Effect of temperature on tuning

[Little John]

46 minutes ago, David Barnert said:

... except that the Pythagorean system doesn’t include the pure third at the 5th harmonic.

 

Ah, thank you for this David! I had been under the misapprehension that Pythagorean was just another name for pure. Interesting that it's effectively another mean tone tuning, and one that makes the major third actually worse the equal temperament.

[ttonon]

9 hours ago, David Barnert said:

The phrase “twice the pitch” has no meaning.

Hi Dave, you're right. I remember this now but it was so long ago. Pitch is subjective and is a way of ordering tones along a musical scale, not something amenable to numbers and based on fundamental physics, as is frequency.

 

As a small correction, the argument of the log function in your formula should be F/Fo, where Fo is the starting frequency. The idea of F = 0 as a starting frequency isn't sound (pun intended).

 

I also point out that when we add notes with each half tone, we are actually adding frequencies that are multiples of 1.0595 times the frequency of the previous note. The frequencies are not being added. If that were true, each frequency would be the previous frequency plus a DeltaF constant throughout the octave. The "human part" of this is in our feeling that each half tone added is "equal" interval as all other added notes, as in "equal temperament."

 

An interesting experiment would be to have a person with perfect pitch identify the note he hears, of frequencies say from the low end of the piano to the top. Let's say his perfect hearing is perfect. I believe he'd do very well if he hears pure sine waves. Let's then plot his response, using a dot in a graph with both abscissa and ordinate as double axes, one for frequency and the other for "note." If you plot this, I'm sure you'd get a linear, straight line. If a real piano is used, there would probably be more scatter. But there would be no meaning to the locations between the dots.

 

The above picture is what I was visualizing when I made my previous comments. But my error in looking at it this way is that pitch is not a numerical quantity with which you add octaves one on another. It's just notes, or categories. Regardless, thanks for catching that and helping me to understand it better.

[Steve Schulteis]

22 minutes ago, ttonon said:

Let's then plot his response, using a dot in a graph with both abscissa and ordinate as double axes, one for frequency and the other for "note." If you plot this, I'm sure you'd get a linear, straight line.

 

I'm stepping outside my pay grade here, but is this graph what you're describing?

 

[ttonon]

5 hours ago, Little John said:

 

This is a curious assertion. In my experience "overtone", "partial" and "harmonic" are virtually interchangeable (with some slight differences in usage between the scientific and musical communities). I've never come across "harmonics" as being reserved for the overtones at octave intervals. Also they are not the most common. If F is the fundamental frequency of a note its harmonics are at 2F, 3F, 4F, 5F etc. The ones at octave intervals are 2F, 4F, 8F, 16F etc. So "most" harmonics/overtones/partials are not at octave intervals: 3F, 5F, 6F, 7F, 9F, 10F, 11F, 12F, 13F etc.

 

It is from these "non-octave" harmonics that we derive the intervals and notes of the natural scale we use: 3F gives us the fifth note, 5F gives us the (major) third note for example. [These are the pure, natural or Pythagorean intervals, which differ slightly from the intervals derived from adding 100, 200 etc. cents to the pitch, but that's a discussion for a different place!]

Hi John, I agree with your correction. I'll change my post to read, "... overtones, or partials, often in whole number ratios of a fundamental, in which case they are called harmonics."

 

In Physical Acoustics, these terms have specific meaning. The overtones of a tone generator are generally not harmonics, but with instruments that have sustained tones, such as woodwinds, bowed instruments, and free reeds, we don't hear the full overtones and the upper components of the waveform we do hear, called partials, are harmonic. They must be harmonic because the forcing function of these instruments is periodic, which requires that the musical tone and all its partials be exactly periodic. When these instruments are played, a cooperation among all overtones is achieved, whereby only the value of the overtone at the harmonic frequency is utilized. We don't hear the rest of the overtone.

 

With instruments that produce transient sounds, as with struck or plucked instruments such as pianos, guitars, xylophones, bells, etc., there are no time constraints, and the tone generator is allowed to sound all its overtones, which mostly are not strict harmonics, though they are tuned so that the non-harmonicity doesn't sound more like noise.  But even some instruments, such as cymbals and drums, do produce a kind of pleasing noise when used in the right place. The sounds from all these instruments are interesting and pleasing, much because of these nonharmonic features.

 

But it's often quite a chore to tune bells and bars so that their overtones provide a pleasant musical tone when we hear them as upper partials. With strings, there isn't much of an issue with such tuning, and the stretched overtones we hear (because of stiffness) are most appealing and advantageous in providing us with music. But of course, proper string design eliminates too much stiffness, which would lead to such overtone issues. For instance, as you make a string more stiff or thick, it soon becomes a bar.

