Digital Mixing & Mastering Tutorial Series : Elementary Concepts of Sound

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Digital Mixing & Mastering Series:
Part 1
"Elementary Concepts of Sound"

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"Elementary Concepts of Sound"

Sound is the tangible manifestation of one of the most universal phenomenon, second only to the existence of Space itself, sound in it's most general form is simply a vibration travelling through a medium. In physical terms, that is 'compressions' and 'expansions' of the density of the atoms & molecules of matter it is travelling through, in our case the medium is air. Other factors such as temperature, wind, etc. effect how that vibration will travel, but won't be covered in the scope of these articles and we'll assume fairly normal conditions.

Naturally, knowing sound is a vibration, the question that arises, is "what is a vibration?" Simply stated, a vibration is a "periodically repeated disturbance or stimulation," the important part is 'periodically.' What the 'disturbance' means simply is some type of change in some sort of medium in space (virtual or physical) is occuring and that it's happening at some certain periodic rate. What the particular changing is is of little importance, as it could be anything generally. A periodic rate is measured in Hertz (Hz,) and is simply a normalized value of "how many times something happens in at unit of time," being normalized the unit of time used is typically 1 second, and translates into "how many times something repeats in 1 second of time."

Every note on every instrument is at it's own specific frequency, and is also known as the 'tone' or 'pitch' of a sound in musical terms. The audible range of frequencies the human ear can percieve ranges from roughly 20Hz (wave-forms repeated 20 times a second,) upto around 21,000Hz (twenty-one thousand repetitions a second.) Below 20Hz percieved sound will have the typical percussion/rhymic sound to it, and over 21,000Hz will be inaudible to the human ear. There is one trick for playing tones lower than 20Hz on modern speakers called 'binaural beat rhythms,' which I will go over in the last article.

Each note continuously differs from the next starting by roughly (but not exactly) 1.0Hz in the lower frequencies, continually growing in difference into the higher frequencies (upto around 400-500Hz difference between adjacent tones in the highest-end) on the Western musical scale of 12 subdivisons (notes) per octave (the first perfect-harmonic of the root note.) The reasoning for 12 notes most simply is that it is roughly the difference in pitch the human ear is capable of detecting. The 'standard' note C3 (C note of the 3rd octave,) has a frequency of roughly 130.8Hz (wave-from repetitions per second,) and C4 a frequency of 261.5Hz, and C5 of 523.3Hz, just to give you a basis for comparison.


[edit:] I made an image quickly (please excuse the crudeness) to give some visualization of this difference in pitch. The reason is, the faster something is changing, the less detectable/absolute to the human senses it will be (move your hand in-front of your-face, it will have the same general appearance, but distortion and 'stretched-out' over space in a blur.) For example, when you see the hubcaps of vehicles passing on the high-way at a highspeed they often appear to be standing still or almost moving in slow motion...the same is true of the human sense of hearing (ie: higher pitches will have a similar 'appearance' as previous harmonic equivilents of themselves each increase of octave.) On a side note, music is perhaps one of the best examples that mathematics is the most primary and fundamental of all the energy sciences (and reality itself, as Pythagoras would argue.)

Vibrations also have another property, called "phase." Playing acoustically this concept can almost be ignored in the sense that we'll be with it dealing with in mastering, but is very significant to working with sound on a digital medium. The phase of the vibration means which state of the cycle is currently. Being a repeated pattern, the vibration continually jumps between two polar-opposite states, or 'positive' and 'negative' states, much like the Yin and the Yang. Physically this translates to if the travelling vibration is compressing or expanding the medium (air) it is travelling through.This means any vibration at the same frequency must also have an anti-frequency at the same frequency, and also that any vibration can be at any state of phase in-between the two polar opposites as they change from one into the other periodically. Digitally the phase of any frequency is measured between a normalized value of -1.0 and 1.0, (scaled: +/-1.0 translates into the maximum magnitude of volume a file can store and/or max volume a speakers can emit.)

