Tag Archives: SPL

Loud, Low, Little

You may pick two, maximum.

Please Remember:

The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.

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Most of you have probably heard the old chestnut, “Good, fast, cheap. You may pick two of the three.” The saying is an “iron law” of project management.

There’s a very similar law when it comes to loudspeakers:

A loudspeaker might be inherently efficient (Loud), it might reproduce useful low-frequency information (Low), and it might be compact in size (Little). You can’t get more than two of those things to happen at once.

By way of example, let’s take a gander at the high-frequency horn section in your typical, full-range, live-sound box. In all likelihood, it produces quite a bit of SPL with not very much power – lots of affordable, high-frequency compression drivers won’t handle more than 50 watts of continuous input. Heck, some can barely manage 20! The driver is quite small, especially when compared to a 12″ or 15″ cone.

Loud and little is 100% within that driver’s wheelhouse, but it won’t go low. If it did, there wouldn’t be a low-frequency driver in the cabinet. To prevent that itty-bitty compression driver from being wrecked, a high-pass crossover filter is needed. The corner frequency of that filter might be up at 2.5 kHz or so. There’s nobody on Earth who would confuse the high-midrange/ high-frequency transition zone for “lows.”

The above is fairly intuitive for most, but it can be a bit easier to get bamboozled when you see a big driver. An 18″ driver must be able to make really low-frequency material at high volume, right? Well…maybe. The box that driver is sitting in is a HUGE part of the equation; A large-diameter diaphragm isn’t enough. The smaller the box gets, the more power you have to dump into the driver to get the really deep material to play “loud.” Past a certain point, things get ridiculous in one way or another, which includes the unbridled hilarity of cooking the voice coil or destroying the suspension.

A compact subwoofer is highly unlikely to do a whole lot for you below about 50 Hz. Forty Hz might be doable at “half power” if the manufacturer is using a bandpass design for the box. (A bandpass design is great in a small frequency range, and terrible everywhere else – which is perfectly fine for a subwoofer.)

You have to decide on what you actually need, versus what you think you need.

For rock-band reinforcement, really deep bass actually isn’t a top requirement. Mostly, what we need is high output, though not so high that we run the whole audience out of the room. I haven’t really cared about anything below 50 Hz for a long time, especially because large SPL at low frequency is what annoys the “neighbors” the most easily. “Varsity-Level” EDM, on the other hand, can be HIGHLY dependent on very, very low frequency information (35 Hz or even lower) that has to be at levels exceeding 110 dB SPL C, slow-average. Doing that in a reasonable way demands bigger boxes, or several truckloads of smaller boxes.

So, when you’re out shopping for low-frequency loudspeakers, be wary of anything that claims to be effective for concert sound below 50 Hz, while also fitting easily into the trunk of a compact car. If a single box is going to play low AND loud without a staggering amount of amplifier power, it just can’t be little.


Double Hung Discussion

It’s not magic, and it may not be for you. It works for me, though.

Please Remember:

The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.

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On the heels of my last article, it came to may attention that some folks were – shall we say – perplexed about my whole “double hung” PA deployment. As can be the case, I didn’t really go into any nuance about why I did it, or what I expected to get out of it. This lead some folks to feel that it was a really bizarre way to go about things, especially when a simpler solution might have been a better option.

The observations I became aware of are appropriate and astute, so I think it’s worth talking about them.

Why Do It At All?

First, we can start with that logistics thing again.

When I put my current system together, I had to consider what I was wanting to do. My desire was to have a compact, modular, and flexible rig that could “degrade gracefully” in the event of a problem. I also had no desire to compete with the varsity-level concert systems around town. To do so would have required an enormous investment in both gear and transport, one that I was unwilling (and unable) to make.

What I’ve ended up with, then, is a number of smaller boxes. If I need more raw output, I can arrange them so that they’re all hitting the same general area. I also have the option of deploying for a much wider area, but with reduced total output capability. I wouldn’t have that same set of options with a small number of larger, louder enclosures.

That’s the basic force behind why I have the rig that I have. Next come the more direct and immediate issues.

The first thing is just a practical consideration: Because my transport vehicle isn’t particularly large, I don’t really have the necessary packing options required to “leave gear on the truck.” If I’m getting the rig out, I might as well get all of it out. This leads to a situation where I figure that I might as well find a way to deploy everything all the time. The gear is meant to make noise, not sit around. “Double hung” lets me do that in a way that makes theoretical sense (I’ll say more on why in a bit).

The second reason is less practical. I have a bit of a penchant for the unconventional and off-the-wall. I sometimes enjoy experiments for the sake of doing them, and running a double hung system is just that kind of thing. I like doing it to find out what it’s like to do it.

Running double hung is NOT, by any means, more practical than other deployments. Especially if you’re new to this whole noise-louderization job, going with this setup is NOT some sort of magical band-aid that is going to fix your sound problems. Also, if you’re getting good results with a much simpler way of doing things, going to the extra trouble very well may not be worth it.

At the same time, though, the reality of making this kind of deployment happen is not really all that complicated. You can do it very easily by connecting one pair to the left side of your main mix, and the other pair to the right side. Then, you just pan to one side or the other as you desire.

System Output And Response

Up above, I mentioned that running my system as a double hung made sense in terms of audio theory. Here’s the explanation as to why. It’s a bit involved, but stick with me.

I haven’t actually measured the maximum output of my FOH mid-highs, but Turbosound claims that they’ll each make a 128 dB SPL peak. I’m assuming that’s at 1 meter, and an instantaneous value. As such, my best guess at their maximum continuous performance, run hard into their limiters, would be 118 dB SPL at 1 meter.

If I run them all together as one large rig, most people will probably NOT hear the various boxes sum coherently. So, the incoherent SPL addition formula is what’s necessary: 10 Log10[10^(dB SPL/ 10) + 10^(dB SPL/ 10)…]. What I put into Wolfram Alpha is 10 Log10[10^11.8 + 10^11.8 + 10^11.8 + 10^11.8].

What I get out is a theoretical, total continuous system output of 124 dB SPL at 1 meter, ignoring any contribution from the subwoofers.

