Technical Numeracy

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Waveform graphs

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  • 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.

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Logarithmic Scales

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  • 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.

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13 Terms

1
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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.

2
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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.

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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.

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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.

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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

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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

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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

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Frequency and musical intervals - Octave higher

The octave higher is always double the frequency of the original

SO

F = n x 2

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Frequency and musical intervals - Octave lower

The octave lower is always half the frequency of the original

SO

F = n / 2

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Perfect 5th higher

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

SO

F = n x 1.5

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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

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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 Fh = Harmonic frequency

Where Ff = Fundamental frequency

Where n = number of harmonic

Fh = Ff x n

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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