After writing about frequency domain analysis recently, I thought a brief example of the utility of this technique in a practical audio application would be useful. I digitized an approximately 10 second piece of acoustic guitar performance from a recording dubbed to a Type I cassette tape about 40 years ago from a quarter inch reel to reel tape recording. The source reel to reel recording was made on two tracks of a TEAC 2340 using high quality quarter inch tape and normal bias at 7.5 ips (and quarter track semi-pro  format, i.e., either two or four tracks, as desired, running in the same direction along the length of the quarter inch wide magnetic tape). You can hear the tape hiss noise on the old recording here (use headphones or turn up your volume loud or you may not hear the noise):

I used Audacity (the fantastic open source audio editor) to generate a frequency analysis of that recording:

That spike on the right side of the plot is at about 15 kHz (15000 Hz) and is at -60 dB. I suspect that this is a residual harmonic (subharmonic) of the reel to reel 150 kHz tape bias signal. In order to record in the linear area of magnetic tape it is common to combine a bias signal with the signal being recorded in order to assure there is sufficient magnetic flux to the tape. You can’t hear much over 20 kHz, so this is not a problem in playback; however, since we have a lot of tape hiss, which is higher frequencies, we want to reduce that frequency along with other higher frequencies. You could use a notch filter to target specifically the 15 kHz frequency, but because the tape hiss occupies a much larger range of frequencies, I decided to use a multi-band equalizer to roll off (decrease the level of) all the frequencies in the recording higher than approximately 3 kHz. I used the Equalization Effect in Audacity to decrease the levels of frequencies in the recording, decreasing them by a larger and larger factor as the frequency increased (you can see that I moved the attenuation sliders farther and farther down as the frequency they effected increased in the screen below). I did this because most of the legitimate sound content, that is, the recorded guitar sound, is lower frequency than the tape hiss, but I wanted to keep some of the brightness of the guitar while reducing the perception of the hiss noise. Here’s how I setup the equalizer:

After reducing those high frequencies by applying the above equalization settings, this is how the recording sounds:

You can see the effect of the equalization on the frequency analysis of the edited recording:

See how the 15 kHz noise spike is now about -79 dB? That is 19 dB lower than originally and you can see that all those frequencies higher than 3 kHz or so are now ramping down at a pretty good slope to a much lower level. That is why the edited recording has almost no tape hiss (yet the guitar still sounds almost as bright as it did originally). I should note that another reason eq’ing out the high frequencies a bit took the hissing noise down so well is that the cassette tape was apparently recorded (copied from the reel to reel) in Dolby (B) noise reduction mode on the cassette deck used (the cassette tape Dolby box was checked by the person making the recording, so I believe they did indeed use Dolby).

Magnetic tape has an inherent noise floor (a tape hiss) deriving from the magnetization of the ferrite particles on the tape emulsion even in the absence of a recorded signal, i.e., if you take a blank cassette tape and play it back at full volume, you will hear some hiss. Dolby noise reduction was developed in the 60’s to try to reduce that inherent magnetic tape noise. Basically, when you record a tape with Dolby noise reduction the high frequencies in the audio you are recording are boosted as they are transferred to the magnetic tape, the higher level (loudest) signals less, the lower level (quietist) signals more. When you play the tape back, you want to use the same Dolby noise reduction circuitry to reduce those boosted high frequencies by the same amounts to restore the original dynamic range i.e., reduce the higher level high frequency signals a little, the lower level high frequency signals a lot. Since the tape hiss comes from the playback tape at a constant low level (as a property of the magnetic tape itself rather than the recorded audio), it gets lowered a lot as it enters the Dolby circuit prior to the playback amplifier (since it is a low level high frequency signal) and drops by as much as 10 dB below the actual audio you recorded (since the low level high frequency audio you recorded was boosted when you recorded it). This reduces the level of tape hiss and its perception by the hearer significantly.

In our test case here, the cassette recording was apparently recorded with Dolby noise reduction, so the high frequencies were boosted. However, when I played them back, I did not have access to Dolby circuitry. When I cut the high frequencies (as I described earlier), I probably reduced the tape hiss a lot, but only reduced the guitar recording high frequencies back to their original levels (since they would have been previously boosted during the Dolby recording process years ago when the tape was dubbed from the reel to reel master). In effect, I manually created a Dolby noise reduction filter.

