Monday, September 17, 2012

The Science of Music -- Part Five

Previously we learned two very important concepts which we will now combine into a useful overall idea that is key to all music reproduction and recording. Regardless of whether we used vacuum tubes or transistors or integrated circuits to amplify, this idea is important for everything from stereo amplifiers to public address systems to guitar amplifiers (plus a whole lot more including radio and television receivers, radar, and even digital photography). It is also important to all kinds of recording from phonograph records to wire to tape to digital recording -- of both audio and video signals. Why it is even important in astronomy and physics.

We will combine the idea of electronic “filtering,” the selective attenuation or amplification of discrete frequencies, allowing us to separate an electronic signal into frequency bands of low, middle, and high, and even select in or out very specific bands of frequencies as small as 1/3 or an octave and even smaller.

This idea of filtering will be applied to our knowledge that all complex tones, and therefore, all music, is made up of combinations of individual sine waves which have a specific amplitude and frequency (and phase). These ideas, combined with how the ear and the mind “hears” speech and music (something called psycho-acoustic effects), will be used to mold and shape the tones to match our musical preferences and to compensate for the limits and characteristics of all the devices in the amplifying and recording chain, including everything from microphone to amplifier to speaker and all the other devices in-between including the recording media and electronics.

This is an exciting journey and now that we’re past the flatlands of Kansas and see the mountains of Colorado ahead, it will be a most interesting journey. So lean back and enjoy the scenery. Your friendly tour guide, (that’s me), will discuss some of the points of interest along the way as we dive deep into filters. Here comes the low-pass, the high-pass (high passes is what Colorado is famous for), as well as band-pass, band-elimination, and multi-band equalizers. Look over there! That’s the RIAA record equalization. Isn’t it beautiful.

I’m sure you all recall that the range of human hearing is 20 Hz to 20 kHz. You also remember that audio amplifiers usually match that frequency response range since there is no reason to amplify frequencies above the range of human hearing, and little reason to amplify the frequencies below that range, although, just to be on the safe side, some very high quality audio amplifiers have a relatively flat frequency response from 10 Hz or a little lower up to 30 or 40 kHz. That’s just to make sure no good frequency is “attenuated.”

Oh, “attenuated,” that’s a new word, and it’s one we’ll need to talk about filters. Just as a  coffee filter “filters out” the course coffee grounds by blocking them in the paper, electronic filters “filter out” frequencies we don’t want to pass by attenuating them. Wordnetweb at Princeton University defines attenuation as the weakening in force or intensity; for example, "attenuation in the volume of the sound."

Filters can also also amplify and some fancy electronic filters do include transistors and other amplification devices, but most filters just reduce the intensity or amplitude of frequencies you wish to reject from the overall signal -- and that reduction is called "attenuation."

Old fashioned tone controls which we’ve all used our entire lives are just filters. The bass control can turn down (or up) the lower tones by filtering. Treble tone control is the same except it affects the higher frequencies. A multi-band equalizer is just a very fancy tone control that lets you adjust the frequency response of your amplifier by octave or even one-third of an octave. We used these kinds of equalizing filters to fine tune the frequency response of the sound system at church to eliminate certain resonances and lift up some flat spots that are caused by combinations of the room design and the speaker inequalities. Careful equalization of the sound system's frequency response will eliminate feedback and squeals and make the sound easy to hear and understand.

Most filters are made up of Capacitors and Inductors (coils) which are called passive components since they don’t amplify like transistors or tubes (which are called active components). The most basic passive component is a Resistor. It adds resistance to the flow of an electrical current. Resistors, within limits, are not effected by frequency; they respond the same to all frequencies. Capacitors, on the other hand, also have a resistance to current flow, but the resistance decreases as frequency goes up. Capacitors completely block DC which is considered 0 Hz. Inductors are the opposite, their resistance goes up with frequency. So you can combine capacitors (called “C”) with Inductors (called “L” because “I” was already taken by current -- well, that's because “C” was already taken by ...) and Resistors (thankfully called “R”) to make a filter that responds to different frequencies.

(Technically, the resistance that Capacitors and Inductors have to various frequencies is called Reactance, with the symbol "X" since "R" was taken. Further, if you add "X" + "R" you get Impedance which is "Z." Now you know why you have to study this double "E" stuff for so many years. By the way, transistors are often denoted by "Q" since tubes typically were called "U" since "T" was taken for Transformers and V = Volts and ... never mind!)

