Octaves in Human Hearing
Octaves are groups of frequencies that help quantify how humans distinguish between frequencies.
Octaves represent the overall level of energy over a specific frequency range.
How are octave bands determined?
The term “octave band” is borrowed from music theory where there is a doubling of frequency between notes of the same name.
Octave bands in human hearing are developed in the same manner: the range of human hearing (20-20kHz) is divided into eleven octave bands, each band having double the frequency span of the previous band. These are called the 1/1 octave bands.
To more closely match how humans distinguish frequencies, each 1/1 octave band can be split into three bands. These are called the 1/ 3 octave bands. These smaller bands more closely represent how humans distinguish between frequencies.
Octaves are not equally spaced:
Octaves are often displayed so that the center frequencies of the octave bands are linearly spaced. This is called octave format. This causes the octaves to appear equally spaced in frequency even though they are not.
In Figure 5 below, white noise is expressed in both narrow band (blue) and octave format (green). The x-axis is in octave format (described above). Notice that the octave bands at lower frequencies have less data filling them compared to the octaves at higher frequencies. This is because octave bands at higher frequencies cover a broader frequency range than octave bands at lower frequencies.
The same data is plotted below but the x-axis is in linear format. Notice that an autopower (blue) has the same density at all frequencies. Notice that the range of frequencies each octave band (green) covers gets larger and larger.
Octave bands help determine how the human ear distinguishes between frequencies. At lower frequencies, the ear can more easily distinguish between frequencies. Thus, the octave bands are narrower. At higher frequencies, the ear has difficulty distinguishing between frequencies (even frequencies that are somewhat far apart). Thus, the octave bands are wider. Watch the video below to hear this phenomenon.
NOTE: Critical bands are also used for defining frequency determination by the human ear. The critical band scale is slightly more refined compared to octaves. Critical bands (like octaves) are used in the determination of many sound quality metrics.
How are octaves calculated?
Octaves are calculated using a series of time-domain based, band-pass filters.
Time data is fed into a series of narrow-band filters. Each filter band represents the frequency range of each octave. In Testlab, the filter shapes conform to the ANSI and IEC standards (ANSI S1.11-2011, IEC 61261:2014).
Both octave maps (like in the figure above) and octave sections can be calculated.
For example, the figure below shows how the 12.5 Hz, 20.0 Hz, and 25.0 Hz octave bands change with time.
Calculating Octaves in Simcenter Testlab:
To calculate filter based octaves in Simcenter Testlab (formerly called LMS Test.Lab), go to “Tools -> Add-ins” and turn on “ANSI-IEC Octave Filtering”. This add-in requires 23 tokens.
In Time Data Processing, open the “Acquisition parameters” settings button (“Change Settings”).
Select an averaging method: exponential or linear. The exponential average weights the acquisitions taken later in time more heavily than earlier acquisitions. The linear average calculates the arithmetic mean of all the values.
Select a sound level type: fast (0.125 sec), slow (1.000 sec), impulse (0.035 sec), or user (custom). This parameter changes the length of the averaging frame. The averaging frame is the length of time that is used to calculate an average at every increment. Check out the Simcenter Testlab Throughput Processing Tips article for more information about increment and frames.
In Time Data Processing, open the “Section” settings button by clicking “Change Settings” under “Section. To calculate an octave map, go to the “Octave Maps” tab. Check on the octave band type that needs to be calculated.
A result of this calculation would look something similar to Figure 12 below.
To calculate a single octave section, go to the “Octave Sections” tab. Type in the center frequency of the octave section(s) that is desired to be calculated.
The octave section calculation will calculate how an octave behaves vs. a tracking parameter. Figure 14 below gives an example of the result from this calculation.
NOTE: There are a few additional tabs with the RTO (Real Time Octaves) suffix. Anything with the suffix RTO will used filter-based octaves to do processing. For example, “Psychoacoustic Metrics RTO” uses time-based filters to calculate sound metrics.
Octave displays in Simcenter Testlab:
There is a special display in Testlab called the “Octave” display. The octave display automatically puts the x-axis in octave format. It also automatically puts data into a “block display” format (as octaves are traditionally displayed in). The icon for this display is enlarged in Figure 15 below.
When data is dropped into an octave display, it will look similar to the data in Figure 12 above.