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Natural Science Forum / Physics / Acoustics / September 2004chords versus single notes
Acoustically speaking, how is a chord different from a single note? If a certain acoustic event is produced by simultaneously plucking two or more strings on (for example) a guitar, could the same event be produced by plucking a single string on another guitar that was tuned differently? Can anybody recommend a good resource for learning about the acoustics of music? Any help will be mucho appreciado. Peace Op Wed, 15 Sep 2004 06:19:06 GMT schreef Elaine Jackson: > Acoustically speaking, how is a chord different from a single note? If a certain > acoustic event is produced by simultaneously plucking two or more strings on > (for example) a guitar, could the same event be produced by plucking a single > string on another guitar that was tuned differently? Can anybody recommend a > good resource for learning about the acoustics of music? Any help will be mucho > appreciado. Any note played on any instrument actually consists of a series of frequencies, called the overtones or harmonics. The note you perceive is called the base note, and has a frequency of x Hz. Then the overtones have the frequencies 2x, 3x, 4x, 5x etc. (Exception: clarinets and some organ pipes only have the odd overtones: 3x, 5x, 7x etc.) So if you play a chord, you get two (or more) series of overtones; that's how the ear (or rather: the brain) can distinguish them. So it is not possible to play one note and have it sound as a chord. Plus: when two notes sound together, they donot only produce their own individual overtone series, but each couple of frequencies produce a sum and a differential tone: Say, frequencies y and z are played, then you also hear y+z and y-z. A chord is actually quite a complicated structure...  SignatureJan Willem from Odijk, Netherlands e-mail in From-field is wrong, real e-mail is: jw point van point dormolen on hccnet point nl (change point into dot, on into at) And then there's this: Before Xerox, five carbons were the maximum extension of anybody's ego Jan, > when two notes sound together, they donot only produce their own individual overtone series, but each couple of frequencies produce a sum and a differential tone: < That's true only in the presence of nonlinearity. In a normal system, and surely acoustically in the air away from all electronics, sum and difference frequencies are not generated. If that were so, all music would sound very ugly! Now, you could argue that air is nonlinear and technically you'd be right. But in that case the IM products are so low as to be inaudible and irrelevant to this discussion. --Ethan >Jan, > [quoted text clipped - 12 lines] > >--Ethan Sum and difference tones can indeed be heard in the air. But most acoustical sound sources radiate in very complex ways, varying by direction, and most musical instruments have enough chaos (phase jitter, etc) to mask the effects. Some kinds of electroacoustical instruments and some kinds of droning chants can make the effects more noticeable. SignatureMatthew H. Fields http://personal.www.umich.edu/~fields Music: Splendor in Sound To be great, do things better and better. Don't wait for talent: no such thing. Brights have a naturalistic world-view. http://www.the-brights.net/ Op Wed, 15 Sep 2004 17:31:52 GMT schreef Dr.Matt: >>Jan, >> [quoted text clipped - 12 lines] > effects. Some kinds of electroacoustical instruments and some kinds of > droning chants can make the effects more noticeable. Indeed, I have a clarinet duet somewhere that deliberately uses these tones to create the illusion of a clarinet trio. It's quite effective. SignatureJan Willem from Odijk, Netherlands e-mail in From-field is wrong, real e-mail is: jw point van point dormolen on hccnet point nl (change point into dot, on into at) And then there's this: For THIS I bought a computer? >Op Wed, 15 Sep 2004 17:31:52 GMT schreef Dr.Matt: > [quoted text clipped - 17 lines] >Indeed, I have a clarinet duet somewhere that deliberately uses these tones >to create the illusion of a clarinet trio. It's quite effective. A duet of soprano recorders or piccolos also makes these effects quite evident. SignatureMatthew H. Fields http://personal.www.umich.edu/~fields Music: Splendor in Sound To be great, do things better and better. Don't wait for talent: no such thing. Brights have a naturalistic world-view. http://www.the-brights.net/ >> when two notes sound together, they donot only produce their own >individual overtone series, but each couple of frequencies produce a sum and [quoted text clipped - 4 lines] >frequencies are not generated. If that were so, all music would sound very >ugly! This one's been done to death not that long ago :-) Tell that to a piano tuner, who uses "beats" to set strings just the right amount away from perfect intervals. Or mix two sine waves of slightly different frequencies in a wave editor. You can SEE the difference tones in the waveform, let alone hear them. Guys, > Sum and difference tones can indeed be heard in the air. < I think you guys are confusing a few different issues here. First, there's a big difference between beat frequencies - amplitude modulation - and the generation of new content. Sometimes you can hear sum and difference tones in the air when the original tones are very loud, but in that case the IM products are generated by nonlinearity in your hearing. Or, put another way, it's all in your head. :->) I hear this when I sub for the percussion player in our local symphony, and play the orchestra bells. If I hit two nearby high notes very loudly, nonlinearity in my ears creates new difference tones much lower in pitch. But that's definitely not occurring in the air. Again, if that were the case every two note chord you ever play would sound horribly