29. Room Mode Calculations

I first heard the term ‘room mode’ mentioned when a friend of mine came by our house to audition our newly acquired Martin Logan SL-3 electrostatic loudspeakers with me. Jens, who had spent some years composing music and collecting analogue modules, was not immediately taken in by the large sound canvas of the Martin Logans and instead pointed out that there was an obvious lack of bass-slam from such large speakers. He went on to suggest that this lack might be attributed to room modes and that proper alignment of the speakers and the listening position might fix it. However, as I did not understand what he was talking about, I rather believed the speakers themselves to be at fault. I wondered, if the crossovers had been tampered with, if they needed to be recapped, if perhaps the amp was too weak, or if the Mylar diaphragm had somehow lost its magnetisation. When Jens left later that night, I was therefore feeling quite shattered.

The next person to visit us was my audiophile companion Luigi. He listened to the Martin Logans, was not especially pleased with their ‘tall stage’ impression which resulted from their sheer height, and started moving them around the room with me. He suggested that greater distance to the front wall would improve imaging and stage depth, and I tentatively agreed with him. We found a position about 1.10 meters into our 5.60 meters deep room that worked well, and we both left our session in a mental state of unsettled turmoil. The Martin Logans were not so easily placed because of their dipole nature. Even one centimetre of deviation in wall distance could mess up imaging, tonality, rhythm, phase coherence and speed impression. It then took me another four weeks to determine the exact position for the SL-3 to finally lock in with our listening room. 

I spent the next months upgrading the amplifier and improving the wiring. I also found a CD player that sounded more analogue and a phono cartridge with improved tonality. I sorted out grounding issues, eliminated trailing edge transformers from the proximity of the system and could hear gradual improvements with each step. Upgrading to solid-core silver cinch/RCA interconnects offered superior dynamics, and symmetrical power cords served to bring about the finishing touches. The system had become revealing and tonally rich. The sound stage was impressive, even if a little taller, as Luigi was quick to point out. The position of the speakers had been found by ear over the course of many months. I could hear that 1.12 meters distance worked well, but I did not know why this was. In fact, I was feeling uneasy about swapping speakers to run new tests for eiaudio. Luigi joked that he had some friends who were so scared to lose what they had accomplished that they set their systems up for life. That prospect did sound pretty sad.

I did not want to be that kind of audiophile. Instead, I preferred to stay true to my mission of exploration that is proposed by the title of this blog. I needed to find a solution of how to set up speakers quicker with more assurance of having found the best position. Then, one day, as I was standing at the shack of my favourite audio technician, I heard him speaking to one of his customers inside. I did not want to interrupt, but as I was listening, I noticed that his customer was speaking very soberly about some basic issues in HiFi that had also troubled me for some time. I could feel that we were kindred spirits and decided to step inside. We were quickly introduced and started speaking about the subject of cables, interference, and grounding, carefully checking each other out, because some people can be quite stubborn insisting that their current state of knowledge should be the end of everyone’s explorations. We were both relieved to find that this did not seem to be the case. At the end of our talk, I gave Peter Englisch my eiaudio.de business card and invited him to join the blog discussion. He said that he would have a look, and we went separate ways. 

Some weeks later, I gave Peter a call, and he seemed happy to hear from me. As it turned out, he had read all my articles in the High Fidelity section and was somewhat pleased with the contents he found. He pointed out that, in some of the articles, although my description was accurate, it was also apparent that my grasp of the subject did not yet allow me to present the issue in a nutshell or state the single cause of an issue. I agreed that this was most likely the case, because I had not first studied the subject but instead worked my way towards a solution while moving from the practical application towards the theory. I felt proud of the progress I had made in just over two years, and he offered to help me take it a little further. Peter informed me that he had written a number of Excel sheets that allowed him to enter room dimensions to derive from them the best possible speaker positions. He offered to send me his spread sheets and promptly did so later that day. I confess that it took me a few weeks do get over the shock of seeing so many numbers and graphs on each page. With some time, however, the initial panic subsided and allowed me to work with the sheets.

I took our laser length meter and measured the inner dimensions of our main listening room to be 5.58 meters in depth, 4.78 meters in width, and 2.78 meters in height. The walls had some furnishings which would have some impact on sound, and I considered the resulting alternative measurements where the furniture affected room dimensions at ear level. Most prominently, there was one Ikea Besta cupboard that narrowed the left side wall by 0.43 meters at the listening position, resulting in 4.35 meters width. Upon entering the results of my measurements in the Excel sheet, I saw that each of the three dimensions (h, d, w) was treated separately without apparent effect on the others. The Excel sheet also did not care if the height and the width value were swapped: The results looked the identical, although one would probably notice the mistake in entry when setting up the speakers in this way. I found that a greater wall-to-wall distance always led to lower resonance frequencies, of which there were three: the first room mode, the second, and the third.

