Adrian, it is not clear what you are describing. If I understand you're saying the 2nd and third phases should be 15⁰ out of phase with the previous?
There is a difference in between the phase shift of the generated voltages and the phase shift in between the coil patterns. How much difference depends on the number of armature poles and on the number of phases. Assume that the armature has 12 poles. Assume that the angle in between the shift of the voltages is called alpha and that the angle in between the shift of the coil patterns is called beta. If the armature of a 12-pole armature has rotated 60° from a certain starting position, a north pole is at the same position as at the starting position. A full sine wave is generated for this angle of rotation of the armature. So a rotation angle beta = 60° of the armature corresponds to a phase angle alpha = 360°. So a phase angle alpha = 1° corresponds to an angle beta = 1/6°. This means that if you want a phase angle alpha = 90° in between the phases, you need an angle beta = 90 / 6 = 15° for the phase shift in between the coil pattern of the two phases for a 12-pole armature.
For a 2-pole armature, the angle beta is the same as the angle alpha
For a 4-pole armature, the angle beta is half the angle alpha
For a 6-pole armature, the angle beta is 1/3 of the angle alpha
For an 8-pole armature, the angle beta is 1/4 of the angle alpha
For a 12-pole armature, the angle beta is 1/6 of the angle alpha
For a 16-pole armature, the angle beta is 1/8 of the angle alpha
If you want a 3-phase winding in stead of a normal 2-phase winding with a phase angle of 90°, the phase angle alpha must be 120° in between all three phases. So in this case the angle beta in between the phases must be 120 / 6 = 20° for a 12-pole generator but 120 / 4 = 30° for an 8-pole generator. One gets the same coil pattern if the angle beta is doubled, so if beta = 40° for a 12-pole armature and if beta = 60° for an 8-pole armature. The double angle is always used for a 1-layer, 3-phase winding with separate coils. Figure 5 of report KD 341 shows the 1-layer winding of an 8-pole PM-generator which has six separate coils. In the upper picture, it can be seen that the angle in between the left leg of adjacent coils is 60°.
It may look strange that the phase angle is 90° for a normal 2-phase winding and not 180° but that is because only for a phase angle of 90° you can make a rotating magnetic field for an asynchronous motor. There has been a big struggle in the past in between a DC-grid and an AC-grid and in between a 2-phase AC-grid and a 3-phase AC-grid. Finally the 3-phase AC grid has won but there are still towns in America which have a 2-phase AC-grid and for those towns you need 2-phase asynchronous motors. The voltage fluctuation of a normal 2-phase grid is given in figure 13 of my report KD 340.
I still insist that you get only doubling of the power for a 2-phase winding for which you have 90° phase shift of the voltages in between the phases. For such a winding you use positions of the wires every 15° for a 12-pole armature. Therefore you can use the double amount of copper than for a 1-phase winding. For a 2-phase winding with 180° phase shift of the voltages in between the phases, both phases compete for the same optimal positions at every 30° and therefore every coil can have only half the amount of copper as for a 1-phase winding. But if people don't agree with my conclusion, I can't help them.