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Its only stated reason for being in HTML is to support a non essential case in an algorithm that is not implemented in any browser
<h2>Subheading</h2> <-- also "subheading", not simply "some other header"
If you want a tagline or similar to your header, and are using h2 because it's visually different, then you are using it wrong. h1 and h2 are semantically different.