First recorded in 1615 the word mystique refers to the legendary aura of power or mystery as in the mystique of Alaskan wilderness. It’s derived from the mid-14th century French adjective mystic from Old French mystique which has its roots in the Latin word mysticus who probably took it from the Greek word mystikos meaning "secret, mystic," and from mystes describing "one who has been initiated."

The noun appeared in 1679, from that came mysticism coined 1736 and by the late 1800’s both mystique and mystic were being bandied about in the everyday vernacular.

So why would the French be so interested in using this word? One reason may be due to the history of the region. In 1598, with the expulsion of the last Spanish troops from French territory, the long years of war were at an end signaling for France a period of recovery from the devastation and disruption of the Wars of Religion. That year Henry seeking to assure the domestic tranquility of the realm issued the Edict of Nantes granting freedom of religious conscious for all his subjects. Never before had a ruler formally accorded freedom of religion and worship to his or her subjects.

Prior to this there was an atmosphere of mystery and veneration attending royalty and a practice called the divine right of kings a political canon asserting that monarchy was:

    A divinely ordained institution in which kings and queens were answerable only to God. It therefore followed that it was a sin for the subjects of even the most evil or incompetent monarchs to disobey them.
The doctrine develop in the middle ages, partly to strengthen the hand of monarchs in their dealings with parliaments as well as partially in response to intrusions by the Pope into national affairs. It may well have been these mystical, aspects of the doctrine that can be seen as the anointed king creating a sacerdotal character leading to all the discussion of the surrounding air of mystery. During this time this mystique became personified and reflected in such practices ‘laying on of hands’ of sorts. Believers ascribed to royalty the hereditary power of curing a disease called the king's evil or scrofula what was probably a form of tuberculosis. A cure was bestowed upon the victim by touching them. This practice was eventually introduced in England from France by Edward the Confessor where James I revived the custom of touching sufferers Under Charles II a religious ceremony was commonly linked with the practice of divine right.
    Dynastic rivalry dominated the 15th century (see War of the Roses) and the Tudor monarchs were persistently troubled by plots and the question of the succession. The Tudors, however, gained much from their exploitation of the mystique of kingship (`your majesty' replaced `your grace' as the title of address), from their manipulation of anticlericalism into a doctrine of the royal supremacy, and from their appropriation of church land.

These auras of heightened value, interest, or meaning surrounding the people gave rise to attitudes and beliefs that imputed special power or mystery to the leaders and added to the resources of the rulers land and military service due to the king as feudal overlord. Since medieval monarchy was intensely personal, and a monarch's success depended on a combination of character, military skill, and successful exploitation of the royal estates the divine right persisted throughout Louis XIV's reign and in a less pronounced form until the French Revolution of 1789.

Conservative thinkers tried to justify the restoration of hereditary rulers throughout Europe after the Revolutionary and Napoleonic period revived the theory briefly. It was last practiced in England by Queen Anne.

Today mystique has come to mean a special esoteric skill essential in a calling or activity such as the mystique that surrounds actions, beliefs, celebrities or social groups that are admired by a large number of people.

Sources:

Online Etymology Dictionary:
www.geocities.com/etymonline/m6etym.htm

Market House Books Dictionary of British History,Market House Books Ltd 1987.

The Pocket Oxford Dictionary of Current English, © Oxford University Press, 1996.

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