The Sound of Bells

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Frequency calibration for tonal analysis

The basic principle of frequency calibration is simple. If a reference tone of known frequency is available, it can be recorded along with the bell sound. When the bell sound is later analysed, the frequency of the reference tone is checked at the same time. If there is a discrepancy, work out the ratio of actual reference frequency to that measured on the reocording. All the measured frequencies in the recording then have to be scaled by this factor. Wavanal, if you are using it, includes the facility to resample a recordings to eliminate the discrepancy. For example, I discovered during the calibration exercise explained below that a 600 Hz tone recorded on my laptop resulted in an analysed frequency of 599.7 Hz. The correction factor, 600 / 599.7 = 1.0005, entered into the 'increase frequency' screen in wavanal, resamples the recording to give the correct result.

Discrepancies can arise both because of errors in recorder speed, and digitisation rate errors in the equipment used to digitise the sound (e.g. the sound card). The processor speed of the PC is not relevant to the accuracy. Even if you are recording direct to PC or laptop, it is worth calibrating the device at least once to see if it is giving significant errors, as you will see below.

Sources of reference tones include tuning forks and handbells, both of which are commonly used. Tuning forks have the advantage of portability. Handbells have the advantage that their frequency variation with temperature is probably the same as that of the bells being recorded. Both forks and handbells have the considerable disadvantage that their frequency is not known, and has to be measured somehow for them to be of use. I have learned not to trust the supposed frequency of tuning forks unless they have been measured, I have seen them up to 10 Hz out.

A suggestion from Dave Kelly led me to investigate the availability of broadcast frequency standards. Dave suggested that the frequency of the time signal pips on BBC Radio 4 was 1000 Hz - for those in a part of the world where this station can be received. He and I have both measured the pip frequency on a number of occasions and have found it to be about 1001 Hz. There are three difficulties in using the time signal as a frequency standard. First, the signal is very brief - the only part of it useful in practice is the half-second burst at the end, which is not long enough for accurate measurement. The second disadvantage is that the signal is only available for a brief instant once an hour. Thirdly, the stability of the frequency is not known. I measured the pips on a recording believed to be running to speed and found the frequency to be 985 Hz. On the plus side, all that is necessary to use this signal as a frequency standard is a radio tuned to BBC Radio 4.

In searching for a better standard than this I was led to the US National Institute of Standards and Technology. NIST broadcast standard frequencies, linked to the equipment which produces the US time standard. These broadcasts can also be accessed via telephone. For the price of a telephone call to the US, very accurate frequency standards are available at all times. If a frequency standard is needed when taking recordings in the bell tower, the NIST standard can be accessed using a mobile phone.

A description of the service is available from the NIST Time and Frequency Division website from which the following details are taken. There are two phone numbers that allow you to listen to NIST time. To hear a simulcast of the WWV shortwave broadcast, call (303) 499-7111. This is not a toll-free call, except in the local Boulder/Denver, Colorado area. To hear a simulcast of the WWVH time announcements from Hawaii, call (808) 335-4363. WWV and WWVH also broadcast precise 1 second time intervals (the interval between the "ticking sounds" you hear) and standard audio frequencies of 440, 500, and 600 Hz. To reach NIST from the UK, call 001-303-499-7111. The tones last for almost a minute, giving ample opportunity to measure their frequency.

The schedule for transmission of the tones repeats every hour, at the following times. Only at around quarter to the hour is it necessary to wait more than a minute or so for a reference tone:

Tone Minutes past the hour
600 Hz 1, 3, 5, 7, 11, 13, 17, 19, 21, 23, 25, 27, 31, 33, 35, 37, 39, 41, 53, 55, 57
500 Hz 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, 24, 26, 28, 32, 34, 36, 38, 40, 42, 52, 54, 56, 58
440 Hz 2
none 0, 29, 30, 43, 44, 45, 46, 47, 48, 49, 50, 51, 59

Here is a sample of the transmission from NIST recorded into my laptop from a mobile phone. (The recording has been resampled to compensate for digitisation rate error.) The sample comprises the following:

Though the sound is noisy the 600 Hz tone gives a very clear reference frequency as you will see if you analyse it. However, do not use this recording to calibrate your PC, it came into your computer ready-digitised and bypassed the sound card. Wavanal will report the frequencies as exact whatever the specification of your computer! Likewise, do not play this recording and use it to calibrate a recorder; the playback frequency will depend on the calibration of your sound card. For a valid calibration, the NIST transmission must come into the PC from the phone via your recorder (if used) and sound card.

I used the NIST tones to calibrate the sound interface on my home PCs, by digitising them through a microphone into each machine. The sound from the phone is quiet, I made the recordings by turning the record level on the PCs to maximum and holding the microphone close to the telephone earpiece. I was able to make successful calibrations with ease using a mobile phone. Multiple recordings were taken on each machine, over a period of about 24 hours. The first and most important conclusion is that, once a sound has been digitised on a particular machine, analysis on any machine always gives the same frequency - as one would expect, because frequency analysis is no more than a series of arithmetic operations on a sequence of bytes in a file. The second conclusion is that, over the 24 hour period, the NIST frequencies were stable to the limits I was able to measure them.

I did discover that of the four PCs I tested, those with SoundBlaster or clone sound cards gave precise results to within my ability to measure them. Those with sound integrated into the motherboard showed slight errors (of about 0.05%) in sampling rate. As a final calibration on the NIST transmission, I checked the timing of the one-second pulses by counting samples over the 55 seconds of the sample recording above. The frequency of 600 Hz was accurate to at least 5 significant figures.

Based on these tests, the NIST frequency standard gives a very precise frequency calibration for the price of a telephone call.


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Last updated March 25, 2002. Site created by Bill Hibbert, Great Bookham, Surrey