Tag Archives: music

Zoo Jokes, Symphony Joke

I went to the zoo to see the baguettes…

….They’re bread in captivity.

The had a pig there, sweltering in the sun.

He was bakin’

I dan’t go the symphony anymore, these days …

… It’s all sax and violins.

Robert Buxbaum, Aug. 2, 2023 –It’s summer, what do you expect? Life’s a beach.

Alice’s Restaurant and Nuclear Waste

It’s not uncommon for scientists to get inspiration from popular music. I’d already written about how the song ‘City of New Orleans’ inspires my view of the economics of trains, I’d now like to talk about dealing with nuclear waste, and how the song Alice’s Restaurant affects my outlook.

As I see it, nuclear power is the elephant in the room in terms of clean energy. A piece of uranium the size of a pencil eraser produces as much usable energy as three rail cars of coal. There is no air pollution and the land use is far less than for solar or wind power. The one major problem was what to do with the left over eraser-worth of waste. Here’s the song, it’s 18 1/2 minutes long. The key insight appeared in the sixth stanza: “…at the bottom of the cliff there was another pile of garbage. And we decided that one big pile Is better than two little piles…”

The best way to get rid of nuclear waste would be (as I’ve blogged) to use a fast nuclear reactor to turn the worst components into more energy and less-dangerous elements. Unfortunately doing this requires reprocessing, and reprocessing was banned by Jimmy Carter, one of my least favorite presidents. The alternative is to store the nuclear waste indefinitely, waiting for someone to come up with a solution, like allowing it to be buried in Yucca Mountain, the US burial site that was approved, but that Obama decided should not be used. What then? We have nuclear waste scattered around the country, waiting. I was brought in as part of a think-tank, to decide what to do with it, and came to agree with several others, and with Arlo Guthrie, that one big pile [of waste] Is better than two little piles. Even if we can’t bury it, it would be better to put the waste in fewer places (other countries bury their waste, BTW).

That was many years ago, but even the shipping of waste has been held up as being political. Part of the problem is that nuclear waste gives off hydrogen — the radiation knocks hydrogen atoms off of water, paper, etc. and you need to keep the hydrogen levels low to be able to transport the waste safely. As it turns out we are one a few companies that makes hydrogen removal pellets and catalysts. Our products have found customers running tourist submarines (lead batteries also give off hydrogen) and customers making sealed electronics, and we are waiting for the nuclear shipping industry to open up. In recent months, I’ve been working on improving our products so they work better at low temperature. Perhaps I’ll write about that later, but here’s where you’d go to buy our current products.

Robert Buxbaum, July 4, 2021. I’ve done a few hydrogen-related posts in a row now. In part that’s because I’d noticed that I went a year or two talking history and politics, and barely talking about H2. I know a lot about hydrogen — that’s my business– as for history or politics, who knows.

Making The City of New Orleans profitable

The City of New Orleans is the name of the only passenger train between Chicago and New Orleans. It’s also the name of a wonderful song by Steve Goodman, 1971. Hear it, sung by Arlo Guthrie with scenes from a modern ride.

“Riding on the City of New Orleans
Illinois Central Monday morning rail
Fifteen cars and fifteen restless riders
Three conductors and twenty-five sacks of mail
All along the southbound odyssey
The train pulls out at Kankakee
Rolls along past houses, farms and fields
Passin’ trains that have no names
Freight yards full of old black men
And the graveyards of the rusted automobiles…”

Every weekday, this train leaves Chicago at 9:00 PM and gets into New Orleans twenty hours later, at 5:00 PM. It’s a 925 mile trip at a 45 mph average: slow and money-losing, propped up by US taxes. Like much of US passenger rail, it “has the disappearing railroad blues.” It’s a train service that would embarrass the Bulgarians: One train a day?! 45 mph average speed!? It’s little wonder is that there are few riders, and that they are rail-enthusiasts: “the sons of Pullman porters, and the sons of engineers, Ride[ing] their father’s magic carpets made of steel.” The wonder, to me was that there was ever fifteen cars for these, “15 restless riders”.

