I've shot film professionally and full-time since the early 90's. I got a Panasonic DVX when desktop video hit, and now do mostly corporate video with a big Panasonic camera and (really, primarily) the Samsung NX1, which shoots wicked 4K. My video-niche is "looks like you had a big crew, but done using sort of guerilla-indie filmmaking techniques", IE I own my gear and don't rent and do most audio, video and lighting myself. And my stuff looks very tight, not like kid-with-a-DSLR (all this to let you know where I'm coming from).
LEDs have come a LONG way. The current Aputure stuff renders very well, usually I find it needs like 1/8 green to match my daylight stuff.
But for LEDs with decent power, you have to spend a lot of money. I have a 575 HMI par for fighting daylight in window-offices, a 400 HID setup for softboxes and general use, a couple HID 150 fresnels, but in most cases I
try to use my biax fluorescents - Kino-knockoffs. they're cool, bright, no hot-restart issues, small and affordable. My Aputure (672) is used as a kicker, hair/cheekbones, or for a background wash.
I don't use Kino tru-match tubes, and I've found my lamps need 1/4 CTB and 1/8 minus-green to render excellent 5500k. Often I manually white balance through a mild cooling filter (like a 1/4 CTB) to warm things up a hair. (I test all my daylight stuff by shooting tests with a raw DSLR, looking at the temp and tint sliders it takes to get good daylight, use that as a guide for gels, shoot again and dial it in). I don't shoot film for motion work, but for digital sensors, this approach works perfectly and my fixtures are marked with gel combos needed.
So as far as CRI - to me it's fairly meaningless when you get over 85 and seems like something the inexperienced (or wealthy!) fight about. If the light can be gelled to render well (without killing many lumens), it's fine with me - considering a 4-tube biax is under $200, pulls 220 watts, packs reasonably small and light, is reasonably cool, and puts out about 1k tungsten equivalent (more like 1600 watts if you compare to a tungsten fixture with full CTB - CTB is a light-eater). Kino trumatch tubes are about $28, so add $100+ to a quad biax - I think they render a bit too magenta, and they lose about 20% brightness over a standard film-industry intended tube.
If I location scout and I need my lights to match existing office lighting (current flo tubes and bulbs are fairly consistent at around 3700k with a big hit of green), I shoot raw stills at the location and dial in my gels so the flo's and HMIs match the office lighting - usually some +green and CTO. Then I manually balance at the location. Again, skin tones come out natural, everything's good.
All this to say - for a budget, try some biax fixtures, widely available in duals and quads (and the occasional 6-tube unit). If you need a hard light, the budget answer is a 1k fresnel, some CTB gel and a couple scrims (or some metal windowscreen in a gel frame). Often you want a hard light for non-key uses, and using 1/2 CTB can look really nice and keep the lumens up. A dimmer will warm the light, so often you need a few flavors of CTB to dial it in.
Frame grabs of biax shoots:
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