speakers or room???

There's a mild form of tinnitus where the ringing is triggered only by certain frequencies and volumes. It comes and goes with these sounds. Since its not heard at other times it creates the impression of a spike or ringing coming from the system. A good test is to see if you hear it playing the same music at the same volume with earphones, ear canal phones or earbuds.

If that's what it is, not much you can do, you just learn to live with it. 

If not then next is the room. Slap or flutter echo can create a frequency spike like that. Stand a few feet from a wall, clap, and listen. The sound should decay smoothly. If the walls are unbroken and parallel you may hear a rapid flutter or ringing sound as the clap bounces back and forth very rapidly. That's flutter echo. Try different places around the room. If you find a spot with flutter echo the simplest/cheapest/easiest treatment is buy one 2x3 ft sheet of 1" thick Owens Corning fiberglass panel. These are light enough to temporarily hold in place on a wall with stick pins or masking tape. You only need to treat one wall.

OC is very absorptive. You can easily over damp with it. Experiment to see how small a piece you can get away with.

The better but more involved solution is a diffusor panel. OC costs almost nothing. Its almost for certain you find some place to use it. Mine are in all the corners. Those little triangles are highly effective. https://systems.audiogon.com/systems/8367

Tinnitus? I hope my years playing in rock bands isn't coming back to haunt me! I'll try the headphone test you suggest. 

Always treat the room.  GIK Acoustics

Actually OC fiberglass isnt very effective when compared with an engineered cotton or wool material designed for this purpose. I bought some cotton material from a company called Soundproof Cow which I think is very good. If you want to go cheap then the OC is fine but it doesnt absorb a very wide band of frequencies.

The Tannoys look like lovely speakers, and published measurements don’t show a peak there. But the two octave around 500 Hz are an area sensitive to speaker positioning, especially with ported speakers. So my suggestion is, try moving the speakers away from the wall a little and also moving your listening position. You might be able to fix this that way.

As far as room treatment, that’s something I often recommend, but these frequencies are low enough so that a thin panel or rug isn’t going to do anything to help. I would use panels 6" thick or something like tube traps. Still, I’d experiment with positioning first. You might not need room treatment for this particular issue.

Finally, I have not used one, but many users swear by the Schiit Loki, saying it's a useful and transparent EQ for very little money. One of its bands is centered at 400 Hz, which might be just the ticket if you can't solve the issue with repositioning the speakers.

dtapo... don’t want to ruin your day but at 63 i’ve just realized that my hearing has changed. in the last few months all of my mid fi gear and car systems now have their treble controls at max boost. never needed that before. max treble boost was way too bright maybe as little as a year ago. ain’t happy about it. fwiw

I have the XT8 speakers as well, also fed by some Primaluna gear. I listen to a lot of jazz piano (as I type this actually) and have not had any issues with any midrange spike. I actually used a mic and REW software to do some room measurements and did not see any spike there. So I’m also guessing the room might be in question here. 
Your source might be able to help with EQ. I use Audirvana (on a Mac feeding my DAC) which allows to use some EQ plugins that I set to compensate for the REW measurements. It probably won’t do as well as some of the recommended room treatments, but it’s an easy test to see if you can “adjust” it out. 

First things first...probably get your ears tested by an audiologist.  That's not realistic at this time...so at least do a few sweep tests on youtube.

Then examine the room...then speaker position...then different speakers etc..

I have tinnitus (4000hz notch) from an ear infection at age 25.  Earlier this year (at age 52) I got a bass boost (way too much) in my left ear and then suddenly lost nearly all the bass and mid tones in my left ear. When you loose mid and low bass you can't properly locate who's talking in a room full of people. It sucks...especially when you've just plunked some good money on your first tube amplifier.

Anyway, I like you, had a boost in the mids that were annoying when listening to piano or when vocals hit the right notes.  I think when you loose some frequency spectrum, your brain compensates by turning up
the other frequencies.

I went to an audiologist and was treated with steroid injections in the eardrum and prednisone...lots of follow ups and nothing. I was told that the condition was most likely permanent and that a hearing aid would be necessary. 

The good news is that unlike upper frequency hearing loss, low tone loss can, sometimes, be recovered by itself or through therapy.  In my case it came back by itself only very recently but not to the same level as before...but I got 70% back. When you get it back, your speakers magically regain that lost imaging...a drive in the car sounds completely different...and you're not asking your wife to repeat everything she says. 

I've always worn earplugs to concerts and movies since my first episode of hearing loss at age 25. I've been so careful with my hearing but it's age and trauma that does our ears in. 

Good luck and happy listening all! 

@dtapo - A while back a friend asked me about his listening space - it was an open concept apartment with 12 ft high concrete ceiling and walls and hardwood floor. His kitchen cabinets did not go to the ceiling.

I had achieved a lot of success in my own living space by using a vinyl roller blind behind the listening position.

Since I had some spare vinyl lying around so I took it down to his apartment and tried hanging it in different locations & positions. 

The vinyl was 8ft wide and 24" tall

It turned out that the best position for the vinyl was at ceiling height on the wall facing the speakers and also as a "barrier" between the audio system and the kitchen. 

On further investigation there was considerable reflection issues between his ceiling and the top of his kitchen cabinets.

So now I tend to "look up" when thinking about room treatments. 

A lot of companies that deal with sound issues in commercial spaces have great success with treatment on the ceilings. Vinyl lines drapes are also effective for noise suppression.

Good luck with solving you problem.
 

+1 on hearing test (and me too)

+1 on "the room"

OK I found a tone generator online and using my Sony noise-cancelling headphones, I discovered a few things about my ears. My total range of hearing is from 25Hz to 12.2 kHz, although the extremes are barely audible. There are a couple of hot-spots where it gets almost painful at 2500 and 4100 Hz and around 3000 drops out considerably. I also noticed that there were volume differences between Lt and Rt at certain frequencies. So that's one thing. I haven't had a proper hearing test in 30 years.

Next, I'll run the sweep through my speakers (after my wife leaves} and see what that turns up.

Thanks for all the ideas and comments so far.

Bummer 😕

Has anyone had any luck with a professional ear cleaning / wax removal help with this?

I've used the simple ear wash system for decades...put the hydrogen peroxide based goo in yer ears, let it burble for 10 minutes or so, douche it out with several squirts from the rubber squeeze ball...do it all again if needed...works and is safe.

I also listened with headphones to 2 tracks which present the problems in my system: Chopin waltz in C# by Nina Postolovskya which was recorded without the use of compression or EQ, and Can't Find my way home by Blind Faith where S Winwood's voice creates some earsplitting tones near the end of the song. On headphones, these 2 tracks present  similar problems, in the form of hot spots but to a lesser degree. It seems like my listening room amplifies these anomalies.

I realize some recordings can induce weird resonances into a system/room, and everyone's hearing is different, including the recording engineers. In my case it's beginning to look like my hearing contributes to these problems, but also my room. I'm beginning to look into room treatments now.