Text: "Difference tones were discovered by Sorge in 1745 and again independently by Tartini in 1754. By sounding two tones a fifth apart, the tone an octave below the lower note is resonated. It is in general true that when any two or more pure tones which are sounded simultaneously happen to be harmonics of the same fundamental note, then the ear adds this fundamental note and many of its harmonics, of its own accord - a result of tremendous importance in all branches of pure and applied acoustics. If the pure tones are all the odd-numbered harmonics of a fundamental note, then the ear of its own accord adds all the even harmonics. If the two pure tones differ only slightly in frequency, then their "difference tone" has the same frequency as the BEATs, so that as the two original tones approximate to one another, their difference tone degenerates into beats, while their SUMMATION TONE approaches to their second harmonic. Difference tones are usually concordant, summation tones discordant, with the tones that produce them; these being the KEY NOTE or ROOT. These two tones are always present simultaneously in all tones, the Difference tones being louder and therefore Dominant of the two. Difference tones can be used to create unlimited Physics depth of tones, ultimately appearing as beats when the two original tones are brought more nearer coincidence. Difference tones are positive and DOMINANT, summation tones are Negative." [John Tyndall, 'Sound']

See Also: ACOUSTICS § 17, 18; BEAT, COINCIDENCE, RESONANCE, KEYNOTE, LAW OF SUPERPOSITION, RESULTANT TONES, LAW OF THE TRIANGLE

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