Technical Numeracy

Waveform graphs

• A graph of a waveform shows us how the displacement changes over time, between its maximum positive and maximum negative values and around a zero line

• May also see waveform graphs that show change in voltage over time.

Logarithmic Scales

• A logarithmic scale is used to represent orders of magnitude as a linear change

• The decibel scale and the frequency values on a filter or EQ graph are examples of logarithmic scales.

Logarithmic Scales - EQ

EQs are organised in this way because of our greater sensitivity to lower frequencies and because doubling a frequency means moving an octave higher.

Logarithmic Scales - dB

• The decibel is a unit of sound pressure level. It uses a logarithmic scale because our ears don’t respond to sound pressure in a linear way. Our ears hear logarithmically i.e. a chainsaw is many times louder (when measuring pressure and power) than a conversation, but we don’t percieve it like that

• When we use dB to muasure sound pressure level, we can normally set meters to Peak or RMS mode

• Because of the way in which we perceive sound, we will hear sounds with a consistently higher level as louder than those with a loud peak but no sustained volume

• This type of psychoacoustics is why we sometimes hear a whole drum kit playing a beat as leader than a singer cymbal hit.

Peak

• A transient measure of loudness

• The meter will give a momentary measuer of the highest volume of the signal

• Useful for setting input gains to avoid distortion, or to create pumping effects on compressors

RMS

• Stands for Root Mean Square, an average measure of loudness

• Much slower analysis than peak and is useful if you are looking for the average volume of something

• Useful for measuring the overall volume of audio and is often used to gauge the volume of a track during the mastering process

Period

• Frequency (measured in Hz), is the number of waveform cycles per second

• The period of an oscillation is the amount of time a single cycle takes

• The frequency of an oscillation is directly related to the period of the oscillation.

Where frequency = F and period = T

F = 1 / T

T = 1 / F

Frequency and musical intervals - Octave higher

The octave higher is always double the frequency of the original

SO

F = n x 2

Frequency and musical intervals - Octave lower

The octave lower is always half the frequency of the original

SO

F = n / 2

Perfect 5th higher

The perfect 5th higher is the mid-point between the original and octave higher

SO

F = n x 1.5

Perfect 4th higher

The perfect 4th is the same note name as a perfect 5th but an octave lower

SO

F = n x 0.75

Frequencies from the harmonic series

• If you know (or can work out) the fundamental frequency, you can approximate the frequency of a note in the harmonic series

• The fundamental frequency is also referred to as the first harmonic

• We can calculate the frequency of higher harmonics by using the calculation:

Where F_h = Harmonic frequency

Where F_f = Fundamental frequency

Where n = number of harmonic

F_h = F_f x n

Calculating delay time from BPM

• To calculate the delay time of a crotchet at 100BPM in seconds:

  • Delay time (s) = 60(s) / Crotchet beats per minute

  • Delay time (s) = 60 / 100

  • Delay time (s) = 0.6(s)

• The delay time is for a crotchet (1/4)

• For a quaver (1/8), the delay time would be half as much so 0.3s

• For a minum (1/2), the delay time would be twice as much and so 1.2s