Every musical note is actually a combination of many frequencies called the harmonic series. When you play a note on a piano, guitar, or voice, the fundamental frequency determines the pitch — but the overtones above it shape the timbre (tone color) and explain why certain intervals sound consonant or dissonant.
Click harmonics to toggle them on/off, then press Play to hear the combination. The fundamental is C2 (65 Hz).
Each harmonic is a sine wave at an integer multiple of the fundamental frequency. The combined wave (bold purple) is what you actually hear. Toggle harmonics above to see how the shape changes.
When a string vibrates, it creates standing waves. The fundamental (H1) vibrates as one arc. The 2nd harmonic has 2 arcs with a node (still point) in the middle. Each higher harmonic adds more nodes — dividing the string into equal parts.
Why this matters: When you press a guitar string at the 12th fret (halfway), you kill the fundamental and hear the 2nd harmonic (octave). At the 7th fret (⅓), you get the 3rd harmonic (perfect 5th + octave). Harmonics on a guitar are literally you selecting which standing wave pattern to isolate!
A piano and a flute playing the same C3 have the same fundamental frequency (131 Hz) but different overtone recipes. Click each instrument to hear the difference — all play the same pitch, but the timbre changes dramatically.
Pick a root note and see which actual notes appear as its overtones across octaves. This is why when you play a low C, you can “hear” the G, E, and Bb hiding inside it.
| H# | Frequency | Nearest Note | Musical Role | Cents Off | |
|---|---|---|---|---|---|
| 1 | 65 Hz | C2 | Root | Exact | |
| 2 | 131 Hz | C3 | Root (8va) | Exact | |
| 3 | 196 Hz | G3 | 5th | +2¢ | |
| 4 | 262 Hz | C4 | Root (15ma) | Exact | |
| 5 | 327 Hz | E4 | Major 3rd | -14¢ | |
| 6 | 392 Hz | G4 | 5th | +2¢ | |
| 7 | 458 Hz | A#4 | Flat 7th ⚡ | -31¢ | |
| 8 | 523 Hz | C5 | Root (22ma) | Exact | |
| 9 | 589 Hz | D5 | 9th (2nd) | +4¢ | |
| 10 | 654 Hz | E5 | Major 3rd | -14¢ | |
| 11 | 719 Hz | F#5 | #11 ⚡ | -49¢ | |
| 12 | 785 Hz | G5 | 5th | +2¢ | |
| 13 | 850 Hz | G#5 | b13 ⚡ | +41¢ | |
| 14 | 916 Hz | A#5 | Flat 7th ⚡ | -31¢ | |
| 15 | 981 Hz | B5 | Major 7th | -12¢ | |
| 16 | 1047 Hz | C6 | Root (29ma) | Exact |
Harmonics 1, 2, 4, 8, 16 are all the root note at higher octaves. Every power of 2 is another octave — this is why octaves sound like “the same note, higher.”
Harmonics 3, 6, 12 are all the perfect 5th. The 5th is the second-most prominent overtone after octaves — explaining why power chords (root + 5th) are the most universal sound in music.
Harmonics 4, 5, 6 form a major triad (root, major 3rd, 5th). Major chords aren't a human invention — they emerge from the physics of vibration itself.
Harmonics 7 (♭7), 11 (#11), 13 (♭13) are not in tune with our equal-tempered system. These are the “blue notes” and jazz tensions — naturally occurring dissonances that add color and complexity.
Two notes sound consonant when their frequencies form simple ratios. The simpler the ratio, the more consonant the interval:
2:1
Octave
Perfect
3:2
Perfect 5th
Very consonant
4:3
Perfect 4th
Consonant
5:4
Major 3rd
Sweet
6:5
Minor 3rd
Warm
5:3
Major 6th
Bright
9:8
Major 2nd
Mild tension
16:15
Minor 2nd
Maximum tension
Why? When two frequencies have a simple ratio like 3:2, their waveforms line up regularly — creating a smooth, periodic combined wave. When the ratio is complex (like 16:15), the waves rarely align, creating a rough, “beating” interference pattern that our ears perceive as dissonance.
Consonant intervals share many overtones. The perfect 5th appears as the 3rd harmonic, the major 3rd as the 5th harmonic — these intervals emerge naturally from the physics of vibration.
Different waveforms contain different overtones. A sine wave has no overtones (pure tone), while a sawtooth wave contains all harmonics — making it sound bright and buzzy.
| # | Frequency Ratio | Nearest Note | Interval from Root | Cents Off |
|---|---|---|---|---|
| 1 | 1:1 | C2 | Fundamental | Exact |
| 2 | 2:1 | C3 | Octave | Exact |
| 3 | 3:1 | G3 | P5 + Octave | +2¢ |
| 4 | 4:1 | C4 | 2 Octaves | Exact |
| 5 | 5:1 | E4 | M3 + 2 Oct | -14¢ |
| 6 | 6:1 | G4 | P5 + 2 Oct | +2¢ |
| 7 | 7:1 | Bb4 | m7 + 2 Oct | -31¢ |
| 8 | 8:1 | C5 | 3 Octaves | Exact |
| 9 | 9:1 | D5 | M2 + 3 Oct | +4¢ |
| 10 | 10:1 | E5 | M3 + 3 Oct | -14¢ |
| 11 | 11:1 | F#5 | ~P4 + 3 Oct | -49¢ |
| 12 | 12:1 | G5 | P5 + 3 Oct | +2¢ |
| 13 | 13:1 | Ab5 | ~m6 + 3 Oct | +41¢ |
| 14 | 14:1 | Bb5 | m7 + 3 Oct | -31¢ |
| 15 | 15:1 | B5 | M7 + 3 Oct | -12¢ |
| 16 | 16:1 | C6 | 4 Octaves | Exact |
The harmonic series naturally produces the intervals found in major chords (root, major 3rd, perfect 5th). This is why major chords have sounded “natural” and “resolved” across cultures for centuries — they are literally built into the physics of vibrating strings and air columns. The 7th harmonic (slightly flat minor 7th) hints at why dominant 7th chords create tension that wants to resolve.