A sack of mail being picked up on the fly.

I would be happy to see more trips and a faster speed, at an average speed of at least 60 mph. This would require 85 mph or higher between stops, but it would save on salaries, and it would bring in some new customers. But even if these higher speeds cost nothing extra, in net, you’d still need something more to make the trip profitable; a lot more if the goal is to add another train. Air-traffic will always be faster, and the automobile, more convenient. I find a clue to profitability in the fifteen cars of the song and in the sacks of mail.

Unless I’m mistaken, mail traffic was at least as profitable as passenger traffic, and those “twenty-five sacks of mail” were either very large, or just the number on-loaded at Kankakee. Passenger trains like ‘the city of New Orleans’ were the main mail carriers till the late 1970s, a situation that ended when union disputes made it unprofitable. Still, I suspect that mail might be profitable again if we used passenger trains only for fast mail — priority and first class — and if we had real fast mail again. We currently use trucks and freight trans for virtually all US mail, we do not have a direct distribution system. The result is that US mail is vastly slower than it had been. First class mail used to arrive in a day or two, like UPS now. But these days the post office claims 2 to 4 business days for “priority mail,” and ebay guarantees priority delivery time “within eight business days”. That’s two weeks in normal language. Surely there is room for a faster version. It costs $7.35 for a priority envelope and $12.80 for a priority package (medium box, fixed price). That’s hardly less than UPS charges.

Last day of rail post service New York to Washington, DC. .June 30, 1977.

Passenger trains could speed our slow mail a lot, if it were used for this, even with these slow speeds. The City of New Orleans makes this trip in less than a day, with connections available to major cities across the US. If priority mail went north-south in under one day, people would use it more, and that could make the whole operation profitable. Trains are far cheaper than trucks when you are dealing with large volumes; there are fewer drivers per weight, and less energy use per weight. Still there are logistical issues to making this work, and you want to move away from having many post men handling individual sacks, I think. There are logistical advantages to on-loading and off-loading much larger packages and to the use of a system of standard sizes on a moving conveyor.

How would a revised mail service work? I’d suggest using a version of intermodal logistics. Currently this route consists of 20 stops including the first and last, Chicago and New Orleans. This suggests an average distance between stops of 49 Miles. Until the mid 70s, , mail would be dropped off and picked up at every stop, with hand sorting onboard and some additional on-off done on-the-fly using sacks and hooks, see picture above. For a modern version, I would suggest the same number of passenger stops, but fewer mail pick ups and drop offs, perhaps only 1/3 as many. These would be larger weight, a ton or more, with no hand sorting. I’d suggest mail drop offs and pick ups every 155 miles or so, and only of intermodal containers or pods: ten to 40 foot lengths. These containers plus their contents would weigh between 2,500 and 25,000 pounds each. They would travel on flatcars at the rear of the passenger cars, and contain first class and priority mail only. Otherwise, what are you getting for the extra cost?

The city of New Orleans would still leave Chicago with six passenger cars, but now these would be followed by eight to ten flatcars holding six or more containers. They’d drop off one of the containers at a stop around the 150 mile mark, likely Champaign Urbana, and pick up five or so more (they’d now have ten). Champaign Urbana is a major east-west intermodal stop, by the way. I’d suggest the use of six or more heavy forklifts to speed the process. At the next mail-stop, Centralia, two containers might come off and four or more might come on. Centralia is near St. Louis, itself a major rail hub for trains going west. See map below. The next mail stop might be Memphis. Though it’s not shown as such, Memphis is a major east-west rail hub; it’s a hub for freight. A stripped down mail-stop version of passenger train mail like this seems quite do-able — to me at least. It could be quite profitable, too.

Amtrak Passenger rail map. The city of New Orleans is the dark blue line going north-south in the middle of the map.

