I'm looking for a simple circuit, preferably based on the 555 in order to get continuous configurable fading tones (chimes), just like a "door open warning". It will fade in and fade out, not very annoying.
Doing this with 555 timers is possible but will require at least two and some additional analog circuitry to get "nice" sounds that aren't just amplitude modulated square waves.
A much simpler way is to use a micrcontroller. You can either keep one cycle of the chime sound in memory or perhaps synthesize it from multiple sine waves if you want it to change over time. Once you have the tone, you can multiply it by a much slower signal to get the volume envelope. This would all be done digitally and the result used to adjust the duty cycle of a PWM output. Then you only need to low pass filter that to get the analog signal you want.
My simple way I did what you want was I bought a really cheap small battery power "star trek sounds" toy from a gift shop for around $1 whose sounds were like I wanted, opened it up and took out the tiny circuit board in it and connected one of the three switch wires on the pcb to the output of my circuit with a 1k resistor and connected the voltage and ground lines to a 3.3volt wire and ground from my arduino. Each switch wire on the pcb makes a different sound and I easily found the one that made the sound I wanted.
So I got the sound done quickly and could spend time on function I wanted to make on the arduino instead of spending time in doing the sound part circuit and all. I know this is not a technical great answer like some are on this site but I am self taught so sorry.
You can get this effect using a simple single transistor cirucit as shown below:
AudioIn should be the output from your 555. Voltage input should be below 5V (use a voltage divider if nessesary).
On the trigger input, apply a short 5V to 9V pulse. This will charge C1.
The charge stored in this capacitor will have enough power to supply the amplifier switch built around Q1 for a while, and the output voltage will be proportional to the voltage across C1.
Since C1 is slowly draining over R1 and Q1 you'll get a exponential fade at AudioOut his way.
Note: This circuit won't work for general audio, but it's fine for square waves such as the 555 output.
You can also add a fade-in effect by putting a series resistor in front of D1.