Analog vs Digital
In what regards music making.
Analog

Advantages:
- Inherent non-linearities of real world physics, electro-magnetics, mechanics, create unexpected results and rich sounds.
- Complex sounds with little effort.
- Usually analog devices have a direct control mechanism included (keyboard, faders, knobs) and operate “out of the box” , allowing for quick experimentation and (more or less) intuitive exploration.
- Don’t crash and don’t break that easily.
- Hackable: it’s possible to operate out of the designed specs.
- Future proof: just connect to 220 volts and it’s working 100 years from now (at least if you took good care of it).
Disavantages:
- Heavy, expensive, difficult to substitute if broken. Non-portable.
- Results cannot often be easily replicated (might be a good thing depending on the objective).
- Limited control. Either because of two arms - 100 knobs ratio problem or because of having to patch 100 cables or splice 10000 segments of 1 second of tape takes a lot of time, and limits experimentation of new approaches.
Digital/Computer
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Advantages:
- possibilities are only limited by cpu power and programming capabilities. 100 sine-waves take the same time to “patch” as 1 (not so true in visual programming languages that try to emulate the visual paradigm of analog devices).
- Instant recall of a setup.
- Very portable. A recent powerful laptop can be taken anywhere easily, great for touring, and general traveling.
- Control can be very very complex, much more than anything possible in analog.
Disadvantages:
- Complex sounds are quite difficult to obtain. Without care and expertise, digital synthesis sounds sterile and repetitive.
- Usually doesn’t operate out of the box. Things have to be setup, programs started, presets recalled, drivers loaded, sound cards selected, midi devices connected, etc.
- Cannot be easily hacked to operate out of the range where it was designed to operate. Randomly changing code will just crash the program, not get more interesting results.
- Not future proof: high danger of software becoming obsolete. Running a patch 10 years from now will be no easy task.
Closed boxed digital devices seem to me to join the bad parts of the analog world (poor control, not extendable, etc) with the bad parts of computer/digital (not very complex sound material), but they do operate out of the box, are more future proof and more portable than analog equivalents, and off-course sometimes that’s exactly what is needed in a concert situation or for intuitive approaches.
In terms of sound reproduction I don’t really see any advantages of analog vs digital, the best ad-da converters out there are basically transparent and inaudible, and if one wants the “sound” of vinyl or tape I would consider that part of the music making process and not of the sound reproduction.