Edited January 9 by ttonon

[ttonon]

57 minutes ago, Steve Schulteis said:

 

I'm stepping outside my pay grade here, but is this graph what you're describing?

 

No, but it's helpful. Your abscissa incorporates the idea that octaves are equal intervals, by perception, and that's correct. The distance between each of the "A's" is the same. I was visualizing the axis with frequency as the variable, which would erroneously stretch out where the "A's" occur, resulting in a straight line. Thanks for the example.

Edited January 9 by ttonon

[David Barnert]

1 hour ago, ttonon said:

I also point out that when we add notes with each half tone, we are actually adding frequencies that are multiples of 1.0595 times the frequency of the previous note. The frequencies are not being added. If that were true, each frequency would be the previous frequency plus a DeltaF constant throughout the octave. The "human part" of this is in our feeling that each half tone added is "equal" interval as all other added notes, as in "equal temperament."

 

That’s what I’ve been saying all along, although I rounded 1.0595 to 1.06.

[David Barnert]

1 hour ago, Steve Schulteis said:

I'm stepping outside my pay grade here, but is this graph what you're describing?

 

It’s a perfect illustration of the logarithmic relationship between pitch and frequency and as such supports my argument, but it’s not what @ttonon had in mind (as the result of his thought experiment).

[Richard Mellish]

Meanwhile has anyone actually done the experiment to investigate Steve S's original enquiry?

[Wally Carroll]

I will stay away from the math, physics and electrical engineering discussions, and simply add, as some others have suggested, that humidity change is my guess for the changes in pitch recorded by the OP. The mechanism has less to due with a change in air density than with a change in the pressure the wood reedpan is putting on the reedshoes as the humidity changes. I see this every time I tune an instrument. Changing the amount of pressure I use to hold a note on the tuning jig will definitely change the pitch of a note.  Even small additions of pressure will show a measurable effect. This explanation would only apply to vintage style reeds where the reedshoes are dovetailed into the pans. 

[Chris Ghent]

I’m with Wally.

[ttonon]

9 hours ago, Wally Carroll said:

I will stay away from the math, physics and electrical engineering discussions, and simply add, as some others have suggested, that humidity change is my guess for the changes in pitch recorded by the OP. The mechanism has less to due with a change in air density than with a change in the pressure the wood reedpan is putting on the reedshoes as the humidity changes. I see this every time I tune an instrument. Changing the amount of pressure I use to hold a note on the tuning jig will definitely change the pitch of a note.  Even small additions of pressure will show a measurable effect. This explanation would only apply to vintage style reeds where the reedshoes are dovetailed into the pans. 

Wally, when you say you will "stay away" from the math, physics, etc., then make a statement about what you think the physical quantity "pressure" has on another physical quantity, "frequency," with a trail of invoking other physical concepts such as "humidity" and "air density," you're contradicting yourself. In your mind you have a physical theory, even if you don't recognize it as a physical theory. Thus, you are not "staying away" at all. 

 

In my view, your theory is not only incomplete, but also erroneous. Try making your theory more complete, and I might listen more to you.

 

Best regards,

Tom

[Leonard]

For some people knowledge is not based on theory, but mostly on experience. 

For people whose knowledge is based on theory it can be hard to believe there isn't a hidden theory. 

But that's just my experience....

[Wally Carroll]

Tom,

Alex is a classier guy than I am and probably saved himself a lot of needless misery by not replying above.  As you can tell from my misuse of the word "physics" I am not as smart as he.  So let me clear 3 things up . . . 

1) by "physics" I was referring to the type of computational physics that was being discussed above.  I could have been more accurate but I thought it was pretty clear from the context.  In fact there is nothing I could say about the mechanics of the concertina without invoking general principles of physics. 

2) I stand by my belief that the most likely candidate for the drift in tuning is humidity change and I think I explained it well enough (though certainly not exhaustive) for almost anyone to understand.

3) I really don't care if you listen more to me or not.  My only concern is that you not poison the well for everyone else by creating a toxic atmosphere where people are afraid to engage or where the discourse becomes charged.  There are many ways you can challenge ideas that you disagree with without belittling the other party.  

 

*I've spent enough time on this now so I'm going to walk away.  And yes, Alex is definitely smarter.

 

[ttonon]

1 minute ago, Leonard said:

For some people knowledge is not based on theory, but mostly on experience. 

For people whose knowledge is based on theory it can be hard to believe there isn't a hidden theory. 

But that's just my experience....

Sorry, I hate to drive home the point, but virtually all people who say they are basing their observation on experience provide at least a semblance of a physical theory to support their claim.  

