It makes me wonder: what if we take existing songs, try to find space-filling curves that explain them, and then look for different paths through those curves? In other words: would it be easy / possible to parameterize existing songs as curves, so that we can find which subset of the space of space-filling curves is actually interesting to human ears?
on the same topic, i been also curious of something and wonder if anyone have the answer to this.
lets say i have a track playing just one note (to be specific, a frequency measured in hertz, lets say 528) for one minute and we want this to be as pure sounding as possible.
what is the best approach to do this?
in addition, if the audio file is in WAV and we convert them to mp3, do we still lose a lot of quality even though we are just playing same note for 1 minute?
how cam we achieve playing the purest sound without music file taking up too much space?
Actual sawtooth on the left (done at higher bit rate), tone on right is 2khz tone at 8khz sample rate (audacity won't generate tone right at nyquist). Looks like a triangle wave in audacity, but the tone is fairly pure with just a whisper of harmonics, and those are probably from the speaker.
(tldw: the answer is no, like the other commenter said, if the D/A converter is working properly)
I wonder if space-filling curves tap into the same complexity as a classically-structured fugue in some kind of deep way.
If a piece of music does not obey those constraints, it cannot be back-transformed into a continuous curve in a fixed number of dimensions. You would need to come up with some other, more complex, method of mapping curves to music in order to handle arbitrary musical compositions.