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I am using Ear Master for ear training and at the Chord Progression exercises, there is an exercise called "Various dominant-tonic combinations".

These are the chord progressions that are being played:

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I can understand why VIIdim7 can be played as a dominant, but why is bII 7(b5) considered dominant?

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bII7(b5) is a tritone substitution of the original dominant V7. Note that the roots of the two chords are a tritone apart, and the 7th of one chord equals the 3rd of the other chord and vice versa, so they share the most important chord tones.

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This is a form of tritone substitution, and is considered one of the basic substitutions in jazz. The idea is that you replace a chord (typically a dominant chord) with one a tritone away. (Recall: a tritone, TT, is 3 whole steps, which is the distance of either an augmented fourth or a diminished fifth).

The reason this substitution works lies in the symmetry of the TT - it is exactly half an octave, so it is its own inversion. This lends it to a certain ambiguity. Consider the G7 chord (G B D F). There is a TT between the B (the 3rd of the chord) and the F (the 7th of the chord). But there is also a tritone between the F and the B, so we can reimagine the F as the third of some chord, and the B as its seventh (except now we have to call the B a Cb, to reflect that it is a fifth above the F).

The chord for which F is the 3rd and Cb is the 7th is Db7 (Db F Ab Cb), so we can use that chord. It's root happens to be a TT away from our original G7.

The deal with the (b5) being used just makes it even closer to the original chord. This would replace the Ab with Abb, which is the same pitch as G. So this gives us a very ambiguous chord: It's either a G7(b5) or a Db7(b5), but it has the same pitches both ways (just "spelled" differently):

(G B Db F) vs (Db F Abb Cb)

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    Another motivation for this substitution is the smooth chromatic progression in the bass. Your typical jazz progression is ii7-V7-IM7, where the bass jumps from 2 to 5 to 1. But with this substitution, the bass just walks down by half steps: ii7-bII7(b5)-IM7. – Caleb Hines May 26 '14 at 13:58
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Tritone substitution is the reason, but it could also resolve to a Imaj.It doesn't have to be a Imaj7, the resolution is more marked to a standard major, as the leading note is there in the TTsub. moving to the root, rather than remaining sounded.(The B/Cb stated in Caleb's answer).

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