Simple filters just have a couple of components, while complicated filters can have dozens of components. Some electronics engineers spend their entire careers doing nothing but designing filters. It is a rich area of engineering. By the way, once a signal is digitized, it can be filtered by software without the use of any L or C or R. That is how modern digital editors such as Pro Tools works. But, as usual, I digress.

We describe filters by the effect they have on frequency. A low-pass filter let’s low frequencies “pass through” but it blocks or attenuates high frequencies. Here’s the frequency response curve.

Frequency Response of a Low-Pass Filter with 6 db per octave or 20 db per decade slope or attenuation

High-pass filters block the lows and let the high frequencies pass.

High-pass Filter

You can combine these two filters together and get a band-pass filter which only passes the frequencies within a certain range to pass. That would be the frequencies between the filter cut-off points. There are also band-stop or band-elimination or band-cut -- they all mean the same --  filters which block a small band of frequencies. Most audio amplifiers contain band-pass filters with cut-off frequencies of 20 Hz at the low end and 20 kHz at the high end.

Low-pass, high-pass, band-pass (combined low- and high-pass), and band-cut or "notch" filters.

All of these filters have their use in audio equipment. You can control (or attenuate) the bass tones with a high-pass filter. Conversely you can control treble with a low-pass filter. Fancy, multi-band equalizers are just a bunch of band-pass / band-cut filters. We sometimes call these multi-band equalizers "graphic-equalizers." Note how the controls are designed to represent the frequency response curve controlled by the individual settings.

Graphic equalizers come in octave band controls which typically is 10 or 12 individual controls, duplicated for the left and right channels. One-third octave graphic equalizers have 30 controls per channel most often. I don't know if you need a graphic equalizer on your stereo system, but they are essential in a good sound system to balance out the amplification to match the room acoustics. They're also useful during recording sessions, but mostly it is the software implementation that is used in a recording studio. Equalization is part of most DAW or Digital Audio Workstations.

Multi-band Equalizer

There are also special band-cut filters called “notch” filters that attenuate or "knock out" a very narrow band. For example, one source of noise in music is the 60 cycle hum that can come from the 110 v power source. One way to reduce the hum is to have a very narrow bandwidth filter called a notch set to 60 Hz. (In Europe it would be set to 50 Hz. Do you know why?) Although you may lose a bit of the musical content that is at 60 Hz, it may be worth it to eliminate the annoying hum.

Very low frequencies may also be filtered out by a "rumble filter" which is designed to remove the sounds added by the turntable rotation and motor noise that is coupled through the turntable needle. High quality turntables take great care to remove these mechanical noises through belt drives to reduce the coupling of motor noise and balanced turntables so they turn smoothly.

I said that most filters cut or attenuate, yet equalizers seem to both boost and cut frequency ranges. How is that done? Well, you could amplify all frequencies a certain amount and then set all the band filters to mid-range attenuation. If you adjust for more attenuation, then the level drops, and if you adjust for less attenuation, that seems to be boost. Or, of course, you can combine a filter with an amplifier. It doesn’t make any difference.

By the way, the frequency at which a filter starts to work is called the “cut-off” frequency and it is described as the frequency which the signal is cut by 3 db (which is half power). In a low-pass filter, the 3 db point marks the frequency which the cut starts and all frequencies above that point are attenuated. The curve has a “slope,” and the slope is often measured in decibels of reduction per octave or per decade (times ten).

In addition, some filters are not adjustable, and are used to provide some condition required for engineering reasons. A good example is the RIAA equalization used by phonograph records, also called the "Gramophone." I want to get into more detail about recording, but that will have to wait. For now I’ll just make the simple (and true) statement that the groove in a record is just a representation -- a “picture” if you will -- of the music total waveform. The phonograph needle tracks the “wiggles” in the groove and produces an electrical signal that duplicates the original sound wave.

But, there are problems. First, as we said, the human ear is not very sensitive to bass, so -- frankly -- the bass is recorded LOUD. But that can be a problem. As manufacturers developed modern, LP (for Long Play), 33-1/3 and 45 rpm records, they moved the grooves closer together than they were on 78 rpm records to obtain the longer playing time. But, then the wide excursion or “wiggling” caused by the bass notes made one groove bump into the next groove.

The solution was really quite simple. Reduce the amplitude of the bass frequencies before they are "cut" onto the record. Then have the record player amplifier boost the bass tones back to their original level. That is called equalization. The trick was that all the record companies and all the record player manufacturers had to make all the filters work the same. As I mentioned earlier, that is measured by the cut-off frequency and the slope of the filter curve in db/octave.

