But as many scholars have argued, this image is distorted. Even the Umayyad dynasty, begun by Abd al-Rahman in 756, was far from enlightened. Issues of succession were often settled by force. One ruler murdered two sons and two brothers. Uprisings in 805 and 818 in Córdoba were answered with mass executions and the destruction of one of the city's suburbs. Wars were accompanied by plunder, kidnappings and ransom. Córdoba itself was finally sacked by Muslim Berbers in 1013, its epochal library destroyed.

Andalusian governance was also based on a religious tribal model. Christians and Jews, who shared Islam's Abrahamic past, had the status of dhimmis -- alien minorities. They rose high but remained second-class citizens; one 11th-century legal text called them members of ''the devil's party.'' They were subject to special taxes and, often, dress codes. Violence also erupted, including a massacre of thousands of Jews in Grenada in 1066 and the forced exile of many Christians in 1126.

In fact, throughout Andalusian history -- under both Islam and Christianity -- religious identity was obsessively scrutinized. There were terms for a Christian living under Arab rule (mozarab), a Muslim living under Christian rule (mudejar), a Christian who converted to Islam (muladi), a Jew who converted to Christianity (converso), a Jew who converted but remained a secret Jew (marrano) and a Muslim who converted to Christianity (morisco).

Even in the Umayyad 10th century, Islamic philosophers were persecuted and books burned. And despite the Córdoba museum's message, Maimonides and his family fled Muslim fundamentalism in Córdoba in 1148 when he was barely in his teens. Averroës was banished from Córdoba about 50 years later. Tolerance may have left less of a cultural mark than intolerance: the historian Joel L. Kraemer has suggested that in Andalusia, a sense of precariousness inspired mysticism, esoteric teachings and a ''prudent dissimulation'' before Islamic superiors.

And what of Andalusian cultural interchange? Ms. Menocal cites the ways Islamic styles appear in Spanish synagogues (one, in Toledo, even incorporating Koranic inscriptions) and in the 14th-century Christian palace the Real Alacazar in Seville. But far from exhibiting convivencia, these resemblances display the power of a culture as dominant as American popular culture is now: it is imitated even if otherwise opposed.

None of this, though, reduces the impulse to idealize Andalusia. One reason may be that it looks so good given what followed. In the 1391 pogroms in Christian Spain, for example, an estimated 100,000 Jews were killed, 100,000 converted and 100,000 forced to flee -- a prelude to the 1492 expulsion of all Jews and the 17th-century expulsion of all Muslims. In comparison, many societies might resemble paradise.