[LUTE] Re: Fourier measurements of lute sound.
Le 29 janv. 09 à 01:17, Herbert Ward a écrit : The width of the central peak ... increases as the interval decreases, but I could not come up with any simple mechanism that would shift the maximum of the curve noticeably. I verified this experimentally. In other words, determining frequencies with shorter time intervals in Fourier analysis is like reading a speedometer whose needle get wider -- you're OK if you use the middle of the needle as the hotspot. Maybe the following qualitative argument explains your observed shift to lower frequencies. Initially, all the vibrational energy is in the vibrating string. Then other parts of the lute start to vibrate too, which means that the the body of the lute drains energy out of the string, which provides an effective damping mechanism. If we can consider the vibrating string as a damped harmonic oscillator, it would indeed vibrate at a lower frequency than an undamped string. I find this plausible. We might even cast other harmonics within the same string as dampers (or even antidampers), since energy transfers between the harmonics due to string imperfections such as stiffness and finite stretchability. Are you suggesting that the Fo of the string at a particular tension would be higher without damping, but that damping gives the impression that it is lower? Creaky voice, which can often be heard from English speakers at the end of an intonation unit, could be a form of this. It seems that some of the beats of the vocal chords are partially damped so that the cycle appears longer than it in fact is. about two octaves below the frequency of normal voicing. http://en.wikipedia.org/wiki/Creaky_voice Algorithms for intonation analysis, usually fail to be able to give a curve for such speech. Anthony To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Fourier measurements of lute sound.
Le 29 janv. 09 à 11:09, Anthony Hind a écrit : Le 29 janv. 09 à 01:17, Herbert Ward a écrit : The width of the central peak ... increases as the interval decreases, but I could not come up with any simple mechanism that would shift the maximum of the curve noticeably. I verified this experimentally. In other words, determining frequencies with shorter time intervals in Fourier analysis is like reading a speedometer whose needle get wider -- you're OK if you use the middle of the needle as the hotspot. Maybe the following qualitative argument explains your observed shift to lower frequencies. Initially, all the vibrational energy is in the vibrating string. Then other parts of the lute start to vibrate too, which means that the the body of the lute drains energy out of the string, which provides an effective damping mechanism. If we can consider the vibrating string as a damped harmonic oscillator, it would indeed vibrate at a lower frequency than an undamped string. I find this plausible. We might even cast other harmonics within the same string as dampers (or even antidampers), since energy transfers between the harmonics due to string imperfections such as stiffness and finite stretchability. Are you suggesting that the Fo of the string at a particular tension would be higher without damping, but that damping gives the impression that it is lower? Creaky voice, which can often be heard from English speakers at the end of an intonation unit, could be a form of this. It seems that some of the beats of the vocal chords are partially damped so that the cycle appears longer than it in fact is. about two octaves below the frequency of normal voicing. http://en.wikipedia.org/wiki/Creaky_voice Algorithms for intonation analysis, usually fail to be able to give a curve for such speech. Anthony Or are you talking tonally? Do you mean that upper harmonics are damped, and thus the string sounds tonally lower? AH To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Fourier measurements of lute sound.
On Wed, 28 Jan 2009, Herbert Ward wrote: The width of the central peak ... increases as the interval decreases, but I could not come up with any simple mechanism that would shift the maximum of the curve noticeably. I verified this experimentally. In other words, determining frequencies with shorter time intervals in Fourier analysis is like reading a speedometer whose needle get wider -- you're OK if you use the middle of the needle as the hotspot. I'd say it's more like standing still for half an hour, then going 100 miles per hour for the next 30 minutes, and arguing in court that you do not deserve a ticket because your average speed was 50 miles per hour. Stated differently, I am not sure that our brains can associate a unique pitch with a sound that has lasted for only 0.1 sec any more than you can by looking at the power spectrum obtained by Fourier analysis. Peter. the next auto-quote is: We lock up our poor, our uneducated, our unruly, our unstable and our addicted, where other countries provide treatment, mental hospitals and care. (Jesse Jackson Sr.) /\/\ Peter Nightingale Telephone (401) 874-5882 Department of Physics, East Hall Fax (401) 874-2380 University of Rhode Island Kingston, RI 02881 To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Fourier measurements of lute sound. [Scanned]
... Fourier analysis ... Very Good. But why? I guess it's like combing one's hair -- just a general desire for orderliness. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Fourier measurements of lute sound.
