Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Another check for the low bass-the 7th harmonic

Here is a view of the partials of a M3. The wave-file can be heard here - M3 resultant

You can hear the resultant, using headphones, starting at about 2 seconds into the recording. The resultant is at 66.6309Hz, but does not show up in the Fourier Analysis screen. The beats you hear (3.0bps, Young temperament) is the beating of the 5th and 4th partials.



The analysis screen shows power line artifacts at 60 and 120Hz. They can be ignored.

As Kees has stated above, the ear+brain is non linear.

Here is an analysis of two tones down mixed to a single channel and played simultaneously. As you can see, only two frequencies are detected - 660Hz and 825Hz.

Listen to the wave file.

660-825Hz test

Depending on your equipment/ears/brain, you will hear at least four pitches - 660Hz, 825Hz, 165Hz (825-660), and 495Hz (660-165). It may be possible to detect 330Hz as well (495-165).

Prout

(p.s. - The wave file was recorded with 660Hz in the left channel and 825Hz in the right channel. If you open the file in Audacity and mute one channel or pan the volume fully left or right, the effect will disappear.)

I hear only two tones, one in the left ear and one in the right. If I mix it down to mono, or play it on my computer's speakers and don't sit very close, then I hear the sum and difference tones. It is the ear drums that are the non-linear element where the mixing takes place, not the brain.

Paul.

Try this site or just Google "missing fundamentals"

http://auditoryneuroscience.com/topics/missing-fundamental

The missing fundamental can also be practically observed at the piano. eg: if you were to play a dominant 7th chord in 1st inversion, take Eb7 (so from lowest to highest note we have G,Bb,Db and Eb) you can think of these notes as representing the 5th, 6th, 7th and 8th harmonic respectively of the Eb fundamental. If you play this chord with a hard staccato blow in the temperament section (ie: the G on the bottom is G3) and hold the note Eb1 (the fundamental) down without sounding so the damper is off the string you can faintly hear Eb1 resonating and more clearly the 2nd harmonic at Eb2. At first you would think it was simply air pressure compressions that are causing the free string (Eb1) to vibrate but if you play another adjacent dominant 7th chord (say D7) the open Eb1 string won't resonate. Experiments have been done in fundamental tracking with pure tones where pairs of intervals are played together in a melodic sequence and the test subject hears a resultant fundamental lower down creating its own melody without even sounding these notes - a phantom melody. The test above with the Eb7 produces not only the fundamental but of course the whole partial spectrum along with the longitudinal modes of vibration that you can hear coming and going as the whole thing decays over at least 30 seconds on the piano I was on. This is all so fascinating to enter into this auditory labyrinth where I'm sure there are more mysteries to discover!