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In Reply to: Re: posted by Romy on July 28, 2002 at 14:30:22:
The lowest note of a double bass is 41.2 Hz and a piano goes down to an A at 27.5 Hz. Even a normal acoustic guitar goes down to 82.4 Hz.The standard 440 Hz A is the A above middle C on a piano. The A string on an acoustic guitar is 2 octaves below that which makes it 110 Hz, and the bass E string on the acoustic guitar is a fourth lower than the A string which makes it 82.4. The double bass and bass guitar go an octave lower again.
Any standard reference text giving the frequency range of instruments will confirm these bottom frequencies.
Follow Ups:
David, there is a difference between “bottom frequencies” and fundamental frequency. Fundamental is a lower resonant frequency. I have seen a number of the “standard reference texts” that confused it.For example you 13' x 17' listening room could easily “produce” music that contains 20 Hz. However, the room itself has it own lowest resonant frequency witch would be somewhere around 180 Hz… By the way there is law of acoustic, if you care, saying that a room can’t properly reproduce bass if the bass’ frequency is lower then the lowest resonant frequency of the room. I know, I know… I am with you on it….
Romy,I'm an amateur musician as well as an audiophile and music lover. I tune my guitar with an A=440 Hz tuning fork, and I know which note on the piano is tuned with the same fork. The bottom A on the piano is 4 octaves lower than that. The frequency of the note halves with each octave we go lower so, in order as we descend, the frequencies of each of those lower As are 220,110, 55 and finally 27.5 Hz. The low E string of the double bass is tuned to the E in that lowest octave between 27.5 and 55 Hz, hence it's 41.2 hz tuning.
As A.J. states, some instruments and voices concentrate more energy into overtones rather than the fundamental frequency of the note, definitely changing the tonality and perception of pitch that is given. In some cases performers deliberately do this for artistic purposes. There is an interesting table on page 6 of the liner notes for Stereophiles 2nd test disc. The first 2 tracks for channel identification and phasing are a recording of John Atkinson playing a Fender Precision Bass and the table lists the level of the overtones produced in relation to the fundamental.The first overtone, an E at 82.4 Hz, is 11.8 dB LOUDER than the fundamental at 41.2 Hz while the next 2 overtones 9B at 123.6 Hz and E at 164.8 Hz) are 5.8 dB and 7.8 dB softer than the fundamental at 41.2 Hz. This still represents an enormous amount of energy at those frequencies.
What this means in terms of reproduction is that a speaker which is rolling off at 50 or 60 Hz, as many are, would actually reproduce the 2nd and 3rd harmonics at 123.6 and 164.8 Hz much louder than they would reproduce the fundamental 41.2 hz note. In fact, I doubt that listeners would perceive the fundamental at all with many such speakers. Many people can be confused by this because they listen to music and hear a bass part and think that's it, then go to a live performance or hear the same recording on a different system (or even make a change in their own system) and suddenly hear a totally different bass part to what they've been familiar with and wonder where it came from. It need not even be that the notes start to fall an octave or 2 octaves lower but are the same note, they can actually be different notes if harmonics like the 3rd or 5th, for example, have previously been perceived as the fundamental. The whole shape of the melody of the bass part can change as a result.
It's also worth noting - just ask any double bass player, pianist, acoustic guitarist, or anyone who plays an acoustic instrument - that the sound of their instrument which they hear while playing is significantly different to the sound that they hear if they're at a normal listening distance while someone else plays. This is simply because instruments project unevenly, like a loudspeaker lobing, and different surfaces of the instrument project different harmonic patterns. My guitar doesn't sound as deep to me when playing on the lowest strings as it does when I'm somewhere in front of it while someone else plays. The sound board and sound hole project to the front while the sound coming most directly to my ears is from the sides which are stiffer and favour higher overtones. Most acoustic musicians have a similar experience - instruments are basically designed to project sound to the audience rather than the musician. At least electric musicians can stand in front of their speakers and set the speaker stacks up so that they hear a more representative sound if they wish, and can stand the volume :-(
I repeat - check any reputable text for the frequency range of various instruments and you will find that the lowest note of a double bass is at 41.2 hz and the bottom A on a piano is 27.5. There are any number of reputable authorities you can use to confirm this, in fact the Grove Musical Encyclopedia probably even has this sort of information somewhere if you could figure out what to look for in the index.
Well,you and A.J. both brought some valuable points. Frankly speaking I’m still not convinced. When you are talking about the lowest note of a double bass is at 41.2 Hz then it is a resonant frequency of the entire instrument, the resonant frequency of the sting or just a heist point in the frequency parabola?
I am not quite sure if it is relevant but I think I have to a harass my bass players to learn what the hell is going on here. Thanks for your and for the A.J.'s posts. I will fuggier out the "Truth about the BBS" (big bass secret)...