out of tune. > Tell that to a piano tuner ... You can SEE the difference tones in the waveform, let alone hear them. < As proof of the difference between AM beating and the generation of new content I just created a Wave file having equal amounts of 50 Hz and 200 Hz. I did this in Sound Forge, and then used the Spectrum Analyzer tool to display the content. All I see are two big blips - one at 50 Hz and another at 200 Hz. Nothing at 150 or 250. If you still don't believe me I'll upload a small screen cap of the display, or you can just try it yourself if you have similar tools. --Ethan >Guys, > [quoted text clipped - 24 lines] > >--Ethan Again, check out the nonlinear response of your ears to any piccolo duet. SignatureMatthew H. Fields http://personal.www.umich.edu/~fields Music: Splendor in Sound To be great, do things better and better. Don't wait for talent: no such thing. Brights have a naturalistic world-view. http://www.the-brights.net/ Matt, > Again, check out the nonlinear response of your ears to any piccolo duet.< Yes, but the key is nonlinear response of your *ears*. The sum and difference tones are generated in your ears, not acoustically in the air. Which is what I said originally. --Ethan >Matt, > [quoted text clipped - 6 lines] > >--Ethan But it's certainly audible from normal acoustical sound sources, and if not taken into account, could surprise the composer. I've seen composers who thought the players were playing "ugly" or that somebody was humming a bass line along with 'em.... SignatureMatthew H. Fields http://personal.www.umich.edu/~fields Music: Splendor in Sound To be great, do things better and better. Don't wait for talent: no such thing. Brights have a naturalistic world-view. http://www.the-brights.net/ Matt, I wanted to let you know that I just spent a fair amount of time at your web site and was very impressed. Your music is great! Please let me know when I can buy a CD. I also enjoyed your exchange with Florsheim, and all the related stuff. You and I have an awful lot in common. --Ethan >Matt, > [quoted text clipped - 4 lines] > >--Ethan Thanks for the interest! I'll keep folks posted. SignatureMatthew H. Fields http://personal.www.umich.edu/~fields Music: Splendor in Sound To be great, do things better and better. Don't wait for talent: no such thing. Brights have a naturalistic world-view. http://www.the-brights.net/ I notice that, unfortunately, whenever a cross posted message shows here, spam soon follows. I think the acoustics group regulars are rarely a source of spam, but the cross posted groups may well be more prone, especially the popular avocational groups. So, whenever a cross posted message shows, erase the other groups when responding, as I did here. In that way, we can maintain a more trouble free forum. Angelo Campanella Op Thu, 16 Sep 2004 18:19:24 GMT schreef Dr.Matt: >>Matt, >> [quoted text clipped - 11 lines] > composers who thought the players were playing "ugly" or that somebody > was humming a bass line along with 'em.... Also, who cares where the tones come from? They are there, that's what counts. SignatureJan Willem from Odijk, Netherlands e-mail in From-field is wrong, real e-mail is: jw point van point dormolen on hccnet point nl (change point into dot, on into at) And then there's this: I hate it when people tell me I cannot take criticism. [snip] play the orchestra bells. If I hit two nearby > high notes very loudly, nonlinearity in my ears creates new difference > tones > much lower in pitch. I used to play bells too and noticed this phenomenon. I played orchestral, and played Glock in marching band - that one especially killed my ears. I assume that the low frequency tone produced has to be above roughly 20 hz for us to perceive it (or we hear it as individual beats). A couple of people have mentioned Duets that took advantage of this phenomenon. To get an audible Bass note, I assume the original pitches have to be in a certain ratio, and at a certain pitch/frequency level before we begin to notice them. Are there any charts or tables that anyone knows of that list such combinations or is it working out all of the math? As a guitarist, we often tune using two harmonics, the lowest pair being at E4 - and if they're close, you get very slow beating, and as they get more "out of tune" (approaching a semitone or tone) the beats increase in speed. It seems at that pitch level it's not high enough to get a really useable "bass" note. However, we also do this thing called a unison bend, where the note D might be bent up to E, matching an E on an adjacent string. When doing so, as the lower pitched note approaches the higher pitched note, you get a low tone that descends in pitch (the frequency gets slower, just like the beats, but here the original pair of notes is high enough (E5) to produce a useable (or at lease discernable) low pitch) Now of course, many guitarists tend to use distortion/overdrive of some sort, and this principle is amplified by that - even when I play a fourth or fifth it will usually produce an "undertone" that is the "root" of the dyad. I can bend one or both of the strings to make that lower note move around. So I'm wondering, in the case of the Clarinet, Piccolo, and Recorder Duets that have been mentioned, what aspects will create "bass" or "undertone" notes - does it have to be loud, do both notes have to be close, or will a 7th or 9th work, do they have to be a certain original pitch level, and if so, what might it be, and, will it work only if the instruments are extremely similar in timbre (or harmonic structure)? Thanks for any suggestions. Steve Steve, > A couple of people have mentioned Duets that took advantage of this phenomenon. < The problem with relying on IM products produced by acoustic instruments is the perceived level of the generated tones depends on how loud the