Katy Perry's first album is amazing. Yes it's pop music and it's catchy and super accessible, but there's depth to it too. To prove it, I decided to analyze one of my favorites, Lost.

Intro

            |C       |F   Bb  |C       |F   Bb  |
            |I       |IV  bVII|I       |IV  bVII|
            |+--+----|...
          

The song starts out with some simple acoustic guitar, with the strum pattern specified above by + signs, accompanied by some subtle bells and delayed electric guitar. In the key of C, Perry makes use of a blues/rock-oriented bVII, and uses it to allow the melody in the bells to have some Bbs.

Verse

          |C       |F   Bb  |C       |F   Bb  |C       |Am      |G       |F       |
          |I       |IV  bVII|I       |IV  bVII|I       |vi      |V       |IV      |

          |C       |F   Bb  |C       |F   Bb  |C       |Am      |G       |E       |E       |
          |I       |IV  bVII|I       |IV  bVII|I       |vi      |V       |V-of-vi |-       |
          

Unike the bells, Perry's vocal melody does not take advantage of the Bb chord, and avoids any kind of B, flat or natural, altogether. After the Am and G, the verse sounds like it's going to "go" somewhere, but is brought back home with an easy IV-I resolution.

In the second iteration, she breaks free using the E. Like the Bb, the E does not belong to the C key, but unlike the Bb, this chord marks a transition to the next section. Over the E, Perry finally commits to a B natural, which propels the song into the Chorus.

Note that I marked the E as a V-of-vi. Normally in pop, the III (E) is used to pivot to the vi (Am).Instead, she slides right on up to the IV (F).

Consider if she had used an Em rather than an E. An Em is totally in key, but lacks the tension that the E introduces.

Chorus

          |F       |G       |C       |Am      |F       |G       |
          |IV      |V       |I       |vi      |IV      |V       |
          

Now instead of avoiding a kind of B, she uses it as a pivot note, falling back to it in the "ver" in "ever" and on "so".

The emphases in the melody are not entirely on the downbeats.

Link

          |C       |F   Bb  |
          |I       |IV  bVII|
          

This link is a unit of the intro again. It also adds to the previous chorus to make an even 8 bars.

Verse 2

          |C       |F   Bb  |C       |F   Bb  |C       |Am      |G       |F       |
          |I       |IV  bVII|I       |IV  bVII|I       |vi      |V       |IV      |

          |C       |F   Bb  |C       |F   Bb  |C       |Am      |G       |E       |E       |
          |I       |IV  bVII|I       |IV  bVII|I       |vi      |V       |V-of-vi |-       |
          

The seconds verse adds backing vocals. Harmonically, they don't add too much (just Cs, Fs, and Gs), but a pop song must have layering, so layer it shall.

Chorus 2

          |F       |G       |C       |Am      |F       |G       |C       |Am      |
          |IV      |V       |I       |vi      |IV      |V       |I       |vi      |

          |F       |G       |C       |Am      |F       |G       |
          |IV      |V       |I       |Am      |IV      |V       |
          

This chorus feels cut short, and for good reason. We've been robbed of a full two bars. This kind of wonky non-multiple-of-4 sectioning is not typical of pop songs. ### Bridge

          |C       |F   Bb  |C       |F   Bb  |C       |Am      |G       |Esus4 E |
          |I       |IV  bVII|I       |IV  bVII|I       |vi      |V       |V-of-vi |

          |F       |G       |C       |Am      |F       |G       |C       |Am      |
          |IV      |V       |I       |vi      |IV      |V       |I       |vi      |

          |F       |G       |C       |Am      |F       |G       |Am      |Am      |
          |IV      |V       |I       |vi      |IV      |V       |I       |vi      |
          

The chorus ends the same way the previous did, but Perry alerts us that this time is different by singing a new melody over the first four measures.

Here the E is used to de-escalate, as opposed to how it's used in the verses. It'd be hard not to de-escalate at that point, following Perry's screams that would make my choir teacher roll in his grave if he were dead.

After the E, we're left with a softspoken Perry and simple eighth note keyboard chords, and it's our last climax.

It's worth noting in how many ways Perry uses these chords. This is the 50s Progression (I vi IV V), but starting on the IV. In the second line above, it's quiet and unmoving. In the third line, it's a roar of frustration.

Outro

          |F       |G       |C       |F   Bb  |C       |F   Bb  |C       |F   Bb  |...
          |IV      |V       |I       |IV  bVII|I       |IV  bVII|I       |IV  bVII|... 
          

We're back where we started. Feels a little different given everything we just heard.

Final Thoughts

--- The main cleverness in this song roots around her use of the Bb and B-natural notes. In the verses, the Bb is a root, though Perry never takes advantage of the note not being in key to expand her melodic capabilities. The switch from Bb to B-natural and vice-versa marks the transitions between sections. With the B-natural at her disposal, she's able to distinguish her chorus and bridge melodies from the verse melodies.
Typical pop song checklist:

50s Progression

Verse-Chorus-Verse-Chorus-Bridge

"ONE and two AND" measure emphasis