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Polar chart visualization for coincident techniques
Old 15th November 2015
  #1
Polar chart visualization for coincident techniques

For the longest time I had a hard time visualizing what the pickup patterns of MS stereo rigs, or of XY rigs reduced to mono, would look like. I developed a spreadsheet that allows you to simulate any coincident mic technique and see what the sum and difference results are.

When I first made this spreadsheet, some of the results surprised me and I was afraid that some of the math might be wrong. Thanks to some excellent supplemental reading (courtesy of John Willett) I've seen confirmation for many of these combinations now, and I'm fairly sure that it's all working properly.

So, for anyone who's interested in visualizing MS matrix results or mono sums from XY pairs, check out the attached spreadsheet and see what you think!

P.S. There's a more fluid and intuitive stereo mic technique visualization online at Visualization of Microphone System XY cardioid 120Β° Intensity stereo - Recording angle Level difference Microphone degrees visualization visualizator - sengpielaudio Sengpiel Berlin
I think it's safe to say that the sengpiel link is much nicer than my spreadsheet, except for the lack of mono and MS matrix functions. On the other hand, their system shows good info on spaced pairs, which my spreadsheet can't handle at all.
Attached Files
File Type: xls polar_7.xls (560.5 KB, 220 views)
Old 15th November 2015
  #2
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Nice spreadsheed, thanks for sharing!
Old 16th November 2015
  #3
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Nice piece of Excel work! Thanks for sharing this - it's a super-helpful learning tool (and I can use all the help I can get).

Since you've done the homework in this area, I'll ask a question I've been wanting to for some time: would you know what would be involved in doing something similar to this for single-bar combinations of two pairs of mics, like the boojum/jnorman or Faulkner 47/67 arrays? In other words, taking a calculation like the one your spreadsheet does for the inner pair, and then combining it with a second calculation for the outer pair and figuring out the net result. I for one would be very interested in seeing the pickup patterns for these arrays (and to compare them to my empirical observations).

My algebra and calculus skills are way rusty, but if you, or anyone else, were able to point me at a source that explained the math behind this sort of thing I'd be willing to take a crack at making something like your spreadsheet. And if I'm grossly underestimating the complexity....maybe there's some enterprising grad student in a tonmeister program who needs a thesis topic?
Old 16th November 2015
  #4
That's a great question, and one I'd love to see answered. I'll be interested to see if someone more knowledgeable can give you a good answer.

For my part, I wouldn't know where to start on calculating spaced pairs. The difference in time of arrival (and to a lesser extent the difference in level) defines the perceived stereo imaging. I read something recently about research that sought to establish the relationships between time of arrival, differences in level, and perceived stereo location, but I don't remember where I read it.

I believe any attempt to visualize the result of spaced pairs would be further complicated by the fact that the mic to source distance and the source width both play a role in the perceived results of spaced pair recordings in ways that are more complicated than in coincident pair recordings.
Old 16th November 2015
  #5
For what it's worth, here's a really well done paper outlining a lot of the fundamental concepts and some of the math involved in various stereo techniques (with the bulk of the work focusing on MS pairs.)

https://www.google.com/url?sa=t&sour...h-ihWLoNNP18gA

Last edited by Ebeowulf17; 16th November 2015 at 07:07 AM.. Reason: Typos
Old 16th November 2015
  #6
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Why worry about Mono?
15 years ago I would have given my eye teeth for a chart / info like these but being overly concerned about mono is a thing of the past, please tell me what devices these days are mono?...... Not many

My preferred mic setup for stereo TV broadcasting is cardiod or short shotgun mics spaced at about 1.2 - 1.5m ( the width of a med / large flat screen TV) facing straight out. And panned hard L / R in the mix.
Super wide stereo and sounds AMAZING when watching TV's.

Last edited by OzGizmo; 16th November 2015 at 10:18 AM..
Old 16th November 2015
  #7
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Quote:
Originally Posted by OzGizmo View Post
Why worry about Mono?
Radio.