Phase can also been seen on speakers. When the speaker expands outwards from the diaphragm it compresses (increases the density) of the air in front of it with a magitude directing it to travel outwards, and when it returns back into the diagragam it expands (lowers) the density of air in front of it. In the process of continuous expansions and compressions, there is a space in-between the peaks of the two where they interact equally and sum up to Zero, creating a continuous smooth 'zig-zag' between compressed, undisturbed, and expanded air through space over time. The same can be observed on a guitar. Silent, a string is in a Neutral position. To make a sound it is plucked in one direction and when released travels in the opposite direction and back again continuously until it decays. For a brief moment in time the string will be in the Neutral, "silent," position transversing between the two directions. This also underlines an important fact, that sound and motion are equivilent...to be sound: there must be motion. The same with life, eveolution and reality itself.( ie: sound represents motion, amongst other things.) Wholistically this can be visualized as a continuous repeating sine-wave travelling through space.

Considering a single vibration alone, phase can essentially be ignored. Phase is imporant in how different vibrations travelling through space of all frequencies interact with one another. If vibrations of the same frequency meet at the same location in space (virtual or real,) and their phases are completely opposite of one another, they will 'destructively' interact...meaning when they meet they will obliterate and destroy one another. Acoustically this means no sound will be heard, electronically this means the vibrations (sounds) will be completely absent from the rendered audio file. In other cases, if two vibrations came together in the same space and of the same phase the corresponding magnitude of the volume or amount of compression/expansion of that medium will be doubled, or the sum of the two frequencies magnitudes.

[edit:] The first row shows an interaction between two in-phase waveforms of the same magnitude interacting to double their magnitude. In the second row, another waveform of the same magnitude of the first, except completely out-of-phase, interacts with the original to sum up to Zero (silence):

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This phenomenon is very important to mastering and mixing, and should always be kept in mind while in the process of doing such. It can destroy the mix, or it can make it amazing. If you're lucky enough all the components and elements in your song will fit together nicely, and you'll have little work to do in this part. But more often than not they do not. Sometimes it's hard to hear, almost subliminal, but something about how the final mixdown sounds compared to how each element sounds on its own just doesn't quite sound right. This is one of the biggest parts of the art of mastering. Eventually an intuitive sense of sound can be developed and you'll be able to quickly know what part of the sound needs a boost, cut or any other type of prcoessing.

Another way frequencies can interact I didn't mention above is the case of two vibrations of the same frequency interacting at states other than of the same magnitude, and being completely in- or out-of-phase (ie: not either exactly in-phase or 100% out-of-phase.) When the other cases interact, depending on their state relative to one another, they'll interact in different, sometimes undesireable ways. Two of the same frequencies with magnitudes in the opposite phase will interact with one deminishing the others magnitude (volume,) and is generally undesireable. When they are in phase of the same magnitudes (both + or both -,) the magnitude will be increased (louder,) and is not always desireable, as it can lead to clipping or unwanted flucuations in the mix. When the wave-forms are out-of-phase other than 100% in- or out-of-phase, a more complex interaction of both incrementing and diminishing of magnitude will occur.
[edit: see images below]
When the sound is very artifacted or distorted this is typically called 'interference' or 'distortion' in digital mediums, and is usually unwanted unless used as a specfic effect. In the end it's all about a fine tuned balance between both boosting frequecies and cutting them, and making them interact with each other nicely. That's not quite everything, compression is another fundamental concept and tool vital to a great mix, but I'll be covering that in another article.

[edit:] The first image below shows interactions between wave-forms that are in-phase but of different magnitudes, interacting. They are also of the same frequency. In the row below it is the same, except the inter-acting wave is completely (100%) out-of phase

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This images shows a more-complex interaction between a wave-form in-phase and another 1/4 out-of phase to it, both the same frequency and magnitude. There is a near-infinite possible ways wave-forms can interact, so there's no exact science behind it (other than arithmetic)..what sounds good, is what goes:

{IMG}

The other cases I did not go over in vibration interaction is of different frequencies. This is known as 'harmony' and is not so much in the scope of this article. It is however something that is important to know when mastering through. Generally you never want to boost anything of the same frequency more than once in the same mix, and quite often you may want to cut the same frequency of another instrument as an alternative to boosting that instrument. Alot of mastering and mixing is about space management: there is a finite amount of space for all of these vibrations/sounds to fit within, and you must make sure there is enough space for them all, and they don't get crowded and mashed together too much. And generally you want to boost/cut in accordance to the tuning of the song...ie: boost/cut at frequencies harmonics relative the key/tuning of the song. You also want to spread a sound out nicely over the spectrum. Each element should be clearly audible in each the bass, mid and high ranges (wherever applicable,) clearly and undistorted.

