and you could simplify this, too, by using an easy-to-remember hash algorithm that gives you a string like this, dependant of the service (or service domain), e.g. if this is your Facebook password:
"Facebook"
→ pick every fourth letter, append index of first "e"
→ "ek4"
prepend this to $basePassword
→ "ek4Ykwctam$?"
But, don’t use this exact algorith, of course
And probably don’t use this method. IANASecurityexpert!