At this point, you would be quite right to say that I can supposedly get to that number in one of two ways. The first, simple way, is to just put everything into all four boxes. The second, not simple way is to put some things in some boxes and not in others. Either way, the total summed sound pressure should be basically the same. The math doesn’t care about the per-box content. So, why not just do it simply?

Because there’s more to life than just simply getting to the maximum system output level.

By necessity of there being physical space required for the speakers to occupy, the outer pair of enclosures simply can’t create a signal that arrives at precisely the same moment as the signal from the inner pair, as far as the majority of the audience can perceive. Placed close together, the path-length differential between an inner box and an outer box is about 0.0762 meters, or 3 inches.

That doesn’t seem so bad. The speed of sound is about 343 meters/ second in air, so 0.0762 meters is 0.22 ms of delay. That also doesn’t seem so bad…

…until you realize that 0.22 ms is the 1/2 cycle time of 2272 Hz. With the outer boxes being 1/2 cycle late, 2272 Hz would null (as would other frequencies with the same phase relationship). If everything started as measuring perfectly flat, introducing that timing difference into a rig with multiple boxes producing the same material would result in this transfer function:

combfiltering0.22ms

Of course, everything does NOT start out as being perfectly flat, so that craziness is added onto whatever other craziness is already occurring. For most of the audience, plenty of phase weirdness is going on from any PA deployed as two, spaced “stacks” anyway. To put it succinctly, running everything everywhere results in even more giant holes being dug into the critical-for-intelligibility range than were there before.

Running double hung, where the different pairs of boxes produce different sounds, prevents the above problem from happening.

So, when I said that I was running double hung for “clarity,” I was not doing it to fix an existing clarity problem. I was preventing a clarity problem from manifesting itself.

Running absolutely everything into every mid-high, and then having all those mid-highs combine is a simple way to make a system’s mid-highs louder. It’s also a recipe for all kinds of weird phase interactions. These interactions can be used intelligently (in an honest-to-goodness line-array, for instance), but for most of us, they actually make life more difficult. Louder is not necessarily better.

More On Output – Enough Rig For The Gig?

For some folks reading my previous installment, there was real concern that I hadn’t brought enough PA. They took a gander at the compactness of the rig, and said, “There’s no way that’s going to get big-time sound throughout that entire park.”

The people with that concern are entirely correct.

But “rock and roll level everywhere” was not at all what I was trying to do.

The Raw Numbers

What I’ve found is that many people do NOT actually want everything to be “rock and roll” loud over every square inch of an event area. What a good number of events actually want is a comfortable volume up close, with an ability to get away from the noise for the folks who aren’t 100% interested. With this being the case, investing in a system that can be clearly heard at a distance of one mile really isn’t worthwhile for me. (Like I said, I’m not trying to compete with a varsity-level sound company.)

Instead, what I do is to deploy a rig that’s in close proximity to the folks who do want to listen, while less interested people are at a distance. Because the folks who want more volume are closer to the PA, the PA doesn’t have to have crushing output overall. For me, the 110 dB SPL neighborhood is plenty loud, and I can do that for the folks nearby – by virtue of them being nearby.

Big systems that have to cover large areas often have the opposite situation to deal with: The distance differential between the front row and the back row can actually be smaller, although the front row is farther away from the stacks in an absolute sense. With my rig, the people up close are probably about three meters from the PA. The folks far away (who, again, aren’t really interested) might be 50 meters away. That’s more than a 16-fold difference. At a bigger show, there might be a barricade that’s 10 meters from the PA, with the main audience extending out to 100 meters. That’s a much bigger potential audience, but the difference in path lengths to the PA is only 10-fold.

Assuming that the apparent level of the show drops 6 dB for every doubling of distance, my small show loses about 24 decibels from the front row to the folks milling around at 50 meters. The big show, on the other hand, loses about 20 dB. (But they have to “start” much louder.)

That is, where the rubber hits the road is how much output each rig needs at 1 meter. At the big show, they might want to put 120 dB SPL into the front seats. To do that, the level at 1 meter has to be 140 dB. That takes a big, powerful PA. The folks in the back are getting 100 dB, assuming that delays aren’t coming into the picture.

For me to do a show that’s 110 dB for the front row, my PA has to produce about 119 dB at 1 meter. That’s right about what I would expect my compact setup to be able to do, with a small sliver of headroom. At 50 meters, my show has decayed to a still audible (but not “rock show loud”) 86 dB SPL.

That’s what I can do, and I’ve decided to be happy with it – because the folks I work with are likely to be just as happy with that as I am. People don’t hire me to cover stadiums or have chest-collapsing bass. They hire me because they know I’ll do everything in my power to get a balanced mix at “just enough” volume.

The Specifics Of The Show

Ultimately, the real brass tacks are to be found in what the show actually needed.

The show did not need 110 dB SPL anywhere. It needed a PA that sounded decent at a moderate volume.

The genre was folksy, indie material. A 110 dB level would have been thoroughly inappropriate overkill. At FOH control, the show was about 80 – 90 dB, and that was plenty. There were a few times where I was concerned that I might have been a touch too loud for what was going on. In that sense, I had far more than enough PA for raw output. I could have run a single pair of boxes and been just fine, but I didn’t want to get all the speakers out of the van and not use them. As I said before, I chose “double hung” to use all my boxes, and to use them in the way that would be nicest for people’s ears.


If you’re curious about running a double hung setup, I do encourage you to experiment with it. Curiosity is what keeps this industry moving. At the same time, you shouldn’t expect it to completely knock you off your feet. If you have a good-sounding system that runs everything through one pair of mains, adding another pair just to split out some sources is unlikely to cause a cloud-parting, ligh-ray-beaming experience of religious proportions. Somewhat like aux-fed subwoofers, going double hung is a taste-dependent route to accomplishing reinforcement for a live event. For me, it solves a particular problem that is mostly logistical in nature, and it sounds decent doing it.


Does It Have To Be This Loud?

A love-letter to patrons of live music.

Please Remember:

The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.

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Dear Live-Music Patron,

Occasionally, you have a question to ask an audio human. That question isn’t often posed to me personally, although, in aggregate, the query is probably made multiple times in every city on every night. The question isn’t always direct, and it can morph into different forms – some of which are statements:

“I can’t hear anything except the drums.”

“The guitar on the right is hurting my ears.”

