Global flattening

[MikeW]

Don't know how old this is, but I didn't find any reference to it on TN with the "advanced search" feature...

Whilst the possibility that increased levels of atmospheric carbon dioxide could give rise to global warming has been widely publicised, a concomitant phenomenon of interest to practicioners of early music, namely global flattening of pitch, has hardly received any attention. The pitch of a wind instrument is inversely proportional to its length and to the density of the gas it contains. In calculating the pitch of the many surviving wind instruments from earlier centuries it has hitherto always been assumed that the latter factor is a constant. Clearly however this is not the case: if we calculate the effect of the increase in carbon dioxide levels the change in pitch is by no means negligible. The atomic weight of nitrogen is 14, of oxygen 16 and carbon is 12 (ignoring trace amounts of carbon-14). Nitrogen and oxygen are divalent, so their molecular weights are 28 and 32 respectively. The resulting molecular weight of the mixture of nitrogen and oxygen in the ratio found in air is approximately 28.8. However the molecular weight of carbon dioxide is 44 and thus even small amounts of this compound make a significant contribution to the density of the resulting gas.

Calculation of the fall in pitch resulting from this over the period from 1700 to the present day is a problem too complex for these pages, but an article from the Journal of Theoretical and Applied Accoustics, published at the beginning of this month, suggests a figure of 5.5%. This means that the pitch of a baroque instrument which today is a=415 would at the time of construction actually have been A=438, i.e. almost exactly the modern concert pitch of A=440.

This seems to be saying that if you want your baroque music to sound authentic, you need to play it on a modern instrument.

[iiipopes]

Except that we still have Handel's tuning fork at A=423, and tuning forks have practically nil variation with pressure or temperature.

[MikeW]

Except that we still have Handel's tuning fork at A=423, and tuning forks have practically nil variation with pressure or temperature.

An interesting point, and there goes another three hours I'll never see again....
I gather that in Handel's time, standard "A" ranged anywhere from 392 to 466 Hz (actually, that should probably read "double vibrations per second"), and academics are still wrangling over what Handel actually used his 422.5 Hz tuning fork for. He doesn't seem to have bothered reclaiming it when he left it behind after a gig, so maybe he didn't actually use it that much anyway ?

[MikeW]

Problem is, pitch has NOT fallen over the past few hundred years. If anything, it continues to climb.

Also, pipe organs designed, built and voiced from the baroque and classic period still remain, built to their original A-415 (or even A-390 in some parts of France). Their pitch has not miraculously risen to 440 all these hundreds of years later. If this theory were accurate, the pitch of these historic organs would have changed over time they have not. What's more, unless you take measurements at precisely the same temperature and humidity, your data will be off.

Foll-de-roll !

Assuming this is not a deliberate troll: the original post quotes an article that asserts that as a result of the increase in carbon dioxide in the atmosphere, a wind instrument that played at A=438 when it was built in 1700 would, if it still exists, play at only A=415 Hz in today's atmosphere. The article asserts that the laws of physics dictate that the pitch of a given individual instrument will be lower now than it was when it was made; it does NOT deal with the the frequency to which new instruments are tuned, which as you say always seems to creep upwards.

Thus if the organ-pipes play at A=415 now, they must have played at A=438 when they were first built.. No magic about it, just an increase in the concentration of carbon dioxide in the atmosphere causing a change in the speed of sound, and thus changing the pitch of the organ pipes.

Actually, I'm still not sure if I believe, but it sounds kinda plausible.

I guess the question is, do we know for sure that the organs were calibrated against a 415Hz tuning fork, or are we calculating that pitch from the pipe length, in which case as you mentioned, many factors come into play, one of them being any change in CO2 levels.

I forgot to mention that this factoid appeared on the less serious "Feedback" page in the New Scientist magazine, with a link to bit.ly/global flattening: I don't know if it's a hoax or not, but it looks kind of interesting.

[windshieldbug]

Stringed instruments would presumably NOT be affected by air density so I doubt pitch has been significantly changed, but it does beg the question:

With global warming changes to air density, do Baroque instruments now SOUND louder than they did at the time?...

[ghmerrill]

Stringed instruments would presumably NOT be affected by air density so I doubt pitch has been significantly changed, ...

Because they're not affected by the speed of sound?

Just genuinely curious about the reasoning here.

[windshieldbug]

Stringed instruments would presumably NOT be affected by air density so I doubt pitch has been significantly changed, ...

Because they're not affected by the speed of sound?

Just genuinely curious about the reasoning here.

Aerophones change pitch by area.
Percussive instruments change pitch by mass and/or tension.

Organ pipes, flutes, oboes, horns are aerophones.
Harpsichords, tuning forks, bells are percussive instruments.

[MikeW]

Stringed instruments would presumably NOT be affected by air density so I doubt pitch has been significantly changed, ...

Because they're not affected by the speed of sound?

Just genuinely curious about the reasoning here.

