Golden Ratio is an easy concept of elementary geometry which has had, and
still has, great relevance both in human designs and in Nature.
Recently it has had wide application in HiFi Audio too.
Let me write down a brief survey on Golden Ratio and its amazing history.
Let us take a segment a of lenght 1. Another segment b is said to be the Golden Section of a if it solves the following equation: b2 + b - 1 = 0 that is to say the two segments respect the following proportion: a : b = b : (a-b). In simpler words, given the fact that a has lenght 1, b must be 0.618 approx.
Historically the Golden Ratio was well known to the Egyptians who used it for
building their pyramids but it achieved wider popularity thanks to the Greek
We have to wait till 1496 in order to have that ratio called "Golden Ratio". Actually the mathematician (Friar) Pacioli wrote a paper called "De Divina Proportione" where he referred to that ratio as a God-given number one can find everywhere in Nature.
This paper had a great influence with Leonardo da Vinci, who was one of Pacioli's friends, such that Leonardo's Anatomia artistica was highly permeated by this magic number. For example, the umbilicus is the Golden Section of the entire body.
Just to go back to HiFi and Music (not to mention the applications of the
Golden Ratio in Architecture) let me recall that the standard AES listening room
is a Golden cuboid, that is the sides are in golden ratio each other.
Also, many loudspeakers cabinets have golden ratio "inner" dimensions.
More generally, whenever one has to minimize or optimize harmonic resonances the Golden ratio proves to be the way to go (read further on for George's explainations).
George Cardas received US Pat. No. 4,628,151 and 4,980,517 for creating his proprietary Golden Section stranding technique.
LC > When (and how) did you start using Golden Ratio in cable manufacturing ?
GC > My original prototypes were stranded in Golden ratio.
I had previously used Golden Ratio in Race car port timing, exhaust systems, track width, weight distribution etc. to control harmonic resonance.
I visualized conductor glare as harmonic resonance and Golden ratio was the most elegant solution, I first assembled the machinery to strand in Golden Ratio back in 1983.
LC > Which are if any, the main differences in designing audio cables? I mean, which is the main difference between say, a signal and a power cable (material Geometry and cross-section.
GC > The materials are basically the same for state of the art cables, you always choose the best metal and dielectric you can find. I use extremely soft and pure copper and a combination Teflon and air dielectric for everything. Constant "Q" Golden ratio stranding is ideal geometry for signal power or speaker cable.
Speaker and power cables are optimized for current transfer thus they are of much larger cross-section and the key is lowering resistance while maintaining a high inductive 'Q' . In signal cables capacitance, dissipation factor and shielding are dominant issues so compact constructions are a must, low clean capacitance and resistance.
LC > Let's talk about power cords. Besides the non-resonant construction, which are the most important parameters one should consider when designing an AC cable?
GC > Power cables are similar speaker cables - they must transfer power and choke RF. I think they should be shielded and provide very low resistance and filter RF. Most of the "free" ones are real junk.
LC > Is there any realistic explanation about the (surprising) fact that audio cables (as any other hi fi equipment) sound better after some "burn-in" or "break-in" ?
GC > I don't know sometimes the difference is show shocking! Moving the cable creates unbalanced static charges in the dielectric in signal cables and the mechanical stress in speaker cables. This is why moving the cables is a no no.
LC > Are there any new projects at Cardas? I've read you article on "setting up speakers in a rectangular room " and I have found it very informative. Is Cardas going to design speakers or room tuning devices in the future?
GC > Well, there are always new projects at Cardas but speakers and room tuning devices are not on the table this week, we are working on several new connectors and I am spending a great deal of time on some recording projects with the local Lab band I will be coming out with some "Big Band" recordings hopefully this year.
Courtesy George Cardas
Copyright © October 15th 1996 Lucio Cadeddu