[BoiledCabbage]

Two beams of light of equal intensity and different frequency contain equal energy not differing amounts of energy.

The actual difference in frequency is the composition of that energy.

If of course you compare a dimmer beam of light with a brighter one the dimmer one will have less energy.

So no less energy is due to lower intensity light, not due to different frequency. You can pretty trivially have 5 flashlights each with a different color of light and all with the same energy.

[mindslight]

Sure. The varying "composition" of that energy is what forms the spectrum - it's a single scalar. You're adding one more dimension of dim/bright, making the entire description be two scalars.

Look up the definition of "spectrum", and contrast with "gamut".

[BoiledCabbage]

I disagree - I'm not adding an additional dimension. You're implicitly including the dimension of intensity without calling it out explicitly.

The only way that two different otherwise identical light sources can output different amounts of energy is if they have different intensity.

Or put differently, in your example if you have different wavelengths and hold intensity constant then energy is also constant. It's your example that has implicitly introduced the concept of intensity without explicitly saying so. And the evidence of that is my example. My example is exactly your example, but holding the intensity consistent between the two different light sources. If you do that, then your example fails.

Different wavelengths of light at the same intensity output the same energy. Meaning wavelength does not change the energy output by light.

Even though photons exist, light is fundamentally not a particle. Your statement would hold if light were a particle and only a particle and did not also have wavelike properties. And generally when discussing light as human perception it's the macro scale and wavelike behavior that is being discussed.

[mindslight]

I was talking about the spectrum, not brightness or intensity. The spectrum represents a variation in just a single quantity - energy per photon, or wavelength if you prefer. The spectrum is orthogonal to brightness/intensity/power.