Amethyst almost never forms with its colour evenly distributed. Violet quartz grows in zones, with the saturation concentrated in bands or in the tips of the crystal and the rest running toward colourless, and a cutter working amethyst has to orient every stone so that the strongest zone sits where it will be seen through the table. On a 37 mm Royal Oak set across the dial, the bezel and the entire bracelet, that decision has to be made a great many times over, and the smaller the baguette the less room there is to position the cut around a weak zone. Matching a run of them so that no single stone reads pale beside its neighbours is the real work in this reference. Amethyst is also the only stone in the ten-piece anniversary gem set drawn from a common mineral: quartz is the most abundant gem-forming species on earth, and until Brazilian deposits opened in the early nineteenth century amethyst was traded alongside emerald and ruby before supply collapsed a value that had held for centuries.
The case is 37 mm across and 10 mm thick in white gold, with the octagonal bezel gem-set in baguette-cut amethysts. The plain 37 mm selfwinding Royal Oak of the same generation measures 9.1 mm, so the complete setting costs nine tenths of a millimetre here against the one and one tenth it costs on the 41 mm version, because smaller stones sit in shallower channels cut into the metal. The eight hexagonal screw positions survive and remain the fixed interruptions the continuous run of stones is built around. The dial is white gold set with baguette-cut amethysts across its full surface and carries no applied hour-markers at all. The stones are the dial. Only the white gold Royal Oak hands sit above them. The bracelet continues the same setting along its length, tapering from the case and closing on an AP folding clasp. Quartz is less refractive than the corundums and garnets in the set, so the dial returns light more evenly and with less flash, and at 37 mm across a denser field of smaller stones that evenness reads as a single continuous violet surface rather than as an assembly of individual gems.
The function set is hours, minutes and centre seconds. There is no date, and the omission follows from the dial rather than from the movement: an aperture cut through a continuous stone surface would break the setting at the point where the run most needs to remain unbroken, and on a 37 mm dial that break would occupy a greater share of the field than it does at 41 mm. Centre seconds keeps all three hands on one axis and avoids the second circular interruption a small seconds subdial would impose. Time is read from hand position against the case, since the dial provides no reference points. Amethyst sits at a middle depth of tone and the low flash of quartz works in the wearer's favour here, because a dial that returns light evenly competes less with the hands than a brilliant stone does. This is among the more readable references in the set despite the dial being entirely given over to stone.
The Royal Oak is the collection Audemars Piguet is built on, and the 37 mm anniversary references form a three-step ladder in setting. The 15550 is plain at 9.1 mm, the 15551 adds a diamond-set bezel over an unset dial and holds the same height, and this reference sets dial, bezel and bracelet together and reaches 10 mm. Ten stones were used across the gem-set programme: amethyst, ruby, blue sapphire, emerald, tsavorite, tanzanite, blue topaz, pink tourmaline, yellow chrysoberyl and orange spessartite. Each was issued at 37 mm here and again at 41 mm at reference 15514, producing twenty references on one construction in two sizes. Purple is the only appearance of its colour among the ten, and the nearest relation anywhere in the programme is not another anniversary reference but the smoky quartz used in one of the two non-anniversary 41 mm graded dials, which is the same mineral in a different colour.
This reference suits a collector buying the colour rather than the material argument. Amethyst does not carry the scarcity case that tsavorite or tanzanite carry, and it does not carry the hardness case that ruby and blue sapphire carry, so the reason to choose it is that violet is the colour wanted and nothing else in the set provides it. That is a cleaner motivation than the rarer stones invite, and it removes a layer of justification rather than adding one. The softness has to be accounted for, since amethyst sits at the bottom of the set alongside tanzanite and a 37 mm bracelet takes more contact than a larger one. It appeals to someone who wants a gem-set Royal Oak in a colour the collection otherwise never uses, and who prefers the quieter optical behaviour of quartz to the flash of a garnet or a corundum. The anniversary designation ties production to the occasion rather than to an open catalogue run.