The Gradient Sub Array or reversed end fired as I call it (English only) .   4 comments

So following up on the End Fired Sub Array article i did before this article here is the description of what i call a Reversed End Fired or Gradient as Harry Olsen called it (note : Harry Olsen came up with this set-up as far as i know so it’s not my idea but , as are most of the things i write about , somebody else’s idea . I only put the idea’s to use and by describing them on my blog i hope to understand them better ) .

If you build a end fired array you need more space then building a conventional stack of subs . If your space is limited and you still need to cancel sub leakage at the stage side of the venue there’s a set-up you can try . The Gradient or the reverse end fired as i call it because that’s exactly what it is .

Map strt

Where in a end fired array of 2 subs (the above screenshot) S1 gets delayed to be in phase with S2 @ the mic1 position in a reverse end fired array S2 gets delay to be in phase with S1 @ the mic2 position . After that there’s 1 really important thing to do : POLARITY REVERSAL @ S2 (do not forget the polarity reversal otherwise all the sub frequencies shoot @ the mic2 position) .

So first let’s do the math again (the part i do not like but hey every job has it’s disadvantages) .

Map edit 2strt

Distance S1(centre) to mic1 = 5mt . S1 = 104 dB @ 69Hz @ mic1 .

Distance S2(centre) to mic1 = 6mt .

S2 = 20log(5/6) = 20log(0,833) = – 1,58 dB . S2 @ mic1 = 104 dB – 1,58 dB = 102,42 dB @ mic1 .


Distance S1(centre) to mic2 = 6mt . S1 = 99,2 dB @ 69Hz @ mic2 .

Distance S2(centre) to mic2 = 5mt .

S2 = 20log(6/5) = 20log(1,200) = + 1,58 dB . S2 @ mic2 = 99,2 dB + 1,58 dB = 100,78 dB @ mic2 .

So let’s go to RBV2-9 and see how this would look if the world was a perfect measureable place (no reflections & acoustics to worry about) . I have put in a level offset within RBV of –50dB on all traces to start with to get the frequency response @ around 0 dB . After that i have compensated the level differences due to the difference in distance to the mic1 or mic2 positions . If i have to measure this set-up i always start measuring at the back of the array so in this example the mic2 position .

RBV S1   S2  b mic log nop

Now i have to delay S2(red) to S1(blue) . Remember this is the mic2 position .

S1   S2 2,8ms Bmic rev.ef

S2(red) with 2,8ms delay in phase to S1(blue) . Remember this is the mic2 position .

S1 vs S2 2,8ms delay pol rev sum freq

S2(red) with 2,8ms delay & polarity reversal 180°phase difference @ all frequencies to S1(blue) . Remember this is the mic2 position . The black frequency trace indicates a +/- 12 db reduction @ all frequencies .

So if you take a look @ the MAP predictions you get the next screenshots .

MAP rev vs end fired @40Hz  Reverse end fired versus end fired @ 40 Hz

MAP rev vs end fired @50Hz  Reverse end fired versus end fired @ 50 Hz

MAP rev vs end fired @63Hz  Reverse end fired versus end fired @ 63 Hz

MAP rev vs end fired @80Hz  Reverse end fired versus end fired @ 80 Hz

If you take a look at the difference between a end fired and the reverse end fired it looks like you should always use the reverse end fired . The reverse end fired cancels @ al frequencies . So what’s the down side of this configuration ?

The down side of this array is the time offset on S2 causing a alignment problem @ the mic1 position (the front) . It also sounds different then a end fired configuration . So why ?

In order to explain the problem you get using this type of array we need to go back to RBV .

ef vs ref S1 vs S2 

I pasted the Sum of S1 and S2 in the top screen . You see the dip in the frequency response . At the same point in the bottom screen you see the phase difference of 180° between S1(blue) and S2(red) . The red trace (S2) never aligns with the blue(S1) . You do have additions between +/- 40 Hz to about 150 Hz but almost never the +6 dB you get when S1 and S2 are perfectly aligned except for a small part of the response @ +/- 80 Hz – 100 Hz . Within Virtual sim you can really see the difference between a end fired and a reverse end fired .

Freq resp end fired vs rev end fired fr mic virt. sim 

So a reverse end fired has the advantage of reduction of level @ all frequencies at the back of the array but has the disadvantage of a different sound and can not be aligned properly with a main full range system because of the time offset on S2 . 

Still want more sub array analysis ?






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