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Identical 2-mana red ritual adding RRR, can be spliced.

3-mana ritual adding five red, bigger burst.

1-mana red ritual netting mana cheaply.

Black equivalent burst ritual for mana spikes.

Classic 1-mana ritual producing extra mana.

Red burst mana plus card advantage, premium upgrade.

Massive red ritual scaling with tapped lands.

Red ritual producing mana per creature for big bursts.
Pyretic Ritual is not a mana ability and doesn’t behave like one. You cast it as a spell. It uses the stack. It can be responded to, and it can be countered.
In the same vein, you can cast Pyretic Ritual only at a time when you could cast any other instant, not at a time when you could activate a mana ability. For example, you can’t cast Pyretic Ritual in the midst of casting another spell; you’d need to cast Pyretic Ritual first.