Intermodal, flat-bed trucks would take the mail to sorting locations, and from there to distribution points. To speed things, the containers might hold pre-sorted sacks of mail. Intermodal trucks might also carry some full containers east and west e.g. from Centralia to St. Louis, and some full flatcars could be switched on and off too. Full cars could be switched at the end, in New Orleans for travel east and west, or in the middle. There is a line about “Changing cars in Memphis Tennessee.” I imagine this relates to full carloads of mail joining or leaving the train in Memphis. Some of these full intermodal containers could take priority mail east and west. One day mail to Atlanta, and Houston would be nice. California in two days. That could be a money maker.

At this point, I would like to mention “super-fast” rail. The top speeds of these TGV’s “Transports of Grande Vitess” are in the range of 160 mph (265 km/hr) but the average speeds are lower because of curves and the need to stop. The average speeds are roughly 125 mph on the major routes in Europe, but they require special rails and rail beds. My sense is that this sort of special-use improvement is not worth the cost for US rail traffic. While 60 -90 mph can be handled on the same rails that carry freight, the need for dedicated track comes with a doubling of land and maintenance costs. And what do you have when you have it? The bullet rail is still less than half as fast as air travel. At an average speed of 125 mph, the trip between Chicago and New Orleans would take seven hours. For business travelers, this is not an attractive alternative to a two hour flight, and it is not well suited for intermodal mail. The fuel costs are unlikely to be lower than air travel, and there is no easy way to put mail on or off a TGV. Mail en-route would slow the 125 mph speed further, and the use of intermodal containers would dramatically increase the drag and fuel cost. Air travel has less drag because air density is lower at high altitude.

Meanwhile, at 60 mph average speeds, train travel can be quite profitable. Energy use is 1/4 as high at 60 mph average as at 120 mph. An increase of average speed to 60 mph would barely raise the energy use compared to TGV, but it would shorten the trip by five hours. The new, 15 hour version of “The City of New Orleans” would not be competitive for business travel, but it would be attractive for tourists, and certainly for mail. Having fewer hours of conductor/ engineer time would save personnel costs, and the extra ridership should allow the price to stay as it is, $135 one-way. A tourist might easily spend $135 for this overnight trip: leaving Chicago after dinner and arriving at noon the next day. This is far nicer than arriving at 5:00 PM, “when the day is done.”

Robert Buxbaum, June 21, 2019. One summer during graduate school, I worked in the mail room of a bank, stamping envelopes and sorting them by zip code into rubber-band tied bundles. The system I propose here is a larger-scale version of that, with pre-sorted mail bags replacing the rubber bands, and intermodal containers replacing the sacks we put them in.

Seize the day

It is forbidden knowledge what our term of years, mine and yours.
Don’t scan the tables of your Babylonian seers.
Better far to bear the future, my Leuconoe, like the past.
Whether Jupiter has many years yet to give,
Or this one is our last:

This, that makes the Tyrrhene waves spent against the shore.
Strain your wine and strain your wisdom.
Life is short; should we hope for long?
In the moment of our talking, precious time has slipped away.
Seize the moment. Trust tomorrow little as you may.

by Horace (23 BC Roman poet) Odes, 1.11

This poem by Horace, in 23 BC is the first appearance of the phrase “carpe diem,” translated as seize he day. I’d decided to look over the translation from Wikipedia, and to correct and update the translation as I saw fit, to some extent to extract the meanings better, to some extent to make the grammar less-clunky, and to some extent to make it rhyme. Seen in context, the whole poem looks  romantic, and the intent of the famous phrase seems more like ‘seize the moment’ when read in context. Either translation is acceptable from the Latin, as I understand it.

The phrase, “seize the day” appears in several important movies. Robin Williams speaks it to a class of literature students in the sense that I read it here — seize the moment — in this scene of “The Dead Poets Society,” He’s trying to get the boys to appreciate the purpose of poetry, and the preciousness of their years in prep-school. A well-done movie, IMHO. The newspaper sellers sing the phrase for different intent in this song in “Newsies.” For them, the intent is more like seize the opportunity, or maybe even seize power. It’s not Horace’s intent, but it’s sung in front of the statue of Horace Greeley, and it works.

