You definitely need to upgrade your HMC first, as you've said.  Your 
current HMC version will not support any AL730 versions.  Good news there 
is that you are not so far behind that you have to do multiple stage 
upgrades (at least for your firmware) like I had to when upgrading v5 to 
v7 of hmc and some really old firmware quite some time ago.
<snip>
The Minimum HMC Code level for this firmware (AL730_142) is:  HMC V7 
R7.3.0 (PTF MH01255 or MH01256) with PTF MH01257 (Mandatory efix).
</snip>
Both your firmware and HMC code have been out of service for over two 
years.
You will have to stage your HMC upgrades!!!
HMC Version 7 Release 7.9.0 supports upgrading from the following 
releases, with or without Service Packs or efixes: HMC V7R7.6.0, HMC 
V7R7.7.0, and HMC V7R7.8.0.
http://delivery04.dhe.ibm.com/sar/CMA/HMA/04gm2/2/MH01405.readme.html
It also says:  This package represents the Recovery image that can be used 
to upgrade your HMC from HMC V7R7.6.0 or higher to HMC V7R7.9.0.
While all previous releases say something like:  This package represents 
the Recovery image that can be used to upgrade your HMC from HMC V6R1.3.0 
or higher to HMC V7R7.8.0. 
Other tidbits from that include:
HMC Version 7 Release 7.9.0 requires model CR3 or later model rack-mount 
HMC or C05 or later deskside HMC. Models CR2, C03, and C04 are not 
supported.
HMC Version 7 Release 7.9.0 will be the last version to support HMC models 
CR3 and CR4.
HMC Version 7 will be the last version to support HMCs with 1 GB of RAM; 
4Gig is recommended. 
DVD-RAM is no longer supported for backup and restore of console data.
Basically it looks like your CR6 will work, if it has the right memory.
Make sure you install the 'optional' fixes for your new version of HMC 
code.  Some firmware upgrades have statements in them like: 
"This requires the management console be at a minimum level that has a 
POODLE fix such as  HMC V7 R7.9.0 SP1 with POODLE PTF MH01484."
Since you are going from AL720 to AL730 it will definitely be a system 
down disruptive upgrade.  This will be an upgrade, not an update.  As you 
are going through the install process this distinction will be felt.  Once 
you've upgraded your HMC you should be able to upgrade your firmware in 
one step.
Note:  While HMC 7.7.9 is the 'Maximum Stability Release Level' release, 
the 'Latest Release Level' release of V8R8.1.0 is an option.
https://www14.software.ibm.com/webapp/set2/sas/f/power5cm3/eltablep7.html
Carefully read the upgrade notes at:
http://delivery04.dhe.ibm.com/sar/CMA/HMA/04ko5/12/MH01419.readme.html
Rob Berendt
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