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# Octaves in Human Hearing

Siemens Experimenter

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.

Figure 1: An octave map. Each vertical block is an octave and represents the overall level of sound energy over that range of frequencies.

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.

Figure 2: In music, 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.

Figure 3: The lower, upper, and center frequencies of the 1/1 octave bands over the human hearing range.

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.

Figure 4: The upper, lower, and center frequencies for the 1/3 octave bands.

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.

Figure 5: X-axis in octave format. The same random white noise is expressed in octaves and as an autopower.

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.

Figure 6: X-axis in linear format. The same random white noise is expressed in octaves and as an autopower.

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.

(view in My Videos)

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).

Figure 7: Time data is fed through narrow band filters. Each filter represents an octave band. The overall level of the time data is plotted on a per-octave basis and then plotted.

Both octave maps (like in the figure above) and octave sections can be calculated.

• Octave maps plot the octave bands vs. the overall level of energy in those bands.
• Octave sections track how a single octave band behaves against a tracking parameter.

For example, the figure below shows how the 12.5 Hz, 20.0 Hz, and 25.0 Hz octave bands change with time.

Figure 8: An octave section tracks how an octave behaves against a tracking parameter. In this case, it is tracking the octave against 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.

Figure 9: Turn on “ANSI-IEC Octave Filtering”.

In Time Data Processing, open the “Acquisition parameters” settings button (“Change Settings”).

Figure 10: The change settings dialog for octave averaging.

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.

Figure 11: Calculating octave maps. In this case, 1/3 octaves will be calculated.

A result of this calculation would look something similar to Figure 12 below.

Figure 12: The result of an “octave map” calculation.

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.

Figure 13: Octave sections 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.

Figure14: Example of how various octaves behave vs. time.

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.

Figure 15: The octave display icon overlaid on an octave display.

When data is dropped into an octave display, it will look similar to the data in Figure 12 above.

• ,
• ### Simcenter Testlab

Siemens Phenom

Here is a little bit of octave trivia and piano keyboards:

• Standard piano keyboard has linear key spacing, but logartihmic frequency spacing. The octaves on a standard keyboard are linearly spaced - i.e., each octave has the same width (about 164 mm or 6.4 inches).  As shown in the article, from a frequency point of view, each octave is a doubling in frequency (440 Hz, 880 Hz, 1760 Hz, etc). The standard keyboard is about 48.5 inches, or 1231 mm wide.

• If a keyboard has logarithmic key spacing, with linear frequency spacing, it would 212 feet, or 64 meters wide!

Dreamer

Hello,

I have a query. What exactly is the difference between Octave bands and critical bands? And how can we find sound pressure levels in critical bands if octave data is know? Octave to 1/3rd octave is or any other order octave is fine, but how to convert octave to critical?

Thanks

Siemens Phenom

Hello

https://community.plm.automation.siemens.com/t5/Testing-Knowledge-Base/Critical-Bands-in-Human-Heari...

Dreamer

Hi Kevin_Grenier ,

Thank you for reply. Can you please also tell, what exactly is the difference between octave bands and the critical bands?

Siemens Phenom

Both critical bands and octave bands are related to how the human ear perceives sound.  The 1/3rd octave band was developed earlier in time, and every 3rd octave is an exact doubling of frequency as shown below.

Critical bands do not have an exact doubling, and below 500 Hertz they are more linearly spaced than logarithmically spaced.

Dreamer

Thank you for the clarification @PJS

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