The width of the central peak ... increases as the interval decreases, but I could not come up with any simple mechanism that would shift the maximum of the curve noticeably. I verified this experimentally. In other words, determining frequencies with shorter time intervals in Fourier analysis is like reading a speedometer whose needle get wider -- you're OK if you use the middle of the needle as the hotspot. Maybe the following qualitative argument explains your observed shift to lower frequencies. Initially, all the vibrational energy is in the vibrating string. Then other parts of the lute start to vibrate too, which means that the the body of the lute drains energy out of the string, which provides an effective damping mechanism. If we can consider the vibrating string as a damped harmonic oscillator, it would indeed vibrate at a lower frequency than an undamped string. I find this plausible. We might even cast other harmonics within the same string as dampers (or even antidampers), since energy transfers between the harmonics due to string imperfections such as stiffness and finite stretchability. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Fourier measurements of lute sound.
3. The harmonics' pitches are not consistent with each other, especially during the initial 0.3 second. For example, the fundamental can be at -4 cents, and the first harmonic (an octave above the fundamental) can be at +4 cents. These observations provide an ample hypothesis for tuner instability, but unfortunately suggest no solution. Tune by ear! :-) No tuner can hear harmonics, our ears can. So you get better results in matching different strings with inconsistent harmonics. Try to tune some much to small children's guitars with bad strings every day, and you'll learn, promised :-) Regards, Stephan To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Fourier measurements of lute sound.
Also, you would expect a brief transient regime before the string settled into a nominally stable state (overlaid by ongoing decay as energy is gradually lost). During the transient period, I wouldn't expect a Fourier spectrum to be terribly meaningful, or at least it would be more difficult to interpret. That said, I'm not sure how long the transient regime would last, but something like 0.1 sec or so sounds plausible. What do you suppose would cause this regime? I agree a transient regime's Fourier spectrum would be more difficult to interpret, if only because it is changing so rapidly (on the scale of 0.1 to 0.3 seconds). If we assume that such interpretation is possible, then several interesting questions arise about the transient regime: 1. Whether it might occupy enough of the total lifetime of the note to account for the inconsistent readings I note in non-stroboscopic tuners. 2. Whether/how it might be related to what is called bad tone by lute players (i.e., controllable by RH technique). 3. Whether it is more pronounced with lutes than with guitars. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Fourier measurements of lute sound.
I am a little puzzled by what you write. Guessing at what you might be doing, I would say that your fundamental in roughly at 300Hz. Observing a frequency in that range for 0.3 seconds gives you about 100 oscillations. With 100 oscillations, the accuracy of the measured frequency cannot exceed 1%, because you might have failed to account for roughly a cycle. Whatever your do, Fourier transformations included, suffers from this fundamental limitation, and to get better accuracy you need either more time or a higher frequency. In other words, given that 1200 x log_2(101/100) = 17, a measurement of a frequency in the 300Hz range derived from a 0.3 sec. observation cannot produce a result with an error smaller than about 10 cents, which is bigger than the effects you seem to talking about, but maybe I am incorrectly interpreting your email. Thanks for the note. I did indeed observe that the peaks in the spectrum broadened as the observation region was decreased. However, I made the assumption that the peak centroids remained unmoved despite the broadening, and thus I thought my results unaffected. It seems the validity of my assumption can be easily checked by using a tone from an electronic device and doing the Fourier integral over many different observation times, varying both in length and start time. I'll do this in the next few days. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Fourier measurements of lute sound.
I think the calibration data are important. We are just seeing a picture of a sound with no reference data to compare it to. I would want to pop a couple of waves through to test the equipment, square in, square out, etc. I tested the equipment and program with all 12 tones from a Korg tuner. The Korg happily has a calibration to allow setting its tones to A 416 instead of 415. using this non-standard setting too. All tests were passed. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Fourier measurements of lute sound.
