Q: 2nd gen nano music transfer to iPod touch through 2011 iMac.

Hello jschuier,

I understand that you would like to get your music that is on your iPod nano to your iPod touch. Let's see what options that you have available. 

If the music on your iPod nano was purchased from the iTunes Store then you can transfer it to your computer by following the steps outlined below. Once you have them in iTunes, you can then sync it to your iPod touch. Take a look at the three articles below for more details on each step. 

Redownload or transfer your iTunes Store purchases from an iPhone, iPad or iPod to a computer
https://support.apple.com/en-us/HT201267

Download your past purchases
https://support.apple.com/en-us/HT201272​

Sync your iPhone, iPad, or iPod touch with iTunes using USB
https://support.apple.com/en-us/HT201253​

If the songs were not purchased through the iTunes Store and the songs are on a different computer, then I would suggest moving them over through an external hard drive or USB. Take a look at the article below for more information on how to do that. 

How to move your iTunes library to a new computer
https://support.apple.com/en-us/HT204318

Take care