My favorite post of all time

Marshall Chasin
December 19, 2017

The Mysterious Case of the Missing C#

It was a dark and stormy Thursday when suddenly the telephone rang.  I heard a voice that I didn’t recognize but something about it was familiar.  He said that he had lost something that was very important to him and he had to see me right away.  I gave him an appointment for later that evening.  He said his name was Smith,… John Smith.

I put on a tie and my best pair of detective sun glasses.  I suspected that this would be a very difficult case that needed my very best pair of sun glasses.

I’m missing something and I need to see you tonight.

He showed up a little after midnight wearing a hat and looking rather mysterious.  He was also smoking- not a good sign for a dark and stormy night.  I sent my secretary Betsy home, took out a fresh pad and began by taking a case history.

It seemed that he has lost the C# on his piano.  Something about this was familiar and I searched for more clues.  But first I needed some more information.  “When did you first notice that the C# was missing” skipping over the pleasantries and getting down to business. “For about 5 years now.  It’s just become more of a problem now that I am retired and am playing more music… and it’s all C#s up to the one above the treble clef ”, he almost whispered.

Just when I was about to ask another question, he volunteered more information.  I thought it was strange that he did this.  People like him rarely volunteer free information, unless they want something.  I proceeded with caution.  He said “… but one thing is really odd.  I have no problem if I am listening to music that is being played in another room”.

Ahhh,…, maybe I can use the course I took in room acoustics during my detective training many years ago?  I recalled that high frequencies don’t like to go through walls.  I had actually learned this as the acoustic impedance is proportional to frequency, but that was only for test purposes.  Low frequencies have long wavelengths and as a rule of thumb, an obstruction needs to be at least one half of the wavelength before it is obstructed.  That’s why low frequencies (long wavelengths) go right through thin walls with barely any attenuation while higher frequencies with shorter wavelengths lose much of their energy when going through walls.

If he has less difficulty when listening to music played in another room, perhaps it is because the offending sound(s) are not as intense- they must be a mid or high frequency sound.  Perhaps the culprit is not a low frequency fundamental but a higher one, or even a harmonic of a lower fundamental? 

But I was getting ahead of myself.

All this time, Mr. Smith was just staring at me, with a slight smile, albeit a sad one.  I pulled myself from my reverie and explained what I was thinking.  “It’s actually the same law of physics as seen when we cup our hands behind the ears to enhance the pinna effect- higher frequencies see the hand as an obstruction and reflect back to the ear.” 

Having felt proud of myself for my great ability to explain things, Mr. Smith said, “Law!  Who said anything about the law?”  I quickly changed the subject.

“Let’s talk about this C# that you are complaining about.  There are many C#s on the piano keyboard-  the one near the very middle at 277 Hz, the one above it at 554 Hz, or even the one an octave higher, at 1108 Hz?”  He said “I have no idea what you are talking about.  What is this “hurts” stuff?”.  He was starting to get angry and he started to reach for something in his pocket when I suddenly remembered that musicians don’t usually talk about Hz.  They just talk about C and C#.  I quickly rephrased my question. “Come on over to my piano and show me which C# notes are missing”.  He slowly withdrew his hand from his pocket and being surprised that I happen to have a grand piano in my office, smiled slightly and we went over to the Steinway.  I usually keep both of my Steinways in my office but the Hamburg D-Steinway was out for tuning.  I won them both in a game of craps over in the east end.  With the finesse of a street-smart punk, he sat down and showed me…. They were indeed, the three C#s I had just mentioned (277 Hz, 554 Hz, and 1108 Hz).

When he seemed to calm down a bit I took this as a chance to educate him on the use of Hz instead of just piano notes.  I explained that one only needed to multiply the note below it by the twelfth root of 2  in order to get the exact frequency of the next semi-tone.  If middle C is 262 Hz then C# is 262 Hz x 1.0595 = 277 Hz.  He was not impressed and his hand slowly started reaching for whatever was in his pocket.  I better change the subject again.

So,…, a quick recap:  C# had been missing for quite some time.  It is not a problem when listening to music from another room.  This may mean that the problem is in the mid to high frequency region.  He hates any discussion of Hz.

