COMPARISON OF OCTAVE BANDS
Introduction
The word ‘octave’ is
derived from the Latin word meaning ‘eight’. In the musical world where there
are 7 notes, the 8th note sounds twice as high as the 1st
note. The 8th note is an octave higher than the 1st note.
Similarly in the octave band, the upper limit frequency is twice the lower
limit frequency. Octave bands are very useful in engineering applications
because they reveal the spectral content, meaning they represent the change in
noise levels with respect to the frequency of sound. This helps in identifying
which frequency is responsible for the noise which helps in nailing down the
component in a machine responsible for the frequency.
There are different
types of Octave bands based on the frequency resolution. Octave 1/1 has the
least spectral resolution. Octave 1/3rd band is similar to the
octave 1/1 band but has higher spectral resolution. Octave 1/3rd
band is octave 1/1 band where each frequency band is divided equally into 3
parts. Similarly for Octave 1/6th band, it is divided equally into 6
parts, 12 parts for Octave 1/12th band and 24 parts for Octave 1/24th
band. This helps in increasing the frequency resolution as more accurate
frequency information is available but at the expense of large processing time
and data space consumption. In this post, all characteristics of Octave 1/1,
1/3rd and higher resolution octaves (1/6th, 1/12th
and 1/24th) will be compared.
Equations
The relation between
the next and the previous center frequency is given by,
n = 1 for 1/1 octave
band, 3 for 1/3, 6 for 1/6 and so on.
CF – center
frequency
CFnext –
next center frequency
CFprev –
previous center frequency
The relation between
the upper band and lower band frequency limit for a given frequency band is
given by,
n = 1, 3, 6 for Octave
1/1, 1/3 and 1/6 bands respectively.
CL – lower
band limit for a given center frequency
CU – upper
band limit for a given center frequency
Comparison
Table
Octave
1/1, 1/3 and 1/6 Band Real Time Analysis
To compare the three octave bands, a whistle
experiment is performed with the intent to accurately predict its frequency. A
male human whistle is blown which has a predicted frequency of around 1300Hz
will be analyzed using the three octave band (1/1, 1/3rd and 1/6th)
analysis. The goal is to determine how accurate and feasible each type of
octave band is and conclude which one is the perfect band which has an optimum
trade-off between frequency resolution and data consumption.
Octave 1/1
 |
| Fig .1 Octave 1/1 Real time |
Tone frequency – 1000Hz
Octave 1/3
 |
| Fig .2 Octave 1/3 Real time |
Tone frequency – 1259 Hz
Octave 1/6
 |
| Fig .3 Octave 1/6 Real time |
Tone frequency – 1334Hz
Conclusion
Based on the above results, it can be concluded that
the experimental whistle frequency of 1300 Hz is accurately calculated by Octave
1/3 as 1259 Hz and by Octave 1/6 as 1334 Hz while Octave 1/1 could only display
it as 1000Hz. Although Octave 1/6 has higher spectral resolution, Octave 1/3
could calculate the frequency with very close approximation. Thus despite the
minor error associated with Octave 1/3 at predicting frequency it is still
useful to use Octave 1/3 over Octave 1/6 as the processing time and data
storage space consumed is far less than Octave 1/6 band.
