As much as I hate to tell you, it simply cannot be done. They just come and go, when they please. I too wished to 'summon' one, but they don't work that way, and not once have I ever seen in any Chinese or Japanese folklore that it has been done before. If anything, they warn against them!
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No, a Synchro Summon is a kind of Special Summon.
A tribute summon is a form of Normal Summon. So that means you can only tribute summon OR normal summon ONCE per turn.
Not quite. A Synchro Summon is a Special Summon. A Tribute Summon is the same as a Normal Summon, except that when you Tribute Summon you need to tribute monsters. Also you can Special Summon as many times as you want to in a turn, whereas you can only Normal Summon OR Tribute Summon once per turn, except with a card effect.
No. A Tribute Summon is a kind of Normal Summon. Special Summons are just Special Summons even if the special summon requires some form of Tribute. That does not make it a Tribute Summon.
Yes, you can, as a Synchro Summon is a special summon, you can perform a Normal Summon on the same turn as one or more Synchro Summons.