Posted by Kenneth Sloan on March 09, 2002 at 12:27:58:
In Reply to: Re: Re: Re: Pedal? posted by Sean Chisham on March 09, 2002 at 11:42:24:
Oh dear. I hinted that this was a "can of worms". I quote:
"...any sound made up of sinusoidal components...it will be useful to refer to these components as the *partials* of the sound in question. When this word is used, we will understand that no particular relationship is to be assumed between the frequencies of these partials; their frequencies may or may not have a whole-number relationship. ...
Their components will still be referred to by their serial numbers as *first* partial...,second partial... We turn now to the special case of sounds in which the frequencies of the various sinusoidal partials are whole-number multiples of some basic repetition rate. The sinusoidal component whose frequency matches that of the repetition rate will be referred to as the *fundamental* component and its frequency as the *fundamental frequency*. It is often referred to also as the *first harmonic*. ... We will have to be very strict in our terminolgy or endless confusion can result." [Benade, _Fundamentals of Musical Acoustics_, p. 63] (snipped for what I hope is clarity; any confusion caused is my fault)
My point? In my opinion, it makes sense to speak of "the fundamental". If you play a C (any C) on a CC tuba, then the "fundamental" corresponds to the note 3 octaves below middle C (I hope I got that right). But, there may, in fact, be no "partial" which corresponds to that note. (most will agree that there is no such "partial" when you play middle C - there is a potentially flame-filled debate over whether or not there is such a "partial" even when you play the note 3 octaves below middle C!!!)
Now, it is perfectly natural to extend this definition of "partial" to the instrument itself, rather than a particular sound. That's what we do when we talk about "third partial", etc. The POINT is: the "first partial" may (or, as I happen to believe, may NOT) correspond to "the fundamental". In tubas, just as in the sounds Benade writes about, not all partials are "harmonic", and not all harmonics are "partials".
Sorry about that...we now return to the main question: where are the "pedal notes"? I like Sean's answer: "how low I can play" - different players refer to different notes, depending on how low *they* can play. "Can you play a pedal F?", "yes (by definition)"
Is the F 4 ledger lines below the bass clef staff a "pedal" (on a CC, on a BBb, on a Eb, on an EEb, on an F)?