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Xenon · 1st October 2009

Hi Collo,

Thanks for all these images! By the way, I think I fixed my earlier image, if you check. Looks like your post#92 just above shows about as much of a difference as possible. And also my left-shift-18 looks pretty good. I was able to load your N43. Very elegant design and only about 120cm (4'). so much work went into that... In your 'left-shift-5' above I notice the phase vectors at the center seem to be fairly divergent, compared to the standard 0-shift N23. Looking into this idea further, I wonder if periods like N19 or N17 might have better results?

Also going to N29 (shifted down either 9 or 16 for depth savings), you can see quite a variance in that layout, internally. That would be pretty nice in a larger room (like at least 25' or 750cm).

N17 seems more self-similar, looking quickly at it.

In general, you've got 'turret' sections and 'stepped hemisphere' sections. If you realign turrets over the position of hemispheres, you get divergence. I think the point or the question is, does this break up the lobing. (I think following a Barker code is smart, the problem of symmetrical periodicity seems well documented.) Interesting, your idea to let the design Hz float in building a (Barker) -1 (realigned) N23.

As for a write-up, sheesh, I was thinking the photo links, construction sheet, cut sheet plus this thread would be enough. If you have a thought though let me know. I was hoping to spend my 'extra' time in getting some room measurements, though I doubt they will say much that's good, until I do a lot more acoustic treatment (which will take a couple more months).

I'm thinking seriously of trying one of these realigned N23s instead of N19... (e.g. Shift Left-5, and split the left well (5) which is only 8mm deep in my design, between left and right, so the frame members can be utilized in the well construction). [Edit: No! See below]

Edit !:
Better add to this, after looking at the sections that can be seen in googlebooks here (in Acoustic Absorbers and Diffusers: Theory, Design and Application By Trevor Cox, Peter D'Antonio), pages 289-329. It seems from this that the Modffusor is likely a 'sampled' N-73 PRD (not QRD), which is why it is asymmetric and why it has 8 wells (see below). The example given (on page 311) is for a modified
(asymmetric) N-7 PRD with 6 wells (ratios: 132645), which can be flipped (to 546231), rather than inversed, in creating multiple periods (according to the Barker code).

The concept of inversing is explained here on p. 248: "The curse of periodicity", in part:

"A QRD needs periodicity to form its optimum diffusion of even energy lobes, yet the periodicity lobes cause uneven scattering."

I learned that techniques of altering symmetrical periodicity in however many arrays, is called "a modulation scheme":

"The modulation works best at multiples of the design frequency. Only at these frequencies do the diffuser and its inverse create exactly opposite pressures. At other frequencies, the modulation is likely to help with the scattering as it breaks up periodicity lobes, but in a more uncontrolled manner." (p. 251)

Which implies that you would want to keep the same the design frequency, whatever (inverse/flip/different N-prime) was used, but with the caveat that altering the design frequency will still be effective in the primary goal of breaking up lobes.

It's stated that QRDs are not mathematically asymmetric. And further in the chapter optimization is mentioned (e.g. autocorrelation) and this interesting statement, leading to my supposition as to the Modffusor, on p. 302:

"Consider a primitive root sequence based on prime 73; this will be of length 72. By taking every ninth sample from this sequence, a shorter-length 8 sequence is formed....the flat plate frequency will be at nine times the frequency that a more normal number theoretic diffusor would achieve."

Well, the above could certainly be the Modffusor, couldn't it? A sequence of 8 wells, based on each ninth well of an N-73?

The basic principle of optimization is to "get the computer to search for a sequence with minimum side lobe energy..." A modified primitive root sequence based on N43 (mod. PRD) is mentioned on p. 318. It seems that quite a lot has been done with PRD modification, since Alton Everest, and since the 90s. Then there is this patent on aperiodic repetition of arrays on a wall, "Embodiments of aperiodic tiling of a single asymmetric diffusive base shape," (issued August, 2004) which may relate to our current discussion. And also see p. 248 of the above book. I downloaded the patent (public domain), and you can grab the PDF here and the full text of the patent, in html form, verbatim, here. It's in the patent that,

"The sound diffusor of claim 14, wherein said series includes said first and last half wells of depth zero, and seven wells there between having respective consecutive depths equal to or proportional to the following amounts in inches: 3, 67/16, 37/8, 51/16, 211/16, 45/8, and 13/16."

Can you source it from an N73 PRD of a certain depth? Anyway the point most relevant to our discussion concerns aperiodicity. Reading over the work of Angus, as mentioned in "Acoustic Absorbers and Diffusers," it seems best to work with "two base shapes" as a best 'less-technical' solution to the problem of periodicity -- a problem explained at length in the patent. It seems there is much to explore for the intrepid.

