Difference tones or Tartini tones, named after the 18th century violinist who is often cited for their discovery, occur when two pure tones are played together .  For example if you have a pure tone at 1000hz and another at 800hz, a third tone can sometimes be heard that is 200hz.  You can also use harmonics to figure out the difference tone.  For example if you have the 3rd harmonic and 2nd harmonic playing simultaneously the difference tone is the frequency at the first harmonic or fundamental pitch.  So we can observer the basic formula is to subtract the smaller hz value from the larger one to determine what pitch may be heard. It's interesting to note is that their different theories that exist whether or not Tartini tone's are really physically present.  Are they created in the inner ear, is it strictly a neural phenomena, or  is their something else going on?

Musical Harmony

Using the above example of difference tones with harmonics let's look at major chords in relation to their harmonic construction. Notice how the difference tones equal 1 or 2 which would be the fundamental pitch of chord.  Let's use C as the fundamental at 130.8.  In class demo uses http://www.szynalski.com/tone-generator/ to generate single tones and NCH Tone Generator software.

Note Interval Harmonic Difference Tone
With Above Note(
Harmonic)		 Frequency
C 1 4 6 - 4 = 2 523.2
E M3 5 5 - 4 = 1 654
G P5 6 6 - 5 = 1 784.8

Binaural Beats

Binaural beats are an aural phenomenon  that are generated by difference tones created when, both frequencies lower than 1500hz and less than a 40hz difference between them, and when one frequency is sent to the left ear and one to the right. When binaural beats are listened to in headphones researchers note that brainwaves "entrain" to the difference tone or frequency between the two frequencies.  Brainwaves are measured by an EEG Machine (electroencephalogram) that measures brainwaves and makes it possible to see what brain "states" relate to brainwave activity.  The below chart comes from mindvalley.com:

  • Beta (14-40Hz) — The Waking Consciousness & Reasoning Wave. ...
  • Alpha (7.5-14Hz) — The Deep Relaxation Wave. ...
  • Theta (4-7.5Hz) — The Light Meditation & Sleeping Wave. ...
  • Delta (0.5-4Hz) — The Deep Sleep Wave. ...
  • Gamma (above 40Hz) – The Insight Wave.

Web Resources

Combination Tone - Introduction
Difference Tone Training
Combination Tones as Harmonic Material
Online Tone Generator
Standalone Tone Generator