But the Korg is not accurate as far as dB, dt At 04:17 PM 1/6/2009, you wrote: I think the calibration data are important. We are just seeing a picture of a sound with no reference data to compare it to. I would want to pop a couple of waves through to test the equipment, square in, square out, etc. I tested the equipment and program with all 12 tones from a Korg tuner. The Korg happily has a calibration to allow setting its tones to A 416 instead of 415. using this non-standard setting too. All tests were passed. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Fourier measurements of lute sound.
On Tue, 6 Jan 2009, Herbert Ward wrote: Thanks for the note. I did indeed observe that the peaks in the spectrum broadened as the observation region was decreased. However, I made the assumption that the peak centroids remained unmoved despite the broadening, and thus I thought my results unaffected. It seems the validity of my assumption can be easily checked by using a tone from an electronic device and doing the Fourier integral over many different observation times, varying both in length and start time. I'll do this in the next few days. I calculated the spectral density of a cosine over a finite interval. The width of the central peak does indeed do what it must, i.e., it increases as the interval decreases, but I could not come up with any simple mechanism that would shift the maximum of the curve noticeably. In other words, my calculation seems to confirm your assumption, and the shift needs some explanation other than the being the result of an arbitrary, ill-defined window function (see e.g. http://en.wikipedia.org/wiki/Window_function). Maybe the following qualitative argument explains your observed shift to lower frequencies. Initially, all the vibrational energy is in the vibrating string. Then other parts of the lute start to vibrate too, which means that the the body of the lute drains energy out of the string, which provides an effective damping mechanism. If we can consider the vibrating string as a damped harmonic oscillator, it would indeed vibrate at a lower frequency than an undamped string. After a while the whole object, body and string, approaches a semblance of equilibrium and in the process the frequency increases as the fast initial damping ceases. It would make sense that this whole process happens much faster than the ultimate damping of the sound. Unfortunately, I do not know how verify all of this in a couple of minutes, but it should not be too difficult to come up with a simple model consisting of a bunch of coupled oscillators. Peter. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html the next auto-quote is: When people learn no tools of judgment and merely follow their hopes, the seeds of political manipulation are sown. (Stephen Jay Gould) /\/\ Peter Nightingale Telephone (401) 874-5882 Department of Physics, East Hall Fax (401) 874-2380 University of Rhode Island Kingston, RI 02881
[LUTE] Re: Fourier measurements of lute sound.
Wow! Nice work. Do you have any screen shots of the Fourier analysis? On Jan 2, 2009, at 7:01 AM, Herbert Ward wrote: Using computerized Fourier analysis, I measured spectra of lute sound, using all strings in courses 1-6, plucked with good tone. Several unexpected features cropped up. 1. The pitch of a harmonic often shifts over the duration of the note, up to 10 cents. 2. The volumes of the harmonics often change relative to each other. Sometimes this can be a strong and surprising effect, as when the fundamental is basically absent during the initial 0.3 second, and then assumes dominance over the harmonics as the note dies away. 3. The harmonics' pitches are not consistent with each other, especially during the initial 0.3 second. For example, the fundamental can be at -4 cents, and the first harmonic (an octave above the fundamental) can be at +4 cents. These observations provide an ample hypothesis for tuner instability, but unfortunately suggest no solution. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html Ed Durbrow Saitama, Japan edurb...@sea.plala.or.jp http://www9.plala.or.jp/edurbrow/
[LUTE] Re: Fourier measurements of lute sound.