All this double bass matter is probably due to the fact that your bass player friends do play electric bass. They depend on amplification and speakers for the reproduction of their instrument, so when they are playing the lowest notes of the bass they assume that what listeners hear is the first and second overtones and hardly the fundamental, but if you got the bass plugged into an osciloscope, you could see that the sine wave would be of 41.2 Hz (if you could supress distortion in the bass' electric cart), as David has clearly explained, electronic music reproduction has limitations that one must be aware of.
In fact, since frequency doubles when you play the same note of the next higher octave, many people hardly distinguish as different notes the same E of next octaves.
*** All this double bass matter is probably due to the fact that your bass player friends do play electric bass…
41.2 Hz is the lowest frequency at which a string of that length and weight vibrates. The vibration pattern producing that frequency has fixed points at the bridge and nut (the point where the string is anchored at the top of the neck) and the point of maximum amplitude is at the midpoint of the string.The string also vibrates at frequencies which are harmonically related to that full length vibration. They occur at whole number multiples of the fundamental frequency - twice, three times, four times, five times, etc - and are related to vibration patterns of half, one third, one quarter, one fifth etc of the whole string length.
The string vibrations are transmitted to the sounding board, the top of the instrument's body, via the bridge and the bulk of the sound that people hear comes from the vibration of the sound board which is a mechanical amplifier for the sound of the vibrating string. The volume of a string vibrating on its own is not very loud and the vibration has to be transferred to something else which will vibrate and project the sound more efficiently.
The body of the instrument will have it's own natural resonant frequency which may or may not be the same as the note being played. Actually, the resonant pattern of the body of the instrument can be quite complex with the back, sides, top or sound board, and neck all having different resonant frequencies which you can hear by tapping them.
"The body of the instrument will have it's own natural resonant frequency which may or may not be the same as the note being played. Actually, the resonant pattern of the body of the instrument can be quite complex with the back, sides, top or sound board, and neck all having different resonant frequencies which you can hear by tapping them."And it is all these differences that differentiate the "tone" of double bass A from double bass B. In addition, the type of string used also does affect the 'tone', but to a smaller extent from my experience.
I started to, and the post kept getting more and more complex. In the end I just cut all of that material out.Instrument construction is an arcane art. I used to be friends with a classical guitar maker and owned a couple of his guitars at one stage, and watched him building instruments, including one of mine, over a number of years. Theory is one thing and practice is another, and the practice of building great instruments relies a lot on gut feel and instinct. The theory only gets you so far, but when you get to the point of realising that the timber used in each sound board is different and start to try and extract the most from each individual board, for example, you end up in totally new terrain each time. You've never worked on THIS piece of timber before and it has it's own character. Experience helps to a degree but ultimately you start to do something unique with each instrument, and they each end up with their own individual character even though the instruments of each maker do have their own family characteristics. The range of things that make a difference is quite large and very small variations on a physical level can have a profound effect on the finished product.
excellent post! thanks.but maybe the issue has changed to the difference between the lowest note of a musical instrument vs. the lowest frequency one can hear through a particular audio system in a particular room.
by Johan Sundberg (Academic Press). Then you'll understand what you're talking about because fundamental frequency (aka Fo) is the main frequency on a given note. Every sound source which is not producing pure tones (like a diapason or a clinical audiometer that are capable of producing just one frequency sounds) produces sounds which consist in a fundamental frequency and harmonics, all entire multiples of the Fo, thus if a bass is emitting a 37 Hz fundamental, also produces 74, 148, 296..... overtones, but you don't hear all them, due to resonancy characteristics of each instrument overtones can be amplified and conform formants, these formants are the "signature" of every sound source, they allow you to distinguish an /a/ vowel of an /e/ when speaking, the voice from your grandfather from your father's and a real organ from an electronic one. Sound sources DON'T produce harmonics under the fundamental, but some resonance characteristics of the rooms, specially if static waves are present, can enhance the lower frequencies. It is possible, for some instruments, even for human voice, to produce formants of higher intensity than the fundamental, perhaps what your musician friends meant was that in double bass the first formant has more energy than the fundamental, that's why most listeners only perceive that 140 Hz freq you mention, but that doesn't mean that very low freqs. aren't produced.
Have you ever wondered how can an opera singer to sing louder than the whole orchestra if the maximum SPL of human voice at Fo is 105 dB and the orchestra can go above 110 dB? Have you realized that at the opera most of the time you simply cannot understand the words of what they sing? If you're interested I can explain ;-))
"Have you realized that at the opera most of the time you simply cannot understand the words of what they sing?"And all this time I thought it was because they were in Italian.
It's fun, but I'm from Spain I think I'm fluent in english and I speak french and italian (i've said speak, not to write) and always when going to opera wondered why I couldn't understand a word unless I was reading the booklet with the words, despite I could clearly hear singers' voices on top of the orchestra.
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