I was just reading over some posts on pianoworld.com by students who were looking for ways to make tuning the temperament easier.
Basically, the problem is that, although most techs use a healthy dose of thirds/sixths and fourths/fifths to tune a temperament, beginners like to use fourths/fifths because it is easier for them to hear when the intervals do not sound right, while hearing the thirds/sixths beating may be more difficult.
Many techs however, advocate the use of thirds/sixths for the purpose of producing more accurate tunings.
It is true, however, that they are harder to hear for some technicians.
With that in mind, I would like to share some tricks I used when starting out, that helped me to more easily hear the beats of thirds/sixths, sometimes called Rapid Beating Intervals, or RBI’s.
1. Know Where the Coincidental Partial Is.
That is where the beating will occur. By knowing where the beating should be, you can begin to train your ear to focus at that frequency. I believe, and there have been studies that prove, that the brain of a piano tuner is different. I believe it is constant focusing of the ear that causes the brain to change. But it takes time and focus. Know where the beating is occurring, i.e. at the coincidental partial, and focus on it.
2. Ghosting
Sometimes this works, and when it does, it is awesome. Most of the time, it doesn’t work as well as we would like.
Slowly press down the interval notes, thereby lifting the dampers, and allowing the interval strings to be excited by the ghost note.
Attack the note that corresponds to the coincidental partial, with a loud ff staccato.
If the coincidental partials of each interval note are close to the frequency of the note you played staccato, then each partial should ring, and if the partial frequencies are not the same as each other, then beats will be heard.
This sometimes works well when accompanied by playing the interval mf.
Play the interval. Let it be heard, and then strike the coincidental partial loud and short. Sometimes, it is just enough to bring out the beating when strict ghosting doesn’t.
3. Focus the Ear.
Play the coincidental partial many times, mp. Let it sustain. Let your ear listen to that unique and special frequency. Burn it into your head. Then play the interval moderately soft, without playing the coincidental partial, trying hard to keep hearing that frequency of the coincidental partial you had burnt into your ear.
4. Filter Unwanted Frequencies.
This is why hearing beats is so hard. When an interval is played, there are too many unwanted frequencies that interfere with the hearing of the beats.
Understanding the harmonic spectrum can help. Whenever a note is played, frequencies, or partials, of the harmonic spectrum are created. The tone of a note is determined by the relative intensities (volumes) of each of those partials.
Simply turning your head a few degrees one way or the other, can filter out just enough unwanted partials from reaching your inner ear, that the beating of the coincidental partial is more easily heard.
Also, with tones that contain the harmonic series, there can be nodes, or points/lines of less vibration of specific partials, within the room. Try to shift your head sideways, as well as tilting, to find the “sweet spot” where hearing the beats is easiest.
Finally, it is possible that the beating partial reaches one ear at a different time than the other. This can set up destructive interference where the two waveforms combine in the brain to cancel out the beats. But if the ears are at the right position, they can add up to make the beat louder! (Constructive interference.)
5. Know What the Beat Sounds Like.
The beat is not produced by the piano, per se. It seems to be a phenomenon like condition created by the interaction of two strings of the piano, and as such, the tone of the beat is not like most musical tones. It has a ghost-like quality, or pureness, that does not seem to come from the piano itself, but more often, from [i]behind[/i] the piano. So sometimes focusing your listening at a point behind the piano helps. Listen for that pure, pulsating tone.
G3B3 Unfiltered
This is what the pure beating partial sounds like...
6. Use a Band Pass Filter like Ocenaudio to Help You Know What the Beats Sound Like.
This is an electronic device that you can use to filter out all frequencies except a narrow band around the frequency you are trying to hear. It has the benefit of showing you exactly what the beat sounds like. It shows you exactly what a seasoned aural piano tuner hears.
You can also create a simple Band Pass Filter by cupping your hand around your ear. Point your fingers behind you. Keep your finger tips touching your head and slowly move your palm farther and closer to your head. You can create a band pass filter with a range of about one octave. (Contact me if you would like to purchase one.)
I also have a Real-Time Audio Bandpass Filter I am designing that has a range from about F3 to F#7, 4 octaves!
One analogy that I use to describe the path to hearing beats easier is the theatre curtain analogy.
The beats are like objects behind a theatre curtain, and we are sitting in the audience, trying to see what’s behind the curtain.
When we start trying to see those objects, the curtain is quite opaque, and while there are moments of translucence, most of the time we are just staring at velvet.
As a tuner practices trying to hear beats, the curtain begins to get thinner, and the moments of translucence last longer.
After years of experience, the curtain is virtually transparent.
By using some of the techniques I describe above, you may be able to achieve transparency sooner, rather than later.
Good luck.
