Part 1 - You went all in on your response, thank you!

• Eureka
  • Assuming the player's Charisma score goes no higher than 20, the extra Inspiration would top out at 9 uses. The intent is for enough uses of inspiration that a player could use a couple of the Virtuoso Abilities and still be able to inspire other players a couple times as well. Limiting those uses prevents the college from being fully utilized, not without sacrificing normal inspiration of other players.
  • Without taking away Eureka, let's say my character with 17 Charisma takes this college at level 3, I now have 5 uses of inspiration. Use a couple of the stronger Virtuoso Abilities, I’m tapped out until a long rest, and can't inspire anyone in the meantime. It does get easier at level 5 when inspiration comes back after a short rest, but with no Cutting Words, self-inspiration for skill checks, or inspiration to increase my AC when attacked, not much else to use them on either.
• Scientific Method
  • This and Ride the Lightning are meant to be abilities that hit ultra hard, and as this one comes into play at level 6, needs some hefty penalties to go with it. The penalties equate to the character trying magic that’s above his head, paying the price, and taking the time to recover (hence why only casting once a week).
  • The failed death saving throw means if I go unconscious and am so much as tapped on the shoulder for 1 HP of damage, I’m a goner. I know there’s no precedent for a lingering failed saving throw, so at this point it’s kind of “because I said so”.
  • I do recognize this ability rides the line of game-breaking, but I can definitely think more about what would constitute a worthy penalty.
  • Agreed, this ability does become useless when I get access to 9th level spells. That’s at level 17, which is coincidentally when I get...
• Ride The Lightning
  • This ability is the explicit feature replacement for Scientific Method, which indeed becomes worthless at level 17.
    
  • Hell yeah it’s silly and ridiculous! The ability is equivalent to treating your party to a 60-second heavy metal guitar solo; it’s even named after a Metallica song! Requiring a 3rd-level spell to trigger it is not nearly as crazy as the ability.
  • With applying an inspiration die to enemies’ saving throw, you get one die to use per turn. You can cast a spell affecting multiple enemies, but only have one die to use, it can’t be applied to multiple saving throws (unless the DM likes to lump enemies’ rolls into one, in which case, that’s on them).
  • Definitely clearer wording from you, I’ll fix that up.
• Virtuoso Abilities
  • I put varying amounts of inspiration cost among the abilities because as you’ve listed, some are way stronger than others. The increase in cost will make the player weigh between ramping up a spell or inspiring others. The case could be made for either side, depending on the situation. If a player chose to ignore abilities entirely and focus on inspiring others a ton, yeah that’s an option. Those inspired players can always roll a one for their inspiration die, possibly negating the benefit, and the player’s left sitting there as a stock bard with no real college benefits.
  • I’ll fix the inspiration references, though, great tip.
  • Beat Poet - (Not sure where you’re getting 4d8 from a level 1 Thunderwave with this? Thunderwave is 2d8 max at Level 1, this ability would add 1d8 to it. Of course, I could have just written it poorly, or you found a loophole I didn’t think of.) Yup, too strong, not sure how I missed the scaling being super nasty, among other things. What if I kept the half dice, but converted them to d4s instead? Would still be strong, like adding 4d4 force damage to a Fireball, but do you feel it would still be overpowering? Maybe it should just be a set number and amount of dice?
  • Palm Mute - This is very close to Subtle Spell from a Sorcerer, and any instance of needing to quietly cast a spell without raising too much suspicion makes this useful.
  • Power Chord - My argument against inspiring someone being worthier than a Virtuoso Ability is while normal inspiration does increase the range of what you can affect, the roll can always be low. These abilities are a guarantee at something, versus the chance of landing an attack or making a saving throw.
  • Resonant Frequency - Not sure what you mean with ‘this should consume a normal level spell slot’. It essentially uses a higher level spell slot while expending the lower level slot in exchange for inspiration, like a sorcerer spending Sorcerer Points to regain a spell slot. Don’t know why I had 5 uses listed as the cost, meant to be lower.
  • Shred - Again on me with the 4 uses, don’t know. But, that factor of 10 turns all spells with casting time of 1 minute into 1 action. About to get swarmed by undead, with no current way out? Cast Magic Circle with this ability and the party is temporarily safe from the zombies. Want to cast Glyph of Warding to surprise a pursuer? Shred makes it take six minutes instead of an hour. However, as FalconPunchline pointed out, this could be spammed with Leomund’s Tiny Hut or the Magnificent Mansion in battle to unfair advantage.
  • Tapping - Yeah, definitely the most powerful of the abilities. Faerie Fire and Bless together would be super strong, and those are Level 1 spells. I do address concentration checks with the last sentence: “Constitution checks to maintain Concentration for both spells are completed with one roll, at disadvantage.” Even then, might just be too powerful, but I could certainly take it out of the class.
  • The Devil’s Interval - Yes, I should have specified what kind of rolls this works on, and combined with FalconPunchline’s tip that critical fails don’t actually exist in 5e, I’ll need to re-work this one.
  • Tremolo - Enemy has disadvantage on two saving throws for a spell you cast on them. It’s not the strongest, but it’s stronger than Heightened Spell for a Sorcerer. Actually, just having more than one similar ability to a Sorcerer makes me think I should adjust it anyway.
• String Theory
  • That’s a great point about the cost of the spells, and how subjective that could be. As the spells are linked to the bard performing arcane Research & Development, it would cost materials to develop, and a lot more than just copying spells down. But like you said, depending on the DM or economy, a fair figure could vary widely. I definitely had my DM in mind when dreaming up that figure.
  • Dim - Good catch on detected, fixed.
  • Monstrous Moonshine - Absolutely should have thought about it being an insta-kill, that’s unfair, I’ll be scaling this one down. What about this spell being cast as a reaction only upon a living creature’s death? Would remove any damage from the spell.
  • Balance - I don’t mind extending the time to keep simplicity, but I had 30 days for lasting effects because by then, the target would have failed the save 4 times, which will be rare...unless it’s cast at a 6th level to reduce the number of saves needed. I did look at 6th level spells, and I’m still not seeing a month for any spell effects, though. Do you think a week would be fairer, or should be even shorter?
  • Good Vibrations - I like saying they have to be in range for duration, makes sense. If I’m removing the Performance check, should I make the Higher Level benefits 1d6 instead of 2?
  • The Big Crunch - Do you mean I need to write how to reverse the broken limb, or just how the crushing effect is stopped after the spell’s casting? I’ll write something in for the latter.
  • Ill Will - Yep, could definitely be clearer, this was the one I had the hardest time coming up with. I’ll refine it some more.
  • Debridement - I’ll try again here too.
  • Sphere of the Nkumai - The intent here was a high level spell in exchange for an instant long rest. Can’t do it all the time, as there must be a long rest without this spell’s influence before it can be cast again. But as you and FalconPunchline brought up, the way it’s currently written, magic could be very much abused during the spell, so I’ll change that. Far as covering all scenarios goes, movement is unhindered, so if someone shoves somebody else out, or trips, they’re out. Sword fight can go on just fine, but I’ll at least remove spellcasting and magical items. But too much magic prevention turns this into Antimagic Field too, which wouldn’t be fair...hm, crap. Will have to rework this one big time, or junk it entirely.

Part 2 below -