The Golden Ratio 💫

 

The Golden ratio in audio

Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of 

φ—may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural objects and artificial systems such as financial markets, in some cases based on dubious fits to data. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other parts of vegetation.

For an optimal audio setup, Cardas Audio recommends using the Golden Ratio (1.618) to determine speaker placement, ensuring a superior listening experience. This method minimizes unwanted sound reflections and maximizes clarity, soundstage, and most importantly bass response by positioning speakers in harmony with room dimensions. Key to this approach is placing speakers and listening positions in mathematically precise spots, reducing acoustic interference and improving overall sound quality. By adhering to these principles, audiophiles can create a well-balanced room.

Setting Up Speakers in a

Rectangular Room

Very precise speaker placement can open up a whole new dimension in listening, so I will outline the system that is becoming the standard of the industry. This standardized listening room is a Golden Cuboid and is the model for the math used in this system. This method will work with any box speaker, in any reasonably sized rectangular room. You may find that you have already positioned your speakers this way by ear. 

Active nodes are the main concern when placing speakers in a rectangular room. A node, or the frequency where speakers and parallel walls interact, is proportional to the speaker to the wall distance. 

The three most importance nodes, in order of importance, are proportional to the distance between the speaker and: 

1. The side wall nearest the speaker

2. The rear wall

3. The side wall across from the speaker 

 

A secondary factor is the speaker-to-speaker time constant. 

When you use this Golden Ratio method to set your room up, the speakers are placed so the three nodes progress or differ from one another in Golden Ratio. This eliminates any unison or near unison resonance in the nodes. 

Panel or dipole speakers such as Apogees and Magnepans cancel their side waves, so a formula of .618 x the ceiling height can be used for determining placement from the rear wall. Most box speakers radiate low frequencies in all directions thus a formula that places the speaker to rear wall distance at 1.618 the side wall distance should be used. 

Speaker placement, simply stated:

-The distance from the center of the woofer face to the side walls is: 

Room Width times .276 (RW x .276) 

 

-The distance from the center of the woofer face to the wall behind the speaker is: 

Room Width times .447 (RW x .447) 

 

This is what you need to know to place speakers in a symmetrical, rectangular room!

 Thanks to Cardas Audio 🙏