In either context, there is a certain young masculinity about this phrase. In both movie, the cast experiencing the idea is male and young. I don’t think either movie would work as well with women dancing or singing to this idea.

Robert E. Buxbaum, March 9, 2019. In case you should wonder what happens to Frank Kelly (Sullivan) after the movie ends, I’ve written about that.  Also, a friend of mine notes that the grammar used in these movies is wrong:  “Carpe diem” is singular, for this 3rd declension noun. The equivalent Latin plural is “Carpite diem:” That’s the equivalent of you-all, should seize the moment. Unlike in the movies, much of classic education is spent on pedantic, uninspiring, minutia, like Latin grammar, but that’s what’s necessary to permit distinction of meaning. Thank you, David Hoenig for grammar help.

God bless you Canada

Canada is a fine country, rarely appreciated in the USA because most of it is so similar to us — One of my favorite places to visit in Canada was the museum of Canadiana — a museum dedicated to the differences between the US and Canada. Differences do exist, but they are few and small, as you can tell perhaps from the song below, “God Bless You Canada,” by Lee Greenwood, the same fellow who wrote, “God Bless the USA.” The tunes and words are strongly similar, I’d say.

Canada is much easier to reach than Hawaii for the most part, or Alaska, Puerto Rico, or Guam, it’s just north of Montana and south of Alaska and Detroit. And Canadian English is at least as understandable as a southern drawl or a New Yorker twang. Canada has far fewer murders but far more rapes, armed robberies and assaults. It has the same suicide rate as we do, but by different means. And Toronto’s mayor was on crack like Detroit’s mayor.

Canadian $2 coin, Elizabeth II, by the grace of god, Queen. The last part is in Latin.

Canadian $2 coin, Elizabeth II, by the grace of god, Queen (it’s in Latin).

Canada has a Queen, Elizabeth II, that it shares with several other countries including England, Australia, and Barbados. This is no to say that Canada isn’t quite independent: the main power of Canada’s Queen, like with the US president, is “the bully pulpit”. As in The United States. The press does its best to rein in this power.

If Canada were to join the US as the 51 state, it be the 3rd largest state in population (after Texas and California) and the 3rd largest in GDP (after New York and California). Not that all of Canada is likely to join, but certain parts might (New Brunswick, Newfoundland, Labrador) if Quebec goes its separate way. Québécois like remember that they were originally French. “Je me Souviens” is the Quebec motto, and having an English Queen irks. One of my favorite Canada facts (maybe true) is that the name Canada is French for Ça nada (nothing here) but tit’s not sure, there is stuff and people there. My wife is from there. Listen to the song, “God Bless you, Canada”, I suspect you’ll like it.

Robert Buxbaum, September 17, 2018.

Sex differences in addiction.

Men become addicted and so do women, but the view in popular movies and songs present some clear differences. Addicted men are presented as drunks or stoners. By contrast, the popular picture of an addicted woman is a middle-aged housewife who takes “mother’s little helper“: anti-depressant and pain pills, “mother’s little helper of the classic Rolling Stones song. Male addicts are presented to take their drugs in the company of friends while female addicts are pictured taking their pills in private. A question I have: is there any evidence to back these popular perceptions.

All addiction may not be bad. Though Churchill was addicted to drink, he imagined it as a virtue not a vice.

Not all who are addicted consider their addiction a liability. Though Churchill was addicted to drink, starting the day with a tumbler of whiskey, he imagined it as a virtue. One would be hard-pressed to prove otherwise.

As it happens, if you look at the statistics in a certain way, they do bear out the popular perceptions. About three times as many men as women are in treatment for alcohol or pot, voluntary or court-mandated. Meanwhile, as a percentage of the addicted, women are nearly twice as likely as men to claim pills as their primary addiction. Percentage data is plotted below. The problem with the percentage graph is that it ignores the fact that twice as many men as women are in treatment: 1,233,000 men vs 609,000 women, as of 2011. Multiply the total numbers by the percentages and you find that there are more men than women with primary addiction to pills, or to cocaine, heroin, or meth-amphetamines. For any drug you mention, the real sex-difference is that more men are addicts.

