modulation

I'm kinda torn here, Walt. I like helping people out with learning music - that's why I teach for a living. I've got no problem with the first part, different strategies for modulation.

The smoothest way in this instance is through the tonic minor: go from C to Cm. Cm is the relative minor of Eb.

Other strategies would include these:

1. Through secondary dominants. In C, you've got G7 as a dominant chord, which leads to C. If you substitute C7 for C, that has a tension that leads to F. You can keep going, and get from C to Eb by this route: C7 -> F7 -> Bb7 -> Eb

2. Through common chords. There aren't any chords in both C and Eb, but you can do it in a couple of steps. The principle chords of C are C, Dm, Em, F, G (or G7) and Am. In Eb you have Eb, Fm, Gm, Ab, Bb (or Bb7) and Cm. If you took something like the above strategy to go from the key of C to the key of F for a bit... well, F has a Bb chord. You can use that to pivot directly into Eb.

3. Modulation through a sequence. You could do C-Dm-Em... D-Em-F#m... Eb-Fm-Gm. You can include a Db sequence if you want to do the whole thing chromatically.

4. You can just jump to it. Nothing says key changes must be smooth, and at times a jarring change is best.

The second part of your question I have a problem with, because it doesn't strike me like you're asking for help understanding modulations... it seems like you're asking for help with your homework. If you're the one writing the song, YOU decide how many beats per chord. Whether or not it modulates has nothing to do with it.

Thank you. The second part of the question I seem to have trouble modulating and keeping in time. It just don't have the feel as being in time. It feels like you should come back in singing like one beat before you should. Like before you accually reach your Neh key.

When you harmonize a melody, you generally have chord changes set so the melody consists mainly of chord tones - that way the melody and the harmony aren't fighting each other. But having a melody note as a non-chord tone is common, and having a melody note occur just before the chord is an "anticipation" tone. If you're in C, the melody note Eb will conflict with a C chord, but a chord change that happens immediately after that to Cm (or Eb, Ab, or any other chord that contains an Eb note) gives a sense that the progression is 'catching up' to the melody.

I forget where I learned this, but I've often used the I-I#dim-ii-V-I formula to modulate.

So, from C to C#dim (using the movable shape) - the double tritone in the diminished chord more or less destroys he sense of tonality so you can go anywhere after that - then ii-V-I in the new key which is Fm, Bb (or Bb7) to Eb.

It doesn't quite destroy tonality, Alan, but it gets pretty close on a practical level.

In C7 you have C-E-G-Bb, which has a tritone between E and Bb. In C#º7 you have C#-E-G-Bb, with tritones between E and Bb (so you're subbing for C7) and between C# and G.

The E/Bb tritone is found in C7 and F#7: F#-A#-C#-E (A# enharmonic to Bb); the C#/G tritone is found in A7: A-C#-E-G and Eb7: Eb-G-Bb-Db (enharmonic to C#); these lead naturally to the keys of F, B, D, or Ab, respectively. That's four of the 11 other keys.

You can also sub a #Vº7 for G7: G#-B-D-F, since it has the same tritone as G7; that's the same as the tritone for Db7: Db-F-Ab-Cb (enharmonic to B), and the G#/D tritone is found in E7: E-G#-B-D and in Bb7: Bb-D-F-Ab (enharmonic to G#). Those let you go naturally to the keys of Gb, A, or Eb.

That's 7 keys. Using the Cº7th to go to the four remaining keys (Db, E, G, and Bb) will sound a touch off. If you want one of those modulations, the best bet for that method is to go C -> G#º7 -> Aº7 -> new key, using a chromatic step up. A bit more rarely used would be going C -> C#º7 -> Cº7 -> new key. Since Cº7 and Aº7 have the same notes (C-Eb-Gb-Bbb/A) either will let you access the remaining four keys. You can also use Iº7 directly, but it's not quite as smooth to my ears.

There's a lot more than one way to skin the cat of changing keys.