Quote:
please tell me what devices these days are mono?...... Not many
Few are aware that when FM reception is poor, the system is designed to revert to a mono signal. This is better illustrated with in-car listening where this feature is more pronounced since good reception can be a moving target. AM is still mono as are certain DAB+ broadcasts, especially in the UK.
Old 16th November 2015
  #8
flexibility in post-production

Quote:
Originally Posted by OzGizmo View Post
Why worry about Mono?
15 years ago I would have given my eye teeth for a chart / info like these but being overly concerned about mono is a thing of the past, please tell me what devices these days are mono?...... Not many

My preferred mic setup for stereo TV broadcasting is cardiod or short shotgun mics spaced at about 1.2 - 1.5m ( the width of a med / large flat screen TV) facing straight out. And panned hard L / R in the mix.
Super wide stereo and sounds AMAZING when watching TV's.
Recently I've had a renewed interest in stereo->mono for entirely different reasons. I'm working with a singer-songwriter friend, starting with laying down his guitar and vocals together, with the intent of adding acoustic bass and possibly other instruments on some of the tracks. When it's just him playing, I strongly prefer a good stereo guitar sound to give the finished recording depth and space. However, past experience tells me that stereo guitar doesn't always sit well in a mix, depending on what else is going on with additional instruments. Not knowing for sure how each song will end up being produced, I'm trying to capture a guitar sound that's equally effective in stereo or mono, so that I can collapse it (partially or completely) and pan it around as needed without losing the sound of the guitar.

This project got me very curious about the differences between XY and MS rigs in this context. So far I've had very good results with MS, but I plan to give XY a go on at least one track for comparison. Unfortunately, my mic selection is quite limited, so switching between stereo methods also means significant changes in frequency response, off axis response, etc. which makes it much harder to hear the difference between the stereo techniques as opposed to the difference in the mic sounds.

Naturally, the choice ultimately comes down to what I actually hear from each rig, not what any spreadsheet tells me, but this project did get me more interested in the theory behind it all again. Specifically right now looking at the difference between MS collapsed to mono (simply the original mid channel; in my case a cardioid pattern) vs. XY collapsed to mono (resulting pattern depends on original mic pattern and the angles of the mics; in my case cardioid mics would collapse to something more or less like a very wide cardioid.)
Old 16th November 2015
  #9
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Stereo guitar sound is also attainable by splitting a mono input, delaying the split and then hard panning the delayed sound...the width is variable by the panning chosen. I'm not sure how well this would collapse to mono however, probably a few factors would come into play here, but easy enough to try out ?

True stereo recording of sources (which are collapsible down to mono with minimal phase injury, such as MS or XY) will give you the max flexibility during mixing, I'm guessing ?
Old 16th November 2015
  #10
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Quote:
Originally Posted by OzGizmo View Post
Why worry about Mono?
15 years ago I would have given my eye teeth for a chart / info like these but being overly concerned about mono is a thing of the past, please tell me what devices these days are mono?...... Not many.
What about PA systems? Most PAs are operated in mono. Whenever you play canned music between sets, recorded live music to help set up, EQ the system in a new venue...mono is your friend.
Old 16th November 2015
  #11
Background music systems too, like in restaurants, stores, etc. Admittedly not a hi-fi situation by any stretch, but why not make your music sound as good as possible no matter where/how it's heard?
Old 16th November 2015
  #12
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Come on seriously...... The sporting broadcasting that I'm doing has an audience of 100,000 to 1 Million viewers whether its a local production or a national production, do you think I'm interested in just a few people playing it on a small PA system or on radio?
The networks I work for want the best possible sound for their viewing audience. They invest HUGE $$$$ into productions so they can get what they want.

Do you honestly think the person / people mixing feature films are the slightest bit concerned about the person watching it several years later on an iPad and listening on headphones?...... No
Yes in the early days of stereo broadcasting we were concerned about mono / stereo compatibility, that then changed to mono / stereo acceptability and since then with the push for bigger screen TV's the sound needed to change to a much wider sound image.

Just like video has changed from Standard def to High Def and toward 4k and above do you think the Cammo's and technicians are checking to see what the picture looks like in B/W or what it looks like on a mobile phone.
Old 17th November 2015
  #13
I have no idea if it's true, but I've heard that tv production is emphasizing closeups more because viewers using mobile devices can't tell what the actors' faces are doing.