I have the impression that the sound of a string instrument is governed by the length and mass of its strings, the elastic properties of the sound board, and to some extent the resonances of the air inside the sound box. Only the third of these would be affected by a change in the speed of sound in air, so if I were forced to guess, I would say that probably the pitch of the instrument would not change, but there may be an effect on the relative strengths of the overtones.

[pgym]

A few questions:

- what is the molecular mass of the atmosphere;
- how is the molecular mass of the atmosphere calculated;
- what is the percentage of CO2 in the atmosphere;
- how large, according to global warming advocates, is the increase in parts per million volume of CO2 between the dawn of the Industrial Revolution and now;
- assuming for the sake of argument that the numbers cited by global warming advocates are correct, how much has the molecular mass, and consequently the density, of the atmosphere changed since the Baroque period;
- is a change of < 0.018% in the molecular mass of the atmosphere "significant"?

[GC]

Molecular mass of the atmosphere? The atmosphere is a mixture and varies somewhat depending on humidity, altitude, proximity to things that are spewing stuff into the air, and so on.

Much of what you ask can be found with search engines.

[MikeW]

A few questions:

- what is the molecular mass of the atmosphere;
- how is the molecular mass of the atmosphere calculated;
- what is the percentage of CO2 in the atmosphere;
- how large, according to global warming advocates, is the increase in parts per million volume of CO2 between the dawn of the Industrial Revolution and now;
- assuming for the sake of argument that the numbers cited by global warming advocates are correct, how much has the molecular mass, and consequently the density, of the atmosphere changed since the Baroque period;
- is a change of < 0.018% in the molecular mass of the atmosphere "significant"?

From the original posting:

Calculation of the fall in pitch resulting from this over the period from 1700 to the present day is a problem too complex for these pages, but an article from the Journal of Theoretical and Applied Accoustics, published at the beginning of this month, suggests a figure of 5.5%.

I believe the article in question appeared some time in 1998. I can't find this on the internet - maybe I'll try the public library.

[mclaugh]

A few questions:

- what is the molecular mass of the atmosphere;
- how is the molecular mass of the atmosphere calculated;
- what is the percentage of CO2 in the atmosphere;
- how large, according to global warming advocates, is the increase in parts per million volume of CO2 between the dawn of the Industrial Revolution and now;
- assuming for the sake of argument that the numbers cited by global warming advocates are correct, how much has the molecular mass, and consequently the density, of the atmosphere changed since the Baroque period;
- is a change of < 0.018% in the molecular mass of the atmosphere "significant"?

From the original posting:

Calculation of the fall in pitch resulting from this over the period from 1700 to the present day is a problem too complex for these pages, but an article from the Journal of Theoretical and Applied Accoustics, published at the beginning of this month, suggests a figure of 5.5%.

I believe the article in question appeared some time in 1998. I can't find this on the internet - maybe I'll try the public library.

Dude, buy yourself a clue: if you understood what molecular mass is, how it's calculated, and the relationship between the molecular mass and density of a gas, or bothered trying to educate yourself, you'd realize the fallaciousness of the underlying premise that a < 0.02% change in the CO2 content of the atmosphere "make a significant contribution to the density of the resultant gas."

Congratulations, dude: you've been clowned.

[iiipopes]

Pipe organ pipes for the most part are made of a lead/tin alloy. Soft metal. If the pitch has fallen, it is because the languid has sagged, impeding the airway, and/or the toe has compressed under the weight of the pipe, impeding the airflow.

[MikeW]

A few questions:

- what is the molecular mass of the atmosphere;
- how is the molecular mass of the atmosphere calculated;
- what is the percentage of CO2 in the atmosphere;
- how large, according to global warming advocates, is the increase in parts per million volume of CO2 between the dawn of the Industrial Revolution and now;
- assuming for the sake of argument that the numbers cited by global warming advocates are correct, how much has the molecular mass, and consequently the density, of the atmosphere changed since the Baroque period;
- is a change of < 0.018% in the molecular mass of the atmosphere "significant"?

From the original posting:

Calculation of the fall in pitch resulting from this over the period from 1700 to the present day is a problem too complex for these pages, but an article from the Journal of Theoretical and Applied Accoustics, published at the beginning of this month, suggests a figure of 5.5%.

I believe the article in question appeared some time in 1998. I can't find this on the internet - maybe I'll try the public library.

Dude, buy yourself a clue: if you understood what molecular mass is, how it's calculated, and the relationship between the molecular mass and density of a gas, or bothered trying to educate yourself, you'd realize the fallaciousness of the underlying premise that a < 0.02% change in the CO2 content of the atmosphere "make a significant contribution to the density of the resultant gas."

Congratulations, dude: you've been clowned.

Thank you. Given the source and treatment of the original assertion, I was expecting an answer like this. It might still be interesting to see if the quoted Journal actually exists, and whether any vaguely relevant article appeared in it (possibly on April 1st ?)

[MikeW]

.

[MikeW]

PM substitute for "the elephant"

You have PM's blocked so I can't send you this privately -- sorry

The over-sized picture you posted above sends my browser into coniptions. It may be causing inconvenience for other users too.

A little editing may be beneficial ?

