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FM Single Operator Waveshapes

FM Single Operator Waveshapes
Single Operators are still sine wave generators but each can be used to generate complex wave shapes by modulating themselves... This is called Feedback.

According to Dr. Chowning, the Father of FM, one of the major innovations that Yamaha engineers brought to the table was the Feedback loop. Basically, routing the output back to the input to generate more complex tones. While this is similar to having additional modulators, it is not exactly the same thing - but will get you similar sonic results. In the reface DX each of the four Operators can be fedback on itself; this means a single operator can be a complex wave source. In the original DX7, for example, you had some ability to use Feedback. When all Operators are simply sine wave generators, if you wished to modulate a Carrier with a Sawtooth or Square Wave you would need to create a two Operator Modulator "stack" to generate that modulation wave to feed into the Carrier. Now any single Operator can generate the Sawtooth Wave or a Square Wave.

What this will translate into is you can build more complex waveshapes with fewer Operators; you can use your Operators to add fine details to your sound because it take less of them to create complex tones. You can simply build really phat sounds, quickly and easily. It's something new to explore. Let's begin with an Initialized Voice.

Navigate to screen #4
Select "YES"
Press [ALGO]

ALGO12This time lets select Algorithm #12... where each Operator is a Carrier (which means it is capable of audio output). Again, only Operator 1 has its Output Level set to 100, in an initialized Voice.

Playing the keyboard, you will hear the pure (and lonely) sine wave - no harmonics. Let's apply some Feedback: Much like a microphone in front of a speaker column or an electric guitarist standing up close to the amplifier, Feedback is the process of signal traveling in a loop, output back to input, over and over again. What the engineers designed this time is a way to channel that energy specifically toward creating Sawtooth type Waves (those that contain every whole integer multiple of the Fundamental - ie, all harmonics) or toward creating Pulse type Waves (those missing certain odd numbered harmonics according to the width of the pulse). A Pulse Wave that is 1:2 (square) will be missing every other harmonic; it contains only the odd numbered harmonics. A pulse that is 1:3 will be missing every third harmonic, a pulse that is 1:4 will be missing every fourth harmonic and so on.

Press [FB] Feedback
FB 0You arrive at a screen showing the four Operators set to 0 (0 here means sine wave). As you swipe up in touch column 1 you will be sending the output of Operator 1 back into itself and thereby generating a Sawtooth Wave output. The higher the value toward 127, the brighter the result. The wave will contain all harmonics.

Notice that there is a "law of diminishing returns" in effect here: as you increase the value, the sound gets richer and brighter, however, once you exceed a certain value the sound starts to over modulate and thin out. Hint: when setting Output Level - use your ears, they will serve you better than the mathematics!
FB 95
Try the opposite direction, again, as you increase the value by swiping down from the 0 centerpoint, the sound gets richer and rounder, as it tends toward the Square/Pulse Wave output. FB 95sqAnd again as you near the extreme the sound begins to thin out again. 

Extra Credit: We mentioned that only Carrier Operators can be heard - Modulators are only heard by how they impact the timbre of the Carrier. You will discover when working with Operators and creating basic wave shapes, it is useful to use the ability to switch Algorithms. When you want to hear your Operator you can switch to an Algorithm, like #12, where all Operators are Carriers and will output audio. The integrity of your programming within the Operator is maintained even though you switch it from Modulator to Carrier, for example. In general, the more complex the Modulator's waveform the more radically it will influence the Carrier you route it through. If your Modulator is very complex, it may quickly result in generating so many sidebands (all frequencies) it will begin to approach non-musical sound (Noise). Noise contains all frequencies simultaneously. Sometimes the best sound is obtained through subtle use of this modulating "influence"... like applying vibrato to a violin or to a synth lead, sometimes a little is all you need. Applying too much can lead to a bit of chaos. The "Modulation Index" is a fancy way of saying the "amount" of modulation you are applying to the Carrier (Modulation Index = the Output LEVEL of the Modular). As we go forward, we'll show you how to isolate the contribution of each of your Operators. Next we'll look at the Amplitude Envelope Generator - how loudness or output is controlled over time. The old "ADSR" (Attack-Decay-Sustain-Release).

If you have any questions or comments about this article, please let us know in this forum thread.

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