The original building was a chapel, attached to the Holy Spirit hospital next door, and built sometime in the fourteenth century when Alkmaar was still establishing itself as the market town for the agricultural country to its north. In 1566 the Bishop of Haarlem - in one of those bureaucratic decisions that quietly changes a city - granted permission for the hospital to re-purpose part of the building for the weighing of goods. By 1582 the actual weighing had been moved into the larger Holy Spirit Chapel itself, which had stopped being used for services. The conversion was finished in 1583. The choir of the chapel was demolished, and a richly carved Renaissance facade was put up where the apse had been. Today, if you stand on the Waagplein and look down at the pavement, you can still see the outline of the vanished choir traced in the cobbles. The facade you see is a careful 1884 copy of the original. Between 1597 and 1603 the modest spire was replaced by the much larger Waagtoren that dominates the square.

Across the front of the building runs the inscription SPQA RESTITVIT VIRTVS ABLATAE JVRA BILANCIS. The acronym is a deliberate echo of the Roman SPQR, but Alkmaar's version reads Senatus Populusque Alkmaris - the Council and People of Alkmaar. The full line translates roughly as: "By virtue of its courage and strength, [Alkmaar] restored the rights of the balance that had been taken away." The balance here is the literal weighing scale, and the claim is specific. After the failed Spanish siege of 1573, when Alkmaar held out and the tide of the Dutch Revolt began to turn, the citizens won back the right to operate their own weigh-house - a right that had legal and tax consequences. The truce that recognized this was signed on 8 October 1573. Nine years later the conversion of the chapel into the official town weigh-house began. The Latin inscription, in other words, is not classical decoration. It is a small civic boast about a recent military victory, carved into the building that the victory made possible.

The carillon now in the Waagtoren contains forty-seven bells. The largest, the bourdon, keyed as a low C but pitched at E-flat, weighs about 1,375 kilograms. The historic meantone tuning, rather than equal temperament, has been retained - so the chords ring with the slightly purer thirds and slightly sourer fifths that Bach would have known. Getting to this point took three centuries of expensive failure. An earlier eleven-bell chime by Jacob Waghevens of Mechelen, dating to the 1540s, was kept in service even after the Hemony brothers worked out how to actually tune bells properly in the 1640s. In 1671 the city tried to hire Pieter Hemony himself, then refused his demand to remove the bars enclosing the belfry; the deal collapsed. After Hemony's death, Claude Fremy was hired in his place, melted down some of the old bells for metal, and produced a carillon so badly tuned the city rejected it and made him repay the cost of the bronze. Some of Fremy's rejected bells ended up, by a long route through an Amsterdam merchant in 1695, in the tower of the Loreto convent in Prague, where they still play. In 1688 Melchior de Haze of Antwerp finally delivered a thirty-five-bell carillon that the city accepted. On 26 October that year, at 3 p.m., the city carillonneur Gerard van der With played the first concert. The 1967 Royal Eijsbouts expansion to forty-seven bells used the surviving de Haze bells as the foundation. Twelve bells de Haze cast that Alkmaar rejected for tone are now in the turret of the Grote Kerk; another set, mixed with Eijsbouts and Taylor bells, plays in the Kapelkerk. Alkmaar therefore has three working carillons, all descended from the same 1688 commission.

The clock in the tower was made in 1541, with Gothic angle pillars that still mark its frame. The drum mechanism - the great metal cylinder studded with bronze pins that lifts the hammers onto the bells - was added by clockmaker Willem Spraackel around 1690. The same year, the clock was converted to use a pendulum, an invention popularized by the Dutch polymath Christiaan Huygens only a few decades earlier. Every quarter hour, the drum strikes the bells in what is called the Hollandse slag, the Dutch strike: a short melody on the quarters, a fuller passage on the half-hour, and the deep bourdon on the hour itself. Twice a year the city carillonneur changes the tunes by physically removing the pins from the drum and inserting new ones at new positions - a process called versteken. The other animated feature, the ruiterspel or horsemen's play, has knights on horseback performing a brief tournament during the full hour strike, while above them a wooden trumpeter blows a melody. The trumpet sound comes from a small reed organ behind the figures, fed by its own miniature drum. The organ has double pipes for every note - one labial, one reed - and must be retuned regularly by the city carillonneur, because temperature changes pull it out of pitch. Christiaan Winter has held the post since 2009.

Inside the Waag, on the ground floor, the original weighing room still holds its great balance scales. Today they weigh ceremonial wheels for the Friday morning cheese market on the square outside, which from late March through late September stages the rituals of a guild that no longer trades cheese in any commercial sense. The Dutch Cheese Museum occupies the upper floors and tells the story of how the Edam and Gouda wheels that built this region's fortune were made, traded, and aged. The tourist information office - the local VVV - sits inside the same building. The square has bars and tapas places along its edges. On most evenings the carillon plays a concert; on Saturday mornings at eleven, and during the cheese market on Friday mornings, the city carillonneur performs live from the keyboard above. The bells, the clock, the trumpeter, the cheese market, and the museum all happen inside one building. None of them happen by accident.