 

Wally is one example. He reports his observation that variations of pitch occur with changes in humidity. That's fine, in itself and I have no objections to it. But he goes  far beyond that when he asserts his theory that the swelling of the wood because of changes in humidity causes changes in clamping pressure on the reed assembly, and that's what causes changes in tuning.

 

It's comical, like shooting at someone in the dark. He says he doesn't want to get into the science of it all but expects us to accept his scientific theory on why he observes what he does.

 

Wally, let me ask, why don't you just state your observation and leave it to more technically competent posters to devise a physical explanation? 

[ttonon]

38 minutes ago, Wally Carroll said:

Tom,

Alex is a classier guy than I am and probably saved himself a lot of needless misery by not replying above.  As you can tell from my misuse of the word "physics" I am not as smart as he.  So let me clear 3 things up . . . 

1) by "physics" I was referring to the type of computational physics that was being discussed above.  I could have been more accurate but I thought it was pretty clear from the context.  In fact there is nothing I could say about the mechanics of the concertina without invoking general principles of physics. 

2) I stand by my belief that the most likely candidate for the drift in tuning is humidity change and I think I explained it well enough (though certainly not exhaustive) for almost anyone to understand.

3) I really don't care if you listen more to me or not.  My only concern is that you not poison the well for everyone else by creating a toxic atmosphere where people are afraid to engage or where the discourse becomes charged.  There are many ways you can challenge ideas that you disagree with without belittling the other party.  

 

*I've spent enough time on this now so I'm going to walk away.  And yes, Alex is definitely smarter.

 

Hi Wally, in my latter years, I've become more direct and to the point. I wasn't always so, but I find it to be the best overall approach because when I become too concerned with how people choose to react to my writing, I waste a lot of time. 

 

I've learned that people who say they are "belittled" by others are most often choosing to feel belittled, and they are motivated for that. Most often it's because they have no factual or rational defense, and so attacking the other person is the only way they can keep asserting their erroneous position.  So why do you choose to feel belittled?

 

I had no intention of belittling you. I addressed only what you wrote, not you personally, and even you (now) acknowledge that you made errors in what you wrote. So why condemn me for pointing out your errors, your incompleteness, and the unusual physical theories you put forth, and still do put forth? (By the way, you can't belittle me because I know who I am.)

 

Have you noticed that people who claim to be belittled accuse the other person of behaving in the displeasing way they themselves are behaving? Your comment about me poisoning the group is a good example. It's you who is poisoning the group with your language and with your attack on me. It seems you want this group to be poisoned, because when it is, you believe most everyone will see me as the miscreant. I think you're probably wrong. 

 

When people correct me for my erroneous thinking, I usually thank them. You can look through this thread for proof of that. Why do you choose instead to throw a tantrum? Why are you asserting that you cannot make any error regarding the laws of physics, at the same time you're denying any reference to physics? This is childish behavior. I ask you this because I still have hopes you can reconnect with your inner self who happens to be a well-meaning, adult human being. I think you just lost sight of that.

 

Best regards,

Tom

 

 

[Stephen DOUGLASS]

Bringing it back to the original post. There is an interesting thread in bagpipe maker Jon Swayne's page, which relates to air speed and temperature. Scrolling down there is an interesting table on change of pitch depending on temp. As a skilled 'pipemaker' he will have done his homework.

https://www.jonswayne.com/_files/ugd/6788c4_901e3df0e96f41c8a1a3a169b9700740.pdf

[ttonon]

51 minutes ago, Stephen DOUGLASS said:

Bringing it back to the original post. There is an interesting thread in bagpipe maker Jon Swayne's page, which relates to air speed and temperature. Scrolling down there is an interesting table on change of pitch depending on temp. As a skilled 'pipemaker' he will have done his homework.

https://www.jonswayne.com/_files/ugd/6788c4_901e3df0e96f41c8a1a3a169b9700740.pdf

Stephen, thanks for the info, but this is really not directly related to free reeds. The chanter of bagpipes in Western Europe are double reeded, and thus resemble oboes and bassoons. I understand that in other countries they are single reeded, like clarinets. But in all cases, they are beating reeds and not free reeds. I'm sure many here know that beating reeds regulate the pressure pulses to a vibrating air column, and the acoustic vibration modes of this air column are what produce the musical tone. That's why the speed of sound is a relevant parameter in the tuning of these instruments. 

 

Such is not the case with western free reeds, whose sound source is the vibrating cantilever of the reed tongue, and this vibration doesn't on the vibrations of an air column. With the Asian (symmetric) free reeds, however, there is an acoustic coupling between the reed and an air column, so there, the speed of sound is relevant. The effects of temperature on western (unsymmetric) free reeds, however, is thus an entirely different effect than the effects of temperature on the vibrating air columns of woodwinds and Asian free reed instruments. 

 

Best regards,

Tom