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I downloaded OS X Yosemite the other night. It wouldn’t let me use the Macintosh Hard Drive as my startup disk so I partitioned space for Macintosh HD 2 and downloaded Yosemite on that.

I didn’t partition enough space to transfer all of my files from Macintosh HD over to HD2, so all of my music is still on the Macintosh HD, but I want it on Macintosh HD 2.

I want to delete the Macintosh HD (or merge them?) but I don’t want to delete my music. Is there anything I can do? I have an external hard drive if that helps.

1. Resizing can possible but not moving the partition. Yosemite partition can only be moved with the help of the third party utility. And a better solution is to back up the data, then delete the partition, recreate it and reinstall it.

2. Yosemite usually is an upgrade installation which will replace your current OS X version. Therefor I am a bit puzzled that you were unable to install it on 'Macintosh HD' but on a newly created partition 'Macintosh HD 2'.

   What was your previous OS X version?
   What partitions are on your hard drive now and what do they contain?
   Did Yosemite migrate your user account, data and settings or was it a 'fresh' installation?

   Technically you cannot merge partitions, you can only delete one and then resize the other to take it's space. But my understanding is that this is not an option for you right away.
   You could transfer your music to the external disk, then delete the 'Macintosh HD' partition and finally resize the 'Macintosh HD 2' using the free space you gained from the deleted one.

   However, without knowing more about your current situation I suggest not to do so before you can confirm all your data is either on the external drive or on the 'Macintosh HD 2'.

3. OS X Yosemite, Core Storage, and partition woes.
   http://awesometoast.com/yosemite-core-storage-and-partition-woes/

By default, your Mac starts up from its built-in hard disk, but a startup disk can be any storage device that contains an operating system compatible with your Mac. For example, if you install macOS on an internal or external drive, your Mac can recognize that drive as a startup disk. You can then follow the steps in this article to start up from it.

Use Startup Disk preferences

When you use Startup Disk preferences to select a startup disk, your Mac starts up from that disk until you choose a different one.

1. Choose Apple menu  > System Preferences, then click Startup Disk.
2. Click the lock and enter your administrator password.
3. Select your startup disk, then restart your Mac.

If you see a message that your security settings do not allow this Mac to use an external startup disk, check the External Boot setting in Startup Security Utility.

Use Startup Manager

When you use Startup Manager to select a startup disk, your Mac starts up from that disk once, then returns to using the disk selected in Startup Disk preferences.

1. Press and hold the Option (Alt) key immediately after turning on or restarting your Mac.
2. Release the Option key when you see the Startup Manager window.
   If your Mac is protected by a firmware password, you can release the key when you're asked to enter the password.
3. Select your startup disk, then click the arrow under its icon, or press Return.
   If you press and hold the Control key during this step, your selection is saved in Startup Disk preferences, so it persists until you change it.

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If your Mac is using OS X Lion 10.7.3 or later, you can also use this method to start up from your Time Machine backup disk. Startup Manager identifies your Time Machine backup as ”EFI Boot.”

If you can't select your startup disk or start up from it

Check for these possibilities if you can't see your disk in Startup Disk preferences or Startup Manager, or your Mac won't start up from it.

Check for a compatible operating system on the startup disk

Make sure that your startup disk is using a version of macOS that is compatible with your Mac.

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To start up from an external disk with macOS Catalina 10.15 or later, the disk must connect via USB-A, USB-C, or Thunderbolt, not FireWire.

Check startup security settings

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If you're using a Mac that has the Apple T2 Security Chip, check the settings in Startup Security Utility. These settings determine whether your Mac can start up from another disk.

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Check for Option ROM firmware

If you're in Startup Manager and can't see a third-party startup disk, the startup disk could be using Option ROM firmware. To enhance system security, Mac computers with up-to-date software don’t show devices that use Option ROM firmware until you load their firmware. To do that, press Option-Shift-Command-Period while in Startup Manager. If your startup disk appears, do that each time you want to start up from it or from another disk connected to it.

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If you're using a firmware password, the ability to load Option ROM firmware is disabled as an additional security protection.