The 9th

14 semitones — color above the octave

Prove it — just do the practice exercise.
C → D 14 semitones
C (root) D (Maj 9th)
The 9th = octave + major 2nd = 14 semitones:

• Extends 7th chords into 9th chords (Maj9, 9, m9)
• Sounds colorful and modern
• In rootless voicings, the 9th often replaces the root

Example: C → D (next octave) = major 9th

♭9 = 13 semitones → very tense (Dominant ♭9)
#9 = 15 semitones → the Hendrix sound