“It’s hard to talk to my girlfriend/ boyfriend in here.”

“Can you keep everything the same, but turn the mains down?”

“Can you make it so the mic doesn’t make that screech again?”

And so on.

Whenever the conversation goes this way, there’s a singular question lying at the heart of the matter:

“Does it have to be this loud?”

There are a number of things I want to say to you regarding that question, but the most important bit has to come first. It’s the one thing that I want you to realize above everything else.

You’re asking a question that is 100% legitimate.

You may have asked it in one way or another, only to be brushed off. You may have had an exasperated expression pointed your way. You may have been given a brusque “Yes” in response. You may have encountered shrugging, swearing, eye-rolling, sneering, or any number of other responses that were rude, unhelpful, or downright mean.

But that doesn’t mean that your question is wrong or stupid. You’re right to ask it. It’s one of the minor tragedies in this business that production people and music players talk amongst themselves so much, and yet almost never have a real conversation with you. Another minor tragedy is that us folks who run the shows are usually not in a position to have a nuanced discussion with you when it would actually be helpful.

It’s hard to explain why it’s so loud when it’s so loud that you have to ask if “it has to be this loud.”

So, I want to try to answer your question. I can’t speak to every individual circumstance, but I can talk about some general cases.

Sometimes No

I am convinced that, at some time in their career, every audio tech has made a show unnecessarily loud. I’ve certainly done it.

As “music people,” we get excited about sonic experiences as an end in themselves. We’re known for endlessly chasing after tiny improvements in some miniscule slice of the audible spectrum. We can spend hours debating the best way to make the bass (“kick”) drum sound like a device capable of extinguishing all multicellular life on the planet. The sheer number of words dedicated to the construction of “massive” rock and roll guitar noises is stunning. The amount of equipment and trickery that can be dedicated to, say, getting a bass guitar to sound “just so” might boggle your mind.

It’s entirely possible for us to become so enraptured in making a show – or even just a small portion of a show – sound a certain way that we don’t realize how much level we’re shoveling into the equation. We get the drums cookin’, and then we realize that the guitars are a little low, and then the bass comes up to balance that out, and then the vocals are buried, so we crank up the vocals and WHAT? I CAN’T HEAR YOU!

It does happen. Sometimes it’s accidental, and sometimes it’s deliberate. Some techs just don’t feel like a rock show is a rock show until they “feel” a certain amount of sound pressure level.

In these cases, when the audio human’s mix choices are the overwhelming factor in a show being too loud, the PA really should be pulled back. It doesn’t have to be that loud. The problem and the solution are simple creatures.

But Sometimes Yes

The thing with live audio is that the problems and the solutions are often not so simple as what I just got into. It’s very possible, especially in a small room, for the sound craftsperson’s decisions to NOT be the overwhelming factor in determining the volume of a gig. I – and others like me – have spent lots of time in situations where we’ve had to deal with an unfortunate consequence of the laws of physics:

The loudest thing in the room is as quiet as we can possibly be, and quite often, a balanced mix requires something else to be much louder than that thing.

If the instrumentalists (drums, bass, guitars, etc) are blasting away at 110 dB without any help from the sound system, then the vocals will have to be in that same neighborhood in order to compete. It’s a conundrum of either being too loud with a flat-out awful mix, or too loud with a mix that’s basically okay. In a case like that, an audio human just has to get on the gas and wait to go home. Someone’s going to be mad at us, and it might as well not be the folks who are into the music.

There’s another overarching situation, though, and that’s the toughest one to talk about. It’s a difficult subject because it has to do with subjectivity and incompatible expectations. What I’m getting at is when some folks want background music, and the show is not…can not be presented as such.

There ARE bands that specialize in playing “dinner” music. They’re great at performing inoffensive selections that provide a bed for conversation at a comfortable volume. What I hope can be understood is that this is indeed a specialization. It’s a carefully cultivated, specific skill that is not universally pursued by musicians. It’s not universally pursued because it’s not universally applicable.

Throughout human history, a great many musical events, musical instruments, and musical artisans have had a singular purpose: To be noticed, front and center. For thousands of years, humans have used instruments like drums and horns as acoustic “force multipliers” – sonic levers, if you will. We have used them to call to each other over long distances, or send signals in the midst of battle. Fanfares have been sounded at the arrivals of kings. On a parallel track, most musicians that I know do not simply play to be involved in the activity of playing. They play so as to be listened to.

Put all that together, and what you have is a presentation of art that simply is not meant to be talked over. In the cases where it’s meant to coexist with a rambunctious audience, it’s even more meant to not be talked over. From the mindset of the players to the technology in use, the experience is designed specifically to stand out from the background. It can’t be reduced to a low rumble. That isn’t what it is. There’s no reason that it has to be painfully loud, but there are many good reasons why a conversation in close proximity might not be practical.

So.

Does it have to be this loud?

Maybe.


Danny’s Unofficial Sound System Taxonomy

Actual “concert rigs” are capable of being really loud. They’re also really expensive.

Please Remember:

The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.

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There’s a question in this business that’s rather like the quandary of what someone means when they say “twice as loud.” It’s the question of how a PA system “classes.”

To a certain degree, the query is unanswerable. What might be a perfectly acceptable rock-band PA for one group might not be adequate for a different band. Even so, if you ask the first group whether or not they play through a “rock-band” system, they will probably say yes. In the end, it all comes down to whether a rig satisfies people’s needs or not. The systems I work on are just fine for what I need them to do (most of the time). If you gave them to Dave Rat, however, they wouldn’t fit the bill.

Even if the question can’t be definitively put to rest, it can still be talked about. In my mind, it’s possible to classify FOH PA systems and monitor rigs by means of acoustical output.

Right away, I do have to acknowledge that acoustical output is a sloppy metric. It doesn’t tell you if a rig sounds nice, or is user-friendly, or if it’s likely to survive through the entire show. Reducing the measure of a system to one number involves a LOT of other assumptions being made, and being made “invisibly.” It’s sort of like the whole problem of simple, passive loudspeakers. The manufacturer suggests a certain, broadband wattage number to use, all while assuming that major “edge cases” will be avoided by the end user.

But one-number metrics sure do make things simple…

Anyway.