Regardless, I understand your point and don't really care to argue the importance of mono either way. As I said before, my interest in the subject primarily stems from two things: interest in the theory of adding and subtracting polar patterns, and interest in what options collapsing stereo tracks to mono gives me in post production.
Old 17th November 2015
  #14
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Quote:
Originally Posted by OzGizmo View Post
The sporting broadcasting that I'm doing has an audience of 100,000 to 1 Million viewers whether its a local production or a national production, do you think I'm interested in just a few people playing it on a small PA system or on radio?
In some territories, Radio is all certain audiences have access to. And we're not talking 100,000 to a Million either. We are talking multiple Millions. Often the Radio feed is fed from the same OB unit as the television broadcast to cut costs. QC is always critical.

Quote:
Do you honestly think the person / people mixing feature films are the slightest bit concerned about the person watching it several years later on an iPad and listening on headphones?...... No
...
do you think the Cammo's and technicians are checking to see what the picture looks like in B/W or what it looks like on a mobile phone.
Certain Directors and Producers QC and approve on the move due to circumstances they are not always in control of and therefore are unable to change. Often all they have is an iPhone or an iPad. Often it is readily apparent from their change logs that certain decisions are based on viewing on a smaller screen with a mono or pseudo-stereo speaker.

I am aware of at least three major live internet broadcasting services that QC in 4K, the main HD broadcast, as well as on PC screens, iPads and iPhones. All QC on different connection speeds to constantly monitor the quality differences as bandwidth use and connection speeds fluctuate. This has resulted in changes in the choice of codec employed and source code rewrites for multiple devices.

If you're taking any of this seriously you will QC for all audiences, not just those you think use a service in that one particular way you may think they do. More often than not, they're not.

Place shifting (i.e viewing on one device and later switching to another to continue watching) is the biggest change in consumer behaviour since mobile data use surpassed traditional computer internet data usage (which only happened in the last four years).

Research has shown that in Ireland, Spain and Russia currently, the average viewer spends more than 6 hours weekly viewing on-demand content at the expense of live broadcasts. If you think that market is tiny, consider that by 2020 90% of the global population over the age of six will own a mobile phone. By the end of the year, Africa as a whole will have already signed the billionth mobile subscriber (it only had 500 million subscribers in 2010).

Ericsson Research has just released a report predicting that by 2021, 70% of all mobile data traffic will be from video. In 2014, that figure was 45% of traffic.

Mobile devices haven't made QC any easier, in fact they've made a lot of things more difficult and much more time consuming.

Last edited by reynaud; 17th November 2015 at 01:06 PM..
Old 17th November 2015
  #15
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Quote:
Originally Posted by Ebeowulf17 View Post
For what it's worth, here's a really well done paper outlining a lot of the fundamental concepts and some of the math involved in various stereo techniques (with the bulk of the work focusing on MS pairs.)

https://www.google.com/url?sa=t&sour...h-ihWLoNNP18gA
I have serious questions about the content of this thesis. In his reply to the candidate, Ron Streicher warned the calculations only work in the horizontal plane. For the vertical plane the distance between the figure of eight and the used M component are causing phase cancellations, because of the distance between the M and and 8 pattern, which I cannot see back in the patterns in this papers. What the paper does show, in the theoretical horizontal plane the result polar patterns look worse than the original patterns of the single microphones, and my conclusion is that it is a miracle MS anyway can sound so convincing.
Old 17th November 2015
  #16
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Quote:
Originally Posted by Adorno View Post
I have serious questions about the content of this thesis. In his reply to the candidate, Ron Streicher warned the calculations only work in the horizontal plane. For the vertical plane the distance between the figure of eight and the used M component are causing phase cancellations, because of the distance between the M and and 8 pattern, which I cannot see back in the patterns in this papers. What the paper does show, in the theoretical horizontal plane the result polar patterns look worse than the original patterns of the single microphones, and my conclusion is that it is a miracle MS anyway can sound so convincing.
I think this paper is very well written and clearly explains the fundamentals of stereophony. The capsule separation distance in MS is certainly its most significant flaw and I am always amused at people using KM86 and U87's in MS pairs and saying how wonderful they sound. I used to own a KM86 and tried it as a side 8 in an MS pair once.

