I was reading a lesson on modulation elsewhere and it said:

For instance to modulate from C major to e minor, we could use the progression

C - F - G - a - B - e

In this context, a is the pivot chord - it is approached as vi of C major but quitted as iv, in the cadential progression iv - V - i, of e minor.

My question relates to that Bmajor****er right there.

C major key - Cmaj, dmin, emin, Fmaj, G7, Amin, Bdim
E minor key - Emin, Fdim, Gmaj, amin, bmin, Cmaj, D7

So we're rocking in a I, IV, V in Cmaj and having a great time and everything, then we begin our modulation to e minor by using a minor as the pivot chord, we then go up to Bmajor which becomes the new V, and then complete the modulation by moving the tonal centre to Emin.

I know that the perfect cadence (Bmaj to Emin) is stronger than a v-I ending, but how comes the Bmaj creates resolution when it is neither present in both keys?
Yeah Bmaj is in neither key, but remember the major 3rd of Bmajor is D# (E flat). This means that when you play the Bmaj chord you are playing the D# so when you play the Eminor next, the note is being resolved as you are going from the notes D# to E. Hence the perfect cadence.

Thats what I can gather from the question.
B major is diatonic to the key of E minor, it comes from the harmonic minor scale.
Quote by Calibos
[...]
I know that the perfect cadence (Bmaj to Emin) is stronger than a v-I ending, but how comes the Bmaj creates resolution when it is neither present in both keys?

What micardo said. The Bmaj chord contains the D#, which is a semitone away from E. The `being a semitone away' bit is what's important here. It's used most notably in jazz all the time, where if you want to resolve to something you tend to approach it with chords that contain notes that are only a semitone away from the important notes in the next chord.

Makes sense?
I was gonna say if it were B7 to Emajor it would be the tritone resolving,

D# and A to E and G#
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How dare you attack the greatness of the augmented sixth?
TS, you answered your own question. It's a dominant. Who cares if it's "not in either key." It's a dominant to E minor.
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So how would you modulate to, say, D minor from C major?

Cmaj, Fmaj, Gmaj, Amaj, Dmin?

I'm guessing the C# in Amaj leads quite nicely into the D?
.
Quote by Calibos
So how would you modulate to, say, D minor from C major?

Cmaj, Fmaj, Gmaj, Amaj, Dmin?

I'm guessing the C# in Amaj leads quite nicely into the D?
.

That's one good way of doing it. The C# in Amaj is a semitone away from the D, so it would make sense doing that. Ofcourse it's not the only way to do it.
Quote by willemhdb
That's one good way of doing it. The C# in Amaj is a semitone away from the D, so it would make sense doing that. Ofcourse it's not the only way to do it.

Could you provide another example please? Modulation is one of those things i'm never too sure about so any help would be much appreciated.

I've read also that the diminished chord can also be exploited because of it's instability.

Also, as noted earlier, the VIIm can sometimes substitute for VIIº, as these chords have two notes in common.

Can anyone provide an example?
Quote by Calibos
Could you provide another example please? Modulation is one of those things i'm never too sure about so any help would be much appreciated.
Ok, here's an example without the use of the dominant:

C F G Am Bb C (Dm). In this case Am is the pivot chord. It separates the major cadence from the minor cadence.

Quote by Calibos
I've read also that the diminished chord can also be exploited because of it's instability.
The diminished seventh chord definitely. Because of it's construction (stacked minor thirds) its root is very ambiguous. Its inversions are all diminished seventh chords of their own. Because of this, it can be used as a dominant to any of four other chords (a half-step above any given chord tone).

The diminished triad is pretty unstable itself, due to the diminished fifth. I personally don't like diminished triads as much because I feel they are basically just rootless dominant seventh chords. Like dominant seventh chords, though, they are pretty unstable and can be used for multiple purposes. For example, you can use a dominant seventh chord as either a V7 or a bII7 (tritone sub). Likewise, you can omit the root of these and they become diminished triads, which can be used for the same two functions.

