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.

High quality, easily accessible frequency standards are available from 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 be accessed via telephone at the price of a telephone call to the US. If a frequency standard is needed when taking recordings in the bell tower, the NIST standard can be accessed using a mobile phone. Now that mobile telephony is digital, the utility of the standard may be dependent on the accuracy of the clock rates of intervening equipment. For our purposes, this can be ignored.

A description of the service is available from the NIST Time and Frequency Division website from which the following details are taken. To hear these broadcasts, dial (303) 499-7111 for WWV (Colorado), and (808) 335-4363 for WWVH (Hawaii). Callers are disconnected after 2 minutes. These are not toll-free numbers; callers outside the local calling area are charged for the call at regular long-distance rates. 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:

ToneMinutes past the hour
600 Hz1, 3, 5, 7, 11, 13, 17, 19, 21, 23, 25, 27, 31, 33, 35, 37, 39, 41, 53, 55, 57
500 Hz4, 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 Hz2
none0, 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:

  • 30 seconds of the 600Hz reference tone, with a one-second tick
  • 8 seconds of silence with a one-second tick
  • a time announcement
  • 1 second of a 1000Hz tone
  • the start of a weather announcement.

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 audio input. 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 audio output. For a valid calibration, the NIST transmission must come into the PC from the phone via your recorder (if used) or audio input – it must follow the same route as used for bell recordings.

I regularly calibrate my laptop, USB pre-amp and mobile phone using the NIST tones but the quality of modern equipment is such that the calibration is always accurate to better than 0.05Hz. The NIST frequency standard gives a very precise frequency calibration for the price of a telephone call.