Reported are the emission properties (energy-time distributions) of high-order harmonic generation (HHG) calculated for lasers of different pulse durations (τL, in units of radian) in full width at half maximum (FWHM) and different carrier-envelope phases (CEPs,Φ). Calculations demonstrate that the cutoff energy of HHG spectrum produced by a few-cycle laser is less than that by an infinite duration laser (ωmax=3.17Up+Ip, where　ωmax is the angular frequency of the photon, Up the ponderomotive potential of the laser field, and　Ip the atomic ionization potential). A τL＝4π rad,　Φ＝15° laser can produce a single distribution pulse peaked at 0.94 rad and spanning 1.29 rad with a cutoff energy ωmax=2.90Up+Ip and a bandwidth 0.86Up. For the same laser but with Φ＝-75°, double distribution pulses occur with equal amplitudes, cutoff energy　ωmax=2.70Up+Ip and bandwidth 0.70Up. These two pulses are peaked at -0.58 rad and 2.43 rad，span 1.22 rad and 1.33 rad, respectively. Calculations also demonstrate that the bandwidth of a selected distribution pulse decreases much faster than its duration as the laser duration grows. The CEP dependence of the single distribution pulse parameters (its energy and time positions) show interesting 180° periodic structures. These features enable us to select attosecond pulse parameters and temporally control them by adjusting CEP. Theoretical analysis shows that the influences of CEP instability on the measured photoelectron spectra and the experimental results may be weakened to the maximum extent or even eliminated by choosing appropriate energy bandwidths of X-rays in attosecond measurements. All these results are helpful in realizing the HHG dynamic process. They can be used as new references in optimizing and selecting single and double attosecond pulses.