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Yup... bad typing.....
What I intended to say was that a speaker at 95 dB efficiency with 10 watts would be as loud as a speaker at 85 dB efficiency with 100 watts.
(So adding 10 dB in speaker efficiency is equivalent to adding 10 dB of power.)
Hmm, this is not correct. Most (read: all subtractive) synthesizers generate the signal in the time domain, i.e. they simply output the samples directly. It simply flips on and off at the frequency you tell it to. This signal is a "perfect" square wave as represented in the audio buffer until it's band-limited by the DAC or another filter in the digital side. Or, it's at least as perfect a square wave as can be represented in PCM format. I don't know if the argument as to whether that counts as "perfect" is actually an academic or philosophical one... but you get my drift.
Additive synthesizers operate in the frequency domain and don't (can't) output this type of signal, they're band-limited by nature, and in that case your objection of infinite harmonics would be correct. However in practice you only need a few hundred harmonics at most to create a passible (in audible terms) approximation of one. This type of synth is popular currently, but is still in the minority as far as how many of them use this method. And, as you note, they certainly do not output perfect square waves or anything close.
I guess you missed my post of the YMCK track, a band that has obviously square-ish synths in every song they make. Probably not in terms of dangerous harmonic content, but in terms of the audible sound, it's unmistakable. They are a fun band if you have any personal nostalgia for the 8-bit era of gaming (certainly not a universal thing I admit!)
Overall my point is not about what's normal or common, what I was trying to get at is that you have to design audio equipment to be able to handle arbitrary audio signals, because people will play whatever horrible sounds they want through them, not just music. I think you would be surprised at what kinds of horrible audio people produce when messing around with soft synths. Even if you exclude the (common) times when a bug in a free plugin wrecks the audio, there is a lot of messed up stuff that happens before a finished album comes out.
As to whether musicians mostly only use patches and don't build their own - I guess you're probably right, but the pros (whose music we actually listen to) are much more likely to write their own, and therefore begin with raw waveforms. You think Vangelis just scrolls through presets all day?
I just wanted to elaborate on a few things... and take a step back on one or two...
First, Pinnahertz is quite correct in that the extra amount of energy you get in the harmonics from any reasonable level of clipping does not account for a huge amount of energy.
Therefore, it really shouldn't account for a significant number of blown tweeters... and probably does not nowadays.
In the old days, it was quite common to see small low cost tweeters, used only for relatively high frequencies, and that actually could only handle two or three watts of continuous power.
And, yes, those could actually be killed by a few extra watts reaching them for too long.
However, most modern domes and planar tweeters can withstand a reasonable amount of power, so this really shouldn't be a problem.
I rather suspect that the cause of most blown tweeters today - especially with low powered amps - is more psychological....
For most of us, the onset of clipping serves as a sort of warning that we're playing things a bit too loud.
It is commonly accepted, as a rough approximation, that with pop music, the average level is usually around 10% of the peak level.
Therefore, if you have a 200 watt amplifier, that starts clipping at 300 watts, your average level will be only 20-30 watts at the onset of clipping.
However, if you have a less powerful amplifier, yet you insist on "playing it loud", it's going to start clipping at a much lower level.
For many people, the result of this seems to be that, without any warning provided by the ONSET of clipping, they just keep turning it up louder.
With an amplifier playing cleanly, the onset of clipping provides a warning that you're playing it too loudly.
With an amp that's ALREADY clipping, you don't get that warning... it just keeps sounding gradually worse as you turn it up.
(Rather like when people who burn the toast too often learn to ignore the smoke detector.)
A significant part of the problem could also be that a lot of people honestly believe that "they can't damage their 200 watt speakers with a 100 watt amplifier"... so they don't pay attention at all.
I talk to a lot of people on the phone who ask which amplifier they should purchase to use with a certain set of speakers.
Their question is OFTEN phrased in therms of "what amplifier they should get if they don't want to have to worry about damaging their speakers if they turn it up too high".
(They are literally looking for an amplifier that, even if they or the kids accidentally turn it up too high unintentionally, CAN'T hurt their speakers.)
The usual advice to them is that, in most cases, if they use common sense they won't have a problem, but most amplifiers can in fact damage most speakers if you ignore when they start to clip and keep cranking them up.
Also, on a side note, there is a reason why most modern amplifiers have limited dynamic power - and it has to do with efficiency and economics.
The maximum power a typical solid state amp can deliver before clipping is limited by the power supply rail voltage - which is fixed.
Once the output is swinging up to the rails it simply cannot go any further.
However, this is also the point of best efficiency for Class A/B amps.
(Remember that, in a Class A/B amp, the output devices must dissipate the difference between the voltage at the output and the rail voltage as heat.)
If you have a Class A/B amp that can deliver 200 watts peak, then it is MOST EFFICIENT at 200 watts output, and much less efficient at 100 watts output.