I have always thought that one of the reasons the Schoeps MS pairs sound the best to my ears is that they have the lowest separation distance between the capsules, only about 12mm. The cancellation and combing should mainly be a problem when the wavelength or half wavelength is of the order of the separation distance. 20kHz wavelength is 17mm and 16kHz is 21mm, the diameter of a Schoeps body.

The complaints of the asymmetry in the Schoeps fig 8 response at 16kHz is the least of its problems at that frequency, because when matrixed, it shares the same more significant issues as any other MS pair at that frequency.
Old 18th November 2015
  #17
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Quote:
Originally Posted by OzGizmo View Post
Why worry about Mono?
Amazon Echo

http://www.amazon.com/Amazon-SK705DI-Echo/dp/B00X4WHP5E
Old 18th November 2015
  #18
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Quote:
Originally Posted by David Spearritt View Post
I think this paper is very well written and clearly explains the fundamentals of stereophony. The capsule separation distance in MS is certainly its most significant flaw and I am always amused at people using KM86 and U87's in MS pairs and saying how wonderful they sound. I used to own a KM86 and tried it as a side 8 in an MS pair once.

I have always thought that one of the reasons the Schoeps MS pairs sound the best to my ears is that they have the lowest separation distance between the capsules, only about 12mm. The cancellation and combing should mainly be a problem when the wavelength or half wavelength is of the order of the separation distance. 20kHz wavelength is 17mm and 16kHz is 21mm, the diameter of a Schoeps body.

The complaints of the asymmetry in the Schoeps fig 8 response at 16kHz is the least of its problems at that frequency, because when matrixed, it shares the same more significant issues as any other MS pair at that frequency.
I know of only one engineer who hears the asymmetry of the Schoeps fig 8 in recordings. It's possible that the mid mic evens out the asymmetry somewhat. I find it to be the most ideal fig 8 side mic out of the ones I've tried, so transparent and clear.

Combined with a Sonodore omni, produces a lovely cardioid.
Old 12th November 2016
  #19
Updated polar scaling.

Almost a year later, I finally realized one big reason my polar charts never looked quite like I expected: I was plotting them with linear, instead of logarithmic, scaling. The updated spreadsheet I've attached now plots with logarithmic scaling, like we're all used to seeing. The concentric circles are the standard 5dB per division. None of the underlying math has changed, just the scaling of the visualization.

EDIT:
I've uploaded another minor tweak. Sometimes the polar charts suddenly generate 360 radial axis lines, which severely clutter the chart area. I think this update should eliminate them.
Attached Files
File Type: xls polar_9_xls.xls (578.5 KB, 81 views)
Old 8th February 2019
  #20
Latest update includes outputs with angles and numeric representation of polar patterns for the "virtual mics" that result from the decoding process.

The attached images also demonstrate the root cause of some common misconceptions. People often assume that MS with a cardioid mid converts back and forth to XY with cardioids. In fact there are numerous interchangeable sets, but that's not one of them. Two sets with cardioids involved would be:
1) MS with cardioid mid = XY with supercardioids at 55 degrees (depending on blend ratios)
2) MS with sub-cardioid = XY with cardioids at 55 degrees (depending on blend ratios)

Note that you can have cardioid on one side or the other, but not both at once!
Attached Thumbnails
Polar chart visualization for coincident techniques-polar_12_screenshot_01.png   Polar chart visualization for coincident techniques-polar_12_screenshot_02.png  
Attached Files
File Type: xls polar_12_libre.xls (512.0 KB, 41 views)
Old 2nd August 2020
  #21
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Thank you for sharing this spreadsheet. I was actually just trying to build my own janky version, and luckily came across your gorgeous one while googling how to do polar plots in Excel. So, needless to say, I've found it exceedingly helpful

That said, I'm having a bit of trouble understanding what the "abs(abs(A) + abs(B))" graph is showing. It seems to be summing together the two original patterns (A and B), but making it so that any overlap sums (rather than cancelling, if they're of opposite polarisation). If so, why? Is it to understand the overall directionality of the inputted mic setup (i.e. how much we can perceive in any direction when listening in stereo)?

