Question: What is the tonal range of the melody for Part of Me?
About the article "Part of Me (Katy Perry song)", section "Composition and lyrical interpretation".

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This occurs when an added part imitates the shape of a portion of the melody (or other portion of the song) at a higher or lower pitch and after the initial musical phrase but overlapping with it.
Due to tonal inflections (in the regions using tonal languages), the shape of the new musical phrase is similar to, but not necessarily identical with, that of the previous one.
The use of imitation accounts for a wide variety of interval combinations within the scale system being used in African musics. 
A melody (from Greek μελῳδία, "melōidía", "singing, chanting"), also tune, voice, or line, is a linear succession of musical tones that the listener perceives as a single entity.
In its most literal sense, a melody is a combination of pitch and rhythm, while more figuratively, the term can include successions of other musical elements such as tonal color.
It may be considered the foreground to the background accompaniment.
A line or part need not be a foreground melody.
Melodies often consist of one or more musical phrases or motifs, and are usually repeated throughout a composition in various forms.
Melodies may also be described by their melodic motion or the pitches or the intervals between pitches (predominantly conjunct or disjunct or with further restrictions), pitch range, tension and release, continuity and coherence, cadence, and shape. 
Post-tonal music theory is the set of theories put forward to describe music written outside of, or 'after', the tonal system of the common practice period. 
When applied to melodies, the "inversion" of a given melody is the melody turned upside-down.
For instance, if the original melody has a rising major third, the inverted melody has a falling major third (or perhaps more likely, in tonal music, a falling "minor" third, or even some other falling interval).
See m. 24 of Bach's C#m fugue Shockwave movie, "Well-Tempered Clavier 2," for an example of the subject in its melodic inversion.
Similarly, in twelve-tone technique, the "inversion" of the tone row is the so-called "prime series" turned upside-down, and is designated T"n"I. 
Barbershop vocal harmony, as codified during the barbershop revival era (1930s–present), is a style of a cappella, or unaccompanied vocal music, characterized by consonant four-part chords for every melody note in a predominantly homophonic texture.
Each of the four parts has its own role: generally, the lead sings the melody, the tenor harmonizes above the melody, the bass sings the lowest harmonizing notes, and the baritone completes the chord, usually below the lead.
The melody is not usually sung by the tenor or baritone, except for an infrequent note or two to avoid awkward voice leading, in tags or codas, or when some appropriate embellishment can be created.
Occasional passages may be sung by fewer than four voice parts.
According to the Barbershop Harmony Society (BHS), "Barbershop music features songs with understandable lyrics and easily singable melodies, whose tones clearly define a tonal center and imply major and minor chords and barbershop (dominant and secondary dominant) seventh chords that resolve primarily around the circle of fifths, while making frequent use of other resolutions."
Slower barbershop songs, especially ballads, often eschew a continuous beat, and notes are often held (or sped up) ad libitum.
With the exception of the bass, the voice parts in barbershop singing do not correspond closely to their classical music counterparts; the tenor range and tessitura are similar to those of the classical countertenor, the baritone resembles the Heldentenor or lyric baritone in range and a tenor in tessitura, and the lead generally corresponds to the tenor of classical repertoire, with some singers possessing a tessitura more similar to that of a high baritone.
Barbershop singing is performed both by men's and women's groups; the elements of the barbershop style and the names of the voice parts are the same for both (although women's groups generally have a different standing arrangement than their male counterparts).