Equal temperament

[Jens]

If I am not mistaken, violinists avoid open strings when the fingered notes are tweaked to fit the music. The treble clef A can be played by fingering the D string and tweaking it as needed.

My horn is neither exactly just in any key nor exactly equal tempered. That is the nature of the beast with wind instruments. I just tune it slightly sharp and bend the notes down as needed. That is done with the lips along with the right hand in the bell, and becomes a reflex like singing in tune. Because of the acoustic characteristics it is much easier to bend the pitch down than up. A trombone must be tuned so none of its first position notes are flat.

That makes sense. Of course, in the real world (with the exception of tuners and synthesizers) nothing is really perfectly tuned. Pianos sometimes have two or three strings playing the same note, and they are never perfectly in tune, and aerophones fluctuate significantly depending on temperature since their pitch is based on the speed of sound in air.

[Jens]

Hello Jens.

Big Doh! I suppose he hears the fundamental tone. Just like when I hear a string. But he has perfect pitch.

Just an interesting point, but there is something called a "missing fundamental". Sometimes we hear a sound as being lower than it actually it, because we are imagining a fundamental when there actually isn't one. You can hear it in this YouTube video. I guess that you probably mean that he has perfect pitch and can hear what a note is absolutely. Because with some sound, like white noise, there isn't really a fundamental to hear.

[7cscb]

Just an interesting point, but there is something called a "missing fundamental". Sometimes we hear a sound as being lower than it actually it, because we are imagining a fundamental when there actually isn't one. You can hear it in this YouTube video. I guess that you probably mean that he has perfect pitch and can hear what a note is absolutely. Because with some sound, like white noise, there isn't really a fundamental to hear.

Hello again Jens,

Yeah, very interesting to me.

Years ago I read a book which alluded to this "missing fundamental" by pointing out that we hear the fundamental if it is filtered from, say, a violin tone. I sorta tried to understand this but did not. A few years later I was working on a presentation on signal losses and, with Excel, drew a square wave with the fundamental removed and realized the information for the missing fundamental is still there as per the attached.

Cheers,

sq-fund.png

[Hornblower]

I did a variation on that missing fundamental theme while riding in a military C-130 transport plane, which has four large propellers droning a low D, around 72Hz. I hummed an A a perfect fifth above it and got the sensation of a D an octave below the droning of the props. I not only heard it but felt it as a throbbing in my chest. Organ builders use that phenomenon to simulate a 32' pipe by sounding a 16' pipe and another one tuned a perfect fifth above it, that is, and exact 3:2 ratio. That is a handy trick for a space that does not have room for a real 32-footer. We feel these notes more than hear them.

[profloater]

I did a variation on that missing fundamental theme while riding in a military C-130 transport plane, which has four large propellers droning a low D, around 72Hz. I hummed an A a perfect fifth above it and got the sensation of a D an octave below the droning of the props. I not only heard it but felt it as a throbbing in my chest. Organ builders use that phenomenon to simulate a 32' pipe by sounding a 16' pipe and another one tuned a perfect fifth above it, that is, and exact 3:2 ratio. That is a handy trick for a space that does not have room for a real 32-footer. We feel these notes more than hear them.

Do you think the 72 Hz is the shaft frequency or the blade frequency? In tuning a piano you use the beat frequency of the three strings which has a distinctive null, (And volume as the three reinforce) and then you tune the fifths, which generates another Beat, perhaps the missing fundamental. Starting with the A octaves, then the E and so on. All the time there are the even harmonics from striking at 1/12 length. I don’t think piano tuners develop perfect pitch but they do learn these feelings from the intervals and harmonics. There must be a role for the missing fundamentals. Then in concert work they can tweak for the key of the piece.

[ngc3314]

I did a variation on that missing fundamental theme while riding in a military C-130 transport plane, which has four large propellers droning a low D, around 72Hz. I hummed an A a perfect fifth above it and got the sensation of a D an octave below the droning of the props. I not only heard it but felt it as a throbbing in my chest. Organ builders use that phenomenon to simulate a 32' pipe by sounding a 16' pipe and another one tuned a perfect fifth above it, that is, and exact 3:2 ratio. That is a handy trick for a space that does not have room for a real 32-footer. We feel these notes more than hear them.

This sometimes comes up in physics classes where superposition of waves is discussed. Two superimposed sine waves generate power at their sum and difference frequencies (as in heterodyne signal processing, come to think of it). Brass players occasionally make use of this by playing one note, humming the second, and having the third note produced in this way (I've never encountered all four, but that may be because the Dennis Brain recordings are old and not up to later fidelity standards...). At least I've heard it done with horn and trombone, maybe because most players are male so I've heard fewer players who could hum at typical trumpet pitch.

[Hornblower]

Do you think the 72 Hz is the shaft frequency or the blade frequency? In tuning a piano you use the beat frequency of the three strings which has a distinctive null, (And volume as the three reinforce) and then you tune the fifths, which generates another Beat, perhaps the missing fundamental. Starting with the A octaves, then the E and so on. All the time there are the even harmonics from striking at 1/12 length. I don’t think piano tuners develop perfect pitch but they do learn these feelings from the intervals and harmonics. There must be a role for the missing fundamentals. Then in concert work they can tweak for the key of the piece.

The 72Hz is the blade frequency from 4-bladed propellers spinning about 1,100 rpm. The Allison T56 turboprop engines are spinning at 13,800 rpm and are geared down 12.5:1 to drive the props.

I knew a piano tuner who used two methods, depending on the wishes of the customer. For a reduced price he would do a quickie tuning with a strobe tuner, which was satisfactory for many customers. For the best possible sound for expert musicians he tuned by ear, knowing from experience how the tempered intervals sounded. This took more time and was accordingly more expensive. The strobe tuner did not allow for the overtones of piano strings that are not absolutely perfect harmonic oscillators. No two pianos are exactly alike, and it is my educated guess that when tuned to equally satisfying sound they might have looked off by different amounts with the strobe.

To digress a bit, I was in the middle of an amusing piano tuning situation. The piano movers got lost when delivering a Steinway grand to a concert venue for a piano concerto and got it onto the stage less than a half hour before show time. The piano tuner did a hurry-up tuning and the piano ended up slightly sharp. He came into the orchestra's rehearsal room and asked the principal oboe player if she could play a 443 A. (The oboe has virtually no tuning range with any given reed.) She looked at the dozen or so reeds she kept ready and said, "This little short one should get us there." I had to push the tuning slide on my horn in about 1/2 inch from its regular position. Since the horn is built a bit sharp that was not a problem.