How can I get rid of a 4khz-8khz room spike?

I have a similar room - 13' x 15' and highly reflective. Nasty 8 dB peak in same area you have. At one point I had the room entirely covered with carpets and blankets and such and still the same peak. Didn't matter which speakers I used until.....
I have now solved the problem by changing speakers - and no acoustic treatment. I went to a single driver speaker which beams over 3kHz so no room reflections. Works GREAT in a small room such as yours. It's like listening to headphone but with great soundstaging.
Some good full range drivers:
Jordan JX92s (~$310/pr)
Adire WR-125 or FR-125 from www.creativesound.ca ($150/pr)
Tang-Band W4-1320 available July from www.partsexpress.com ($75/pr.)
Other brands: PHY, AER, and Fostex FR-120 or FR-200.

Nanotweeter...If you must use the RS meter, use it with the Rives Audio CD that has tracks which are corrected for the RS meter error.

My personal experience is that a spectrum analyser (such as the Behringer DEQ2496) is a thousand times better.

Nanotweeter, if you launch the link in Herman's post above, you will see a 2001 thread that was initiated by Sean and that includes a compensation chart of adjustments that need to be made at each 1/3 octave interval in order to adjust for the inaccuracies of the Shack meter. Those compensation adjustments are summarized below:

10Hz.....+20.5
12.5Hz...+16.5
16Hz.....+11.5
20Hz.....+7.5
25Hz.....+5
31.5Hz...+3
40Hz.....+2.5
50Hz.....+1.5
63Hz.....+1.5
80Hz.....+1.5
100Hz....+2
125Hz....+0.5
160Hz....-0.5
200Hz....-0.5
250Hz....+0.5
315Hz....-0.5
400Hz....0
500Hz....-0.5
630Hz....0
800Hz....0
1kHz.....0
1.25kHz..0
1.6kHz...-0.5
2kHz.....-1.5
2.5kHz...-1.5
3.15kHz..-1.5
4kHz.....-2
5kHz.....-2
6.3kHz...-2
8kHz.....-2
10kHz....-1
12.5kHz..+0.5
16kHz....0
20kHz....+1

Add the above numbers to your SPL meter readings in order to obtain the actual SPL level in your room at each 1/3 octave interval. Given the -2dB compensating adjustments required at your problematic treble frequencies, I think you will find that you still have a reduced but still very sizable 8dB or so frequency response spike throughout those frequency bands.

Thanks for the replies and comments. I think my approach will be to install some 4khz+ traps on the walls and see if this makes any difference. Maybe remove and/or reposition some room tunes as Edle suggests. If no significant effect, I will then look at power supply per comments of Cincy bob.

Herman: how do I properly set up a nearfield measurement?

Cincy bob: please advise how you compensate for RS SPL meter inaccuracies.

Onhwy61: I measured using the meter mounted on a tripod positioned at my head location on my listening chair and on the tripod in the same location with the chair removed from the room. No noticable change in response. Measurements were taken using 10s weighted average readings (C-weighted). I repositioned speakers two more times by up to 18" each with only a slight reduction in the magnitude of the spikes. Used both Paradigm S60V3 and Triangle Antal XS speakers - results were relatively the same with the hotter Antals having higher peaks within the same general range.

Thanks.

Last year I consistently measured a treble frequency response spike in my system in the range of 5kHz to 6.3kHz. The treble frequency spike remained in the range of 5dB to 8dB (measured with the Radio Shack analog SPL meter with measurements adjusted to compensate for the inaccuracy of the meter) despite various room treatment experiments, component changes and cable changes. Throughout this period, the spike was most apparent when listening to string sections in orchestral music where the violins would exhibit a coloration that made them sound "hot" and forward.

I was convinced that my problem was inherent in the treble response of my speakers until about six months ago when I was surprised to discover that the problem was primarily an issue with my AC electric. Apparently, there was high frequency noise riding along on my AC electric lines. I managed to solve the problem and revert the treble frequency response to flat with the upgrade of my AC electric system, including the addition of a 7.5 kVA isolation transformer.

If you find that your problem is not inherent in your speakers and is also not related to room reflections, you might find that your AC electric supply is the culprit. If you are interested in more detail, check my virtual system thread.

Good luck.

Are you sure it is the room? Perhaps some nearfield measurements will reveal that your speakers have a peak in their response.

Ten dB is quite a bit and can be heavily influenced by your measuring technique. Is the meter clear of anything reflective including you that could be skewing the readings. If you hold it in your hand or lay it your chair then that can affect the accuracy. It's not that accurate in the first place. Assuming this data on the Radio Shack SPL meter is correct then take this in to account. A 10dB spike above the reading at 1Khz may be a problem but a 10dB spike in relation to lower frequencies may just be showing how inaccurate the meter is?

May be you have too many room tunes....take 1/2 of them out and check again.

Listing your equipment and a photo of the room would be very helpful. Also describe how you measured the speaker's frequency response.