So, the Record Industry Association of America or RIAA defined the required bass reduction and labeled it "RIAA Equalization." All the record producers and record player manufactures follow that equalization specification and the net result is that bass is reduced before recording on the record disk to allow grooves to be close together, then the bass frequency levels are restored in the amplifier by equalization.

While the RIAA was at it, they were also able to address another problem called “noise.” Recall that noise is any signal we don’t want. One very common noise in electronic amplifiers is “hiss” which is a high frequency noise. One source of “hiss” is the tiny irregularities in the record groove from manufacturing and also from dust that has settled in the grooves. No matter how smooth the cutting is, there will be tiny imperfections and that will produce noise in the record player output. In addition, these imperfections, dust, and even scratches can cause all kinds of unwanted noise including pops and ticks. All these problems are made up of mostly high frequencies, so a pre-emphasis of highs before recording allows a de-emphasis in playback, thereby reducing most of these sonic artifacts.

The idea is to boost the high frequencies before recording them on the record. This is called "per-emphasis." Then the record player can reduce these high frequencies, and that will restore the music to its normal level, but it will reduce the noise frequencies caused by the record groove irregularities. It is a simple thing to do, and so the RIAA also added treble boost to the RIAA equalization spec. Here is an example of the frequency response of a modern record player to compensate for the bass reduction and treble boost during recording. The equipment that made the record had an equalization curve exactly the opposite, it reduced bass and boosted the treble.

RIAA Equalization Curve

A lot of very modern audio amplifiers do not have this required RIAA equalization circuit because not many people play records any more in this age of tape and CDs. This equalization was applied to an amplifier input usually labeled "phono." These modern amps often don't have a "phono" input.

If you have a turntable, you will need an amplifier with a phono input which includes the RIAA equalization. Or, you can purchase a preamp that has the required equalization. In addition, the output from the needle or phono cartridge on the turntable is very low level, so you need additional amplification and it needs to be high quality, low noise amplification. Some modern turntables have the required amplification and equalization built into the turntable base and provide a high level, properly equalized output that can be connected to you amplifier "tape in" or other inputs. I have an old Dynaco preamp I built back in the 60's that I use with my turntables, and it is still working pretty well even after 50 years of use. I wish I could say the same about my knees!

The RIAA equalization curve has been in use since 1954. Before that there were many standards that did the basically the same thing. It wasn't a new idea. Even 78 rpm records had equalization similar to the RIAA standard, but they had a little different cut-off frequency or a little different filter slope. It doesn’t matter much, but serious high fidelity enthusiasts that play those old records from the 30’s and 40’s use amplifiers with adjustable equalization so they can compensate and that bunch knows what values to use for Columbia or Decca or Victor recordings since each recording company used slightly different equalization. So RIAA wasn't really new, it was just a standardized specification to make the process simpler.

Other organization, such as the National Association of Broadcasters or NAB were also involved in setting record standards. Remember, most radio broadcasts in the 40's and 50's were put on records for distribution to individual radio stations and overseas to the military. If you're a fan of "old time radio," you've been listening to "transcriptions" or recording that were on large records. Tape recorders didn't become popular until well after the end of World War Two.

All record companies and audio equipment manufacturers now follow the 1954 standard. Foreign companies had some variation, but it was small. Since the 70's everyone, world-wide, has used the RIAA standard. You might want to adjust your system for older English or Japanese records. I know some of you out there are collecting those foreign disks. If you want to learn more, then here's some more: check out this website.

By the by, similar equalization to control amplitude and minimize noise are in use in everything from FM broadcast to video cameras and even in Photoshop (Unsharp filter anyone?)

So, there you have it. A brief course in electronics from R to L to C and beyond from Richard Lee Cheatham -- that's me. We’ve cut-off db’s and octaves and boosted our trebles through pre-emphasis. If you are interested, dig deeper. A few Google searches and a few hours spend on Wikipedia and you’ll know all about Reactance and Impedance or Zobel, Chebyshev, Butterworth, and Elliptic filters, and pi and tee designs. Why you’ll even learn about acoustic filters using crystals. Next thing you know you’ll be reading about Hammond spring reverb units, and you’ll be writing your own “Music of Science” or something like that. I look forward to reading it.

Originally written on Feb. 19, 2012 during a visit to my Dad's home in Hillsboro, Oregon and posted on Facebook. During my two week visit with my dad, I wrote an article a day. I started with a long series on the Science of Photography which had thirteen individual articles. I then started this series on the Science of Music. It isn't finished and I have a lot more to say. I hope to add to this series in the future.

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