Guitar Harmonics Calculator
| Harmonic | Frequency | Note | Fret | Cents |
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What Your Result Means
- Harmonic frequency: Each row shows the vibrational frequency in Hz. Harmonics are integer multiples of the fundamental, so the 2nd harmonic is exactly twice the frequency.
- Note name: The closest musical note in equal temperament tuning. Most natural harmonics align closely with standard notes, but some (especially the 7th) drift measurably.
- Fret position: The approximate fret or fractional position where you can touch the string lightly to isolate that harmonic. "Open" means the fundamental played normally; "12" means the 12th fret (one octave up).
- Cents deviation: A cent is 1/100 of a semitone. Positive values are sharp (higher pitch), negative values are flat (lower pitch). The 7th harmonic is notably ~31 cents flat, which is why artificial harmonics sound slightly out of tune to trained ears.
How This Calculator Works
Enter a guitar string's fundamental frequency—either by selecting a standard tuning (E2 through E4) or entering a custom frequency in Hz. The calculator multiplies the fundamental by each harmonic number (1–16) to find the frequency of each harmonic. Each frequency is converted to its nearest equal-temperament note and compared to that note's "perfect" frequency to calculate the cents deviation. Fret positions show where you can touch the string to emphasize each harmonic.
Quick Questions
What's the difference between a harmonic and a note?
A harmonic is a frequency that's an integer multiple of the fundamental. A note (like C4 or A3) is a specific pitch in the chromatic scale. Most harmonics align closely with standard notes, but not perfectly—that's why the 7th harmonic sounds "out of tune."
Why is the 7th harmonic flat?
The 7th harmonic has a frequency ratio of 7:1 with the fundamental. In just intonation (pure ratios), this creates a pitch about 31 cents flat compared to equal temperament's tempered intervals. This is a mathematical consequence of how whole-number ratios relate to the 12-tone chromatic scale.
How do I play natural harmonics on guitar?
Touch the string lightly (don't press down) at the fret position listed in the "Fret" column, then pluck near the bridge. The string will vibrate in segments, amplifying that harmonic. The 12th fret (octave) and 7th fret (harmonic 3) are easiest for most players.
Can I use custom frequencies other than standard tunings?
Yes. The "Custom Frequency" field accepts any value in Hz. This is useful if your string is tuned lower or higher than standard (e.g., a dropped tuning or a capo effect), or if you want to analyze harmonics for any frequency source.
Why does the cents value matter?
Cents measure how far a harmonic drifts from equal temperament. A trained ear can detect deviations over ±10 cents. High deviations (like the 7th harmonic's −31 cents) explain why some harmonics sound slightly out of tune compared to the chromatic scale.
What's "inharmonicity" and why does it matter?
Real strings aren't perfectly flexible, so they have slight stiffness that causes higher harmonics to be slightly sharper than ideal. This effect grows stronger with thicker strings and shorter lengths. It's why acoustic guitars sound richer but less "perfect" than synthesizers.
Sources
- Wikipedia: Harmonic Series (definitions and mathematical ratios)
- Wikipedia: Just Intonation (frequency ratios and their relationship to equal temperament)
- Wikipedia: Cent (Music) (cents as a unit of pitch deviation)
- Wikipedia: String Vibration (physics of harmonics and inharmonicity)
Method & review
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.