If you want any kind of quality audio (not just buzz and hiss), then you will need a well filtered and well regulated power supply.
You can either learn about power supply design (an interesting and useful subject), or you can buy a module that does it for you.
I have this Recom 1215D DC/DC converter, that ripple from 50mv is to much for me, i dont want HF ripple at all.
I also going to avoid mains voltage, thats why i do this with wall adapter.
If i connect the Recom 1215D Vin- to COM, the ripple is gone, only slow peaks that go higher then the ripple voltage.
I've seen this arrangement being used in several commercial audio products, but only for low power applications (sub 100mA).
What are your power requirements?
Not so much, i build a few drumsounds + maybe mixer with eq, about 100mAh each + & - 15v.

Thats about what i trying to do for the power supply, without those extra diodes and bigger caps.
My advice would be don't.
As you're building this from scratch, avoid having to use a dual power supply in the first place, so a single, rail, efficient switched mode power supply can be used.
Do you already have the schematic? If it states it needs a dual supply, it's very likely it can be converted to work off a single supply with minimal effort.
I,m making this schematic ( maybe twice if it works ), and another drumsound, it cannot be done without symmetrical power supply,
if you wanto figure it out how it will cost you more then a week, your welcome to make this schematic single supply if you like, or tell me why it is not possible :