My Proposed “Rule Of Quarters”

So, as I present my personal taxonomy of audio rigs, let me also mention some of my other assumptions for a “pro” PA system:

1) I assume that a system can be tuned such that any particular half-octave range of frequencies will have an average level of no more than +/- 6 dB from an arbitrary reference point. Whether the system is actually tuned that way is a whole other matter. (My assumption might also be too lenient. I would certainly prefer for a rig’s third-octave averages to be no more than +/- 3 dB from the reference, to be perfectly frank. I’d also like a $10 million estate where I can hold concerts.)

2) I assume that the system can provide its stated output from 50 Hz to 15000 Hz. Yes, some shows require “very deep” low-frequency reproduction, but it seems that 50 Hz is low enough to cover the majority of shows being done, especially in a small-venue context. On the HF side, it seems to me that very few people can actually hear above 16 kHz, so there’s no point in putting superhuman effort into reproducing the last half-octave of theoretical audio bandwidth. Don’t get me wrong – it’s great if the rig can actually go all the way out to 20 kHz, but it’s not really a critical thing for me.

3) I assume that the system has only a 1:100 chance (or less) of developing a major problem during the show. To me, a major problem is one that is actually a PA equipment failure, is noticeable to over 50% of the audience, and requires the space of more than 5 minutes to get fixed.

If all the above is in the right place, then I personally class PA systems into four basic categories. The categories follow a “rule of quarters,” where each PA class is capable of four times the output of its predecessor. Please note that I merely said “capable.” I’m not saying that a PA system SHOULD be producing the stated output, I’m only saying that it should be ABLE to produce it.

Also, as a note about the math I’m using for these numbers, I do make it a point to use “worst case” models for things. That is, I knock 12 dB off the peak output of a loudspeaker just to start, and I also treat every doubling of distance from a box to result in a 6 dB loss of apparent SPL. I also neglect to account for the use of subwoofers, and assume that full-range boxes are doing all the work. I prefer to underestimate PA performance, because it’s better to have deployed a Full-Concert rig and wish you’d brought a Foreground Music system than to be in the opposite situation.

Spoken Word

Minimum potential SPL at audience center, continuous: 97 dB

This isn’t too tough to achieve, especially in a small space. If the audience center is 25 feet (7.62 meters) from the PA, and they can hear two boxes firing together, then each box has to produce about 112 dB at one meter. A relatively inexpensive loudspeaker (like a Peavey PVx12) with an amp rated for 400 watts continuous power should be able to do that with a little bit of room left over – but not much room, to be brutally honest.

Also, it’s important to note that 97 dB SPL, continuous, is REALLY LOUD for speech. Something like 75 – 85 dB is much more natural.

Background Music

Minimum potential SPL at audience center, continuous: 103 dB

This is rather more demanding. For a 25-foot audience centerpoint being covered by two boxes, each box has to produce about 118 dB continuous at close range. This means that you would already be in the territory of something like a JBL PRX425, powered by an amp rated for 1200 watts continuous output. (It’s a bit sobering to realize that what looks like a pretty beefy rig might only qualify as a “background” system.)

Foreground Music

Minimum potential SPL at audience center, continuous: 109 dB

Doing this at 25 feet with two boxes requires something like a Peavey QW4F…and a lot of amplifier power.

Full Concert

Minimum potential SPL at audience center, continuous: 115 dB

If you want to know why live-sound is so expensive, especially at larger scales, this is an excellent example. With $4800 worth of loudspeakers (not to mention the cost of the amps, cabling, processing, subwoofer setup, and so on), it’s actually possible to, er, actually, NOT QUITE make the necessary output. Even in a small venue.

Also, there’s the whole issue that just building a big pile of PA doesn’t always sound so great. Boxes combining incoherently cause all kinds of coverage hotspots and comb filtering. It’s up to you to figure out what you can tolerate, of course.

And, of course, just because a system can make 115 dB continuous doesn’t mean that you actually have to hit that mark.

Don’t Be Depressed

Honest-to-goodness, varsity-level audio requires a lot of gear. It requires a lot of gear because varsity-level audio means having a ton of output available, even if you don’t use it.

In the small-venue world, the chances of us truly doing varsity-level audio are pretty small, and that’s okay. That doesn’t mean we can’t have a varsity-level attitude about what we’re doing, and that doesn’t mean that our shows have to be disappointing. We just have to realize where we stack up, and take pride in our work regardless.

As an example, at my regular gig, “full-throttle” for an FOH loudspeaker is 117 dB SPL at one meter. “Crowd center” is only about 12 feet from the boxes, so their worst-case output is 106 dB continuous individually, or 109 dB continuous as a pair. According to my own classification methods, the system just barely qualifies as a “foreground music” rig.

But I rarely run it at full tilt.

In fact, I often limit the PA to 10 dB below its full output capability.

“Full Concert” capability is nice, but it’s a difficult bar to reach – and you may not actually need it.


Loud Doesn’t Create Excitement

A guest post for Schwilly Family Musicians.

Please Remember:

The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.

amped

The folks in the audience have to be “amped up” about your songs before the privilege of volume is granted.

The full article is here.


How Much Output Should I Expect?

A calculator for figuring out how much SPL a reasonably-powered rig can develop.

Please Remember:

The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.

howloudWant to use this image for something else? Great! Click it for the link to a high-res or resolution-independent version.

As a follow-on to my article about buying amplifiers, I thought it would be helpful to supply an extra tool. The purpose of this calculator is to give you an idea of the SPL delivered by a “sanely” powered audio rig.

A common mistake made when estimating output is to assume that the continuous power the amp is rated for will be easily applied to a loudspeaker. This leads to inflated estimations of PA performance, because, in reality, actually applying the rated continuous power of the amp is relatively difficult. It’s possible with a signal of narrow bandwidth and narrow dynamic range – like feedback, or sine-wave synth sounds, but most music doesn’t behave that way. Most of the time, the signal peaks are far above the continuous level…

…and, to be brutally honest, continuous output is what really counts.


This Calculator Requires Javascript

This calculator is an “aid” only. You should not rely upon it solely, especially if you are using it to help make decisions that have legal implications or involve large amounts of money. (I’ve checked it for glaring errors, but other bugs may remain.) The calculator assumes that you have the knowledge necessary to connect loudspeakers to amplifiers in such a way that the recommended power is applied.


