Question: A boyar was a member of a system that flourished in medieval Europe between what centuries?

Context paragraphs:
Horsebread: Horsebread was a type of bread sometimes consumed in medieval Europe.  This bread was, at the time, considered a low-quality bread, made from legumes such as dry split peas as well as or instead of grains, and was one of the cheapest breads available.  It was fed to horses but also eaten in times of famine by the indigent and those who could not afford white bread (which was the most labour-intensive, and therefore expensive, bread) or other breads like rye or barley breads. White breads were generally only eaten by the wealthy, because of the labor involved in refining flour and because of the lower nutritional content.  This is in contrast with modern whole grain breads, which are typically seen as premium-priced health foods or gourmet foods.  This is in part because modern flour has a higher gluten content than flour produced in medieval Europe, and thus bread made from less refined flour is more palatable than it would have been during the Middle Ages.

Medieval technology: Medieval technology refers to the technology used in medieval Europe under Christian rule.  After the Renaissance of the 12th century, medieval Europe saw a radical change in the rate of new inventions, innovations in the ways of managing traditional means of production, and economic growth.  The period saw major technological advances, including the adoption of gunpowder, the invention of vertical windmills, spectacles, mechanical clocks, and greatly improved water mills, building techniques (Gothic architecture, medieval castles), and agriculture in general (three-field crop rotation).

Feudalism: Feudalism was a combination of legal and military customs in medieval Europe that flourished between the 9th and 15th centuries.  Broadly defined, it was a way of structuring society around relationships derived from the holding of land in exchange for service or labour.

Hindu–Arabic numeral system: The Hindu–Arabic numeral system (also called the Arabic numeral system or Hindu numeral system) a positional decimal numeral system, is the most common system for the symbolic representation of numbers in the world.  It was invented between the 1st and 4th centuries by Indian mathematicians.  The system was adopted in Arabic mathematics by the 9th century.  Influential were the books of Muḥammad ibn Mūsā al-Khwārizmī ("On the Calculation with Hindu Numerals", 825) and Al-Kindi ("On the Use of the Hindu Numerals", 830).  The system later spread to medieval Europe by the High Middle Ages.

Medieval household: Neither Greek nor Latin had a word corresponding to modern-day "family".  The Latin "familia" must be translated to "household" rather than "family".  The aristocratic household of ancient Rome was similar to that of medieval Europe, in that it consisted – in addition to the "paterfamilias", his wife and children – of a number of clients "(clientes)", or dependents of the lord who would attend upon him, counsel him and receive rewards.  Where it differed from its medieval equivalent was in the use of slaves rather than paid servants for the performance of menial tasks.  Another difference was that, due to the relative security and peacefulness within the borders of the Roman Empire, there was little need for fortification.  The aristocratic household of medieval Europe, on the other hand, was as much a military as a socio-economic unit, and from the 9th century onwards the ideal residence was the castle.

Mestnichestvo: In Russian history, Mestnichestvo (Russian: Ме́стничество , ] ; from ме́сто, a position) was a feudal hierarchical system in Russia from the 15th to 17th centuries.  "Mestnichestvo" was a complicated system of seniority which dictated which government posts a "boyar" could occupy.  It was based on the individual's seniority within an extended Russian aristocratic family on the one hand, and on the order of precedence of the families, on the other.  The hierarchy of families was calculated based on the historical records of senior appointments, going back to 1475.  For example, the Odoevskys clan was ranked higher than the Buturlins, but a senior Buturlin could be appointed to a position equivalent to that occupied by a junior member of the Odoevsky family.  The mestnichestvo seniority system was most visibly represented in the order of seating of the boyars at the tsar's table.  The clans jealously guarded their status.  This often led to bitter disputes and physical violence among nobles about their ancestry and their services to the monarch.  According to eminent Russian 19th century historian Vasily Klyuchevsky, "you could beat a boyar up, you could take away his property, you could expel him from government service, but you could never make him accept an appointment or a seat at the tsar's table lower than what he is entitled to."

Emilia Jamroziak: Emilia Jamroziak is professor of medieval religious history at the University of Leeds.  Jamroziak is a specialist in medieval British and European religious history of the 12th to the 15th centuries, the Cistercian order, and frontiers and borders in medieval Europe.  She became the director of the Institute for Medieval Studies at the University of Leeds in 2016.

Great Stirrup Controversy: The Great Stirrup Controversy is the academic debate about the Stirrup Thesis, the theory that feudalism in Europe was largely the result of the introduction of the stirrup to cavalry.  It relates to the hypothesis suggested by Lynn Townsend White, Jr. in his 1962 book, "Medieval Technology and Social Change."  White believed that the stirrup enabled heavy cavalry and shock combat, which in turn prompted the Carolingian dynasty of the 8th and 9th centuries to organize their territory into a vassalage system, in which these mounted warriors were rewarded with land grants for their service.  White's book has proved very influential, but he has also been accused of speculation, oversimplification, and ignoring contradictory evidence on the subject.  Other scholars have debated whether the stirrup actually provided the impetus for this social change, or if the rise of heavy cavalry was a result of political changes in Medieval Europe.

Droit du seigneur: Droit du seigneur ( ; ] ) ("lord's right"), also known as jus primae noctis ( ; ] ) ("right of the first night"), refers to a supposed legal right in medieval Europe, and elsewhere, allowing feudal lords to have sexual relations with subordinate women (the "wedding night" detail is specific to some variants).  There is no evidence of the right being exercised in medieval Europe, and all known references to it are from later time periods.  Overall, medieval "jus primae noctis" can be considered a historical fiction fabricated after that era.

Boyar: A boyar was a member of the highest rank of the feudal Bulgarian, Kievan, Moscovian, Wallachian and Moldavian and later, Romanian aristocracies, second only to the ruling princes (in Bulgaria, tsars), from the 10th century to the 17th century.  The rank has lived on as a surname in Russia, Ukraine and Romania, and in Finland, where it is spelled "Pajari".

Supporting paragraphs: Boyar Feudalism
Answer: 9th and 15th