Would I be right to assume, then, that the other "abs(abs(A) - abs(B))" graph is showing everything not picked up by the inputted mic setup?
Old 2nd August 2020
  #22
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Quote:
Originally Posted by md2802 View Post
Thank you for sharing this spreadsheet. I was actually just trying to build my own janky version, and luckily came across your gorgeous one while googling how to do polar plots in Excel. So, needless to say, I've found it exceedingly helpful

That said, I'm having a bit of trouble understanding what the "abs(abs(A) + abs(B))" graph is showing. It seems to be summing together the two original patterns (A and B), but making it so that any overlap sums (rather than cancelling, if they're of opposite polarisation). If so, why? Is it to understand the overall directionality of the inputted mic setup (i.e. how much we can perceive in any direction when listening in stereo)?

Would I be right to assume, then, that the other "abs(abs(A) - abs(B))" graph is showing everything not picked up by the inputted mic setup?
Perhaps it is to rectify the signal to ignore the effects of phase in the addition.
https://physics.stackexchange.com/qu...nds-add-up-6db
Old 2nd August 2020
  #23
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Quote:
Originally Posted by David Spearritt View Post
Perhaps it is to rectify the signal to ignore the effects of phase in the addition.
https://physics.stackexchange.com/qu...nds-add-up-6db
In the real world you'd get interference patters at high frequencies, because there's always some physical distance between the capsules (and so time-of-arrival will vary depending on where the sound is coming from); but in this simulation the two mics are at the exact same point in space, so there shouldn't be any difference in phase between the two recorded signals. The data only seems to show rejection based on direction (and a polarity inversion where appropriate).

The only difference between the "abs" graphs and the normal ones is that the polarity inversion you see in the back side of fig-8 / supercardioid patterns is ignored when being summed.

More specifically: Ebeowulf17 is using the ABS function to convert negative numbers to positive ones; e.g. "-0.855" becomes "0.855". This is necessary because there's logarithms being used to calculate the data, and you can't take the log of a negative number. The result is a graph that's agnostic to polarity; which is perfectly fine for an individual pattern. However, when summing two together, you need to take this polarity into account to know whether to add or subtract values; and with the graphs that show normal summing, Ebeowulf17 is doing that calculation before using the ABS function (i.e. he's doing it right, and returning correct results). But with the "abs" graphs, the summing is happening after the ABS function is applied.

I think I understand what the "abs" graphs are showing mathematically; I'm just confused about what they relate to in the real world. The spreadsheet has already been very helpful to me; I'd just love to know what I'm missing!
Old 2nd August 2020
  #24
The abs() function is simply to guarantee a positive value for plotting in polar coordinates; otherwise the plotted point gets reflected through the origin. As md2802 stated, we get to ignore inter-channel phase because the mics are coincident. So the formula used is a special case of vector summing that applies to identical phase angles. It would not work for spaced pairs, which calculation would need to account for the phase shifts due to path length difference. BTW, in a spaced-pair simulation one needs to treat the direct and reverberant sound differently: the latter sums as SQRT(A^2+B^2).

I think writing a program like Ebeowulf17's must be some kind of right-of-passage for academically-trained audio engineers. I wrote one 40 years ago in Fortran -- on punch cards!

David L. Rick
Old 2nd August 2020
  #25
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Punch cards! I remember those. And the "everyone has one" story of the poor computer sciences student that dropped the huge box of punch cards, exploding on the ground. Apocryphal? Probably. But a great mental image.

I think my biggest project had 20 cards. But then again, I bought a Timex Sinclair 1000 a few years later. Cutting edge. 2KB (kilobytes) RAM. Wow!

https://en.wikipedia.org/wiki/Timex_Sinclair_1000

The cool thing is that the nightmares of computers haven't gotten any better. Just different.

D.
Old 3rd August 2020
  #26
Quote:
Originally Posted by md2802 View Post
Quote:
Originally Posted by David Spearritt View Post
Perhaps it is to rectify the signal to ignore the effects of phase in the addition.
https://physics.stackexchange.com/qu...nds-add-up-6db
In the real world you'd get interference patters at high frequencies, because there's always some physical distance between the capsules (and so time-of-arrival will vary depending on where the sound is coming from); but in this simulation the two mics are at the exact same point in space, so there shouldn't be any difference in phase between the two recorded signals. The data only seems to show rejection based on direction (and a polarity inversion where appropriate).

