Help Me Understand Pedal Point

I know how a pedal six-four chord is used, but that's different from a pedal point right? My theory book left me a little confused about them.

My theory book shows an example in G major. There is a I chord with G in the bass. The G is sustained on the bottom all the way through the measure but the chords above it change from I to IV to vii, and back to I.

Can you do the same thing but invert the I chord and put B or D in the bass, sustaining it under a I-IV-vii-I progression?

Does the pedal point have to occur on I? Would a pedal point on a root position ii chord work; sustaining it under some progression?

Does the pedal point have to come back to the original chord it started on? The two examples in my book show it doing that.

Are they most often used in specific places, or use them wherever you want?

Pedal point is used to stabilize the key. Notes for pedal are the tonic or the dominant. A tonic pedal using second inversion (D in your example) would be still a dominant pedal. First inversion (B in your example) would contradict the purpose of tonal stabilization of the pedal, since it is a weak position.

The pedal usually starts and ends with the regular chord that you would use to connect the chord previous to the pedal to the chord that comes next.

The usage of pedal depends on the type of compositon, whenever you want static harmony to consolidate the key. You could write a piece entirely based on pedal (or drones); for instance a musette or a tambourin; in fugues and sonatas there there are often pedal sections. dominant pedal is good for retransition to the recapitulation in the home key, and tonic pedal is good for coda sections. Also, tonic drones or pedals are used to harmonize modal music (such as medieval tunes).

The pedal note does not need to be the bass, it can be some other voice. It does not need to be a sustained note, either, but it can be rhythmically patterned, or use two notes forming a fifth.

"The pedal usually starts and ends with the regular chord that you would use to connect the chord previous to the pedal to the chord that comes next."

Can you explain that?

Let me see if I'm understanding correctly.

The the only notes you can use as a pedal point are the tonic and dominant pitches of the key you are in.

You can have a pedal point on a root position I chord, a second inversion I chord, or a Root position V chord.

The pedal point doesn't have to be in the bass, but it must be the tonic or dominant pitch of the key you are in.

no

a pedal point can be on any note or chord, in any voice

that said in tonal music a pedal other than tonic or dominant is quite rare.

- the supertonic (2nd scale degree) only really appears as a fifth above the dominant, turning a pedal point into a pedal chord.

- a mediant (3rd scale degree) pedal is only likely to appear in the middle voices, usually in sections where the harmony oscillates between I and vi/iii. (a good example of a mediant pedal is Laurie Anderson's O Superman)

- a subdominant (4th scale degree) pedal will sometimes happen in preparation for a strong perfect authentic cadence, due to the emphasis placed on the subdominant as a preparation for the dominant, or sometimes after said cadence by way of coda (a plagal "Amen" cadence), often involving modal mixture. (i'm pretty sure there's a good one near the end of the Hammerklavier)

- if there are any pieces with submediant or leading tone pedals i'm not aware of them

- ok i lied. there are submediant pedals all over the finale of beethoven's string quartet op. 59 no. 2

- a tonic pedal strongly confirms the key, particularly in a section where the harmony oscillates between I and IV (for an even stronger confirmation/stabilization use the tonic plus the dominant (see Schumann's Romanze op. 28 no. 2))

- a dominant pedal in an interior voice also confirms the key, particularly in a section where the harmony oscillates between I and V (see Schubert's Sonata d. 960)

- a dominant pedal in the bass increases tension, acting as a preparation for I (see the waldstein sonata)

if you're not writing music that adheres to common practice tonality you can do whatever makes sense according to the established "rules" of your piece though

Everything has pretty much been covered above me but I just want to say, don't forget that a pedal doesn't have to be just one note. You can have what Messiaen would call a "pedal group" (basically an ostinato) allowing you to be a bit more creative. If you wanted the same effect as say, a dominant pedal, you would just base your pedal group around the dominant chord with chord tones, passing notes, auxiliaries etc.