For example, it's a good idea to boost a bass kick in the very-low end bass to really add alot of 'whack' that can be felt physically, but also up in the mid-ranges so it can still be audibly heard clearly, especially for small speakers that can't play lower-end frequencies, which would emit the kick as almost-inaudible if it were not also boosted in the mid-ranges. It's also better practice of instead of blunty increasing the volume of an element in the mix, to rather boost certain frequencies of that element instead in the areas it lacks. Using the scalpel instead of the hammer.

The last concept and property of a vibration, which I'v already mentioned, is the "magnitude" or "volume," in audio terms. This is the most obvious and well-known of all the properties of sound, so I won't go over it too much. Each sound/vibration in addition to being a frequency, is at a certain phase, and is also at a certain magnitude/volume at any instance of time of it's existence. Every element/instrument emits vibrations. The note that is being playing is typically the main and loudest (of greatest magnitude)emitted. In addition to the root note being played, an instrument will usually emit a series of peaks of harmonics of that root across the entire spectrum of possible frequencies, and sometimes frequencies out-of-harmony with the root. All-in-all an instrument can be seen as a collection of emitted vibrations, that often can change over time (where 'mixing'comes in.)

Below is an image with labels pointing out each of these concepts and how they appear in a typical audio analyzer. It shows both the left and right channels, where the labels appear does not matter, as the concepts apply to both the left and right channels. The frequency can be seen as patterns repeating over time:

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What you can't see unless you zoom-in is that each point is at only one point on the vertical (magnitude & phase) axis direction per each point on the horizontal (time) axis. When zoomed in the distinction between phase of a wave-form can be seen clearly and how it can only be either Positive or Negative (but not both,) or Zero at each frequency at any particular point in time. The volume (distance the bar extends from the centre-line) specifies "how positive" or "how negative" a vibration is:

{IMG}

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In summary:

Each element or instrument in your song is a collection of vibration emitters. Each of these vibrations emitted is at a certain frequency, and usually has one predominate "root" frequency, as well as a series of harmonics (unless you're using a pure tone or tuning fork,) each of yhese frequencies will also have a dualistic-state known as "phase," and the maximum reached peak in either domain (positive, negative,) direction's value is known as the "magnitude" or "volume," and essentially describes how much energy the vibration has.

From this perspective, the process of "Mastering" is a static one. It is editing and analyzing individual "vertical slices" or "depth" of the sound, over the frequency spectrum. It is making each element at any instance of time fit together nicely...carving and polishing each element, and making them all fit nicely together over the frequency spectrum over time. And then "Mixing" is the more dynamic process. How each element will relate to each other dynamically at any instance of time and how it will change over time in relation to one another and to itself (ie: such as which element will predominate and which will take the background, vice-versa, or which frequency range...high/mid/low the element will predominate in or shift towards, etc.). Each requires both element be considered in relation to itself and all of its properties, and how each element will relate to every other element and their properties, and how they will interact.

Not covered in this article is alot. Compression/Expansion, EQ, Reverb, Delay, Panning&Dynamics, Stereo-Imaging, Mixing and to to a lesser degree Chorus, Flanger and Distortion and many other concepts and tools are covered with practical guides to their use, and philsophical &physical analysis of them, will be covered in future follow-up articles to this one. That's all for now, good-night and have a good tommorrow.
-Scott Rennie

Follow-up Articles:

http://www.spaceandmotion.com/mathematical-physics/logic-truth-reality.htm

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