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Message: [QUOTE="Bombastus, post: 91692, member: 2178"] Multiplying two sine waves in a ring modulator removes the original tones and produces energy at their sum and difference frequencies. A 300 Hz tone multiplied by a 100 Hz sine therefore gives you components at 200 Hz and 400 Hz, not a tidy blend of the two inputs. Simple enough on paper. Trouble starts when the input is music instead of a laboratory sine wave. A piano note, synth patch, vocal, or distorted bass already contains a stack of partials, and each one gets shifted by the carrier frequency. Feed several notes at once, and the arithmetic gets crowded fast. The [B][URL='https://goldmidi.com/community/threads/unusable-engineering-introduced-quadrant-modulator.77074/']four-quadrant multiplication used by Quadrant Modulator[/URL][/B] follows this basic spectral rule whenever its modulating shape crosses above and below zero. You are not merely adding another tone on top of a chord. You are rebuilding the chord's spectrum from new frequency relationships. [HEADING=2]Two sine waves hide the real spectral mess[/HEADING] Introductory explanations usually begin with one carrier and one modulator because the result is easy to calculate. If the frequencies are 440 Hz and 100 Hz, the audible sidebands land at 340 Hz and 540 Hz. Neither original sine needs to remain in the ideal ring-modulated output. A complex tone changes the scale of the problem. Multiply a source containing five significant partials by a sine carrier, and each source partial produces its own upper and lower sideband. Use a carrier that also contains several partials, and every meaningful component in one spectrum can interact with every meaningful component in the other. The possible component count grows fast. For inputs containing N and M frequency components, the basic sum-and-difference model can produce as many as two times N times M component relationships before coincidences, cancellations, filtering, and inaudible frequencies thin them out. A chord gives the process more starting frequencies before overtones even enter the picture. Nominal note names tell you less than expected here. C major is not simply C, E, and G once real instruments are involved. Each note arrives with its own overtone structure, so a single fixed carrier can shift dozens of components into places that no longer line up with the chord's original harmonic framework. [HEADING=2]Chords make sidebands collide in awkward places[/HEADING] Harmonic relationships can keep ring modulation surprisingly orderly. If a source and carrier share carefully chosen integer relationships, many resulting frequencies can still fall onto a common harmonic grid. Move the carrier away from those relationships and the lower and upper sidebands start landing between the positions your ear expects from a stable pitched tone. Chords make this harder because one carrier ratio cannot be equally tidy for every note and every overtone at once. A carrier that gives a useful relationship against the root may produce rougher intervals against the third, while upper partials generate another set of sums and differences above them. Dense voicings expose the problem faster. Subtraction adds a less obvious complication. When a carrier frequency is higher than a source partial, the signed mathematical difference can be negative, while the audible real-signal spectrum contains the corresponding positive-frequency component. Lower sidebands can therefore turn up in frequency regions that are easy to misread if you only picture two neat lines around a carrier. A study of live ring modulation in a scored piano and percussion work runs into the same issue with acoustic sources. The [B][URL='https://ro.ecu.edu.au/ecuworkspost2013/2990/']interaction of complex overtones under ring modulation[/URL][/B] matters because rich instrumental spectra produce results with properties of both harmony and timbre, not merely a clean pair of extra tones. [HEADING=2]Carrier shape decides how crowded the spectrum becomes[/HEADING] A sine carrier is the controlled case because it contributes one main frequency. Change the carrier to a square-like, saw-like, folded, or hand-drawn waveform, and its own harmonics enter the multiplication. Each added carrier partial creates another set of shifted versions of the source spectrum. Square-wave modulation makes the mechanism easy to hear. Its odd harmonics act as additional carrier frequencies, so a source component can generate sidebands around the fundamental carrier, then around three times that frequency, five times it, and higher odd multiples at progressively different levels. Rich carrier shapes can make a chord sound far more crowded without changing a single played note. For musical work, restraint often beats another turn of the depth control. Start with a sine or otherwise sparse carrier when the input is already harmonically dense, then choose the carrier frequency by listening to what happens to the root, third, and strongest upper partials. Filtering before multiplication can also remove source components that would otherwise generate unwanted sidebands. Monophonic material gives you another degree of control because the carrier relationship only has to suit one note at a time. Polyphonic pads, piano chords, and distorted buses are less forgiving. A modest carrier with a simple waveform can preserve some pitch identity, while a harmonically rich carrier can turn the same chord into a dense inharmonic texture within a few cycles. [/QUOTE]

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