So, if I have a 100 watt amplifier that can deliver 200 watts of dynamic power, when running at 100 watts it will be less efficient and run hotter than a 100 watt amp that can really only deliver 100 watts maximum.
(Because, in order to enable it to deliver 200 watts peak, I had to use higher power supply rails, which means that, at 100 watts, the output devices are dissipating more power.)
How this actually affects the cost of manufacturing the amp will depend on the cost of the transformer and of the heat sinks.
Virtually all transformers can safely deliver far above their average ratings short term - so a 100 watt transformer will cheerfully deliver the power necessary for an amplifier rated at 100 watts continuous and 200 watts peak.
However, because I've raised the rail voltage to support the higher peak power, the amplifier will be less efficient at lower power levels, and so will run hotter and require bigger heat sinks.
The way the costs of the various parts balance out....
If you were going to make an amplifier that would be rated 100 watts continuous and 200 watts peak.... it doesn't cost much more to enable it to simply deliver 200 watts continuously.
It used to make sense in the old days - when a 200 watt transformer cost a lot more than a 100 watt transformer - and the transformer was a major portion of the total cost.
(Virtually all modern output transistors are capable of handling massive amounts of power - so they're not usually a limiting factor at all these days.)
However, today, this is not the case.
Another factor is simply that overall costs have dropped so much lately.....
Power has simply gotten so cheap lately that most people can easily afford that amp that can deliver 200 watts continuously...
So there's little incentive to save a few dollars and get one that can only deliver 200 watts short term... but has a lower continuous rating.
(And, because of the reasons I mentioned above, the price difference won't necessarily be much at all.)
Note that Class H addresses the efficiency trade off by allowing the amplifier to operate from lower supply rails when putting out lower power.
This eliminates a lot of the loss of efficiency when the amplifier is delivering less than full power.
However, it does result in more complex, and so more expensive, circuitry and design.
Many modern designers would simply say that:
"An amplifier that can deliver 100 watts continuous and 200 watts peak is really just a 200 watt amplifier with an undersized transformer and not enough heat sinks."
You seem to be assuming that your device will be "building the waveforms from harmonics"... however that's not the way everybody would do it.
(Looking at the harmonics and summing them is one way of visualizing a square wave.... but far from the only way of creating one.)
I could create a square wave by summing the proper harmonics in the proper proportions and with the correct phase relationship.
And, yes, this would be a lot of work.
But, if I was generating a square wave using hardware electronics, I would simply use an electronic switch to switch a DC voltage on and off.
I would use a digitally controlled clock to turn the switch on and off at the proper rate (that rate determines the frequency of my square wave).
Many signal generators and "discrete synthesizers" do it this way.
Two dollars worth of parts can switch cleanly enough that the harmonics will be correct up into the gigahertz range.
(And, since you are effectively "drawing the wave" rather than "assembling it" - the phase relationships and harmonic amplitudes simply "turn out right".)
Alternately, I could use some sort of oscillator to make a different waveform, like a sine wave, and then "clip" it into a square wave.
To do this I would use a twenty cent chip called a comparator... which is specially designed to convert variable voltages into on/off conditions.
And, yes, a typical low cost comparator has a gain rated in the MILLIONS and can switch in BILLIONTHS of a second... so it really can produce a fair approximation of a square wave.
I can do something similar using a computer program.
1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0
That string of numbers represents a square wave.
It is "what a perfect square wave would look like if you digitized it" - except that we can skip most of the steps and simply "calculate what the values would be" directly.
For example, I can go into Abobe Audition and instruct it to "generate a square wave".
It will then produce the numbers that define what a perfect square wave would be, at the frequency I request, and within the limits of the sample rate and bit depth I tell it.
What comes out will be exactly what I would get if I actually had a perfect square wave, and then converted it into a digital signal, also perfectly within the limits I've chosen.
(Once you know what the picture should look like, you simply work backwards and figure out what numbers will make the picture you want.)
The programming is quite simple.... so any software synth can do it easily enough....
I don't know how the majority of soft synths "handle" their samples.
However, a sample is simply a digital recording of a sound.
What I described in 3. is essentially "manufacturing" that recording directly - using math - without even having an original to record.
The reason most soft synths use samples is because they WANT to introduce the imperfections and limitations of the original physical source.
All "perfect 1 kHz square waves" at a given sample rate are exactly the same.... it is the flaws and variations that add "personality" to the different samples.
Indeed, a synthetic audio signal from scratch. You could almost say it's "synthesizing" the audio. Hmmm... Maybe they would call this program a "synthesizer"... more research is needed.
That square wave signal is "illegal". If you bandlimit and sample a "perfect" analog squarewave, it doesn't give you this. This is what proper 4410 Hz square wave at 44100 Hz sampling rate looks like:
You're exactly right... as an audio signal it is "illegal", and you should never encounter it in a digital audio device.
