Can you provide some examples of music with a free form structure?

Likewise, Russian composer Nikolai Rimsky-Korsakov's composition “Sheherezade” contains a sequence of musical passages with skeletal framework provided, allowing free-form to both soloist and strings in pizzacato. Rimsky-Korsakov's notation is most fascinating to see..and hear. The passages of which I write take place in Mvt. 2 of this astonishing work.

Below are images of the respective passages of which I speak.

“Sheherezade”:

Is there a type of function where every point has exactly one tangent line passing through it? If yes, what is this type of function called?

Typically, within a symphonic score, free-form structure is instructed via a Composer's indication of “Cadenza”. In musical terms, a cadenza is an improvised, ornamental passage performed in a “free” rythmic style, typically by a solo performer. To some extent, the musical indication of “a piacere”, (at your pleasure), also allows a performer to abide by the tempo, rhythm and dynamic level of their decision.

“The Lark Ascending”: (the indication “Sur la touche” advises the Violinist to play on the finger board of the instrument).

Ralph Vaughn-Williams’ timeless, ethereal “The Lark Ascending” begins with a cadenza for solo Violin with quite the duration of free-form allowed by the Composer. Vaughn-Williams' notation is quite interesting to view. Violinist Hilary Hahn best infuses this cadenza with the most favorable tone and technique.

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