They can also be used as rootless diminished seventh chords, which opens up the possibilities I mentioned at the beginning.

Quote by Calibos
Can anyone provide an example?
What do you mean? Bm in the key of C would be a substitution of this type. Do you want to see how this might function in a progression?
Only play what you hear. If you don’t hear anything, don’t play anything.
-Chick Corea
Quote by food1010
Ok, here's an example without the use of the dominant:

C F G Am Bb C (Dm). In this case Am is the pivot chord. It separates the major cadence from the minor cadence.

Sorry, but i've not heard of a major or minor cadence, but i'm guessing the major is the tone from G to A and minor the semitone to Bb?

The diminished seventh chord definitely. Because of it's construction (stacked minor thirds) its root is very ambiguous. Its inversions are all diminished seventh chords of their own. Because of this, it can be used as a dominant to any of four other chords (a half-step above any given chord tone).

So in Cmaj - C, F, G, a, Bdim7, F#?

What do you mean? Bm in the key of C would be a substitution of this type. Do you want to see how this might function in a progression?

Yeah I was meant to ask how it would function, sorry.

Where can I learn this stuff? Or what should I know to better understand this, I know the circle of 5ths and I know what chords are in which keys, what else do I need to know? cos this is like looking at MT for the first time and it's pissing me off my feeble brain cannot comprehend.
Quote by Calibos
Sorry, but i've not heard of a major or minor cadence, but i'm guessing the major is the tone from G to A and minor the semitone to Bb?
Well I kind of just made up those phrases. What I mean by "major cadence" is a part of a progression that is in a major key, and what I mean by "minor cadence" is a part of a progression that is in a minor key.

C F G is a progression in C major. Bb C Dm is a progression in D minor. That's all I meant by that.

Quote by Calibos
So in Cmaj - C, F, G, a, Bdim7, F#?
Yes sort of. Although, it's still going to take a little more than that to modulate by a tritone. The problem is that C major and F# major only share two notes (C/B# and F/E#) in common, plus these are only enharmonics anyway. You need a little more than a diminished seventh chord to make that transition. As odd as it may sound, you could use G as a pivot chord and the Bdim7 to confirm the resolution. Try this:

C Am F G A G F# Bdim7 (F#)

As (I think) I was talking about earlier, the G now functions kind of like a tritone substitution. This is using that Spanish-sounding bIII bII I progression. In fact, the A major chord can be seen as a pivot chord as well (even though it's not diatonic, it's a V/ii or VI, which is pretty easily usable in major keys).

Quote by Calibos
Yeah I was meant to ask how it would function, sorry.
Well it could always function as some odd sort of dominant. It contains the key's 7 2 and #4, all which resolve pretty well to the notes of the tonic. It could also be seen as a substitution from G major (iii/V if you were to use the idea of secondary dominant notation).

Quote by Calibos
Where can I learn this stuff? Or what should I know to better understand this, I know the circle of 5ths and I know what chords are in which keys, what else do I need to know? cos this is like looking at MT for the first time and it's pissing me off my feeble brain cannot comprehend.
A lot of the stuff you can learn from studying music, then asking here or looking up whatever questions you have about things that are unfamiliar.
Only play what you hear. If you don’t hear anything, don’t play anything.
-Chick Corea
Quote by Calibos
Could you provide another example please? Modulation is one of those things i'm never too sure about so any help would be much appreciated.

I've read also that the diminished chord can also be exploited because of it's instability.

Say, you're playing something in C major. The usual way to resolve back to the tonic is to play a V-I progression. In this case this is Gmaj (or G7) followed by Cmaj.

Now take that V, and replace it with a bVIdim7, in our case this would be a Abdim7. Now play that progression instead of the V-I.

It works because Abdim7 has so three notes in common with G7. The only unstable note in there is the Ab itself, which gets resolved once you play the I.