This sort of thing has been explored pretty deeply by, among other people, Conlon Nancarrow. He used player pianos to perform pieces which would most likely have been too complex for anyone to perform organically. One way in which he complicated things was that he used what he called a tempo canon. As discussed here, one such piece was his Study for Player Piano 41a. It used multiple voices, each with its own tempo and the ratios were on a strict, but irrational ratio. If the ratio between tempos was rational, it would line up, or converge, so that two notes could fall at the same time. However, if the ratio was irrational, they would never converge and dance around each other until the piece ended.

This basic concept, although the effect can be jarring, is really not very different from polyrhythms and polymeters. It's just obfuscated by using complicated ratios. For example, if you have a bar and a main voice hit four evenly spaced beats, you have the standard quarter note pulse in 4/4. You can fit 3 notes evenly into that same bar in a second voice and the second voice will be playing half-note triplets. For every four notes in the main voice and every three notes in the second voice, the voices will play together. That's your bar. And that's a polyrhythm. That would be a 4:3 ratio. I'm not sure that's how it's typically notated, but the idea translates. You can imagine how this can be seen as two voices at different tempos. Say maybe one voice in 4/4 at 120 and another voice in 3/4 at 90. They would line up the same way.

Here's another example. If your main voice plays 8 eighth notes before repeating and your second voice plays 7 eighth notes before repeating, they will line up every 56 (7×8) eighth notes. In other words, after your main voice repeats seven times and your second voice repeats eight times. That's a polymeter. Now you can see how these concepts can get mixed up. As the ratios get more complicated (ie 128:73) or less rational (ie √2:φ), the tempos line up less and less and the individual tempos will get closer and/or less distinguishable. That is where you cross the line into tempo canon territory.


  Note: I understand that 'irrational ratio' is a terrible oxymoron, but
  I can't think of better terminology. Also, this is just the one conceptualization of
  the multiple tempo idea. There is world music where this is done organically and many
  people have already mentioned other composers who have worked with the idea. But hopefully this helps.


What is it called when a music has two concurrent tempos
I've been trying for pretty much the whole day now to install milewise's nodejs Soap client.  I'm simply running the following from the cmd as an administrator:

cd: c:\Program Files\nodejs
npm install soap


It keeps getting stifled at the node-gyp rebuild file. I've received several different errors, but currently I am getting the following error:

error MSB4019: The imported project "C:\Microsoft.Cpp.Defaul.props" was not found.  
Confirm that the path in the &lt;Import&gt; declaration is correct and that the file exists on disk.


This is driving me crazy.  I'v tried several iterations of installing the Windows 7 dependencies for node-gyp.  Unfortunately, after successfully installing VS C++ 2010 express, MS Windows SDK + .NET Framework 4 will not install.  

Has anyone out there had success installing this or any other Soap client for Nodejs on Windows 7?