The first room mode was the strongest and the result of the speed of sound of around 340 m/s interacting with the space between the room walls. The other two were harmonic resonances that occurred at double and tripple the frequency of the first room mode. Since sound waves peaked along the room walls where they were reflected backward, the nulls were spread across the room. For the first room mode, the null was at half the room depth (at 2.79 meters in the case of our room example). I learned that sound waves were different from electrical waves, as the floor of a listening room folded the bottom half of the potential sine wave upwards, thus placing the first resonance frequency at half the calculated resonance. The resulting calculation for the room depth resonance was: 

340m/s (speed of sound) ÷  5.58m (room depth) = 60.93 Hz (sine wave)

60.93 Hz (sine wave) ÷ 2 = 30,47 Hz (1st Resonance)

The second depth resonance was at 60.93 Hz and produced three peaks in the room. Next to the natural peaks at the walls, the third peak was in the room center. The resulting two nulls were at the center of each room half, as if there was a wall between the halves where they could also accumulate. The third resonance was at 91,40 Hz and acoustically divided the room in three. The graph looked as if two separating walls were separating the three parts producing a null in each center and a peak at each imaginary wall. This created three nulls and four peaks over the total room depth.

Since resonances could accumulate or cancel each other out, the best positions for setting up speakers and for the listening position were those in which the specific room resonances produced a natural balance in the relevant frequencies. In his descriptions, Peter referred to these locations as preferential positions. And although their factors remained the same for normal rooms, the resulting value would change with the dimensions of each listening room. The factors for the calculation of the preferential positions were:

Factors: (+3) 0.125 — (+2) 0.2 — (+1) 0.45 — (-1) 0.55 — (-2) 0.8 — (-3) 0.875

Results: (+3) 0.70 m — (+2) 1.12 m — (+1) 2.51 m — (-1) 3.07 m — (-2) 4.46 m — (-3) 4.88 m

The distances provided in meters underneath each factor show the preferential positions for our room depth of 5.58 meters with all distances being relative to the front wall. The factors with negative numbers are actually mirror images of the first three factors and could more easily be measured from the back wall using the first three values. The mirror axis being at 0.5, which is half the room’s depth. I could see that the room dimensions had an effect on the first resonance frequency and the two harmonic counterparts, with larger rooms having lower resonance frequencies. The lower the frequency, the easier it was to place speakers in the room without interfering with our ear’s most critical frequencies, which are commonly around the spectrum of the human voice.

Doing the calculations for our upstairs listening room produced far lower resonances than our main listening room. The upstairs room, which also served as our office, measured 15 meters in depth and 11 meters in width. There were no parallel walls, and also the ceiling elements were of various heights. The room depth resonance frequencies were 11.3 Hz, 22.67 Hz, and 34 Hz correspondingly. The resulting preferential positions were:

Factors: (+3) 0.125 — (+2) 0.2 — (+1) 0.45 — (-1) 0.55 — (-2) 0.8 — (-3) 0.875

Results: (+3) 1.88 m — (+2) 3.0 m — (+1) 6.75 m — (-1) 8.25 m — (-2) 12 m — (-3) 13.13 m

When looking for the preferential positions for loudspeakers with respect to the width of the room, placing the speakers in mirrored positions along the room’s center axis would have produced a null in the listening position, because the latter was then located in the center of the room to form an isosceles (if not equilateral) triangle with the speakers. To avoid this effect, positions of varying wall distances had to be preferred. For our smaller 4.78 meters wide room, this could for example be a combination of factor 0.125 = 0.60 m and factor 0.2 = 0.96 m. The width distances were measured from each speaker’s center axis to the wall, whereas the depth distances was measured from the woofer’s voice coil to the front wall.

In larger listening rooms, the highest order resonances were quite frequently produced by the limited ceiling height of the room. In our 2.78 meters high room, the resonances were 61.15 Hz, 122,30 Hz and 183,45 Hz. Preferential positions were calculated to be at factor 0.125 = 35 cm and factor 0.2 = 56 cm. The vertical distances were measured from the central axis from the largest woofer to the floor of the room and had to be identical for both speakers.

The main listening position ought to form an isosceles triangle with the speakers. If the result was an equilateral triangle, this was even better. For the tonal balance, however, it was of far greater importance that the listening position corresponded with one of the preferential positions in the room. Once we began positioning the speakers and ourselves according to these factors, the first outcome was already quite acceptable. And it was from this assurance the we were able to begin with the fine tuning of the speakers to the wall materials, carpeting, and various furniture by moving the them a few centimetres or moving the listening position slightly in order to compensate for unwanted room accents. I found Peter’s method highly useful and will keep it in my toolbox for any upcoming adjustments.

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