The only difference between the "abs" graphs and the normal ones is that the polarity inversion you see in the back side of fig-8 / supercardioid patterns is ignored when being summed.

More specifically: Ebeowulf17 is using the ABS function to convert negative numbers to positive ones; e.g. "-0.855" becomes "0.855". This is necessary because there's logarithms being used to calculate the data, and you can't take the log of a negative number. The result is a graph that's agnostic to polarity; which is perfectly fine for an individual pattern. However, when summing two together, you need to take this polarity into account to know whether to add or subtract values; and with the graphs that show normal summing, Ebeowulf17 is doing that calculation before using the ABS function (i.e. he's doing it right, and returning correct results). But with the "abs" graphs, the summing is happening after the ABS function is applied.

I think I understand what the "abs" graphs are showing mathematically; I'm just confused about what they relate to in the real world. The spreadsheet has already been very helpful to me; I'd just love to know what I'm missing!
I don't think you're missing anything - I think you've got it!

The first graph you mentioned is indeed attempting to gauge the perceived total pickup pattern of the stereo pair, as experienced when listening in stereo (not summing to mono.) I honestly never did figure out if I believe that this graph is meaningful or not, but that's what I was attempting.

The second one that's subtracting abs values is probably nothing. It took me several attempts at this project before I got accurate results, and I tried a lot of weird graph ideas along the way - this was one of them that I just never got around to deleting. I often wondered if there might be some meaning to be gleaned from it, but I suspect there isn't. I think it's a fun piece of math with no real world value.

In fact, if you look at the latest updates I posted, you'll see that I eventually abandoned both of those extra graphs. I have a pretty high degree of confidence that the MS->XY matrix calculations (and their reverse) are implemented reasonably well here, but those other graphs were always dubious!
Old 3rd August 2020
  #27
Quote:
Originally Posted by David Rick View Post
I think writing a program like Ebeowulf17's must be some kind of right-of-passage for academically-trained audio engineers.

David L. Rick
I've often wished I'd gotten better audio training - I got a degree in "media communications" with an emphasis in audio production, but it was a very soft, artsy liberal arts program - good for my ears and artistic sensibilities, but totally worthless for acoustics, electronics, anything to do with the engineering side of things. I had to teach myself that stuff as best I could later on from books and by number crunching with spreadsheets until things made sense. I understood some theory, but there was also some trial and error to get things like this spreadsheet to work.

Coincidentally, a similar thing happened to me recently as I gained interest in both electronics and programming. I decided to write a C program to find the best resistor values for any desired ratio in a voltage divider, and I kind of thought I was doing something creative and unusual... when I posted it to my favorite electronics forum, ten different engineers came out and told me about how they'd done the same thing years or decades earlier (one in Fortran, one on a graphing calculator, one in basic, a few others in C.) It seems there are several of these DIY rites of passage!
Old 4th August 2020
  #28
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Hello Ebeowulf17, the rejuvenation of this thread reminded me that I should quickly thank you for taking the time to produce this spreadsheet. I have used, with gratitude, the most recent version for a number of things over the past several months, and have found it very useful.
Old 4th August 2020
  #29
Quote:
Originally Posted by lukedamrosch View Post
Hello Ebeowulf17, the rejuvenation of this thread reminded me that I should quickly thank you for taking the time to produce this spreadsheet. I have used, with gratitude, the most recent version for a number of things over the past several months, and have found it very useful.
Thanks for the kind words! I'm glad you've found it useful.
Old 4th August 2020
  #30
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Actually, without wishing to hijack this thread in any way, maybe some of the knowledgeable folks here would be aware:

A few months back I was messing around with some of the various MatLab-like visualization tools for 3-dimensional graphing etc. I was hoping to do something similar to your chart, but visualizing microphone directivity (and coincident combinations) in three dimensions at various frequencies.

Any ideas/tips/shortcuts? I certainly don't want to reinvent the wheel if something like this is out there in open source land and can perhaps be tweaked for these purposes.
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