[RPG] How to calculate the Black Blade’s skills

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I am playing a Bladebound Magus in a campaign with very quick level advancement, necessitating frequent recalculation of my stats. The only part of my character advancement that's confusing me is calculating my Black Blade's skill ranks. From the PFSRD:

Upon reaching an Intelligence of 12, it gains a bonus language of the GM’s choice, and gains 1 rank in Knowledge (arcana). Each time the sword gains a bonus to Intelligence, it gains another language and another rank in Knowledge (arcana). [Empahsis mine]

The wording of the second sentence is the issue and I feel as if I may be aproaching my advancement incorrectly. Does the way the entry is worded mean every time my Blade's INT score increases it gains another skill rank and language (ie. from 12 to 13 with no increase in modifier)? Or every time its INT modifier increases (ie. from 13 to 14 and from a modifier of +1 to +2)?

Best Answer

PFSRD says this about Attribute modifiers:

Each ability, after changes made because of race, has a modifier ranging from –5 to +5. [...] A positive modifier is called a bonus, and a negative modifier is called a penalty.

Compare to these sections from Black Blade Basics:

Languages and Skills: A black blade starts with Common as a language. As the black blade increases in Intelligence, it manifests knowledge of languages and arcane lore. Upon reaching an Intelligence of 12, it gains a bonus language of the GM’s choice, and gains 1 rank in Knowledge (arcana). Each time the sword gains a bonus to Intelligence, it gains another language and another rank in Knowledge (arcana).

Black Blade Arcane Pool: A black blade has an arcane pool with a number of points equal to 1 + its Intelligence bonus.

Hence, you get extra skills every time the bonus (or modifier) increases (the same as with characters).

If it was every time the score increases, they would say "Each time the sword increases in Intelligence..." similar to the start of the Languages & Skills paragraph.

Also, it starts gaining skills at Int 12, ie Int modifier (or bonus) of +1

And, its Arcane Pool size is 1 + Int bonus. If this is not the same as Int modifier, then what is it? If this is the same as Int modifier, why isn't it in the previous paragraph?

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