours of the four 251 options I wrote, you could sing the 6, 7 and 8 of the scale while the 251 harmony happens underneath. Assuming you're in A minor:
For the natural minor ii° - v - i, you'd sing F G A
For the harmonic minor ii° - V - i, you'd sing F G# A
For the Dorian ii - v - i, you'd sing F# G A
For the Melodic minor ascending ii - V - i, you'd sing F# G# A.