So, I think you can see some immediate applications for these kinds of techniques in audio recording and mixing. For example, if your acoustic guitar track sounds muddy, look at the frequency plot of the recording and see where the lower frequency levels are, then do some equalization in that area. As a matter of fact, before I began the noise reduction process on this test recording, I did reduce the frequency content below 400 Hz (using the Equalization Effect) in order to clarify the sound of the guitar (and compressed and amplified the track, which was recorded at too low a volume). There are some general rules of thumb for eq of common rock instruments, for example, bass guitar tracks muddy up a multi-track mix unless you eq out the general neighborhood of 250 Hz in the bass guitar track. You can, of course, skip the frequency analysis and go entirely by ear. In that case, just increase the slider levels on particular frequencies of your equalizer until the objectionable sound quality becomes even worse, and then lower those same frequency sliders on the equalizer to eq out the undesired frequencies for that track. Or, conversely, adjust the sliders on the equalizer for a particular track at different frequencies until the track punches through the surrounding mix or acquires the type of sound you are looking for.  It is helpful to loop a few seconds of the track (set it up to keep repeating automatically) while you are making this kind of analysis by ear, so you don’t have to keep restarting the track.  

I was talking to some colleagues about EQ, using equalization to make particular tracks on a multitrack recording stand out. In talking about EQ I mentioned the idea of viewing a sound wave as a frequency plot, so I thought it might be interesting (possibly more interesting to me than others, grin) to post an image of a D chord played on my acoustic guitar (click on the image above to see a larger version of that frequency analysis), which includes a wave plot of the actual variation in time of the strings as they vibrate and the other the transformation of that series in time to a spectrum plot, which is a way of looking at the event in a place without time, if you have time, grin.

This is a D chord played with open 5th and 4th, fret 2 3rd, fret 3 2nd, and fret 2 1rst (strings), actually the first chord I played on my recording of Window. Every make of guitar has more or less a unique spectral signature. You can see that the wave of the actual sound wave propagating through the air from the guitar (below the spectrum/Frequency Analysis) is approximately a sine wave with about 4.56 ms (0.00456 second) between each peak. This is about 220 Hz, or approximately the note A3. This was surprising to me, since I was playing a D chord (however, if you consider harmonic content there is additional A3 available as the second harmonic of the 5th string, so perhaps this accounts for the strength of A3 energy). You can see from the frequency analysis that this sound wave actually contains many different frequencies and this is normally the case in nature unless you have a pure sine wave, in which case all of the energy would be in exactly the frequency of that wave.

The vertical height of the purple peaks in the Frequency Analysis is the relative energy at each frequency, higher vertically on the graph equals stronger/louder, however, the labeling is from 0 dB downwards. The larger a negative number, the smaller the quantity, so, for example, -20 dB is larger than -37 dB. I’m not sure which type of dB they used here, probably voltage amplitude, in which case a frequency at amplitude – 20 dB is  approx. 7 times greater than another frequency amplitude at -37 dB) . I labeled the more important peaks.

You can see the open 5th string A2 note about 110 Hz at about -37 dB, the open 4th string D3 approx. 146.83 Hz at about -33 dB, and the 3rd string 2nd fret A3 note approx. 220 Hz very strong at around -20 dB (as we might expect, since the time varying wave is very close to a 220 Hz pure sine wave), and the 2nd string 3rd fret D4 note approx. 293 Hz -38 dB. The A4 440 Hz energy at around -37 dB could be primarily the second harmonic of the 2nd string 2nd fret A3 (the first harmonic is defined as the fundamental frequency of a vibrating string; the second harmonic is 2X that frequency, so 2 X A3 220 Hz = 440 Hz or an A4 note). The A4 note and all of the remaining energy on the frequency analysis are higher vibration multiples of the actual notes played (harmonics). The A4 energy at 440 Hz could include components of the fourth harmonic of the open 5th string 110 Hz, i.e., 4 X 110 Hz = 440 Hz also, but there should be less energy in higher order harmonics than lower so I would assume less of a contribution from the open 5th string fourth harmonic than the 3rd string 2nd fret A3 220 Hz second harmonic.

To actually characterize the timbre of a particular instrument, you can make successive frequency analyses at a number of times after a chord or note is played and then make a 3-d plot or wire frame of that, but I don’t have that capability at present. I note that the software I used to make the analysis here is open source, i.e., free (Audacity). I also use Audacity for producing mp3 files of wav file output from my multitrack recording software.