1st October 2009	#96
Xenon Gear nut Joined: Jul 2008 Location: Japan Posts: 77 Thread Starter	Hi Collo, Thanks for all these images! By the way, I think I fixed my earlier image, if you check. Looks like your post#92 just above shows about as much of a difference as possible. And also my left-shift-18 looks pretty good. I was able to load your N43. Very elegant design and only about 120cm (4'). so much work went into that... In your 'left-shift-5' above I notice the phase vectors at the center seem to be fairly divergent, compared to the standard 0-shift N23. Looking into this idea further, I wonder if periods like N19 or N17 might have better results? Also going to N29 (shifted down either 9 or 16 for depth savings), you can see quite a variance in that layout, internally. That would be pretty nice in a larger room (like at least 25' or 750cm). N17 seems more self-similar, looking quickly at it. In general, you've got 'turret' sections and 'stepped hemisphere' sections. If you realign turrets over the position of hemispheres, you get divergence. I think the point or the question is, does this break up the lobing. (I think following a Barker code is smart, the problem of symmetrical periodicity seems well documented.) Interesting, your idea to let the design Hz float in building a (Barker) -1 (realigned) N23. As for a write-up, sheesh, I was thinking the photo links, construction sheet, cut sheet plus this thread would be enough. If you have a thought though let me know. I was hoping to spend my 'extra' time in getting some room measurements, though I doubt they will say much that's good, until I do a lot more acoustic treatment (which will take a couple more months). I'm thinking seriously of trying one of these realigned N23s instead of N19... (e.g. Shift Left-5, and split the left well (5) which is only 8mm deep in my design, between left and right, so the frame members can be utilized in the well construction). [Edit: No! See below] Edit !: Better add to this, after looking at the sections that can be seen in googlebooks here (in Acoustic Absorbers and Diffusers: Theory, Design and Application By Trevor Cox, Peter D'Antonio), pages 289-329. It seems from this that the Modffusor is likely a 'sampled' N-73 PRD (not QRD), which is why it is asymmetric and why it has 8 wells (see below). The example given (on page 311) is for a modified (asymmetric) N-7 PRD with 6 wells (ratios: 132645), which can be flipped (to 546231), rather than inversed, in creating multiple periods (according to the Barker code). The concept of inversing is explained here on p. 248: "The curse of periodicity", in part: "A QRD needs periodicity to form its optimum diffusion of even energy lobes, yet the periodicity lobes cause uneven scattering." I learned that techniques of altering symmetrical periodicity in however many arrays, is called "*a modulation scheme": "The modulation works best at multiples of the design frequency. Only at these frequencies do the diffuser and its inverse create exactly opposite pressures. At other frequencies, the modulation is likely to help with the scattering as it breaks up periodicity lobes, but in a more uncontrolled manner." (p. 251) Which implies that you would want* to keep the same the design frequency, whatever (inverse/flip/different N-prime) was used, but with the caveat that altering the design frequency will still be effective in the primary goal of breaking up lobes. It's stated that QRDs are not mathematically asymmetric. And further in the chapter optimization is mentioned (e.g. autocorrelation) and this interesting statement, leading to my supposition as to the Modffusor, on p. 302: "Consider a primitive root sequence based on prime 73; this will be of length 72. By taking every ninth sample from this sequence, a shorter-length 8 sequence is formed....the flat plate frequency will be at nine times the frequency that a more normal number theoretic diffusor would achieve." Well, the above could certainly be the Modffusor, couldn't it? A sequence of 8 wells, based on each ninth well of an N-73? The basic principle of optimization is to "*get the computer to search for a sequence with minimum side lobe energy..." A modified primitive root sequence based on N43 (mod. PRD) is mentioned on p. 318. It seems that quite a lot has been done with PRD modification, since Alton Everest, and since the 90s. Then there is this patent on aperiodic repetition of arrays on a wall, "Embodiments of aperiodic tiling of a single asymmetric diffusive base shape," (issued August, 2004) which may relate to our current discussion. And also see p. 248 of the above book. I downloaded the patent (public domain), and you can grab the PDF here and the full text of the patent, in html form, verbatim, here. It's in the patent that, "The sound diffusor of claim 14, wherein said series includes said first and last half wells of depth zero, and seven wells there between having respective consecutive depths equal to or proportional to the following amounts in inches: 3, 67/16, 37/8, 51/16, 211/16, 45/8, and 13/16." Can you source it from an N73 PRD of a certain depth? Anyway the point most relevant to our discussion concerns aperiodicity. Reading over the work of Angus, as mentioned in "Acoustic Absorbers and Diffusers,"* it seems best to work with "two base shapes" as a best 'less-technical' solution to the problem of periodicity -- a problem explained at length in the patent. It seems there is much to explore for the intrepid.