Hello,
I used to work on Rayleigh's formula. My pruprose was to have the smallest interval between 2 consecutive resonances.
This study produced the attached graph.
The optimal shapes points on that garph form a red line.
Good shapes that spread optimally the resonances frequencies seem to be :
1 : 1.3 : 1.5
1 : 1.5 : 2.0
1 : 1.9 : 2.5
1 : 2.3 : 3.0
1 : 2.5 : 3.5
1 : 3.0 : 4.0
Best regards from Paris, France
Jean-Michel Le Cléac'h
I used to work on Rayleigh's formula. My pruprose was to have the smallest interval between 2 consecutive resonances.
This study produced the attached graph.
The optimal shapes points on that garph form a red line.
Good shapes that spread optimally the resonances frequencies seem to be :
1 : 1.3 : 1.5
1 : 1.5 : 2.0
1 : 1.9 : 2.5
1 : 2.3 : 3.0
1 : 2.5 : 3.5
1 : 3.0 : 4.0
Best regards from Paris, France
Jean-Michel Le Cléac'h
Attachments
But it looks like that approach compares the first dimension to the second and the second to the third, but not the first to the third. As an example 1:1.5:2 would have lots of overlapping modes from the 1 and 2 dimensions.
Isn't the cube root of 2 approach guaranteed to be the most uniform distribution?
(Not that I still think any of this matters when damping is applied.)
David
Isn't the cube root of 2 approach guaranteed to be the most uniform distribution?
(Not that I still think any of this matters when damping is applied.)
David
GL shows up all over as was noted; for some reason it is a pleasing proportion. I have no doubt the ancients had just as good an eye for portion as we do. A concert hall or cathedral is not a speaker box. If you want to read about cathedral acoustics, search on Harris. Yea, over time the did know what they were doing.
My mid cabinets are highly stuffed and if I was worried about overlapping standing waves, I would just angle a wall. I don't find it to be necessary.
My mid cabinets are highly stuffed and if I was worried about overlapping standing waves, I would just angle a wall. I don't find it to be necessary.
Does it matter. As long as the driver fits i'll happily use any face epending on the context of the installation.
dave
re. Fibinacci
The concept is to get the most even spacing between the modes (fundamental and harmonics) of the standing waves of the 3 dimensions of a speaker cabinet (or listening room). Since each dimension has multiple modes at integral multiples (1/2 wavelength frequency, 2 x that, 3 times that) the modes actually get closer together as you go up in frequency (at least on a log graph). As such you can only worry about the spacing for the first mode or two. Since even thin wall lining will easily kill upper modes I think worrying about the fundamental and second mode are the only ones that could possibly be justified.
As such, looking at the longest dimension, we should strive to have the 2nd and third modes equally spaced between the long dimension first mode and its second harmonic. The only approach that guarantees that is the cube root of 2 approach. It places the three dimension's fundamental modes 1/3 Octave apart in the first Octave.
And I still don't think it matters if the cabinet is well damped!
David S.
The concept is to get the most even spacing between the modes (fundamental and harmonics) of the standing waves of the 3 dimensions of a speaker cabinet (or listening room). Since each dimension has multiple modes at integral multiples (1/2 wavelength frequency, 2 x that, 3 times that) the modes actually get closer together as you go up in frequency (at least on a log graph). As such you can only worry about the spacing for the first mode or two. Since even thin wall lining will easily kill upper modes I think worrying about the fundamental and second mode are the only ones that could possibly be justified.
As such, looking at the longest dimension, we should strive to have the 2nd and third modes equally spaced between the long dimension first mode and its second harmonic. The only approach that guarantees that is the cube root of 2 approach. It places the three dimension's fundamental modes 1/3 Octave apart in the first Octave.
And I still don't think it matters if the cabinet is well damped!
David S.
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Not sure I agree with you, Dave. Even spacing will get you some cancellation, but you will end up with an augmented sequence and those chord tones often sound dissonant.
I'd rather go with Jean-Michel's 1:1.5:2, which apparently causes a lot more cancellation, and produces a dyadic "power chord" which is less likely to generate unpleasant overtones in whatever resonances remain undamped.
