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Magical Lineage says:

Benefit: Pick one spell when you choose this trait. When you apply metamagic feats to this spell that add at least 1 level to the spell, treat its actual level as 1 lower for determining the spell’s final adjusted level.

Arcane Bloodline's Bloodline Arcana says:

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. This bonus does not stack with itself and does not apply to spells modified by the Heighten Spell feat.

If I apply "+1 spell level" metamagic (such as Extend Spell) to the spell chosen with Magical Lineage, does the DC of the spell increase, even though the final adjusted level of the spell remains the same as that of the base spell?

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Both the trait Magical Lineage and the arcane bloodline bloodline arcana are looking for metamagic feats that do the same thing: they're seeing if you're applying to a spell the benefit of a metamagic feat increases the spell's slot level by at least +1.

It doesn't matter if you actually increase that slot level by at least 1 or not when you cast or prepare the spell; the trait and the arcana only care if the metamagic feat itself would increase that slot level by at least 1 if the metamagic feat were applied normally.

In other words, if Ekaj the sorcerer takes a full-round action to cast web bolt modified by the feat Extend Spell, and he possesses the trait Magical Lineage, he'd expend a 1st-level spell slot. And if Ekaj the sorcerer takes a full-round action to cast web bolt modified by the feat Extend Spell, and he possesses the arcane bloodline bloodline arcana, he'd expend a 2nd-level spell slot and the saving throw DC against that web bolt spell would be increased by +1.

And, finally, if Ekaj the sorcerer takes a full-round action to cast web bolt modified by the feat Extend Spell, and he possesses both the trait Magical Lineage and the arcane bloodline bloodline arcana, he'd expend a 1st-level spell slot and the saving throw DC against that web bolt spell would be increased by +1.

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  • \$\begingroup\$ That's pretty obvious in the case where the spell slot has actually increased. What about if it was metamagic that only added one level (and therefore added no levels once Magical Lineage was applied)? That seems to be the core of the question, and your example skips around it. \$\endgroup\$ – Ben Barden Oct 9 '19 at 18:47
  • \$\begingroup\$ @BenBarden Sorry about that. I mistook in the question Extend Spell for Empower Spell. The example should clear things up more now. \$\endgroup\$ – Hey I Can Chan Oct 9 '19 at 18:50
  • \$\begingroup\$ Err... Burning hands doesn't have a duration, and therefore can't be extended. \$\endgroup\$ – Ben Barden Oct 9 '19 at 18:52
  • \$\begingroup\$ Also, and pertinently, the counterargument is: We're told this applies when you "apply a metamagic feat to a spell that increases the slot used by at least one level" We've applied a metamagic feat, but the slot used has not increased. do you have any responses to that that go beyond "Ignore that. My interpretation is the correct one."? \$\endgroup\$ – Ben Barden Oct 9 '19 at 18:58
  • \$\begingroup\$ @BenBarden Actually, I don't think we are told that exactly. What we're told is that whenever a metamagic feat of a specific kind is applied, something happens. The word that in both examples is the beginning of an adjective clause answering the question What kind of metamagic feat? rather than an adverb phrase answering the question To what extent must the metamagic feat be applied? \$\endgroup\$ – Hey I Can Chan Oct 9 '19 at 20:44
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The text is unclear, and the "yes it works" argument has already been espoused, so I'll take the contrarian view.

Bloodline Arcana says "Whenever you apply a metamagic feat to a spell that increases the slot used by at least one level". In the case of applying Extend Spell to a spell that is enhanced by Magical Lineage, the slot used is not increased. Therefore the requirement is not met.

By contrast, Magical Lineage has the requirement "When you apply metamagic feats to this spell that add at least 1 level to the spell". Bloodline Arcana is referring to the actual slot used, as a result of applying the feat. Magical Lineage is referring to an aspect of the feat(s) - that they are magical feats that add a level to the spell. Indeed, they do add a level to the spell, which is then removed again by Magical Lineage itself, which results in no change to the slot used.

The real answer, however, is that both are valid interpretations. There is no clear official answer on the subject. It is thus best handled via DM adjudication, preferably during the chargen process.

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