I have a question about some specifics examples in a few songs, where my knowledge of music theory fails as an explanation as to why something sounds good. Here is a sorta of long winded question I have about a Paul Gilbert song.



Alright, starts out simple enough. It's a cute little riff in E Major. I understand how the modes work, and I get that the first riff works out, because even as the apparent 'root' changes, all of the notes are still relative to one another in the same diatonic scale. But then at 0:14, he literally plays the exact same riff, only in G major instead of E major. I am scratching my head was to why this form of modulation works. G is not found anywhere in the E major scale. G major and E major are not relative scales at all, and in fact, G major and E minor are. Is there some kind of rule that states what number of semi-tones a pattern can shift, in order to sound mildly disjointed but still appropriate for a song? I know there are supposed to be a few tricks for modulating from whatever key/mode to whatever other key/mode you want, but I don't really know what they are, and I suspect they are much trickier than this.

Here, I have a few other examples with minor scales moving by major thirds:



Here, at 1:29, there's a chromatic riff (which feels pretty close to minor, and it get's harmonized later on.) Then at 1:47 it switches to a similar riff, but the root is a major third higher. The only reason I could see this making sense is because all of the notes from both riffs almost fit into like a half-whole diminished scale or something. Other than that, it seems like a totally random choice of notes which happen to sounds cool, but I don't really know why.



Classic example! Alright, pretty much the whole song is just the root, a minor first, minor third, and major third. Again, making good use of the half-whole scale lol. But again, at 2:40, an altered version of the chorus riff plays, and momentarily after that, it's repeated note for note, only four semitones higher.

I've fooled around with the latter two examples and found that playing any minor scale pattern, and shifting that pattern uniformly through an augmented cycle (for example, playing in E, G# and C in any order) is a good way to change up a song. But for the life of me it still doesn't seem apparent as to why it works so smoothly.

I'm sure there are a lot of examples where you can find other songs modulating by any number of semitones, but can it just be done spontaneously? Why is it that when I try to pick two arbitrary scales in two arbitrary keys, and jam/shred them back to back, it doesn't sound fluid at all, but in these youtube examples, some riffs are moved up/down by intervals which aren't in the starting scale at all, and it sounds good?

Well, thirds are popular intervals for harmonizing two melodies, so it's pretty much taking that concept but applying it melodically. I have no idea why the interval used to shift is of opposite tonality as the scale in question (as far as major/minor goes), though.

Also, as far as the Dark Angel song and diminished scales goes, If you take a given note in either form of a diminished scale, the major third of that note is going to be in the same position (as far as its place in the pattern goes) in the other diminished scale. I.e, D in a half/whole diminished scale falls in the same place as F# in the whole/half diminished. Yay symmetrical scales.

Umm.

#1. harmonizing a scale does not mean playing the exact same notes a third above the root, it means playing the same number of steps in that scale above the root. That's why you have to shift positions when you play chord scales.

#2. I understand that phenomenon with the diminished scale. That's why it's the diminished scale. But I didn't ask about the diminished scale, I asked about why this works specifically with minor scales also, considering the major third would not appear in any of those like it does in the half/whole scale.

It's in the tricks. Rhythmic and melodic tricks to change scales using a two-note overlap in the scales, and using the rhythm to emphasize the change which was already in progress.
I'll use this tab for reference: http://tabs.ultimate-guitar.com/p/paul_ ... up_tab.htm

The transition from the first part to the second is a descending run in E major grouped into three groups of three notes on the first line. Nine notes there, plus the first note of the next line, which needs to be considered. Look at how these ten notes fit the scales:
-The first nine are E major, while the last one is firmly in the new key. The timing separates them too, so the first note that isn't in E major is the start of a new line.
-The last three are G major. He plays through the seven notes of E major, then once the octave repeats, there are two notes that overlap between EM and GM, while the last one the first that doesn't fit EM, there is a three note run at the end that fits GM
-The last note falls on the first beat of the next measure/line, which reinforces the key change. It is the third note in the key of GM. That's a three-note pattern, and the last measure ended with three patterns of three notes each. Two notes overlapped, and the final one fell on the first note of the next measure/line, a rhythmic trick to emphasize a key change that has already been in progress for a few shared notes.

Two tricks used here that make this key change work:
-Find notes that overlap between the two keys you're changing between and use those to make the transition. Set up the transition before you change key, so you're already into the shared notes with the new key.
-Use timing and percussion to support the change. If the first note of a new key comes on the first beat of a measure, it feels right, better than doing it a few notes into the measure.
-Extra note: When the rhythm pattern is the same in both parts, the transition feels less abrupt. Changing one of melody/rhythm at a time can help make both smoother transitions and interesting variations on parts.