Numeracy
Technical numeracy is probably not the most exciting thing to learn about, but it is very important that you have a good understanding of what units are used to measure various features of a sound. It is also essential that you can display and interpret data about sound in a graphical form and make calculations about sound.
Contents
Specification 👇
Component 3 Specification
Component 4 Specification
Graphs
Waveform Graph
This graph is a visual depiction of a sound wave. Sound waves propagate through the compression and rarefaction of molecules in the air or material. The compression part of the wave is drawn above the zero-crossing line and the rarefaction part is drawn below the line.
The height of the wave, from the zero-crossing line to the peak or trough, represents the amplitude of the sound. It is measured in decibels (dB) and it determines the volume of the sound.
The pitch of the sound is determined by the length of the cycle of the wave. The cycle is measured in hertz (Hz) and this refers to how many cycles are completed in a second. The more cycles, the higher the pitch.
The wavelength measures the distance between the peak or trough of one wave to the next peak or trough.
The zero-crossing line is the line that goes through the centre of this graph and it represents the times at which the molecules in the air are neutral and there is no sound. The nodes are the points at which the sound wave intercepts with the zero-crossing line.
EQ Curves
This is an EQ or equalisation graph. All the information you need to know about EQ can be found on this page here, but to summarise, this graph depicts the filters and parameters that you can apply to a sound to alter its tonal qualities.
The blue filters are shelf filters; they can boost or attenuate frequencies at the low or high end of the frequency spectrum.
The red filter is a bell/notch filter and it can be used to boost or attenuate frequencies at any point along the frequency spectrum.
The green filter is a cut/pass filter. It can be used to cut frequencies at either the low or high end of the frequency spectrum.
Compressor Graph
Again, all the information you need to know about compression is on this page here on dynamic processing. This graph represents the amount of compression that is being applied to a signal and when.
ADSR
This graph is a visual depiction of an amplitude envelope. Amplitude envelopes like this one are used to change the amplitude of a sound at different points; when the sound is started, when the key is released or instrument isn’t playing any more and when the sound stops.
More information on ADSR can be found here on this page about synthesis.
Polar patterns
Polar response pattern graphs are 2D depictions of the 3D pickup area of a microphone. 0º is the front of the microphone, 180º is the rear of the microphone and 90º and 270º represent the sides of the microphone. The circles show that the sensitivity or responsiveness of the microphone decreases the further away you are.
It is also important to know how the quality of the captured sound changes, depending on where in the polar pattern the sound source is. The closer you are to the microphone, the more low frequencies are captured. This is known as the proximity effect. Therefore, the closer to the edge of the polar pattern radius you are, the less low frequencies will be captured, and it is likely that the signal will sound thinner.
More information on polar patterns can be found on this page on the capture of sound.
Frequency Curves
Frequency curve graphs display information on the frequency response of microphones. Much like an EQ graph, frequency (Hz) is on the X-axis and volume (dB) is on the Y-axis. “The Y-axis frequency curves are also measured in both a positive and negative direction."
As shown on the graph below, the SM57’s ability to pick up frequencies varies along the frequency spectrum; it is not even. The microphone cannot pick up any sounds below 50Hz, but has a boosted response between 1KHz and 6KHz. This is generally the range of frequencies at which vocals sit, which is why the SM57 is quite often used for capturing vocals.
Numeracy
Units of Measure
Everything you need to know in terms of units of measure is detailed in the table below.
Binary
One of the requirements of A Level Music Technology is that you understand what binary is and how to calculate it. Binary is what all computers use to process information, meaning that as computers have become more heavily used in music production, audio has had to be ‘binary’ compatible.
This is where converting analogue signals (sound waves) into digital signals (binary), sample rate and bit depth come in, but that won’t be explained here as this concept is explained in better detail on this page about sampling.
MIDI also works using binary. More information on MIDI and binary can be found on this page about sequencing.
Logarithms
It is also important to have an knowledge of logarithms and be able to understand that frequency and decibels use a logarithmic system, rather than a linear system.
An example of how frequency works on a logarithmic scale is calculating the frequency of the note an octave above of below a note. For instance, A4 has a frequency of 440 Hz. To calculate what the frequency of the note an octave above is, you must double the original frequency. This means that A5 has a frequency of 880 Hz. This is a difference of 440 Hz. Using this same principle, A6 must have a frequency of 1760Hz (880 Hz x 2). This is a difference of 880 Hz. With every octave increase, the gap between the frequencies increases. If you plotted this on a graph, you would get what is known as a logarithmic curve.
Calculations
Relationship Between Frequency and Period
Frequency, as discussed, is the number of the cycles per second. A period is the amount of time that it takes for a cycle to be completed.
The frequency of an oscillation is directly related to the period of the oscillation. For example, the frequency of A4 is 440Hz, meaning that the waveform vibrates at 440 cycles per second and that the period of each cycle must last a 440th of a second.
Frequency = ƒ and period = T
ƒ = 1 ÷ T
T = 1 ÷ ƒ
Relationship Between Frequency and Musical Intervals
As explained above, you can calculate the frequency of a note if you know the frequency of the note an octave above or below it. To work out the octave above, the frequency is doubled and to work out the octave below, the frequency is halved.
You can also work out the higher perfect fifth of a note by multiplying the starting frequency by 1.5. This can be done because the perfect 5th is 7 semitones above the root note and at the midpoint of the twelve note octave.
You can also work out the lower perfect 4th, as it is the same as the perfect fifth but an octave apart (G is the perfect 5th above C and is also the perfect 4th below). You can do this by multiplying the starting frequency by 0.75.
ƒ = n x 1.5
ƒ = n x 0.75
Example:
440Hz (A4) x 1.5 = 660Hz (E5) = higher perfect 5th
440Hz (A4) x 0.75 = 330Hz (E4) = lower perfect 4th
Measuring and Labelling Amplitude on a Waveform Graph
The only thing that you need to remember in order to accurately measure the amplitude of a wave on a waveform graph is that the measurement goes from the zero-crossing line to the peak or trough of the wave (not both). The unit you use should dB and this can be read from the Y-axis of the graph.
Calculating the Phase Difference Between Different Waveforms
See this page for information on phase.