Welcome to: Tutorials page - mix with mathematical equalization

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About...

This tutorial is for the last equalization proccese to be taken befor "compleating" the mix, this mixing technique should be last in the chaine, that means - after effects, after normalization and dithering and after proper compression.
This is NOT mastering.

In this tutorial I will explain mathematical mixing technique. 5 parts will guid you in a step-by-step process with image examples of each step taken.

The parts are:

Part 1: Finding and definding the frequencies of the main instrument of the entire mix. - in this tutorial we will tread vocal track as main instrument.
Part 2: Finding the frequencies of the other instruments of the mix by using n-root formula based on the main instrument.
Part 3: Adding the values from the formula to the equalizers. - the whole data values will be added e.g. frequency values (hz), gain values (db), 'Q' thickness values (octaves width), low-cuts/high-cuts.
Part 4: Getting the instruments match harmonicaly and acousticaly to each other in the mix.
Part 5: Finalizing the mix.

[ ATTENTION !!! ]
This tutorial is not yet completed !
Offline version in .pdf format also available. [soon!]

The formula:

[Do not afraid of the looks of this formula!]

y = serial number of the instrument in the mix range (1... 2... 3... etc.)
b = start frequency
a = end frequency
x = total number of instruments in the mix or calculated part
F = frequency

Part 1:

Finding and definding the frequencies of the main instrument of the entire mix - This instrument should be defined basing on the instrument importance - in this tutorial we will tread vocal track as the main instrument.

Let's say our mix frequency range going to be from 30 Hz to 16000 Hz - based on human hearing abilities. We are going to calculate mix with the following instruments:

Vocal track - (Main instrument of the mix)
Guitar track
Piano track
Bongo track
Crash hits track - (played accasionaly)

We need to create a graph similar to the one bellow:

In the graph we choose 2 frequencies (based on main instrument of your choise, usualy vocals or bass): low-mid and hi-mid. The frequencies can be declared without any measurements, however the 440 hz (the middle C) and 3000 hz frequencies are the "easiest" on the human ear, so i chouse to use them for the vocal track. The placement of the frequencies should divide the graph into 3 main parts (in our case): 30-440 hz, 440-3000 hz, 3000-16000 hz as it apeares at the picture bellow.

Part 2:

Finding the frequencies of the other instruments of the mix by using n-root formula based on the main instrument.

Now we are going to decide and state the other instrument placement on the graph (for visual reference only). The placement is based on high/low instrument frequencies, e.g. bongos are bassy, so theire place should be closer as possable to the left side of the graph part. The 30 hz and 16000 hz frequencies are already exist - so we will asign some instruments for them. I chouse the bongos for the 30 hz and the vocals for 16000 hz.

Here comes the math part:

Now we need to find the frequencies of the rest of the instruments (that marked with the red mark on the picture above). Inserting data into the formula.

Calculating the 1-st part of the graph:
Range: 30 hz - 440 hz
Frequncies to find: Gutar1, Piano1.

y=(1 for Gutar1 and 2 for Piano1) = serial number of the instrument in the mix range (1... 2... 3... etc.)
b=(30 hz) = start frequency
a=(440 hz) = end frequency
x=(2) = total number of instruments in the mix or calculated part
F=(the answare) = frequency (hz)

Gutar1

The frequency of Guitar1 is 58.70 hz.

Piano1

The frequency of Piano1 is 224.83 hz.

After we get the results of the frequencies of the 1-st part - we can now insert them into the graph.

Calculating the 2-nd part of the graph:
Range: 440 hz - 3000 hz
Frequncies to find: Bongo2, Gutar2, Piano2.

y=(1 for Bongo2, 2 for Gutar2 and 3 for Piano2) = serial number of the instrument in the mix range (1... 2... 3... etc.)
b=(440 hz) = start frequency
a=(3000 hz) = end frequency
x=(3) = total number of instruments in the mix or calculated part
F=(the answare) = frequency (hz)

Bongo2

The frequency of Bongo2 is 605.89 hz.

Guitar2

The frequency of Guitar2 is 1148.91 hz.

Piano2

The frequency of Piano2 is 2178.59 hz.

After we get the results of the frequencies of the 2-nd part - we can now insert them into the graph too.

Calculating the 3-rd (and the last) part of the graph:
Range: 3000 hz - 16000 hz
Frequncies to find: Bongo3, Gutar3, Piano3.

y=(1 for Bongo3, 2 for Gutar3 and 3 for Piano3) = serial number of the instrument in the mix range (1... 2... 3... etc.)
b=(3000 hz) = start frequency
a=(16000 hz) = end frequency
x=(3) = total number of instruments in the mix or calculated part
F=(the answare) = frequency (hz)

Bongo3

The frequency of Bongo3 is 3965.40 hz.

Guitar3

The frequency of Guitar3 is 6928.20 hz.

Piano3

The frequency of Piano3 is 12104.68 hz.

After we get the results of the frequencies of the 3-rd part - we can now add them and complete the graph.

Part 3:

Adding the values from the formula to the equalizers - the whole data values will be added e.g. frequency values (hz), gain values (db), "Q" thickness values (octaves width), low-cuts/high-cuts.

Equaizer: The equalizer shoud be used as "insert" (not send). It is impossable to use parametric equalizer for this kind of mixing technique because of specificated amounts of values. It is also recomended to use equalizer with as much as possible bands for achiving the results in faster and more eficient way - one track can have at least 9 values to be entered into and not all hosts/sequencers are capable of this amound of "insert" slots in case of small portion of bands per EQ plug-in.
Gain: The ±3db of gain is not affecting the entire sound, but colorises it with a specified frequencies.
Q: the "Q" should be wider at the low spectrum and thinner at the high, this is due to thicknesses of the high spectrum's frequencies.

This is typical graphic equalzer, the one in the picture is a native equalizer from CubaseLE with settings of the "vocal" track from this tutorial.

This tutorial will be using Electri-Q [posihfopit edition] to demonstrate the technique.

Due to desent amount of information to be proccesed during the creation of this tutorial - the final 2 parts will come in smaller portions for now.