Herb, I am a little puzzled by what you write. Guessing at what you might be doing, I would say that your fundamental in roughly at 300Hz. Observing a frequency in that range for 0.3 seconds gives you about 100 oscillations. With 100 oscillations, the accuracy of the measured frequency cannot exceed 1%, because you might have failed to account for roughly a cycle. Whatever your do, Fourier transformations included, suffers from this fundamental limitation, and to get better accuracy you need either more time or a higher frequency. In other words, given that 1200 x log_2(101/100) = 17, a measurement of a frequency in the 300Hz range derived from a 0.3 sec. observation cannot produce a result with an error smaller than about 10 cents, which is bigger than the effects you seem to talking about, but maybe I am incorrectly interpreting your email. Peter. On Thu, 1 Jan 2009, Herbert Ward wrote: Using computerized Fourier analysis, I measured spectra of lute sound, using all strings in courses 1-6, plucked with good tone. Several unexpected features cropped up. 1. The pitch of a harmonic often shifts over the duration of the note, up to 10 cents. 2. The volumes of the harmonics often change relative to each other. Sometimes this can be a strong and surprising effect, as when the fundamental is basically absent during the initial 0.3 second, and then assumes dominance over the harmonics as the note dies away. 3. The harmonics' pitches are not consistent with each other, especially during the initial 0.3 second. For example, the fundamental can be at -4 cents, and the first harmonic (an octave above the fundamental) can be at +4 cents. These observations provide an ample hypothesis for tuner instability, but unfortunately suggest no solution. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html the next auto-quote is: True virtue is life under the direction of reason. (Baruch Spinoza) /\/\ Peter Nightingale Telephone (401) 874-5882 Department of Physics, East Hall Fax (401) 874-2380 University of Rhode Island Kingston, RI 02881
[LUTE] Re: Fourier measurements of lute sound.
Also, you would expect a brief transient regime before the string settled into a nominally stable state (overlaid by ongoing decay as energy is gradually lost). During the transient period, I wouldn't expect a Fourier spectrum to be terribly meaningful, or at least it would be more difficult to interpret. That said, I'm not sure how long the transient regime would last, but something like 0.1 sec or so sounds plausible. Guy -Original Message- From: Peter Nightingale [mailto:n...@pobox.com] Sent: Friday, January 02, 2009 4:59 AM To: Herbert Ward Cc: lute@cs.dartmouth.edu Subject: [LUTE] Re: Fourier measurements of lute sound. Herb, I am a little puzzled by what you write. Guessing at what you might be doing, I would say that your fundamental in roughly at 300Hz. Observing a frequency in that range for 0.3 seconds gives you about 100 oscillations. With 100 oscillations, the accuracy of the measured frequency cannot exceed 1%, because you might have failed to account for roughly a cycle. Whatever your do, Fourier transformations included, suffers from this fundamental limitation, and to get better accuracy you need either more time or a higher frequency. In other words, given that 1200 x log_2(101/100) = 17, a measurement of a frequency in the 300Hz range derived from a 0.3 sec. observation cannot produce a result with an error smaller than about 10 cents, which is bigger than the effects you seem to talking about, but maybe I am incorrectly interpreting your email. Peter. On Thu, 1 Jan 2009, Herbert Ward wrote: Using computerized Fourier analysis, I measured spectra of lute sound, using all strings in courses 1-6, plucked with good tone. Several unexpected features cropped up. 1. The pitch of a harmonic often shifts over the duration of the note, up to 10 cents. 2. The volumes of the harmonics often change relative to each other. Sometimes this can be a strong and surprising effect, as when the fundamental is basically absent during the initial 0.3 second, and then assumes dominance over the harmonics as the note dies away. 3. The harmonics' pitches are not consistent with each other, especially during the initial 0.3 second. For example, the fundamental can be at -4 cents, and the first harmonic (an octave above the fundamental) can be at +4 cents. These observations provide an ample hypothesis for tuner instability, but unfortunately suggest no solution. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html the next auto-quote is: True virtue is life under the direction of reason. (Baruch Spinoza) /\/\ Peter Nightingale Telephone (401) 874-5882 Department of Physics, East Hall Fax (401) 874-2380 University of Rhode Island Kingston, RI 02881
[LUTE] Re: Fourier measurements of lute sound.
