Frquency

[John Bertotti]

What is the lowest frequency coming out of a octave mandola? I am actually curious to the lowest harmonic not the frequency of the lowest string. I am a firm believer that although there are upper and lower thresholds to the human ear we still perceive frequencies lower then those we hear. Not sure how I'll use this info yet but feel like it's needed info. Am I the only one who gets a bug in his ear and has to chase it? Actually I ask because I notice that when instruments are amplified the ones that have a freq response below what I can hear still sound fuller and that to me is better. Thanks John

[Chris Baird]

Since stringed instruments project a sawtooth like wave pattern we can detect frequencies that are lower than we can actually hear. This is because, although we can not hear the fundamental, we can create in our heads a pitch based on the partials that we can hear. This phenomenom doesn't occur but in the very lowest instruments like the double bass and even larger(unconventional) instruments. You should be able to hear the lowest fundamental tone of an octave mandola. The reason lower frequency tones sound "fuller" on a mandolin family instrument is because the partials lay more fully in the "loudest" frequency spectrum. In other words, we hear the partials better than those on the higher strings. Our ear canal is shaped such that we hear frequencies in the 1-3k range as being much louder than any other frequencie range of the same decibal rating. There are also other internal functions and systems which further tune our hearing in on certain frequency ranges.

[John Bertotti]

Thank Chris I'll have to turn that over in my head for awhile. It is a bit different then I had it figured based on what I think I'm hearing. hanks John http://www.mandolincafe.net/iB_html/non-cgi/emoticons/smile.gif

[Dave Cohen]

Chris, where on earth did you get that sawtooth stuff? I have never seen anything in the literature to support that. The only sawtooth waveform that I know of in stringed instruments is the "Helmholtz motion" which occurs as a result of the pull/slip action of the bow on the strings in bowed stringed instruments. If by "project" you mean "radiate sound", then none of the instrument families do that.

[Martin Jonas]

Without wanting to second-guess Chris, I read his post as referring not to the waveform but to the amplitude envelope. Mandolins and other plucked string instruments have a very sudden attack and a more gradual decay and that envelope shape may well be called "sawtooth".

Martin

[Chris Baird]

By sawtooth I am refering to the wave shape which contains the fundamental and all of its partials(thoeoritcally) in decending amplitudes. #Of course a string doesn't impart a perfect sawtooth wave form onto the intrument and the instrument certainly doesn't accept a perfect sawtooth but, that is the wave that is most closely related to what is going on. #You have a fundamental and related partials in descending amplitudes. #That is what I meant by "sawtooth". #I got this information from several wave anaylisis programs. #If I am wrong in my terminology I would certainly welcome a correction. #Here is a quote from one of my programs.

"A sawtooth wave's sound is harsh and clear and its spectrum contains both even and odd harmonics of the fundamental frequency. Because it contains all the integer harmonics, it is one of the best waveforms to use for constructing other sounds, particularly strings, using subtractive synthesis."

An FFT graph of a sawtooth at a certain frequency will have many of the same peaks at certain harmonic intervals and relative amplitudes as an FFT of a plucked mandolin string. #I'm sure it wouldn't look anywhere near the same on a scope but there are enough similarities to refer to it as "sawtooth like".

[Martin Jonas]

I see -- I was wrong in my interpretation then. #I was thinking of a sawtooth shape in the time domain, whereas what you describe is a sawtooth shape in the frequency domain (i.e. the Fourier transform of the wave spectrum). #I wouldn't know whether either usage is standard amongst acoustic engineers (I'm a physicist), so I can't help with what would be the consensus terminology (if indeed there is one). With your explanation, your meaning is clear to me, although I've never looked at an FFT spectrum of a mandolin tone.

Martin

[Chris Baird]

Perhaps this will facilitate some kind of peer review. #This is easily reproducable. #These are two ffts taken with a microphone. #The bottom image is a plucked G string and the top is a sawtooth from a tone generator at 196hz. #As can be seen the similarities warrant the use of "sawtooth like" in describing the sound radiating from a mandolin.

[Dave Cohen]

Textbook stuff: In the time domain, the dacay pattern of a plucked string is an exponential decay (except in the case of multiple courses of strings, i.e., the piano). In the frequency domain, the 2nd harmonic will have 1/4 the amplitude of the 1st harmonic; the 3rd harmonic will have 1/9 the amplitude of the 1st harmonic, & so on. See, e.g., Fletcher & Rossing, The Physics of Musical Instruments, 2nd Ed., Springer, 1998, pp 40-44. If either or both of the scales on your graph are logarithmic, that may account for the confusion.

[Chris Baird]

Dave,
#Please elaborate on your last post. #I didn't understand the point. #What confusion are you speaking of? #The amplitude comparison in those graphs is irrelevent because I didn't control the test in that way. #I would have to factor in the worn speakers and also the cheap mics shortcomings to make any decent amplitude comparison. #My point for comparison of a plucked string to a sawtooth wave is in the relation of hamonic partials as has to do with frequency; which happen to be almost identical. #

[Dave Cohen]

Chris, what are the labels on your axes? The frequency scale looks linear, but I can't make out what the units are on the vertical axes. If they are decibels, then the vertical axis is logarithmic.

[/QUOTE]My point for comparison of a plucked string to a sawtooth wave is the relation of hamonic partials as has to do with frequency; which happens to be almost identical[QUOTE]

The relative amplitudes of the succesive harmonics vary as the inverse square of the number of the harmonic, for which I referred you to a textbook. They don't decrease in a "sawtooth" fashion, which would be a repetitive linear decrease. However, as long as you are doing this kind of thing, try the following: Vary the position at which you pluck the string. You will find some interesting things. If the string is plucked in the middle, i.e., over the 12th fret, all of the even harmonics, i.e., the 0th, 2nd, 4th, 6th,..., will be missing, or at least very weak. If you pluck the string at one fifth of the distance from the bridge to the nut, every fifth harmonic, i.e., the 5th, 10th, 15th, etc., will be weak or absent. Similarly, if you pluck the string at one eighth of the distance from the bridge to the nut, every eighth harmonic, i.e., the 8th, 16th, 24th,..., will be weak or absent, and so on. Another thing is that if the string is plucked close to the bridge, the resulting fft will show the amplitudes of the higher harmonics to be relatively greater than if you pluck the string near its center, i.e., over the 12th fret.

You don't need to apologize for your equipment. What you are saying is that you haven't calibrated. But frequency domain spectra often aren't calibrated anyway. A cheap mic may add a little "coloration" to what you see, but will still allow you to see what I described above.

[Chris Baird]

The vertical axis is amplitude. In my first post I was using the sawtooth comparison to show why it is possible to "hear" a pitch below what one can hear as a pure sine wave. So I disregarded that the amplitude decrease was different for a string as compared with a sawtooth. I do have a "sawtooth" programmed into my tone generator which does take into account the amplitude decrease as you described above for a string. I use this psuedo sawtooth to excite my mandolins when using a piezo transducer to gather information.

[Dave Cohen]

Eep! I got one thing backwards. If you pluck a string in the middle, the even harmonics will be weak or missing, and the odd harmonics will be present. Always good to check the source.