Nominal or Hum

[Bill Hibbert]

RO:

>Just out of interest, at what diameter do you swap from nominal to 
hum?

One of the experiments in my PhD thesis deals specifically with this 
point. The experiment was done on 17 test subjects, all musically 
competent, at a range of nominal frequencies between 315Hz and 
4,000Hz. There is no clear breakpoint, but rather a gradual 
transition from one mode of listening to another. There is a neat 
graph showing the results but I'm not able to post it from work. As 
well as pitching by the hum, prime or nominal, for big bells we have 
the secondary strike effect (pitching by partial I-7, the first rim 
partial above the octave nominal, sounding about a 4th above the 
primary strike). The results were as follows:

315Hz nominal: 2/3 hear secondary strike, 1/3 pitch from nominal
397Hz nominal: about 50/50 secondary strike / nominal
Nominals from 500Hz to 1260Hz: most peple pitch by the nominal
1587Hz nominal: 50/50 between nominal and prime
2000Hz nominal: 2/3 prime, 1/3 nominal
2520Hz nominal: 3/4 prime, 1/4 hum
3175Hz nominal: 50/50 between prime and hum
4000Hz nominal: 3/4 hum, 1/4 prime.

For pitches arising from secondary strike and nominal, the effect is 
independant of the loudness of the partials. For pitching by prime 
and hum, the louder partial wins, other things being equal. Results 
are potentially different for every listener, because the pitches 
heard are generated in the individual's auditory system.

These results also help explain why small old-style bells sound 
worse than large old-style bells; in small bells, the various 
pitches compete and sound discordant. In true-harmonic bells, all 
the pitches are the same 'note'.

This is all explained in my thesis, of course . . .

Cheers,

Bill H

PS there is a recording on 'Called Home' of a peal of small bells, I 
forget where, where for my ears an octave jump upwards occurs half-
way round the circle. In rounds, I hear the back bells an octave 
higher than the small bells.