I think the calibration data are important. We are just seeing a picture of a sound with no reference data to compare it to. I would want to pop a couple of waves through to test the equipment, square in, square out, etc. dt At 09:39 AM 1/2/2009, you wrote: Also, you would expect a brief transient regime before the string settled into a nominally stable state (overlaid by ongoing decay as energy is gradually lost). During the transient period, I wouldn't expect a Fourier spectrum to be terribly meaningful, or at least it would be more difficult to interpret. That said, I'm not sure how long the transient regime would last, but something like 0.1 sec or so sounds plausible. Guy -Original Message- From: Peter Nightingale [mailto:n...@pobox.com] Sent: Friday, January 02, 2009 4:59 AM To: Herbert Ward Cc: lute@cs.dartmouth.edu Subject: [LUTE] Re: Fourier measurements of lute sound. Herb, I am a little puzzled by what you write. Guessing at what you might be doing, I would say that your fundamental in roughly at 300Hz. Observing a frequency in that range for 0.3 seconds gives you about 100 oscillations. With 100 oscillations, the accuracy of the measured frequency cannot exceed 1%, because you might have failed to account for roughly a cycle. Whatever your do, Fourier transformations included, suffers from this fundamental limitation, and to get better accuracy you need either more time or a higher frequency. In other words, given that 1200 x log_2(101/100) = 17, a measurement of a frequency in the 300Hz range derived from a 0.3 sec. observation cannot produce a result with an error smaller than about 10 cents, which is bigger than the effects you seem to talking about, but maybe I am incorrectly interpreting your email. Peter. On Thu, 1 Jan 2009, Herbert Ward wrote: Using computerized Fourier analysis, I measured spectra of lute sound, using all strings in courses 1-6, plucked with good tone. Several unexpected features cropped up. 1. The pitch of a harmonic often shifts over the duration of the note, up to 10 cents. 2. The volumes of the harmonics often change relative to each other. Sometimes this can be a strong and surprising effect, as when the fundamental is basically absent during the initial 0.3 second, and then assumes dominance over the harmonics as the note dies away. 3. The harmonics' pitches are not consistent with each other, especially during the initial 0.3 second. For example, the fundamental can be at -4 cents, and the first harmonic (an octave above the fundamental) can be at +4 cents. These observations provide an ample hypothesis for tuner instability, but unfortunately suggest no solution. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html the next auto-quote is: True virtue is life under the direction of reason. (Baruch Spinoza) /\/\ Peter Nightingale Telephone (401) 874-5882 Department of Physics, East Hall Fax (401) 874-2380 University of Rhode Island Kingston, RI 02881
[LUTE] Re: Fourier measurements of lute sound.
On Thu, Jan 1, 2009, Herbert Ward wa...@physics.utexas.edu said: Using computerized Fourier analysis, I measured spectra of lute sound, using all strings in courses 1-6, plucked with good tone. The lute is a complex generator. You have cross-couplings between the strings of a course, and other courses as well as with the top. The act of plucking stretches the string, raising the fundamental pitch, as the string vibrations yield energy the tension decreases, lowering pitch. I suspect the reflection of each wave develops the harmonics, they may not be present initially, so some time-lag will be seen in their history; perhaps different time lags for each harmonic. Try more experiments with some strings dampened by felt to isolate coupling issues. -- Dana Emery To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Fourier measurements of lute sound.
The fundamental should be present in your data set. Are you using a measurement microphone? dt At 02:01 PM 1/1/2009, you wrote: Using computerized Fourier analysis, I measured spectra of lute sound, using all strings in courses 1-6, plucked with good tone. Several unexpected features cropped up. 1. The pitch of a harmonic often shifts over the duration of the note, up to 10 cents. 2. The volumes of the harmonics often change relative to each other. Sometimes this can be a strong and surprising effect, as when the fundamental is basically absent during the initial 0.3 second, and then assumes dominance over the harmonics as the note dies away. 3. The harmonics' pitches are not consistent with each other, especially during the initial 0.3 second. For example, the fundamental can be at -4 cents, and the first harmonic (an octave above the fundamental) can be at +4 cents. These observations provide an ample hypothesis for tuner instability, but unfortunately suggest no solution. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