Well, no, but I'm thinking of all those people who won't listen to you about damping.
Hello David,
The ratio on the graph are just the ratio between the combined L, W and H in Rayleigh's formula :
http://www.bobgolds.com/Tangental/EverestRayleighModeEquation.GIF
Taking a given dimension as 1 allows to apply the formula whatever the size of the resonator, so the formula applies for parallelipipedic enclosures as well as parallelepipedic auditoriums (only the values frequencies are differents but not their progression).
Comparisons with Louden's real measurements and classification of the best shapes of auditorium is excellent.
Best regards from Paris, France
Jean-Michel Le Cléac'h
The ratio on the graph are just the ratio between the combined L, W and H in Rayleigh's formula :
http://www.bobgolds.com/Tangental/EverestRayleighModeEquation.GIF
Taking a given dimension as 1 allows to apply the formula whatever the size of the resonator, so the formula applies for parallelipipedic enclosures as well as parallelepipedic auditoriums (only the values frequencies are differents but not their progression).
Comparisons with Louden's real measurements and classification of the best shapes of auditorium is excellent.
Best regards from Paris, France
Jean-Michel Le Cléac'h
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Yes, I understand the origins of the formula, but you are comparing dimension 1 to dimension 2, then dimension 2 to dimension 3, while ignoring the 1 to 3 comparison. Optimizing those two while ignoring the third has taken you down a wrong path.
Clearly for the case of 1:1.5:2, the 2 to 1 dimensions will have every one of the short dimensions resonances coincident wth half of the long dimension's resonances. Not exactly the solution for optimum spacing.
I've worked in the field of architectural acoustics. Unlike small room acoustics, nobody talks of room dimension ratios. Dimensions are relatively long and standing waves hence are dense and not a consideration. (i'd be happy to read a contrary reference if you can find one.)
Room length and width are determined by audience considerations ( seat count, sight lines, legal requirements for exit rows, distance to stage) and then the ceiling is raised until he RT is to target.
David
You have made a huge jump to saying we perceive chords in resonances. I'd ask you to substantiate that. Even in rooms were the resonances are relatively undamped and high Q nobody suggests that chordal qualites are perceived.
Getting a little absurd...
David
Hello Dave,
Sorry to have to say that but your question is a silly question,
You have to think more about the problem... (think 1 degree of freedom... so it is obvious ration between dimension 1 and 3 is perfectly defined knowing the ratio D1/D2 and D2/D3...).
From the point of view of resoannt frequencies, it doesn't matter if the room is elongated along x, y ou z...
Best regards from Paris
Jean-Michel Le Cléac'h
Sorry to have to say that but your question is a silly question,
You have to think more about the problem... (think 1 degree of freedom... so it is obvious ration between dimension 1 and 3 is perfectly defined knowing the ratio D1/D2 and D2/D3...).
From the point of view of resoannt frequencies, it doesn't matter if the room is elongated along x, y ou z...
Best regards from Paris
Jean-Michel Le Cléac'h
Of course. But a dimension ratio of 2 to 1 is clearly the worst possible choice if well spaced harmonics are desired.
You do understand that, right?
Probably absurd, yeh, I'm working with musicians!
I can build two pine guitar cabinets of different dimensions that resonate noticeably, and one will be preferred to the other. They'll say it sounds "sweeter".
It's known that some concert halls sound better than others, no? And they're not dead. I don't think it's just the RT60, I think content matters, as well.
Granted, I'm talking euphonics on a hifi forum, and that's always thin ice.
O yeah, lots of factors beyond RT60 are considered important. Most have to do with signal difference between the ears, strength of direct signal, RT balance from low to high, early reflection patterns, etc. But nobody looks at standing waves due to hall dimensions because the dimensions tend to be big and the modes start very low.
Granted, I'm talking euphonics on a hifi forum, and that's always thin ice.
But it is nice to think about music every once in a while, and consonance and dissonance related to intervals is worth knowing about.
David
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