Comparison of various Octave bands

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 8^th note sounds twice as high as the 1^st note. The 8^th note is an octave higher than the 1^st 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 1/3^rd band is similar to the octave 1/1 band but has higher spectral resolution. Octave 1/3^rd band is octave 1/1 band where each frequency band is divided equally into 3 parts. Similarly for Octave 1/6^th band, it is divided equally into 6 parts, 12 parts for Octave 1/12^th band and 24 parts for Octave 1/24^th 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, 1/3^rd and higher resolution octaves (1/6^th, 1/12^th and 1/24^th) 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.

C_F – center frequency

C_Fnext – next center frequency

C_Fprev – 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.

C_L – lower band limit for a given center frequency

C_U – 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, 1/3^rd and 1/6^th) 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.