Enter the sensitivity (SPL @ 1 watt @ 1 meter) of the loudspeakers you wish to use:

Enter the peak power rating of your speakers, if you want slightly higher performance at the expense of some safety. If you prefer greater safety, enter half the peak rating:

Enter the number of loudspeakers you intend to use:

Enter the distance from the loudspeakers to where you will be listening. Indicate whether the measurement is in feet or meters. (Measurements working out to be less than 1 meter will be clamped to 1 meter.)

Click the button to process the above information:

Recommended amplifier continuous power rating at loudspeaker impedance:
0 Watts

Calculated actual continuous power easily deliverable to each loudspeaker:
0 Watts

Calculated maximum continuous output for one loudspeaker at 1 meter:
0 dB SPL

Calculated maximum continuous output for one loudspeaker at the given listening position:
0 dB SPL

Calculated maximum continous output for entire system at the given listening position:
0 dB SPL

How The Calculator Works

First, if you want to examine the calculator’s code, you can get it here: Maxoutput.js

This calculator is intentionally designed to give a “lowball” estimate of your total output.

First, the calculator divides your given amplifier rating in half, operating on the assumption that an amp rated with sine-wave input will have a continuous power of roughly half its peak capability. An amp driven into distortion or limiting will have a higher continuous output capability, although the peak output will remain fixed.

The calculator then assumes that it will only be easy for you to drive the amp to a continuous output of -12 dB referenced to the peak output. Driving the amp into distortion or limiting, or driving the amp with heavily compressed material can cause the achievable continuous output to rise.

The calculator takes the above two assumptions and figures the continuous acoustic output of one loudspeaker with a continuous input of -12 dB referenced to the peak wattage available.

The next step is to figure the apparent level drop due to distance. The calculator uses the “worst case scenario” of inverse square, or 6 dB of SPL lost for every doubling of distance. This essentially presumes that the system is being run in an anechoic environment, where sound pressure waves traveling away from the listener are lost forever. This is rarely true, especially indoors, but it’s better to return a more conservative answer than an “overhyped” number.

The final bit is to sum the SPLs of all the loudspeakers specified to be in the system. This is tricky, because the exact deployment of the rig has a large effect – and the calculator can’t know what you’re going to do. The assumption is that all the loudspeakers are audible to the listener, but that half of them appear to be half as loud.


Loud Thoughts

“Loud” is a subjective sort of business.

Please Remember:

The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.

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The concept of “loud” is really amorphous, especially when you consider just how important it is to live shows. A show that’s too loud for a given situation will quickly turn into a mess, in one way or another. Getting a desired signal “loud enough” in a certain monitor mix may be key to a great performance.

And yet…”loud” is subjective. Perceived changes in level are highly personalized. People tolerate quite a bit of level when listening to music they like, and tolerate almost no volume at all when hearing something that they hate. One hundred decibels SPL might be a lot of fun when it’s thumping bass, but it can also be downright abrasive when it’s happening at 2500 Hz.

Twice As Loud

Take a look at that heading. Do you realize that nobody actually, truly knows what “twice as loud” means?

People might think they know. You’ll hear statements like “people generally think 6 dB is about twice as loud,” but then later someone else will say, “people perceive a 10 dB difference to be twice as loud.” There’s a range of perception, and it’s pretty sloppy when you actually do the math involved.

What I mean is this. The decibel is a measure of power. (You can convert other things, like voltage and pressure, into power equivalents.) Twice the power is 3 dB, period. It’s a mathematical definition that the industry has embraced for decades. It’s an objective, quantitative measurement of a ratio. Now, think about the range of perception that I presented just now. It’s a little eyebrow raising when you realize that the range for perceiving “twice as loud” is anywhere from 4X to 10X the power of the original signal. If a 1000 watt PA system at full tilt is the baseline, then there are listeners who would consider the output to be doubled at 4000 watts…and other folks who wouldn’t say it was twice as loud until a 10kW system was tickling its clip lights!

It’s because of this uncertainty that I try (and encourage others to seriously consider) communicating in terms of decibels. Especially in the context of dialing up a PA or monitor rig to everybody’s satisfaction, it helps greatly if some sort of quantitative and objective reference point is used. Yes, statements like “I need the guitar to be twice as loud,” or “I think the mix needs 10% more of the backup singers” ARE quantitative – but they aren’t objective. Do you need 3dB more guitar? Six decibels? Ten? Do you want only 0.4 dB more of the backup singers? (Because that’s what [10 log 1.1] works out to.) Communicating in decibels is far less arbitrary.

(The irony of using a qualitative phrase like “far less” in the context of advocating for objective quantification is not lost on me, by the way.)

The Meter Is Only Partially Valid As An Argument

Even if nobody actually knows what “twice as loud” means, one thing that people do know is when they feel a show is too loud.

For those of use who embrace measurement and objectivity, there’s a tendency that we have. When we hear a subjective statement, we get this urge to fire up a meter and figure out if that statement is true. I’m all for this behavior in many scenarios. Challenging unsubstantiated hoo-ha is, I think, one of the areas of pro-audio that still has some “frontier” left in it. My opinion is that more claims need to be challenged with the question, “Where’s your data?”

But when it comes to the topic of “loud,” especially the problem of “too loud,” whipping out an SPL meter and trying to argue on the basis of objectivity is of only narrow appropriateness. In the case of a show that feels too loud for someone, the meter can help you calibrate their perception of loud to an actual number that you can use. You can then decide if trying to achieve a substantially lower reading is feasible or desirable. If a full-on rock band is playing in a room, making 100 dBC at FOH without the PA even contributing, and one person thinks they only ought to be 85 dB C…that one person is probably out of luck. The laws of physics are really unlikely to let you fulfill that expectation. At the same time, you have to realize that your meter reading (which might suggest that the PA is only contributing three more decibels to the show) is irrelevant to that person’s perception.

If something is too loud for someone, the numbers from your meter have limited value. They can help you form a justifying argument for why the show level is where it is, but they’re not a valid argument all by themselves.


It’s Not Actually About The Best Sound

What we really want is the best possible show at the lowest practical gain.

Please Remember:

The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.

