Question: The father of Pietro de' Medici was the Duke of Florence between what years?

Context paragraphs:
Lorenzo de' Medici, Duke of Urbino: Lorenzo di Piero de' Medici (] ), (12 September 1492 – 4 May 1519) was the ruler of Florence from 1516 to his death in 1519.  He was also Duke of Urbino from 1516 to 1519.  His daughter, Catherine de' Medici, became Queen Consort of France, while his illegitimate son, Alessandro de' Medici, became the first Duke of Florence.

Eleonora di Garzia di Toledo: Eleonora di Garzia di Toledo (March 1553 – 11 July 1576), more often known as "Leonora" or "Dianora", was the daughter of García Álvarez de Toledo, 4th Marquis of Villafranca, Duke of Fernandina, and the wife of Don Pietro de' Medici, a son of Cosimo I de' Medici, Grand Duke of Tuscany.  Leonora was born in Florence, where she was brought up by Cosimo and Eleanor of Toledo, her aunt and namesake.  Betrothed to their son Pietro at the age of 15, she blossomed under the wing of Pietro's older sister, the artistic patron Isabella, into a vivacious and witty beauty.  Her marriage, like Isabella's, was not a success, and she followed her mentor's example of taking lovers.  For this reason, Pietro had her brought in 1576 to the country retreat of Cafaggiolo, where he strangled her to death with a dog leash.  Cosimo's successor, Francesco I, tacitly approved the murder, and Pietro was never brought to justice for it.

Giovanni Gualberto Magli: Giovanni Gualberto Magli was an Italian castrato who had an active singing career during the first quarter of the 17th century.  Born in Florence, he studied voice with Giulio Caccini before becoming a musician for the House of Medici on 23 August 1604.  He participated in the world premiere of Claudio Monteverdi's "L'Orfeo" in 1607 at the court of Prince Francesco IV Gonzaga, Duke of Mantua, portraying the roles of La Musica and Proserpina and possibly one other part.  The musicologist and historian Hans Redlich mistakenly allocates Magli to the role of Orfeo.  In 1608 he sang for the wedding festivities of Cosimo II de' Medici, Grand Duke of Tuscany and Archduchess Maria Maddalena of Austria.  In October 1611 he was granted two years paid leave by Antonio de' Medici to pursue further studies in Naples.  He left Medici service in 1615 to join the musicians at the court of John Sigismund, Elector of Brandenburg.  He remained there until September 1622.  He was buried in Florence on 8 January 1625.

Duchy of Florence: The Duchy of Florence (Italian: "Ducato di Firenze" ) was an Italian principality that was centred on the city of Florence, in Tuscany, Italy.  The duchy was founded after Emperor Charles V restored Medici rule to Florence in 1530.  Pope Clement VII, himself a Medici, appointed his relative Alessandro de' Medici as Duke of the Florentine Republic, thereby transforming the Republic of Florence into a hereditary monarchy.

Pietro de' Medici: Don Pietro de' Medici (3 June 1554 – 25 April 1604) was the youngest son of Cosimo I de' Medici, Grand Duke of Tuscany and Eleonora di Toledo.

Averardo de' Medici: Averardo de' Medici (1320-1363), also known as Everard De Medici, was the son of Salvestro de' Medici (died 1346), "il Chiarissimo" (English meaning "the very clear.")  and the father of three children: Giovanni, Francesco, and Antonia.  Giovanni di Bicci de' Medici would later become the first historically relevant member of Medici family of Florence and the eventual founder of the Medici bank.

Medici: Masters of Florence: Medici: Masters of Florence is an Italian-British television drama series about the Medici dynasty set in 15th-century Florence, starring Dustin Hoffman as Giovanni di Bicci de' Medici, Richard Madden as Cosimo de' Medici, and Stuart Martin as Lorenzo de' Medici ("The Elder").  The series was co-created by Frank Spotnitz ("The X-Files" and "Man in the High Castle") and Nicholas Meyer ("").  Sergio Mimica-Gezzan ("The Pillars of the Earth") directed all eight episodes.  Episodes 1 and 2 aired on Rai 1 (Italian TV) on 18 October 2016.  According to Italian ratings compiler Auditel, it attracted a record 7.6 million viewers.  The first season consists of eight episodes.

Taddea Malaspina: Taddea Malaspina (1505 - ?)  was an Italian marchesa.  She was the mistress of Alessandro de' Medici, Duke of Florence from the early 1530s to about 1537 and was likely the mother of at least two of his children, Giulio di Alessandro de' Medici and Giulia de' Medici.  Giulio de' Medici was associated with the Malaspina family at different points throughout his life.  Taddea was the younger daughter of Alberico Malaspina, sovereign marquis of Massa, and Lucrezia d'Este.  She married Count Giambattista Boiardo di Scandiano.  After his death and the death of her father, Malaspina lived with her mother in Florence and had a number of lovers, including Alessandro.  Her sister Ricciarda inherited the title after their father's death.  Through Ricciarda's marriage, the family was related to Pope Innocent VIII.  Ricciarda was probably also one of Alessandro de' Medici's lovers.

Cosimo I de' Medici, Grand Duke of Tuscany: Cosimo I de' Medici (12 June 1519 – 21 April 1574) was the second Duke of Florence from 1537 until 1569, when he became the first Grand Duke of Tuscany.

Giovanni di Bicci de' Medici: Giovanni di Bicci de' Medici (c. 1360 – February 20/28, 1429) was an Italian banker, a member of Medici family of Florence, and the founder of the Medici Bank.  While other family members, such as Chiarissimo di Giambuono de' Medici, who served in the Signoria in 1201, and Salvestro de' Medici, who was implicated in the Ciompi Revolt of 1378, are historically significant, Giovanni's founding of the family bank truly began the family's rise to power in Florence.  He was the father of Cosimo de' Medici ("Pater Patriae"), grandfather of Piero di Cosimo de' Medici, great-grandfather of Lorenzo de' Medici (the Magnificent) and great-great-great-grandfather of Cosimo I de' Medici, Grand Duke of Tuscany.

Supporting paragraphs: Pietro de' Medici Cosimo I de' Medici, Grand Duke of Tuscany
Answer: 1537 until 1569