Bach's 'Orgelbüchlein' (O=B) has so far been regarded as a musical torso. Only 46 out of the total 164 chorale titles recorded in the autograph were actually composed. Felix Pachlatko provides evidence, based on newly discovered arithmetic structures in the work, that the O=B must not only be seen as planned in its current form but also as complete. The way Bach structured the O=B is not innovative. The foundations of this connection between music and mathematics are rooted in Pythagorean thinking. Examples of this can be found in music from the mid-14th century to Bach's immediate predecessors. In addition to integer ratios and golden sections, the O=B also demonstrates magical squares and a magical cube for the first time. However, the most complex construct is likely to be an extremely precise golden section.