After reading the Wikipedia article about pedal point, to me it seems pedal with pedal point you'd be playing the key's root when other instruments would be playing chords according to modal theory (so the chords have their own root that is not the tonic root) and pitch axis rests totally on the root by only changing the harmonizing notes within the chord and using the same root.
Well, you don't have to play the key's tonic (root refers to chords primarily)--the dominant is also sometimes used. But note that the fact that other chords may be played that have their own root has absolutely NOTHING to do with "modal theory." It's in the nature of harmonic progressions.
So with Pedal point it would be in C, playing C throughout I-IV-V-I
Cmaj7-Fmaj7-G7-Cmaj7 (C is not a chord tone with G7).
So with this the C would create a dissonance within the V.
Yeah, that's a reasonable example. Generally you proceed from consonance to dissonance and resolve to consonance.
With Pitch Axis (if I'm correct) playing I-IV-V-I would incorporate 3 scales, C Ionian, C Lydian, C Mixolydian which are CDEFGABc, CDEF#GABc and CDEFGABbc.
So you could basically fill the I-IV-V slots with any suitable chords, probably with those that use the identifying notes, F# and Bb and keeping the C as the "note in the background" but still in the chord.
I wouldn't say this is right. What you describe is not I-IV-V. That terminology refers to root movement, and if the root never changes, you can't have I-IV-V, by definition. If you're doing C ionian, C lydian, C locrian, C altered, there's no root movement. What's more, that terminology (I, IV, V, and so on) mostly makes sense within a key structure (ie, functional harmony) or an overarching modality, though you could technically derive those relations from any specified starting point. The whole point of pitch axis, it seems to me anyway, is that you're not really working with a key or its attendant functionality, you're dealing with a succession of harmonic spaces that revolve around (hence "axis") a
note rather than a key or modality (hence "pitch"). IOW, you could say they don't exactly have a key as such, in the way in which we usually employ the term; rather, they have a
key note, or a tonal center, and perhaps a general flavor. Through shorthand, you could refer to a tune of this type that is based on the pitch E as being "in E", but it won't necessarily be analyzable as being in E major in terms of functional harmony. So trying to impose those functional harmonic concepts onto this kind of progression won't always be that productive.
The consequence of this is that since the changes are not really tied together by a key, you often can't approach them by thinking in terms of a key. They don't have the same kind of relationships that the chords in a key have in functional harmony. So you may have to approach them one by one, as they happen--rather as if each one is its own key or mode. This is different from the way pedal point is generally used, because that usually involves some level of functionality. But I suppose you could say that at a basic level--that of harmonies shifting over a constant bass--it's the same idea. But in practice I'd say most people mean somewhat different things by it.