It could be argues that rehab attendance is a bad measure of addiction, but I would argue that this is the best measure, not only are the numbers are more accurate, rehab is an indication that the addict feels that his or her addiction is a problem. It is a mistake, I think, to include people who feel their addiction is not ruining their lives with people who do not, e.g. Churchill. Any person who believes he or she is benefiting, and who has managed to avoid running afoul of the police, it could be argued, does not have a serious problem. Friends and employers may disagree in terms of diagnosis, but in terms of statistics, other measures like self-reporting come to the same conclusion: if it’s a stupid addiction, more men do it than women. Men self-report that they smoke more, binge-drink more, and use drugs more. Men also commit suicide more and end up in jail more.

Main addiction of men and women. percent based on rehab records, 2011. From the TEDS Report 4/3/14. Twice as many men as women go to rehab.

Main addiction of men and women. percent based on rehab records, 2011. From the TEDS Report on substance abuse. 4/3/14. The most significant sex difference, as I see it: twice as many men as women go to rehab.

In terms of age of prescription drug use, the graph below shows a difference between men and women. There is a slight tendency for women to persist with prescription drugs, but that may reflect the tendency for men to move on to some other stupid behavior.

While more female than male addicts consider opioids their main addiction, since there are twice as many male addicts as female, it comes out that the number using opioids is about the same. Interestingly, a greater fraction of men seem capable of switching out from opioids -- likely to some other addiction.

While more female than male addicts consider opioids their main addiction, since there are twice as many male addicts as female, it comes out that the number using opioids is about the same. A greater fraction of men switch out from opioids, perhaps to another addiction. Source: ibid.

A few cheerful bits of news are in order. One is that smoking, the most deadly of the addictions, is on the decline. It seems like vaping is a contributor to this, and much safer. Similarly, with illicit drug addictions, while use is on the upswing, and while an amazingly large share of Americans have used such drugs — see graph below from Statista — only a small fraction remain users into middle age. Most seem to quit on their own — they even seem to quit heroin when it ceases to serve a purpose. At present, only 60,000/year total die of overdose out of some 120,000,000 who’ve used illicit drugs. Ringo Starr’s song, “I don’t smoke it no more“may be cited, especially when paired with his “Oh my my” song about quitting through dance. If you want to quit and dance doesn’t work for you, I’d suggest AA or NA. To quote Ringo: “You can do it if you try.”

Number of people in the US using different drugs as of 2016. The vast majority have not used in the last year.

Number of people in the US who have used different illegal drugs as of 2016. It’s about 1/3 of America. The vast majority from every category have quit, and are not using. 89% of heroin uses have quit. You can too. Statista.

As for why men more than women do drugs, all I can say is that they do all sorts of stupid things. They fight in wars more often, they go over Niagara Falls in barrels more often, and they start new businesses more often. Sometimes it works for them; usually not. Here is a more detailed article with the same semi-conclusion: men are stupid, risk takers. I suspect that’s their language of love.

Robert Buxbaum, June 11, 2018

Marijuana, paranoia, and creativity

Many studies have shown that marijuana use and paranoid schizophrenia go together, the effect getting stronger with longer-term and heavy use. There also seems to be a relation between marijuana (pot) and creativity. The Beetles and Stones; Dylan, DuChaps, and Obama: creative musicians painters, poets and politicians, smoked pot. Thus, we can ask what causes what: do crazy, creative folks smoke pot, or does pot-smoking cause normal folks to become crazy and creative, or is there some other relationship. Dope dealers would like you to believe that pot-smoking will make you a creative, sane genius, but this is clearly false advertising. If you were not a great artist, poet, or musician before, you are unlikely to be one after a few puffs of weed.

