From the SoundCloud API Guide, this is how to get the streaming URL of a sound:
import soundcloud
# create a client object with your app credentials
client = soundcloud.Client(client_id='YOUR_CLIENT_ID')
# fetch track to stream
track = client.get('/tracks/293')
# get the tracks streaming URL
stream_url = client.get(track.stream_url, allow_redirects=False)
# print the tracks stream URL
print stream_url.location
Is there any way to command the API to return a URL for the sound at a different speed or better yet, at a different tempo?
Thats not a feature from SoundClouds API. You need to somehow analyze your track to change the tempo / speed / bpm. For that you can use the EchoNest / Spotify APIs.
Check this question:
How to get BPM and tempo audio features in Python
If you change to JavaScript you can use the browser built-in WebAudio / WebMIDI API on Chrome and/or FireFox.
API description by Mozilla:
https://developer.mozilla.org/en-US/docs/Web/API/Web_Audio_API
Examples by Google:
http://webaudiodemos.appspot.com/
Hackday project based on Samplr + SoundCloud API using WebAudio + WebMIDI (Chrome only):
http: // dope-dj-culture.com/ No longer a valid URL.