On the surface, this seems like a simple question. At quick glance, you might immediately say: "Yes, changing the speed of a song is a derivative work".
According to wikipedia, a transformed work is possibly viewed as fair use:
In United States copyright law, transformation is a possible justification that use of a copyrighted work may qualify as fair use, i.e., that a certain use of a work does not infringe its holder's copyright due to the public interest in the usage. Transformation is an important issue in deciding whether a use meets the first factor of the fair-use test, and is generally critical for determining whether a use is in fact fair, although no one factor is dispositive.
While it is completely clear that simply speeding up or slowing down a song, which would change both the pitch and speed, is clearly a derivative work. My question is regarding transforming it using youtube's speed controls.
Youtube's speed algorithm uses a phase vocoder. When the speed of a song is lowered to 0.25 it is virtually unrecognizable as the original work due to the effects the phase vocoder introduces to the original audio. The phase vocoder works by transforming the audio, which seems to match the legal language around what is considered fair use. In fact, the basis for a phase vocoder is a mathematical transformation function called a Short-time Fourier transform.
In youtube's speed control algorithm, while the pitch is retained, the duration of the notes is altered, and the effect of of the phase vocoder on slowing the video to 0.25 adds audio effects that transforms even the color of the notes to the point that it's difficult to tell what instrument is being played.
Further, once this transformation is performed on the audio, if a recording is made of the audio in this state, returning it to the original speed is a near impossibility.
Also, the reason I'm asking this overall, is I would like to do this and then add several layers of tracks of different instruments and effects to the song, which could be considered criticism or parody perhaps?