I've been in a discussion with another individual over this, and would like to see the general consensus on it. The Arcane Bloodline Arcana reads as such:
Whenever you apply a metamagic feat to a spell that increases the slot used by at least one level, increase the spell's DC by +1.
We come to a disagreement based on the sentence's structure when it comes to interactions with stuff such as Magical Lineage or Spell Perfection. I'll try to get the evidence for both in a relatively fair manner.
Event: An arcane-blooded sorcerer has a metamagic feat that increases the spell's level by +1. They have Magical Lineage, and cast the spell attached to said lineage with the metamagic feat applied as well (resulting in a final net change of +0).
Does the Arcane bloodline's Arcana activate in this case or not?
Choice A: No it does not.
Reasoning: The wording of the bloodline arcana states the slot used must be increased by at least one level. Therefore, it does not.
Choice B: Yes, it does.
Reasoning: The metamagic feat is the actual subject of the sentence for the bloodline arcana, not the spell. Removing all prepositional phrases from the first half of the sentence results in the following:
Whenever you apply a metamagic feat (to a spell) that increases the slot used (by (at least) one level), increase the spell's DC by +1.
Therefore, as long as a metamagic feat of at least +1 is applied to a spell, the bloodline's arcana should activate, regardless of whether the character has found a way to reduce the metamagic's actual impact on spell slots.
Since we can both see the other side of the argument being a fair enough one, I'd like to see what this forum generally thinks.
I would say 'A' ,for the reasons you stated.Magical lineage prevents the metamagic feat from moving the spell to a higher level slot..making it ineligible.
Even without the preposition it still says the meta magic feat must increase the spell slot used.
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Most certainly choice B. Remember, there is a metamagic feat that adds +0 to the casting level (merciful spell), so I think it is clearly intended to be able to work like this.
I'd also note that the bonus to DC is the same as other bloodlines which add DC to spells of a certain school. Seems reasonable they are intended like this.
On a side note, the sorcerer's spell DC is normally at a disadvantage per their level as their spell DC is 10+mod+spell level because they get access to each level of spells at a higher level than wizards do. This bloodline arcana means a 9th level sorcerer can cast their max spell level spells with the same DC as a wizard of 9th level.