Index Room & AcousticsListening Triangle

Listening Triangle

Lay out speakers and seat to scale and find the side-wall reflection points.

Ear to each speaker2.20m

Seat from front wall2.71m49% of the length

Space behind the head2.79m

Side reflection point1.39malong the wall from the front

Reflection arrives3.7ms late

Toe-in to aim at ears30°

Plan view, to scale

Listening triangle
Speakers
Seat
First side reflection

Place absorbers or bookshelves on the side walls at the marked points.

Input

Room widthm

Room lengthm

Speaker spacing, centre to centrem

Speakers from the front wallm

Measured to the front of the cabinet.

Angle between speakers at the seat°

60° is the equilateral triangle that stereo was designed around.

How it works

The triangle

Stereo recordings are mixed with the speakers about 60° apart as seen from the engineer's chair. With the speakers a distance $s$ apart and the angle between them $\theta$ , the seat sits on the centre line at

d_{\perp} = \frac{s/2}{\tan(\theta/2)}

d_{ear} = \frac{s/2}{\sin(\theta/2)}

At 60° the three sides are equal. A narrower angle gives a firmer centre image; a wider one a broader stage with a weaker middle.

First reflections

Sound also reaches you by bouncing off each side wall. The bounce point is found by mirroring the speaker in the wall and drawing a straight line to the ear. For a speaker at distance $x_s$ from the wall and a seat at $x_l$ :

y_r = y_s + (y_l - y_s)\,\frac{x_s}{x_s + x_l}

The reflection travels further and arrives late by

\Delta t = \frac{\sqrt{(x_s + x_l)^2 + (y_l - y_s)^2} - d_{ear}}{c}

Reflections inside the first 5 ms or so blur the image most. Treating the marked points, or moving the speakers away from the side walls, pushes them later and lower.

Front to back

Bass standing waves along the room have nulls at half and quarter length. A common starting point puts the ears 38% of the room length from either end wall, shown as the dotted line. Keep at least a metre between your head and the wall behind when you can.

References

H. Haas, “Über den Einfluss eines Einfachechos auf die Hörsamkeit von Sprache,” Acustica, vol. 1, pp. 49–58, 1951 (Göttingen dissertation, 1949). English translation: “The Influence of a Single Echo on the Audibility of Speech,” J. Audio Eng. Soc., vol. 20, no. 2, pp. 146–159, 1972. AES