Undertone series

While overtones naturally occur with the physical production of music on instruments, undertones must be produced in unusual ways.

[2] The complex tones of acoustic instruments do not produce partials that resemble the subharmonic series, unless they are played or designed to induce non-linearity.

While harmonics can "... occur in any linear system", there are "... only fairly restricted conditions" that will lead to the "nonlinear phenomenon known as subharmonic generation".

The overtone series can be produced physically in two ways – either by overblowing a wind instrument, or by dividing a monochord string.

Singers often describe it as feeling like stable points below regularly sung notes where it snaps or jumps specific intervals.

String quartets by composers George Crumb and Daniel James Wolf,[citation needed] as well as works by violinist and composer Mari Kimura,[3] include undertones, "produced by bowing with great pressure to create pitches below the lowest open string on the instrument.

Also third bridge preparations on guitars cause timbres consisting of sets of high pitched overtones combined with a subharmonic resonant tone of the unplugged part of the string.

Elizabeth Godley argued that the minor triad is also implied by the undertone series and is also a naturally occurring thing in acoustics.

[11] Henry Cowell discusses a "Professor Nicolas Garbusov of the Moscow Institute for Musicology" who created an instrument "on which at least the first nine undertones could be heard without the aid of resonators.

[16] Kathleen Schlesinger pointed out, in 1939, that since the ancient Greek aulos, or reed-blown flute, had holes bored at equal distances, it must have produced a section of the undertone series.

[14] She said that this discovery not only cleared up many riddles about the original Greek modes, but indicated that many ancient systems around the world must have also been based on this principle.

[17] Most experiments with undertones to date have focused largely upon improvisation and performance not compositional design (for example the recent use of negative harmony[18] in jazz, popularised by Jacob Collier and stemming from the research of Ernst Levy), although in 1985/86 Jonathan Parry used what he called the Inverse Harmonic Series (identical to the Undertone Series) as one stage in his process of Harmonic Translation.

If feelings are instead based on the high "fundamental" of an undertone series, then descending into a minor triad is not felt as melancholy, but rather as overcoming, conquering something.