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As it happens, there’s a bit of a trilogy forming around my last article – the one about gain vs. stability. In discussions like this, the opening statement tends to be abstract. The “abstractness” is nice in a way, because it doesn’t restrict the application too much. If the concept is purified sufficiently, it should be usable in any applicable context.

At the same time, it’s nice to be able to make the abstract idea more practical. That is, the next step after stating the concept is to talk about ways in which it applies.

In live audio, gain is both a blessing and a curse. We often need gain to get mic-level signals up to line-level. We sometimes need gain to correct for “ensemble imbalances” that the band hasn’t yet fixed. We sometimes need gain to make a quiet act audible against a noisy background. Of course, the more gain we add, the more we destabilize the PA system, and the louder the show gets. The day-to-day challenge is to find the overall gain which lets us get the job done while maintaining acceptable system stability and sound pressure.

If this is the overall task, then there’s a precept which I think can be derived from it. It might only be derivable indirectly, depending on your point of view. Nevertheless:

Live sound is NOT actually about getting the best sound, insofar as “the best sound” is divorced from other considerations. Rather, the goal of live sound is to get the best possible holistic SHOW, at the lowest practical gain.

Fixing Everything Is A Bad Idea

The issue with a phrase like “the best sound” is that it morphs into different meanings for different people. For instance, at this stage in my career, I have basically taken the label saying “The Best Sound” and stuck it firmly on the metaphorical box containing the sound that gets the best show. For that reason alone, the semantics can be a little difficult. That’s why I made the distinction above – the distinction that “the best sound” or “the coolest sound” or “the best sound quality” is sometimes thought of without regard to the show as a whole.

This kind of compartmentalized thinking can be found both in concert audio veterans and greenhorns. My gut feeling is that the veterans who still section off their thinking are the ones who never had their notions challenged when they were new enough.

…and I think it’s quite common among new audio humans to think that the best sound creates the best show. That is, if we get an awesome drum sound, and a killer guitar tone, and a thundering bass timbre, and a “studio ready” vocal reproduction, we will then have a great show.

The problem with this line of thinking is that it tends to create situations where a tech is trying to “fix” almost everything about the band. The audio rig is used as a tool to change the sound of the group into a processed and massaged version of themselves – a larger than life interpretation. The problem with turning a band into a “bigger than real” version of itself is that doing so can easily require the FOH PA to outrun the acoustical output of the band AND monitor world by 10 dB or more. Especially in a small-venue context, this can mean lots and lots of gain, coupled with a great deal of SPL. The PA system may be perched on the edge of feedback for the duration of the show, and it may even tip over into uncontrolled ringing on occasion. Further, the show can easily be so loud that the audience is chased off.

To be blunt, your “super secret” snare-drum mojo is worthless if nobody wants to be in the same room with it. (If you follow me.)

Removed from other factors, the PA does sound great…but with the other factors being considered, that “great” sound is creating a terrible show.

Granularity

The correction for trying to fix everything is to only reinforce what actually needs help. This approach obeys the “lowest possible gain” rule. PA system gain is applied only to the sources that are being acoustically swamped, and only in enough quantity that those sources stop being swamped.

In a sense, you might say that there’s a certain amount of total gain (and total resultant volume) that you can have that is within an acceptable “window.” When you’ve used up your allotted amount of gain and volume, you need to stop there.

At first, the selectivity of what gets gain applied is not very narrow. For newer operators and/ or simplified PA systems, the choice tends to be “reproduce most of the source or none of it.” You might have, say, one guitar that’s in the PA, plus a vocal that’s cranked up, and some kick drum, and that’s all. Since the broadband content of the source is getting reproduced by the PA, adding any particular source into the equation chews up your total allowable gain in a fairly big hurry. This limits the correction (if actually necessary) that the PA system can apply to the total acoustical solution.

The above, by the way, is a big reason why it’s so very important for bands to actually sound like a band without any help from the PA system. That does NOT mean “so loud that the PA is unnecessary,” but rather that everything is audible in the proper proportions.

Anyway.

As an operator learns more and gains more flexible equipment, they can be more selective about what gets a piece of the gain allotment. For instance, let’s consider a situation where one guitar sound is not complementing another. The overall volumes are basically correct, but the guitar tones mask each other…or are masked by something else on stage. An experienced and well-equipped audio human might throw away everything in one guitar’s sound, except for a relatively narrow area that is “out of the way” of the other guitar. The audio human then introduces just enough of that band-limited sound into the PA to change the acoustical “solution” for the appropriate guitar. The stage volume of that guitar rig is still producing the lion’s share of the SPL in the room. The PA is just using that SPL as a foundation for a limited correction, instead of trying to run right past the total onstage SPL. The operator is using granular control to get a better show (where the guitars each have their own space) while adding as little gain and SPL to the experience as possible.

If soloed up, the guitar sound in the PA is terrible, but the use of minimal gain creates a total acoustical solution that is pleasing.

Of course, the holistic experience still needs to be considered. It’s entirely possible to be in a situation that’s so loud that an “on all the time” addition of even band-limited reinforcement is too much. It might be that the band-limited channel should only be added into the PA during a solo. This keeps the total gain of the show as low as is practicable, again, because of granularity. The positive gain is restricted in the frequency domain AND the time domain – as little as possible is added to the signal, and that addition is made as rarely as possible.

An interesting, and perhaps ironic consequence of granularity is that you can put more sources into the PA and apply more correction without breaking your gain/ volume budget. Selective reproduction of narrow frequency ranges can mean that many more channels end up in the PA. The highly selective reproduction lets you tweak the sound of a source without having to mask all of it. You might not be able to turn a given source into the best sound of that type, but granular control just might let you get the best sound practical for that source at that show. (Again, this is where the semantics can get a little weird.)

Especially for the small-venue audio human, the academic version of “the best sound” might not mean the best show. This also goes for the performers. As much as “holy grail” instrument tones can be appreciated, they often involve so much volume that they wreck the holistic experience. Especially when getting a certain sound requires driving a system hard – or “driving” an audience hard – the best show is probably not being delivered. The amount of signal being thrown around needs to be reduced.

Because we want the best possible show at the lowest practical gain.


The Board Feed Problem

Getting a good “board feed” is rarely as simple as just splitting an output.