I-IV-V sincere-strum-soliloquy style songs don't touch me at all, except to the extent I appreciate the message in the lyrics. Perhaps musicians are often selecting what is comfortable and natural to perform, personally. In this case, the chords and rhythm are uncomplicated and the vocal is really relying on the tonal quality and phrasing of the singer (and the personal appeal of the singer perhaps) rather than a striking melody. Set, the set of expectations we bring to bear on a particular experience, is important also, e.g., I enjoy a Bentley-Thomas song, "You're the Only One," (a I-IV-V of this same genre basically) though I probably would not seek it out were it not for the personal connection (to the composer, Chas Thomas, with whom I recorded the song for the 2010 Out of Time album), as well as the interesting lyric device (reversing the person of the lyrical narrator) and the great studio production and instrumentation (grin). In psychology, set has been famously demonstrated in the case of subjects rating the telephone conversation of a person associated with an attractive picture as more intelligent and pleasant than the identical conversation with a remote party associated with a less attractive image. I don't intend to say this particular form of set is at work here; it is merely an accessible example of how expectations color perception, and music is a complex perception.

But, returning to the chord pattern of I-IV-V, the simple harmonic motion between I and IV (for example, G and C) is a common element in American gospel music, which is one of the fundamental bases from which American musical styles evolved. Insert the V chord and you seek the tonic (another way of referring to I) from a fourth below, and have the I-IV-V which is the primary progression of the 12 bar blues, most 50’s and 60’s rock and roll, and American folk and country. You can modify the way in which you use these three chords and obtain new expressions, e.g., I to V, then down to IV, then back to V before resolution. Chord progressions are simply harmonic routes leading the music towards or away from a particular tonic chord (the key center) that we can choose to traverse to suit our own artistic direction, with a particular style of music offering its template of chords within which to operate---or to depart from when a new style is created. "A song has a few rights, the same as other ordinary citizens. If it feels like walking along the left hand side of the street, passing the door of physiology or sitting on the curb, why not let it? If it feels like kicking over an ashcan, a poet's castle, or the prosodic law, will you stop it?" [A quote from American composer Charles Ives]

 So, as The Preacher claimed so long ago, is there nothing new under the sun and all that will be done has been done before? I don’t believe so. For travelling a well-known set of paths, chord progressions, we can create new sequences of notes dancing in, out and among these paths---the melody: Now there’s the crux of the biscuit (using Zappa’s inscrutable but oddly appropriate phrase) for me! A song using the I-IV-V chords can completely transcend the common routes and cause you to forget you have ever heard it before, for example, the great gospel song (there is a lesson here also, i.e., why do the gospel songs offered in recent years lack melodic soul---when the host culture lacks soul is it possible to express such a melody?), How Great Thou Art. If you place the song in the key of C, it begins with the I chord, C, but the melody immediately catches your attention by repeating a G note three times (“O Lord my”) and dropping to an E note (“God”), possibly because this represents kind of a reverse arpeggio on the triad of which the C chord is composed (C note + E note + G note is the normal ordering of a C chord). …and so on, the melody of this song just moving me, making me actually feel the awesome wonder spoken of by the lyrics from the first time I heard it in a Baptist church a half century ago.

I don’t think about music theory when I’m listening to a song (I’m referring to the musical composition rather than the lyrical composition here, though the two are related ideally, the music of the composition helping others to get to the same place we are in the story we are telling, the poem we are expressing, with the lyrics) and I normally rely on intuition when I’m writing a song. A portion of a chord progression or melody might come to me on its own (from my muse, or Moose as we jokingly referenced, grin) and only afterwards might I consider music theory in order to pursue elaboration of this core (if the Moose is stingy at that point). I’ve found you can kick the Moose in the ass by running through music theory scales or chord progressions and letting Him (His Mooseness) tell you what has potential (by what you feel intuitively on hearing those, often in the context of the lyrics mood). Chas and I used that technique in composing many of the songs on the Out of Time and Just One More Time albums (after Chas complained about our use of I-IV-VII on a couple of songs, e.g., Shattered Apple Pie, Blind Man’s Vision---he feared falling into that formulaic chording pattern…though John Cougar, among others, made a career out it).

A good melody is what draws me in…and to some degree the judgment of what is a good melody is a matter of personal experience, i.e., what makes the particular listener feel something notable.