John Tyndall
"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 keynote 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']
Ramsay
A grave harmonic is a secondary note which spontaneously arises when two different notes are sounded together. It is a note whose mathematical number is the difference of the two which awaken it; e.g., F2 and C3, the interval of the fifth, awakens a grave harmonic whose number is 1, which is the difference of 2 and 3; and this 1 strengthens F2, for it is its lower octave. But the interval of F2 and F4, or any other octave, does not awaken a grave harmonic, since there is no difference-number between the two. - Editor. [Scientific Basis and Build of Music, page 36]
See Also
1.23 - Power of Harmonics through Summation Tones
9.9 - Sympathy or Harmony Between Harmonics or Overtones
12.06 - Mid-Tones and Neutral Centers
12.42 - Tone
Figure 4.16 - Break-out of Colors Tones and Attributes
Figure 4.17 - Musical Relationships of Colors Tones and Attributes
Figure 7B.02 - Colors and Tones
Figure 8.5 - Summation Tones
Figure 8.6 - Difference Tones
Figure 12.03 - Scale Showing Relations of Light Color and Tones
Figure 14.01 - Overtones Developed Musically Showing Up as Isotopes along the Vertical Axis of this Chart
Figure 18.06 - Hubbard Tone Scale of Degrees or Levels of Consciousness
grave harmonic
Master Tone
Overtone
Overtone series
Power of Beat Harmonics
Ramsay - Nature refuses Man's Dictation
resultant tone
Table 11.02 - Fifth is Double Tone
TARTINIS TONES
Tone
Undertone
Wolf Tone