The Freak Brothers, by Gilbert Shelton. While these boys were not improved by dope, It would be a shame to put the artist in prison for any length of time.

The Freak Brothers, by Gilbert Shelton. What’s the relationship?

When things go together, we apply inductive reasoning. There are four possibilities: A causes B (pot makes you crazy and/or creative), B causes A (crazy folks smoke pot, perhaps as self medication), A and B are caused by a third thing C (in this case, poverty culture, or some genetic mutation). Finally, it’s possible there’s no real relationship but a failure to use statistics right. If we looked at how many golf tournaments were won by people with W last names (Woods, Wilson, Watson) we might be fooled to think it’s a causal relationship. Key science tidbit: correlation does not imply causation.

The most likely option, I suspect is that some of all of the above is going on here: There is an Oxford University study that THC, the main active ingredient in pot, causes some, temporary paranoia, and another study suggests that pot smoking and paranoid insanity may be caused by the same genetics. To this mix I’d like to add another semi-random causative: that heavy metals and other toxins that are sometimes found in marijuana are the main cause of the paranoia — while being harmful to creativity.

marijuana -paranoia

Pot cultivation is easy — that’s why it’s called weed– and cultivation is often illegal, even in countries with large pot use, like Jamaica. As a result, I suspect pot is grown preferentially in places contaminated with heavy metal toxins like vanadium, cadmium, mercury, and lead. No one wants to grow something illegal on their own, good crop-land. Instead it will be grown on toxic brownfields where no one goes. Heavy metals are known to absorb in plants, and are known to have negative psychoactive properties. Inhalation of mercury is known to make you paranoid: mad as a hatter. Thus, while the pot itself may not drive you nuts, it’s possible that heavy metals and other toxins in the pot-soil may. The creativity would have to come from some other source, and would be diminished by smoking bad weed.

I suspect that creativity is largely an in-born, genetic trait that can be improved marginally by education, but I also find that creative people are necessarily people who try new things, go off the beaten path. This, I suspect, is what leads them to pot and other “drug experiments.” You can’t be creative and walk the same, standard path as everyone else. I’d expect, therefore, that in high use countries, like Jamaica, creative success is preferentially found in the few, anti-establishment folks who eschew it.

Robert E. (landslide) Buxbaum, September 4, 2014. The words pot, marijuana, dope, and weed all mean the same but appear in different cultural contexts. To add to the confusion, Jamaicans refer to pot as ganja or skiff, and their version of paranoid schizophrenia is called “ganja psychosis”. I’m not anti-pot, but favor government regulation— perhaps along the lines of beer regulation, or perhaps the stricter regulation of Valium. My most recent essay was on the tension-balance between personal freedom and government control. I was recently elected in Oak Park’s 3rd voting district. My slogan: “A Chicken in every pot, not pot in every chicken”. I won by one vote. For those who are convinced they’ve become really deep, creative types without having to create anything, let me suggest the following cartoon about talent. Also, if pot made you smart, Jamaica would be floating in Einsteins.

The speed of sound, Buxbaum’s correction

Ernst Mach showed that sound must travel at a particular speed through any material, one determined by the conservation of energy and of entropy. At room temperature and 1 atm, that speed is theoretically predicted to be 343 m/s. For a wave to move at any other speed, either the laws of energy conservation would have to fail, or ∆S ≠ 0 and the wave would die out. This is the only speed where you could say there is a traveling wave, and experimentally, this is found to be the speed of sound in air, to good accuracy.

Still, it strikes me that Mach’s assumptions may have been too restrictive for short-distance sound waves. Perhaps there is room for other sound speeds if you allow ∆S > 0, and consider sound that travels short distances and dies out far from the source. Waves at these, other speeds might affect music appreciation, or headphone design. As these waves were never treated in my thermodynamics textbooks, I wondered if I could derive their speed in any nice way, and if they were faster or slower than the main wave? (If I can’t use this blog to re-think my college studies, what good is it?)

