Research Soft Synths and really cool Android apps - wrightflyer/Synth GitHub Wiki
In reality, if you want to "tinker with synths" then these days you don't actually really need very much than your PC or even just your tablet/mobile phone. These things have CPUs with insane power and can easily synthesise multi-voice sounds.
PC's (and Macs etc) have "VST" which are each just a loadable module that is some kind of instrument or effect. You just need a VST host (such as most Digital Audio Workstations - DAW) that have the ability to load any number of VST then route the inputs (could be a real USB MIDI keyboard device) to the various simulated instruments.
Even mobile phones (and tablets) have apps in their libraries that can synthesize sound. I'm a dedicated Android fan so I would pick items from the Google Play store but almost all of these (and more) are in the Apple app store too.
Now what I am trying to do here is make a "modular synth". It's a bit like a "Lego synth". There are fundamental building blocks and you just wire up paths (patch coords) between them in various ways to make an audio path to start the generation of a sound and then "shape" it in various ways. Most such synths have as a minimum an Oscillator that acts as a sound source, a "gated" amplifier and the final audio output device. The oscillator gets told which key has been pressed and plays that frequency continuously but the amplifier only lets the output "get through" for as long as the "gate" tells it the key is pressed. When the key is released it stops the sound. But that just makes very simple sounds so usually another device called an ADSR (Attack-Decay-Sustain-Release) envelope is inserted between the keyboard gate and the amp. So when a key is pressed then released it doesn't just immediately switch the amplifier on-off but instead the key going down starts an "attack" phase and the volume ramps (quickly or slowly) to some peak level, then a decay segment starts and the sound starts to die away. But if the key is still pressed the level is held at some "sustain" level (which is likely lower than the initial peak) and finally when the key is released (envelope is told "note off") it goes into a final "release" phase and the sound dies away either rapidly or gradually.
In the jargon the oscillator that makes the noise in the first place is a "VCO" (voltage controlled oscillator), the level controllable amplifier is a VCA (voltage controlled amplifier) and the envelope generator is simply an "ADSR". Another module that is in common use is an LFO (Low Frequency Oscillator). This doesn't create the actual sounds you here but is typically fed to filters and VCAs to cause them to "come and go" at a regular rate (usually something between a fraction of 1Hz and 20Hz).
If you download "analog"/"modular" software synthesizers for Android/iOS you will typically see many of these items as separately controlled units in the synth but generally the connection between the things is in some fixed order (though fancier ones may be software patchable).
In the PC/VST land there's all kinds of software simulated synthesizers but if you look hard enough you'll find that some are very specifically simulations of "analog"/modular and of these quite a few really good ones are completely free. I found many articles comparing the best of them and perhaps this summary is one of the best...
https://www.attackmagazine.com/reviews/the-best/ten-of-the-best-modular-software/
Some of the best ones there are:
Blocks Base within Native Instruments Reaktor 6 (this bit of Reaktor is free) VCV Rack - this is the main open source (free!) development for rack synthesizers Cherry Audio Voltage Modular
I've used all of these a bit and perhaps it's just a personal thing I think "Voltage Modular" wins by a country mile! What's more, until Covid, it was commercial and cost real money but in a fit of philanthropic altruism the developers announced that since every one was locked up in doors they'd make it free so you had something to do in isolation. It's got be worth getting for that reason alone! See:
https://cherryaudio.com/news/2020-03-17/covid-19-voltage-modular-nucleus-free-for-all
On my Android tablets and phones I tried out a few of the offerings (obviously things are more "playable" on a tablet than a phone!). There are many free options. The ones currently on my phone are:
- Caustic
- Common Analog Synth
- DRC
- EasySynth
- Hexen
- ModSynth
- ORG 2021
- QiBird
- Synth FM
Now again maybe it's a personal thing but for me "ModSynth" stands out by a country mile. It's actually EXACTLY what I want to build in hardware. In fact I like it so much that I immediately paid for the in-app upgrade (£5 I think?) to get access to other "Lego building blocks". Get the "free" one from this link:
https://play.google.com/store/apps/details?id=com.gallantrealm.modsynth&hl=en
This image gives an idea of the way it's used with blocks and lines defining how the synth is wired together...
If I can generate something in hardware with Teensy as the sound engine that is even just 1/10th as good as that I will feel I have succeeded. I can't recommend it highly enough.
But, to be clear, I didn't see that and think "I want to build one of those". I initially thought "I want to build a modular synth that is portable (like a VL-Tone). Then while I was doing background reading and research I happened to download that app and thought "tickle me pink and call me Gertrude, but this is exactly the kind of thing I want to do". If my final design ends up looking and behaving a lot like that I'm afraid I can't help it because, by a coincidence, it was an existing implementation of almost exactly what I had independently thought of.
Other research
Reading around about synth topics in general I thought the following is a brilliant series of articles about the core components of synthensizers:
Also synthesizers.com is a site trying to sell real modular synth systems but they also have a great set of educational videos that basically explain things from the ground up:
https://synthesizers.com/tutorials.html leading to... https://www.youtube.com/playlist?list=PLvm7myerzlkAuECUHK9qiicbpyXQG0wlT
Oh and while talking about synthesizers.com I have to share this picture:
Top end system at synthesizers.com

This bad boy will cost you $15,249.50 (love the .50 on the end of that!!). I hope to end up with something similar ;-)