It will never be produced as the output of an A/D converter because the band-limiting filters at the input won't pass that signal.
No proper digital audio application would create it... and any normal editor would "fix" it if you imported it.
But, strictly speaking, nothing would prevent a computer program from generating it, and any DAC can technically play any stream of numbers you feed it.
However, it would be interesting to see what would come out if you played it through a DAC with filters specifically optimized for digital audio.
(Much as when you submit an impulse signal to a DAC, which is also an illegal signal, something would come out, and it would be informative, it just wouldn't be "legitimate" digital audio.)
1. Yes my bad, I meant additive synthesis. But ...
2. If we are talking about subtractive synthesis then of course there MUST be a filter and not just "in the digital side" but in the soft-synth itself, as that is the very definition of subtractive synthesis.
3. And in practice a subtractive soft-synth must also be band-limited.
4. Correct but firstly, a "passable approximation" of a square wave is not a "theoretically perfect square wave" and secondly, with say a 1kHz square wave at 44.1kHz sample rate we do not get "a few hundred harmonics" we only get eleven and two or three of those are inaudible anyway!
1. A square wave and something that sounds "square-ish" are two VERY different things! To sound square-ish you just need a few harmonics (as few as 3 or so) but of course in reality that's barely even square-ish, let alone a "theoretically perfect square wave".
2. No, we don't have to design audio equipment to handle arbitrary audio signals, only audio signals which are audible, and that doesn't include "theoretically perfect square waves" or anything even particularly close.
2a. I very much doubt I'd be surprised. I worked for a number of years with music technology students, a fair number of whom were into techno, hardcore and various other electronic sub-genres and were creating material which made "The Prodigy" sound like Mozart! While they often used square-ish sounding effects, in reality the waveforms they ended up with were not remotely square and it wasn't really any more surprising than what Stockhausen was doing 50+ years ago, just more consistently louder.
2b. Yes, there is a great deal of "messed up stuff" that happens before a finished album comes out. Therefore: even if we did start with nothing but a square wave then it's going to be "messed up" and nothing like a square wave when the "album comes out" and if we don't start with a square wave, the "messing up" is not magically going to turn it into a square wave. So no square waves, why then the obsession with square waves??
3. I'm not sure you want to go there! I worked with Vangelis several times in the 1980's, so I don't have to guess, hypothesise or assume what he did all day. Obviously there weren't soft-synths back then but yes, Vangelis (or people who worked for him) often designed their own patches, as some pros do today but the starting point was often another patch and where the starting point was just a basic signal, it was fairly rarely a square and it never exited the synth as square wave, it was always modulated, filtered and processed in some other way first. So again, no square waves.
In effect, that IS the "way everybody would do it"! How many people who create digital audio music do you know (or have even heard of), who do not use an ADC, DAC, DAW, Audio Editor or any other "digital device"? As you admit, a square wave is an illegal signal and a digital device would alter it.
You could in a sense call that "synthesizing" audio but that's NOT what a synthesizer actually is or does. A Synthesizer is a musical instrument, which requires at a minimum: Filters, envelope controls and audio oscillators! "This program" would essentially be a signal generator and would NOT be called a "synthesizer"!
Again, why the continuing obsession/nonsense with square waves?
Actually, acknowledged and agreed on the above, I didn't see anything I actually disagree with. (this must be a first on this forum... do I get a medal?) Actually not sure why we're stuck on square waves right now, but it traces back to the earlier post where a user was worried his headphones were damaged by listening to a digitally clipped audio track. We got into clipping, from there excessive harmonics, and then off to the races...
PS Good point on the fact that you only get some tens of harmonics at 44.1, in my head I was thinking of the additive synth Harmor which does (once all the filters and other effects get involved) output some hundreds of harmonics on a musically useful patch, but as you note, that's much more common than trying to use it as a signal generator. Just goes to show that in real life you rarely spend much time on raw basic signals like that.
PPS Jealous that you've got to work with Vangelis before, he's a total champ of the synth world. Bladerunner soundtrack 4 lyfe.
square waves, crossfeed, obscure LP cartridges that go to 30kHz, xeroxes from books with yellow highlighter, dynamic range measurements... these are a few of my least favorite things.
does this mean you're more into raindrops on roses and whiskers on kittens?
Err.... errata corrige ; cartridges that go (only) to 30 kHz are not obscure not at all; change the frequency to 50 kHz ... at least !
But, with that out of the way :
1. Hah! Liam Howlett is a genius so maybe that's why The Prodigy sounds like Mozart in comparison to some other technoheads?
2. All you have to do is to all-pass filter a "square-wave" to produce differing group delays to harmonics and the waveform doesn't look like square at all.
3. Wow. I'm more of a Tangerine Dream fan myself, but wow.
I'd love to see the measurements on a 50kHz signal from a cartridge reading an actual vinyl record. It's just not happening. Ever.