I t can help to think of a shock-wave of sound wave moving down a constant area tube of still are at speed u, with us moving along at the same speed as the wave. In this view, the wave appears stationary, but there is a wind of speed u approaching it from the left.

Imagine the sound-wave moving to the right, down a constant area tube at speed u, with us moving along at the same speed. Thus, the wave appears stationary, with a wind of speed u from the right.

As a first step to trying to re-imagine Mach’s calculation, here is one way to derive the original, for ∆S = 0, speed of sound: I showed in a previous post that the entropy change for compression can be imagines to have two parts, a pressure part at constant temperature: dS/dV at constant T = dP/dT at constant V. This part equals R/V for an ideal gas. There is also a temperature at constant volume part of the entropy change: dS/dT at constant V = Cv/T. Dividing the two equations, we find that, at constant entropy, dT/dV = RT/CvV= P/Cv. For a case where ∆S>0, dT/dV > P/Cv.

Now lets look at the conservation of mechanical energy. A compression wave gives off a certain amount of mechanical energy, or work on expansion, and this work accelerates the gas within the wave. For an ideal gas the internal energy of the gas is stored only in its temperature. Lets now consider a sound wave going down a tube flow left to right, and lets our reference plane along the wave at the same speed so the wave seems to sit still while a flow of gas moves toward it from the right at the speed of the sound wave, u. For this flow system energy is concerned though no heat is removed, and no useful work is done. Thus, any change in enthalpy only results in a change in kinetic energy. dH = -d(u2)/2 = u du, where H here is a per-mass enthalpy (enthalpy per kg).

dH = TdS + VdP. This can be rearranged to read, TdS = dH -VdP = -u du – VdP.

We now use conservation of mass to put du into terms of P,V, and T. By conservation of mass, u/V is constant, or d(u/V)= 0. Taking the derivative of this quotient, du/V -u dV/V2= 0. Rearranging this, we get, du = u dV/V (No assumptions about entropy here). Since dH = -u du, we say that udV/V = -dH = -TdS- VdP. It is now common to say that dS = 0 across the sound wave, and thus find that u2 = -V(dP/dV) at const S. For an ideal gas, this last derivative equals, PCp/VCv, so the speed of sound, u= √PVCp/Cv with the volume in terms of mass (kg/m3).

The problem comes in where we say that ∆S>0. At this point, I would say that u= -V(dH/dV) = VCp dT/dV > PVCp/Cv. Unless, I’ve made a mistake (always possible), I find that there is a small leading, non-adiabatic sound wave that goes ahead of the ordinary sound wave and is experienced only close to the source caused by mechanical energy that becomes degraded to raising T and gives rise more compression than would be expected for iso-entropic waves.

This should have some relevance to headphone design and speaker design since headphones are heard close to the ear, while speakers are heard further away. Meanwhile the recordings are made by microphones right next to the singers or instruments.

Robert E. Buxbaum, August 26, 2014

Musical Color and the Well Tempered Scale

by R. E. Buxbaum, (the author of all these posts)

I first heard J. S. Bach’s Well Tempered Clavier some 35 years ago and was struck by the different colors of the different scales. Some were dark and scary, others were light and enjoyable. All of them worked, but each was distinct, though I could not figure out why. That Bach was able to write in all the keys without retuning was a key innovation of his. In his day, people tuned in fifths, a process that created gaps (called wolf) that prevented useful composition in affected keys.

We don’t know exactly how Bach tuned his instruments as he had no scientific way to describe it; we can guess that it was more uniform than the temper produced by tuning in fifths, but it probably was not quite equally spaced. Nowadays electronic keyboards are tuned to 12 equally spaced frequencies per octave through the use of frequency counters.  Starting with the A below “middle C”, A4, tuned at 440 cycles/second (the note symphonies tune to), each note is programmed to vibrate at a wavelength that is lower or higher than one next to it by a factor of the twelfth root of two, 12√2= 1.05946. After 12 multiples of this size, the wavelength has doubled or halved and there is an octave. This is called equal tempering.

