Harmonics On Stringed Instruments
The following table displays the stop points on a stringed instrument, such as the guitar (guitar harmonics), at which gentle touching of a string will force it into a harmonic mode when vibrated. String harmonics (flageolet tones) are described as having a "flutelike, silvery quality that can be highly effective as a special color" when used and heard in orchestration. It is unusual to encounter natural harmonics higher than the fifth partial on any stringed instrument except the double bass, on account of its much longer strings.
| Harmonic | Stop note | Sounded note relative to open string | Cents above open string | Cents reduced to one octave |
|---|---|---|---|---|
| 2 | octave | octave (P8) | 1,200.0 | 0.0 |
| 3 | just perfect fifth | P8 + just perfect fifth (P5) | 1,902.0 | 702.0 |
| 4 | second octave | 2P8 | 2,400.0 | 0.0 |
| 5 | just major third | 2P8 + just major third (M3) | 2,786.3 | 386.3 |
| 6 | just minor third | 2P8 + P5 | 3,102.0 | 702.0 |
| 7 | septimal minor third | 2P8 + septimal minor seventh (m7) | 3,368.8 | 968.8 |
| 8 | septimal major second | 3P8 | 3,600.0 | 0.0 |
| 9 | Pythagorean major second | 3P8 + Pythagorean major second (M2) | 3,803.9 | 203.9 |
| 10 | just minor whole tone | 3P8 + just M3 | 3,986.3 | 386.3 |
| 11 | greater unidecimal neutral second | 3P8 + lesser undecimal tritone | 4,151.3 | 551.3 |
| 12 | lesser unidecimal neutral second | 3P8 + P5 | 4,302.0 | 702.0 |
| 13 | tridecimal 2/3-tone | 3P8 + tridecimal neutral sixth (n6) | 4,440.5 | 840.5 |
| 14 | 2/3-tone | 3P8 + P5 + septimal minor third (m3) | 4,568.8 | 968.8 |
| 15 | septimal (or major) diatonic semitone | 3P8 + just major seventh (M7) | 4,688.3 | 1,088.3 |
| 16 | just (or minor) diatonic semitone | 4P8 | 4,800.0 | 0.0 |
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“We are all instruments endowed with feeling and memory. Our senses are so many strings that are struck by surrounding objects and that also frequently strike themselves.”
—Denis Diderot (1713–84)