Please Remember:

The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.

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I’ve lost count of the number of times I’ve been asked for a “board mix.” A board mix or feed is, in theory, a quick and dirty way to get a recording of a show. The idea is that you take either an actual split from the console’s main mix bus, or you construct a “mirror” of what’s going into that bus, and then record that signal. What you’re hoping for is that the engineer will put together a show where everything is audible and has a basically pleasing tonality, and then you’ll do some mastering work to get a usable result.

It’s not a bad idea in general, but the success of the operation relies on a very powerful assumption: That the overwhelming majority of the show’s sound comes from the console’s output signal.

In very large venues – especially if they are open-air – this can be true. The PA does almost all the work of getting the show’s audio out to the audience, so the console output is (for most practical purposes) what the folks in the seats are listening to. Assuming that the processing audible in the feed-affecting path is NOT being used to fix issues with the PA or the room, a good mix should basically translate to a recorded context. That is, if you were to record the mix and then play it back through the PA, the sonic experience would be essentially the same as it was when it was live.

In small venues, on the other hand…

The PA Ain’t All You’re Listening To

The problem with board mixes in small venues is that the total acoustical result is often heavily weighted AWAY from what the FOH PA is producing. This doesn’t mean that the show sounds bad. What it does mean is that the mix you’re hearing is the PA, AND monitor world, AND the instruments’ stage volume, hopefully all blended together into a pleasing, convergent solution. That total acoustic solution is dependent on all of those elements being present. If you record the mix from the board, and then play it back through the PA, you will NOT get the same sonic experience that occurred during the live show. The other acoustical elements, no longer being present, leave you with whatever was put through the console in order to make the acoustical solution converge.

You might get vocals that sound really thin, and are drowning everything else out.

You might not have any electric guitar to speak of.

You might have only a little bit of the drumkit’s bottom end added into the bleed from the vocal mics.

In short, a quick-n-dirty board mix isn’t so great if the console’s output wasn’t the dominant signal (by far) that the audience heard. While this can be a revealing insight as to how the show came together, it’s not so great as a demo or special release.

So, what can you do?

Overwhelm Or Bypass

Probably the most direct solution to the board feed problem is to find a way to make the PA the overwhelmingly dominant acoustic factor in the show. Some ways of doing this are better than others.

An inadvisable solution is to change nothing about the show and just allow FOH to drown everything. This isn’t so good because it has a tendency to create a painfully loud experience for the audience. Especially in a rock context, getting FOH in front of everything else might require a mid-audience continuous sound pressure of 110 dB SPL or more. Getting away with that in a small room is a sketchy proposition at best.

A much better solution is to lose enough volume from monitor world and the backline, such that FOH being dominant brings the total show volume back up to (or below) the original sound level. This requires some planning and experimentation, because achieving that kind of volume loss usually means finding a way of killing off 10 – 20 dB SPL of noise. Finding a way to divide the sonic intensity of your performance by anywhere from 10 to 100(!) isn’t trivial. Shielding drums (or using a different kit setup), blocking or “soaking” instrument amps (or changing them out), and switching to in-ear monitoring solutions are all things that you might have to try.

Alternatively, you can get a board feed that isn’t actually the FOH mix.

One way of going about this is to give up one pre-fade monitor path to use as a record feed. You might also get lucky and be in a situation where a spare output can be configured this way, requiring you to give up nothing on deck. A workable mix gets built for the send, you record the output, and you hope that nothing too drastic happens. That is, the mix doesn’t follow the engineer’s fader moves, so you want to strenuously avoid large changes in the relative balances of the sources involved. Even with that downside, the nice thing about this solution is that, large acoustical contributions from the stage or not, you can set up any blend you like. (With the restriction of avoiding the doing of weird things with channel processing, of course. Insane EQ and weird compression will still be problematic, even if the overall level is okay.)

Another method is to use a post-fade path, with the send levels set to compensate for sources being too low or too hot at FOH. As long as the engineer doesn’t yank a fader all the way down to -∞ or mute the channel, you’ll be okay. You’ll also get the benefit of having FOH fader moves being reflected in the mix. This can still be risky, however, if a fader change has to compensate for something being almost totally drowned acoustically. Just as with the pre-fade method, the band still has to work together as an actual ensemble in the room.

If you want to get really fancy, you can split all the show inputs to a separate console and have a mix built there. It grants a lot of independence (even total independence) from the PA console, and even lets you assign your own audio human to the task of mixing the recording in realtime. You can also just arrange to have the FOH mix person run the separate console, but managing the mix for the room and “checking in” with the record mix can be a tough workload. It’s unwise to simply expect that a random tech will be able to pull it off.

Of course, if you’re going to the trouble of patching in a multichannel input split, I would say to just multitrack the show and mix it later “offline” – but that wouldn’t be a board feed anymore.

Board mixes of various sorts are doable, but if you’re playing small rooms you probably won’t be happy with a straight split from FOH. If you truly desire to get something usable, some “homework” is necessary.


The Calculus Of Music

There’s a lot of math behind the sound of a show, but you don’t have to work it out symbolically.

Please Remember:

The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.

Want to use this image for something else? Great! Click it for the link to a high-res or resolution-independent version.

This post is the fault of my high-school education, my dad, and Neil deGrasse Tyson.

In high-school, I was introduced to calculus. I wasn’t particularly interested in the drills and hairy algebra, but I did have an interest in the high-level concepts. I’ve kept my textbook around, and I will sometimes open it up and skim it.

My dad is a lover of cars, and that means he gets magazines about cars and car culture. Every so often, I’ll run across one and see what’s in the pages.

About a month ago, I was on another jaunt through my calculus book when I happened upon a car-mag with an article by Neil deGrasse Tyson. (You know Dr. Tyson. He’s the African-American superstar astrophysicist guy. He hosted and narrated the new version of “Cosmos.”) In that article was a one-line concept that very suddenly connected some dots in my head: Dr. Tyson pointed out that sustained speed isn’t all that exciting – rather, acceleration is where the fun is.

Acceleration.

Change.

The rate of change.

Derivative calculus.

Exciting derivative calculus makes for exciting music.

What?

Let me explain.

Δy/Δx: It’s Where The Fun Is!