Something about this was familiar- something distant, but familiar none-the-less.

I looked through my detective files and found a yellowed article with coffee stains on it.  It was the classic Hallowell Davis et al. 1950 article.   That was it!  Davis studied American servicemen who had volunteered to sacrifice their hearing in one ear, at least temporarily (in a TTS paradigm).  He blasted them with loud noise in one ear while protecting the other one and created a unilateral (temporary) hearing loss.  He then gave them two knobs- one which controlled frequency and the other which controlled intensity.  While listening to a tone in the normal hearing ear, the volunteers adjusted the knob to the matched frequency and intensity that they perceived in the damaged ear.

For the region of hearing that was still normal, there was a good one-to-one correspondence… as the frequency increased in the good ear, the volunteers heard a similar increase in the damaged ear.  However, when the test tone approached the area of sensori-neural damage in the bad ear, as the test frequency increased, the volunteers noted that it was only an increase in intensity, and not frequency.  That is, the tone in the good ear was heard as being slightly louder, but flat, in the damaged ear.  Davis called this diplacusis and it is very rare (about 3% of the hard of hearing population have this).

As I perused this well -thumbed article reprint I noticed that Mr. Smith was starting to get antsy (ANSI?) so before he even started to move his hand towards his pocket, I piped up and said “Let me do an audiogram”.  His hand shot towards his pocket and he stood up and said “nobody ain’t gonna do an audiogram to me”.  I explained that I meant a hearing test- his hand remained in his pocket holding something. I didn’t think that it was wise to correct his grammar.

“Nobody aint gonna do an audiogram to me!”

I walked over to my audiometric sound booth hoping that he would follow.  He did.  A while later, after a bit of “discussion” that included a black eye and a possibly dislocated shoulder, I had a complete audiogram.  He had a moderate sensori-neural hearing loss, most likely related to presbycusis, but possibly to his incessant Walkman playing since the early 1980s.  He also volunteered that he knew how to shoot a Colt .45 gun and then smiled and said “I never wear hearing protection.  I need to hear what’s around me, see”.  I thought that I would save my hearing protection speech for another day.

Diplacusis is typically related to inner hair cell damage so having a moderate hearing loss supported this contention.  If he only had a mild loss, the odds are that it would have been mostly outer hair cell damage so the diplacusis hypothesis would not have fit.

I told him that I thought that he had diplacusis.  His hand immediately went to his pocket, grabbed something deadly, but before he could withdraw it, I told him that he was hearing things flat.  He did not appreciate being called flat, but eventually he calmed down.

I made myself a mental note to never see strange patients after midnight, especially if it was a dark and stormy night.

So, was it C# at 277 Hz, C# at 554 Hz, or C# at 1108 Hz?  I tried him with a pair of broadband WDRC hearing aids but they had the capability of allowing me to use high pass and notch filtering.  A notch filter (as well as a high pass filter) would chop out entire regions.  Reducing the gain in these regions may resolve the problem.

I first tried high pass filtering all sounds below 300 Hz… no improvement.

I next tried notch filtering in the 550-600 Hz region (as well as high pass filtering the sounds below 600 Hz)… no improvement.

I finally tried notch filtering the 1000-1200 Hz region… a big improvement.  He smiled.

So it seemed that the C# (1108 Hz) just above the treble clef was the culprit after all.  Earlier vague comments about C# being flat, were actually related to hearing the second or third harmonics of the lower frequency C# notes, that occurred in the 1108 Hz region.  It was not the lower frequency fundamentals after all.  Just the fundamental at 1108 Hz

It wasn’t a perfect solution, but program #1 was set to a broadband configuration for speech.  Program #2 was set with a notch filter at 1000-1200 Hz for music.

Mr. Smith left my office shortly after 2 AM with a smile on his face.  I nursed my shoulder and put an icepack on my eye.

Case closed.

  1. Be careful crossing streets. If you do not C#, you may Bb.
    I’m too far away to worry about you blackening my eye for the bad pun.

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