I ... if choose impedance of speakers, I will choose 8ohm. 8ohm speakers need half or current but only quieter 3dB. My amplifier will hotter when drive 4ohm spkr.
But I can't understand why many people think 4ohm speaker is higher end than 8ohm while I have saw many tube amp use 8ohm speaker many transistor amp use 8ohm speakers too.
As the other members say, the speaker impedance is designed to match the amplifier V/I characteristics. 15 Ohms was used in the valve days for hi-end amps because it was the best compromise between the output transformer design and speaker coil design. As far as the speaker coil is concerned, 3 Ohm is the best. That is why it was the standard for years- it uses a small number of turns with relatively thick wire which is more rugged, cheaper to manufacture, and better for heat dissipation. Why 15 Ohms then? It's because of the output transformer. The higher the turns ratio the harder it is to get a good performance. 15 Ohms is also better for distributed speaker systems as it has 0.2 the current of a 3 Ohm system for a given power, thus the resistive losses are lower- just like the mains power grid. For weedy amps, like in the early battery-powered transistor radios for example, speaker impedances as high as 300 Ohms were used.
Since the 1970s the trend has been towards 8 Ohms to match the V/I characteristics of solid state amps. In general 3 Ohms allows more power from a solid-state amp because, to a first order approximation, it is easier to provide more current than more voltage.
By the way, the stated impedance of a loudspeaker is only nominal. If you measure the resistance of an 8 Ohm speaker with a multimeter, it is likely to read around 7 Ohms, but this changes, sometimes radically, through the audio frequency spectrum, and some 8 Ohm speakers, with cross-overs, can drop to as low as 2 Ohms, particularly at bass resonance and the cross-over point of 300Hz to 3.5KHz.
4 Ohm, 8 Ohm, 15 Ohm make no difference to the audio quality of a speaker. In fact, it is not uncommon to see the same speaker chassis available in all three impedances.