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Booming blade is a Sword Coast Adventurer's Guide cantrip that allows the spellcaster to make a melee weapon attack with their weapon and add additional power to the attack:

You brandish the weapon used in the spell's casting and make a melee attack with it against one creature within 5 feet of you. On a hit, the target suffers the weapon attack's normal effects and then becomes sheathed in booming energy until the start of your next turn. If the target willingly moves 5 feet or more before then, the target takes 1d8 thunder damage, and the spell ends

Booming Blade, Sword Coast Adventurer's Guide, pg. 142

The Twinned Spell metamagic permits a Sorcerer to take any spell that targets only a single creature, and cast it twice, targeting a different creature.

When you cast a spell that targets only one creature and doesn't have a range of self, you can spend a number of sorcery points equal to the spell's level to target a second creature in range with the same spell (1 sorcery point if the spell is a cantrip).

To be eligible, a spell must be incapable of targeting more than one creature at the spell's current level. For example, magic missile and scorching ray aren't eligible, but ray of frost and chromatic orb are.

Twinned Spell, Player's Handbook, pg. 102

It has been commonly accepted that this is a valid use of this metamagic/cantrip combo, but a recent Errata to the spell has changed its range to "Self (5-foot radius)". Is this spell still eligible to be Twinned?

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A range of Self with an area of effect is a further specification.

Booming blade has a range of Self (5 foot radius). Twinned spell says:

When you cast a spell that targets only one creature and doesn't have a range of self

Xirema's answer has alleged that Self (5 foot radius) is not a range of Self with respect to Twinned Spell. This is not the case. The spell still has a range of Self, and an area of effect is further specified. This is clear from the rules for spellcasting, which state:

Spells that create cones or lines of effect that originate from you also have a range of self, indicating that the origin point of the spell's effect must be you (see “Areas of Effect” later in the this chapter).

This rule tells us that spells having a range of self together with a further specification of an area of effect still have a range of self, so are not eligible to be twinned.

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Yes, Booming Blade can be twinned, because a range of Self is not the same thing as a range of Self (5-foot radius)

When a spell has a range of "Self", it definitionally targets the caster themselves, and no one else. For example, a spell like armor of agathys (PHB, 215), which places Temporary Hit Points on the spellcaster (and cannot be placed on anyone else), has a range of "Self". Conversely, a spell like arms of hadar (PHB, 215), which produces an area of effect, very explicitly does not target the spellcaster, but instead all the other creatures within the radius surrounding the spellcaster; it has a range of "Self (10-foot radius). So by example, we can see that these two ranges do not represent the same concept in 5th edition D&D.

Naturally, a spell like arms of hadar cannot be twinned: the requirement for Twinned Spell is that the spell must be "incapable" of targeting more than one creature, and this is obviously not true for arms of hadar. But booming blade targets a single creature: the creature being attacked, and it doesn't target the caster, because "Self (5-foot radius)" isn't the same as "Self".

As a result, booming blade, post-errata, is still a valid spell to use with the Twinned Spell metamagic.

The Spellcasting Rule about "Spells that create cones or lines of effect" does not apply

This is the rule in question:

The target of a spell must be within the spell's range. For a spell like magic missile, the target is a creature. For a spell like fireball, the target is the point in space where the ball of fire erupts.

Most spells have ranges expressed in feet. Some spells can target only a creature (including you) that you touch. Other spells, such as the shield spell, affect only you. These spells have a range of self.

Spells that create cones or lines of effect that originate from you also have a range of self, indicating that the origin point of the spell's effect must be you (see "Areas of Effect" later in the this chapter).

Once a spell is cast, its effects aren't limited by its range, unless the spell's description says otherwise.

Range, Player's Handbook, pg 202

The reason here is that this rule specifically calls out spells that create cones or lines of effect as also having a range of "Self", but booming blade does neither of these things. It simply makes an effect that targets a single creature within range.

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    \$\begingroup\$ I'm not sure I quite agree with that logic. \$\endgroup\$ – RevanantBacon Nov 11 '20 at 21:34
  • \$\begingroup\$ FWIW, Jeremy Crawford sorta agrees: "A note about D&D spells with a range of "Self (XYZ)": the parenthetical—which says "5-foot radius," "15-foot cone," or something else—means you are the spell's point of origin, but you aren't necessarily its target. You're creating an effect that originates in your space. " and later stated: "Booming blade works with War Caster." (which is different, but related) \$\endgroup\$ – Medix2 Nov 11 '20 at 22:38
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    \$\begingroup\$ I thin kit would help if you addressed the spellcasting rules which state "Spells that create cones or lines of effect that originate from you also have a range of self". I don't see the rules as saying that "self (5')" is different to "self". \$\endgroup\$ – user-024673 Nov 12 '20 at 7:52
  • \$\begingroup\$ "Thankfully, everyone knows I'm not a persnickety person" -Xirema ;) \$\endgroup\$ – Thomas Markov Nov 12 '20 at 13:29
  • \$\begingroup\$ I will fully acknowledge the persnickety-ness of my addressing of that rule. Call it a protest against WotC trying to take my toys away, if you like. I do maintain that the usage of the term in the 2020 errata is in contradiction with how it was used in the original 2014 printing of the PHB, but "I don't think they really meant X when they say X" can't really be justified in a Rules-as-Written answer. \$\endgroup\$ – Xirema Nov 12 '20 at 13:44

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