What do you hear?
José Rodríguez Alvira
This phenomenon has been known for several centuries. The Italian violinist Giuseppe Tartini (1692-1770) spoke of the terzo souno or third sound generated from 2 sounds. The third sound can help with regards to tuning the two original notes. A major third is perfectly tuned if the generated note is two octaves lower than the bass note. Any change in the tuning of the top note will be reflected in the frequency of the third sound:
Organ constructors use of this phenomenon to produce low-pitched sounds with smaller pipes. Two pipes tuned to a perfect fifth will generate a sound one octave lower than the lowest sounding pipe.
The fact that our auditory system can complete missing harmonics, makes possible to listen to music in sound systems that are not capable of producing low frequency sounds.
Tartini Effect
Finally, let's experiment with the Tartini effect. We suggest using headphones. Be careful that the volume is not too high!
- Play C4/C5.
- Add the G4, do you also hear a lower sound? This is Tartini's terzo suono a C3. Continue to the next step even if you do not hear the C3...
- Change the G4 tuning using the + and - buttons. By changing the tuning of the G4, the generated C3 is affected and a beat is produced. If you did not hear the C3 in the previous step, you may notice now that when the G4 tuning is changed, another lower sound also changes. You may also notice that the beat seems to be produced by C3. If you do not hear the beat, carefully raise the volume.
The G4 is a perfect fifth above the C4 and is tuned using the size of the fifth of the harmonic series: 260 x 1.5 = 390. The perfect fifth of the equal temperament system - commonly used today - is 2 cents smaller than the fifth of the harmonic series. Note the effect of this small change in tuning.
If you would like to know why the equal temperament has smaller fifths, follow this link to read about tuning systems...
Reference and additional information:
- Benade, Arthur H. 1990. Fundamentals of Musical Acoustics, 2nd edition. Dover Publications, New York.
- The Harmonic Series. teoria.com.
- 2,500 years of musical temperaments. teoria.com.
- Piano tuning. Wikipedia.
- Beat. Wikipedia.
- Cent. Wikipedia.
- Combination Tone. Wikipedia.
- Missing fundamental. Wikipedia.
- Harmonic Series. Wikipedia.
© 2017 José Rodríguez Alvira. Published by teoria.com
