Free dance is a 20th-century dance form that preceded modern dance. Rebelling against the rigid constraints of classical ballet, Loie Fuller, Isadora Duncan and Ruth St. Denis (with her work in theater) developed their own styles of free dance and laid the foundations of American modern dance with their choreography and teaching. In Europe Rudolf Laban, Emile Jaques-Dalcroze and François Delsarte developed their own theories of human movement and methods of instruction that led to the development of European modern and Expressionist dance.

https://en.wikipedia.org/wiki/Free_dance

'Danza' here doesn't refer to one dance, but the art form in general. I understand 'carácter más abierto de la danza' to mean dancing without the constraints of classical ballet or other formal styles.

Contemporary dance allows the students to experience a freedom of movement quite different from any other style.

In terms of the focus of its technique, contemporary dance tends to combine the strong and controlled legwork of ballet and jazz, powerful allegro (Jumps), floor work, stress on the torso with contract-release, controlled and uncontrolled movement with fall and recovery, and freedom of improvisation movement.

Contemporary is very free in its diverse styles of movement; from grounded, African inspired, athletic, harsh, to smooth, classically controlled, to commercialised modern-inspired movement.

http://www.scpaconline.com/classes/contemporary

I know what I'm talking about because dancing was my life for 35 years.

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Note added at 3 hrs (2017-11-13 19:54:22 GMT)
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I meant to write 'marked interest for'.