The only way I could get back into this thread was to foe you, and I would much prefer that to be as temporary as possible
(oily flattery removed - even I was too embarassed to do that in public)
thank you

[MikeW]

Assuming this is not a deliberate troll:

18+ years as a pipe organ builder.

You mentioned the continuing upward drift in tuning notes, which usually seems to get a rise, so naturally I wondered if you were trolling. Apologies if that was not your intention.

Period wind instruments were typically built to the pitch center of their major city in the area. That pitch center was typically determined by the as built/voiced pitch of the pipe organ.

...

So even as we have historic data showing pitch centers for different regions, and even as A-440 was established by committee (at 65 degrees F), they still postulate that organs were built at A-438?

That does seem to be the implication of the article. I think the crux of the proposition/hoax lies in the question of whether organs of the period were tuned at the time of construction against a standard known to be at 415 Hz, or whether the frequency was determined in modern times by measurement (of the frequency, or of the pipe lengths). I certainly don't know enough to answer that question, and I haven't found anything on that topic on the Internet. I was hoping someone with expertise in your field could settle it, one way or the other.

[MikeW]

Caculating the effect of CO2 on pitch is a chore, but most of the work is already done in the “Handbook for the Speed of Sound in Real Gases, Vol III”.

Atmospheric CO2 before the industrial revolution was fairly steady around 160 to 180 ppm.

Current level is at or about 400 ppm, so the increase is about 220 to 240 ppm (definitely less than 300).

According to the Handbook, increasing the level of CO2 by 100 ppm reduces the speed of sound, and thus the pitch of an organ pipe, by 31 ppm. We are thus fairly safe in saying that pitch has fallen by less than 93 ppm, or 0.0093%.

Comparing this with the 5.5% suggested in the original article, there seems to have been a shift in the decimal place: I guess it must originally have been an April Fool article, but the reference to it was mentioned in a March issue of the New Scientist (which gave fair warning that the references had not been checked).

So ok, I got clowned.

[Art Hovey]

Maybe I have too much spare time on my hands, but....

We know that air density is proportional to the average molecular mass of the air.
We also know that the speed of sound (and hence the resonant frequency of a standing wave) is inversely proportional
to the square root of the air density. That means a one-percent increase in density will cause a 0.5% decrease in frequency.

Going down one semitone means decreasing the frequency of a note by about 5.61%, so the 0.5% decrease mentioned above
corresponds to 0.5/5.61 = 0.089 semitone, or about 9 “cents” on your tuner. Consequently, if the density increases by X%,
the pitch goes down by about 9X cents.

Without the carbon dioxide, dry air is 78% nitrogen, 21% oxygen, and 1% argon, along with insignificant amounts of other gases.
The molecular mass of nitrogen is 28, oxygen is 32, and argon is 40. The average molecular mass of that mixture comes out to 28.96.
(Please check my arithmetic and let me know if I am wrong.)

The molecular mass of carbon dioxide is 44. Before the industrial revolution (around 1760) the carbon dioxide concentration was
about 0.028%. Adding that much CO2 to the pure air described above increases its average molecular mass to:

(28.96 + 0.00028 x 44)/(1.00028) = 28.964.

Today’s CO2 concentration is about 0.0395%, so the average molecular mass is now

(28.96 + 0.000395 x 44)/(1.000395) = 28.966.

Comparing those two values, 28.964/28.966 = 1.000067. That means the air density has increased by about 0.0067% due to the
increase in CO2, which implies a pitch decrease of 9 x 0.0067 = 0.06 cents.

As explained elsewhere, a one-degree (Celsius) change in temperature causes a pitch change of about 3 cents.
So the CO2 effect is roughly equivalent to an air temperature decrease of about 0.02 degrees,
which seems pretty insignificant.

Another factor to consider is humidity. Air can contain up to 5% water vapor, and the molecular mass of water is 18.
So the average molecular mass of humid air is actually less than that of dry air: (28.96 + 0.05 x 18)/(1.05) = 28.44.

Comparing the density of humid air with dry air, 28.44/28.96 = 0.982. That means addition of water vapor can decrease the
air density by about 1.8%, corresponding to a pitch rise of about 16 cents. When you play a cold wind instrument a lot of the
moisture in your breath condenses quickly. When you play a warm instrument less moisture condenses, so more of it remains
as vapor, causing even more rise in pitch than the temperature effect alone would predict. The breath that you exhale may
contain slightly more CO2 than the surroundings, but that effect is insignificant.

These calculations do not in any way imply that the growth of atmospheric CO2 is not a serious issue for global climate.
I am still convinced that this planet is more sensitive than a tuba.

[pgym]

Atmospheric CO2 before the industrial revolution was fairly steady around 160 to 180 ppm.

Source?

Every reputable source I've seen cites the pre-IR atmospheric CO2 level at ~280-300 ppmv. See, e.g., Historical CO2 record derived from a spline fit (20 year cutoff) of the Law Dome DE08 and DE08-2 ice cores; Global Atmospheric Concentration of CO2; Climate Change - European Environmental Agency.

That's a good 50-75% ppmv higher than the figures you're claiming.