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PrecisionAudio 8th October 2012 03:39 AM

The Golden Ratio of 1.618
Do the internal dimensions of 13.335cm, 18.429cm, and 29.818cm follow the Golden Ratio of 1.618? One website calculator says yes, another says no.

13.335cm is my smallest allowable dimension so I started from that number.

I am seeking to construct a dimensionally non-resonant sealed box for a driver.


PrecisionAudio 8th October 2012 03:47 AM

BTW, the numbers of 13.335cm, 21.578cm, and 34.913cm appear to be more correct to meet the 0.618 : 1.000 : 1.618 ratio...

rjbond3rd 8th October 2012 03:57 AM


1. Find the cabinet volume
2. Find the volume's cube root. That's your 1.0 dimension.
3. Multiple the cube root by .618 and 1.618. Those are the other two dimensions.

planet10 8th October 2012 04:59 AM

13.335 x phi = 21.576

21.576 x phi = 34.910

A box a hair over 10 litres.

What do you need an on-line calculator for? One of the ones you used is out-to-lunch.

Robert's algorithm for working from a required volume is bang on

Using the golden ratio will not create a non-resonant sealed box. The use of irrational numbers (phi or not) to determine a boxes dimensions just helps keep them from piling on top of one another (be careful with the squareroot of 2)


T101 8th October 2012 10:41 AM

A non-resonant box is the sphere. B&W Nautilus makes use of long distances behind the driver. For the bass driver they serve as a closed transmission line or a kind of or maybe labyrinth/aperiodic/infinite baffle.

You could install it in a pipe, just make sure the length is one quarter of the lowest reproduced wavelength and fill it with fiberglass or stone wool or a mix of all known wadding.

After all with midranges, your aim is not the LF alignment and as long as you are in the flat area of the response, the enclosure is demanded to do just one thing. Actually it is required not to do anything and specifically not to send reflected waves through the cone.

I remember a discussion between me and one of the reputable members here, we agreed that a good choice for midrange is well stuffed chamber with open back. Slight dipole effect (eliminates the environment due to the side null) and nothing is returned through the cone due to the non-interacting character of the enclosure.
A note of caution is to stuff the chamber well, because otherwise it will act as an U-frame and those always exhibit the so called U-H-frame peak which is not manageable in a bandpass such as the midrange, only low pass or in exotic examples highpass if it occurs low enough which in turn is governed by dimensions.

Best regards!

planet10 8th October 2012 02:51 PM

The inside of a sphere has one very strong standing wave since all distances across the inside are the same. The outside is very nice.


balerit 8th October 2012 05:21 PM


Originally Posted by planet10 (
13.335 x phi = 21.576

irrational numbers (phi or not) to determine a boxes dimensions just helps keep them from piling on top of one another (be careful with the squareroot of 2)


1.41 is the closest to the very desirable ratio for room sizes of 7/5. ref:

Wes Lachot Design || Studio Design and Acoustic Consulting

planet10 8th October 2012 05:56 PM

Thanx for the article.

The trap to avoid when using root-2 is that root-2 x root-2 is a very undesirable ratio.

Toole's work shows that there are no magix ratios for rooms... partly due to the fact that windows, doors, and the construction of the walls, more often than not give resonances that do not correspond to the physical dimension.

A huge step in solving room issues is to cant one of the surfaces (ie vaulted ceiling). If the cant can be in 2 directions you are even further ahead.

This also applies to speaker boxes, but at higher frequencies and the consideration that it is easier to achive a "stiff room" so the actual dimensions have greater coorespondence to functional dimensions.


StigErik 8th October 2012 06:18 PM

There is no such thing as a non-resonant box.

The only thing achieved by using different dimensions for height, length and width is to spread the resonances so they coincidence less. Which dimensions that actually work depends, and should be calculated for each case. And one should look at both axial, tangential and oblique resonant modes.

acefromspace 8th October 2012 07:05 PM

I like golden ratio encolsures for strength. It makes for a very stiff box without adding bracing/panels. It also helps that no single dimension is too small/large, but with all the great "tower" designs out there, I'm not sure golden ratio has any advantage... internal dampening may be more important.

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