mikhailvs - May I help you answer this question?
You can design a frequency synth in many ways. You choose high speed clock and divide by N counter (software or hardware) . THere are decimal and binary counters and "Fractional N counters". Some use variable clocks using digital or analog Voltage control. Others are simply various integer multiples of your lowest output frequency. If you want a CMOS binary counter you can create ~50Hz easily from a simple CMOS clock at 50KHz and 2^10 "CMOS binary counter" In software you can use a single or double precision counts and many embedded chips have hardware counters. The output can be enabled and programmed by input states.
Freq synth's are used everywhere from digital radios, TV's, clocks, watches, microwave, and telemetry channels. Such as 1pps from GPS signals.
If you need more precision, ceramic or watch oscillators can be used or quartz.
PWM is generally a fixed frequency and phase is modulated 0 to 100% to synthesize a linear on off switch. These are used in power supplies, class D audio amps and many other applications.
Without more details I hope this triggers some key words to search for.
Maybe you want to build a MOOG synthesizer instead.
The requirements are understated.
in this case you can use a VCO with different waveforms and filters to create a single tone using a calibrated VCO and DAC. or use one chip per octave .
Then this chip for a smart VCA.
Scrap the idea and learn to use the free MIDI synth on an old PC and use a custom weighted 88 key board to play the synth using the MIDI port for key input. Or simply buy an AXIOM keyboard and play on your Mac AIr in minutes with Darth Vader sound effects singing. Bob Moog eat your heart out using Garage Band.
My buddy Peter Allen in Vancouver blew away Speilberg's Industrial Light and Sound's 1st UCLA course for in Composition for FILM. (e.g. he had more experience than the rest of the class together) Prior to this, Peter studied his Masters in Music at McGill and Bachelors in Winnipeg, and used the Moog in 1975 and now has composed more than 50 (maybe 80 by now) film & music arrangements to his credit. Thanks to Bob Moog's inspiration.
OK no more edits
The AXIOM 88 is inexpensive and can play any music anytime anywhere and WILL do more than simple notes with a software Midi controller.
That's all folks.
Thank you for letting me help you.