Fast
Med
Slow
Very Slow

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555 Timing:  Ra Rb
Duty Cycle >50% 
Duty Cycle <50%
Normally the 555 timer is unable to produce a duty cycle of 50% or less. This is due to the fact that the first half of the cycle both Ra and Rb determine the charging interval (T1); where Rb alone determines the discharge interval (T2).
To allow a Duty Cycle of 50% or less, a Diode D1 is placed in parallel with Rb such that during the charging cycle (T1) Rb is bypassed. This allows Ra and Rb to act independently, allowing a duty cycle of nearly 0% to nearly 100%.
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Triggering of a 555
The Triggering process starts when the negative differentiated pulse edge "dips" below 1/3 Vcc, the capacitor starts charging.

If the trigger is held below 1/3 Vcc longer than the charge time, the output will remain high even though the capacitor charging cycle is complete; and then only goes low when the trigger rises above 1/3 Vcc. 

It can be seen, therefore, that it is desirable to have the negative going trigger pulse to be shorter than the charge time.
 

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Three Cascaded Delays

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Using two 555s as an AM Transmitter
A Word  or Two about using Pulse Width Modulation for AM broadcasting: 
Always keep the Pulse Width of the modulation between 
> 50% & < 100%; 
OR between 
> 00% & < 50%. 

At first blush, the reasoning for this may not be obvious: A transmitter is not broadcasting a varying voltage but a varying POWER. That is, the varying modulation voltage is controlling how much Carrier POWER is transmitted. Although the modulating voltage may have a polarity +/-, the RF power leaving the antenna has no polarity. 

At the receiver the varying power is demodulated/ which is saying it is converted from a varying power to a varying voltage, and if you "AC Couple" the detector's output you again have a varying voltage that has a +/- polarity. --Huh? 

NOW! At this point you should not have experienced an "Ah Ha!" --yet. 
        --BUT,  Stand-By YOU are about to Experience a Genuine "Ah Ha!"  --or your money back.

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Of course, we will need a 
Graphic:--> 

Notice anything Funny? Right, the second harmonic of the modulation signal increases if the [ > 50%, < 50% ] rule is violated!

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Example:  Generating a delay,  using Dual 555s (or one NE556)
Triggering a 555 requires that the "Trigger" input be A.C. coupled. Typical values can be found in the 555's data sheet & app notes.

However, some values: Rp = 10k, Cc = .001ufd.

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Car Tachometer
  
The timer receives pulses from the distributor points. Meter M receives a calibrated current thru R 6 when the timer output is high. After time-out, the meter receives no current for that part of the duty cycle. Integration of the variable duty cycle by the meter movement provides a visible indication of engine speed.  
 
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555 Circuit using 60 Hz as clocking source 
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Using Countdown circuit for LONG delays.

Note relay driving circuit with Protection.

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 Layout of 555 Circuit 
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555 as 
F.M. Xmitter
445 kHz
Oscillator frequency modulated by a 1-kHz tone.
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Method for 
50% Duty Cycle