sound is (and the condition of the listener's hearing). So in a small recital hall most listeners might hear the added tones, but in the back row of a large concert hall they'll hear less or none at all. > Are there any charts or tables that anyone knows of that list such combinations or is it working out all of the math? < Here's a list of all the musical notes in all the octaves, and their associated frequencies: www.ethanwiner.com/misc-content/notefreq.gif > However, we also do this thing called a unison bend < I've been a rock 'n' roll lead guitar player for almost 40 years, so I know those techniques well! In fact, hearing those tones go lower in pitch as I stretched a string upward is one of my earliest memories of understanding this phenomenon. When I discussed it (years ago) with my friend Bill Eppler, the most brilliant EE I've ever known, he explained why this occurs only in the presence of nonlinearity. In this case the nonlinearity is in the overdriven guitar amp. > So I'm wondering, in the case of the Clarinet, Piccolo, and Recorder Duets that have been mentioned, what aspects will create "bass" or "undertone" notes - does it have to be loud, do both notes have to be close < Yes, it has to be loud because it relies on distortion occurring in the listener's ears. --Ethan [steve] >> So I'm wondering, in the case of the Clarinet, Piccolo, and Recorder >> Duets > that have been mentioned, what aspects will create "bass" or "undertone" > notes - does it have to be loud, do both notes have to be close < [ethan] > Yes, it has to be loud because it relies on distortion occurring in the > listener's ears. That's what I was afraid of... I was wondering if the audience perceives those glockenspiel "undertones" and I never remembered hearing them as an audience member, but I always assumed it was that the resultant frequencies were of significantly reduced power, and wouldn't carry very far - only to my ears where it made my ear drums rumble. Maybe have to stick to working it out on guitar where I have some "control" over the frequencies! Thanks, Steve Steve, > I was wondering if the audience perceives those glockenspiel "undertones" and I never remembered hearing them as an audience member < Yes, that's exactly my point, and why I mentioned hearing them when *I play the bells* in an orchestra. --Ethan >Acoustically speaking, how is a chord different from a single note? If a certain >acoustic event is produced by simultaneously plucking two or more strings on >(for example) a guitar, could the same event be produced by plucking a single >string on another guitar that was tuned differently? Can anybody recommend a >good resource for learning about the acoustics of music? Any help will be mucho >appreciado. A note consists of a fundamental frequency, and a set of overtones. A "perfect" source has overtones strictly corresponding to the harmonic series. Real-life notes have a much messier set of overtones and, more importantly, are not uniform over time, having notable initial transients containing inharmonic frequencies. All this helps to explain why, generally, two notes are heard as two notes, not as one composite. You CAN arrange things so that multiple sounds meld into a single perceived note. When you hit a piano key three strings sound, you hear one note. Plucking two strings, one tuned to a harmonic of the first (with carefully controlled volume) can sound like an enrichment of the lower note. Do YOU hear the octaves on a 12-string guitar? Now we're getting into perception, not acoustics! A big subject :-) Can one guitar note sound like a chord? Certainly not by simply tuning it differently. But two guitar notes, carefully chosen and balanced, might sound like an enriched single note. Confused? :-) If you do get into the subject, don't get bogged down with the sort of elementary acoustics that assumes all sounds are built from harmonic overtones. Musical sounds (a) aren't, and (b) are defined largely by their initial transients. > Acoustically speaking, how is a chord different from a single note? > If a certain acoustic event is produced by simultaneously plucking > two or more strings on (for example) a guitar, could the same event > be produced by plucking a single string on another guitar that was > tuned differently? Can anybody recommend a good resource for learning > about the acoustics of music? Any help will be mucho appreciado. Some good books that relate music and physics and are light on mathematics: "The Science of Musical Sound" by John R. Pierce (Scientific American, 1983). "The Science of Sound" by Thomas D. Rossing (2nd ed., Addison-Wesley, 1990). "Science and Music" by James H. Jeans (Cambridge U. Press, 1937; Dover, 1968). Interesting question > simultaneously In practice, unlikely. I would imagine that even a couple of milliseconds spread between the start of the sounds would be enough to give the ear, or rather the brain, the hint to treat is as two sounds, not one. Then, transients. The harmonics on two seperate strings, in the first couple of milliseconds, will be changing radically in different ways; again, the brain will decide that is two sounds, not one. Excellent music acoustics book is Campbell and Greated 'The Musicians' Guide to Acoustics' SignatureJ. Simon van der Walt - Composer <http://www.jsimonvanderwalt.com> Don't forget Benade's wonderful "Fundementals of Musical Acoustics." And also don't forget that most percussion instruments (xylophone bars, bells, etc.) are (a) not generating "even" harmonics in the sense of integer multiples of the fundamental and (b) not always "tuned" to their fundamental, but to their first harmonic because it's a slightly stronger mode of vibration. My $0.02. Best regards, Jeff D. Szymanski Chief Acoustical Engineer Auralex Acoustics, Inc. |
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