The first thing to say here is that there’s no need to be frightened of those symbols in the section heading. The point of all this is not to say that everybody should reduce music to a set of equations. I’m not suggesting that folks should have to “solve” music in a symbolic way, as a math problem. What I am saying is that mathematical concepts of motion and change can be SUPER informative about the sound of a show. (Or a recording, too.)

I mean, gosh, motion and change. That sounds like it’s really important for an art form involving sine waves. And vibrating stuff, like guitar strings and loudspeakers and such.

Anyway.

Those symbols up there (Δy/Δx) reflect the core of what derivative calculus is concerned with. It’s the study of how fast things are changing. Δy is, conventionally, the change in the vertical-axis value, whereas Δx is the change in the horizontal-axis value. If you remember your geometry, you might recall that the slope of a line is “rise over run,” or “how much does the line go up or down in a given horizontal space?” Rise over run IS Δy/Δx. Derivative calculus is nothing more exotic than finding the slopes of lines, but the algebra does get a bit hairy because of people wanting to get the slopes of lines that are tangent to single, instantaneous points on a curve YOUR EYES ARE GLAZING OVER, I KNOW.

Let’s un-abstractify this. (Un-abstractify is totally a word. I just created it. Send me royalties.)

Remember that article I wrote about the importance of transients? Transients are where a change in volume is high, relative to the amount of time that passes. An uncompressed snare-drum note has a big peak that happens quickly. It’s the same for a kick-drum hit. The “thump” or “crack” happens fast, and decays in a hurry. The difference in sound-pressure from “silence” to the peak volume of the note is Δy, and the time that passes is Δx. Think about it – you’ve seen a waveform in an audio-editor, right? The waveform is a graph of audio intensity over time. The vertical axis (y) is the measure of how loud things are, and the horizontal axis (x) is how much time has passed. Like this:

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For music to be really exciting, there has to be dramatic change. For music to be calming, the change has to be restrained. If you want something that’s danceable, or if you want something that has defined, powerful impact regardless of danceability, you’ve got to have room for “big Δy.” There has to be space for volume curves that have steep slopes. The derivative calculus has to be interesting, or all you’ll end up with is a steady-state drone (or crushingly deafening roar, depending on volume) that doesn’t take the audience on much of a ride. (Again, if you want a calming effect, then steady-state at low-volume is probably what you want.) This works across all kinds of timescales, by the way. Your music might not have sharp, high-speed transients that take place over a few milliseconds, but you can still move the audience with swells and decrescendos that develop over the span of minutes.

Oh, and that graphic at the top of the page? That’s actually a roughly-traced vocal waveform, with some tangent-lines drawn in to show the estimated derivatives at those points. The time represented is relatively small – about one second. Notice the separation between the “hills?” Notice how steep the hills are? It turns out that the vocal in that recording is highly intelligible, and I would strongly argue that a key component in that intelligibility is a high rate of change in the right places. Sharp transitions from sound to sound help to tell you where words begin and end. When it all runs together, what you’ve got is incoherent mumbling. (This even works for text. You can read this, because the whitespace between words creates sharp transitions from word to word. This,ontheotherhand…)

Oh, and from a technical standpoint, headroom is really important for delivering large “Δy” events. If the PA is running at close to full tilt, there’s no room to shove a pronounced peak through it all. If you want to reproduce sonic events involving large derivatives, you have to have a pretty healthy helping of unused power at your disposal.

Now, overall level does matter as well, which leads us into another aspect of calculus.

Integral Volume

Integral calculus contrasts with derivative calculus, in that integration’s concern is with how much area is under the curve. From the perspective of an audio-human, the integral of the “sonic-events curve” tells you a lot about how much power you’re really delivering to those loudspeaker voice-coils. Short peaks don’t do much in terms of heating up coil windings, so loudspeakers can tolerate rather high levels over the short term. Long-term power handling is much lower, because that’s where you can get things hot enough to melt.

From a performance perspective, integration has a lot to say about just how loud your show is perceived to be. I’ve been in the presence of bands that had tremendous “derivative calculus” punching power, and yet they didn’t overwhelm the audience with volume. It was all because the total area under the volume curve was well managed. The long-term level of the band was actually fairly low, which meant that people didn’t feel abused by the band’s sound.

This overall concept (which includes the whole discussion of derivatives) is a pretty touchy subject in live audio. That is, it can all be challenging to get right. It’s situationally dependent, and it has to be “just so.” Too much is a problem, and too little is a problem. For example, take this blank graph which represents a hypothetical, bar-like venue where the band hasn’t started yet:

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If the band volume’s area under the curve is too small, they’ll be drowned out by the talking of the crowd. Go too high, though, and the crowd will bail out. It’s a balancing act, and one that isn’t easy to directly define with raw numbers. For instance, here’s an example of what (I think) some reggae bands might look like over the span of several seconds:

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The “large Δy” events reach deep into the really-loud zone, but they’re very brief. Further, there are places where the noise floor peeks through significantly. This ability for the crowd to hear themselves talking helps to send the message that the band isn’t too loud. Overall, the area under the curve is probably halfway to three-quarters into the “comfortable volume” zone. Now, what about a “guitar” band:

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The peaks don’t go up quite as far. In terms of sustained level, the band is probably also halfway to three-quarters into the comfortable zone – and yet some folks will feel like the band is a bit loud. It’s because the sustained roar of the guitars (and everything else) is enough to completely overwhelm the noise floor. The crowd can’t hear themselves talk, which sends the message that the band’s intensity is higher than it is in terms of “pure numbers.”

As an aside, this says a lot about the problems of the volume war. At some point, we started crushing all the exciting, flavorful, “large Δy” material in order to get maximum area under the curve…and eventually, we started to notice just how ridiculous things were sounding.

And then there’s one of my pet peeves, which is the indie-rock idiom of scrubbing away at a single-coil-pickup guitar’s strings with the amp’s tone controls set for “maximum clang.” It creates one of the most sustained, abrasive, yet otherwise boring noises that a person can have the displeasure of hearing. Let me tell you how I really feel…

Anyway.

Excitement, intelligibility, and appropriate volume levels are probably just a few of the things described by the calculus of music. I’ll bet there’s more out there to be discovered. We just have to keep our cross-disciplinary antennae extended.