Currently, many non-electric instruments are also tuned this way.  Equally tempering avoids all wolf, but makes each note equally ill-tempered. Any key can be transposed to another, but there are no pure harmonies because 12√2 is an irrational number (see joke). There is also no color or feel to any given key except that which has carried over historically in the listeners’ memory. It’s sad.

I’m going to speculate that J.S. Bach found/ favored a way to tune instruments where all of the keys were usable, and OK sounding, but where some harmonies are more perfect than others. Necessarily this means that some harmonies will be less-perfect. There should be no wolf gaps that would sound so bad that Bach could not compose and transpose in every key, but since there is a difference, each key will retain a distinct color that JS Bach explored in his work — or so I’ll assume.

Pythagoras found that notes sound best together when the vibrating lengths are kept in a ratio of small numbers. Consider the tuning note, A4, the A below middle C; this note vibrates a column of air .784 meters long, about 2.5 feet or half the length of an oboe. The octave notes for Aare called A3 and A5. They vibrate columns of air 2x as long and 1/2 as long as the original. They’re called octaves because they’re eight white keys away from A4. Keyboards add 4 black notes per octave so octaves are always 12 notes away. Keyboards are generally tuned so octaves are always 12 keys away. Based on Pythagoras, a reasonable presumption is that J.S Bach tuned every non-octave note so that it vibrates an air column similar to the equal tuning ratio, 12√2 = 1.05946, but whose wavelength was adjusted, in some cases to make ratios of small, whole numbers with the wavelength for A4.

Aside from octaves, the most pleasant harmonies are with notes whose wavelength is 3/2 as long as the original, or 2/3 as long. The best harmonies with A4 (0.784 m) will be with notes with wavelengths (3/2)*0.784 m long, or (2/3)*0.784m long. The first of these is called D3 and the other is E4. A4 combines with D3 to make a chord called D-major, the so-called “the key of glory.” The Hallelujah chorus, Beethoven’s 9th (Ode to Joy), and Mahler’s Titan are in this key. Scriabin believed that D-major had a unique color, gold, suggesting that the pure ratios were retained.

A combines with E (plus a black note C#) to make a chord called A major. Songs in this key sound (to my ear) robust, cheerful and somewhat pompous; Here, in A-major is: Dancing Queen by ABBA, Lady Madonna by the BeatlesPrelude and Fugue in A major by JS Bach. Scriabin believed that A-major was green.

A4 also combines with E and a new white note, C3, to make a chord called A minor. Since E4 and E3 vibrate at 2/3 and 4/3 the wavelength of A4 respectively, I’ll speculate that Bach tuned C3 to 5/3 the length of A4; 5/3*.0784m =1.307m long. Tuned his way, the ratio of wavelengths in the A minor chord are 3:4:5. Songs in A minor tend to be edgy and sort-of sad: Stairway to heaven, Für Elise“Songs in A Minor sung by Alicia Keys, and PDQ Bach’s Fugue in A minor. I’m going to speculate the Bach tuned this to 1.312 m (or thereabouts), roughly half-way between the wavelength for a pure ratio and that of equal temper.

The notes D3 and Ewill not sound particularly good together. In both pure ratios and equal tempers their wavelengths are in a ratio of 3/2 to 4/3, that is a ratio of 9 to 8. This can be a tensional transition, but it does not provide a satisfying resolution to my, western ears.

Now for the other white notes. The next white key over from A4 is G3, two half-tones longer that for A4. For equal tuning, we’d expect this note to vibrate a column of air 1.05946= 1.1225 times longer than A4. The most similar ratio of small whole numbers is 9/8 = 1.1250, and we’d already generated one before between D and E. As a result, we may expect that Bach tuned G3 to a wavelength 9/8*0.784m = .88 meters.

For equal tuning, the next white note, F3, will vibrate an air column 1.059464 = 1.259 times as long as the A4 column. Tuned this way, the wavelength for F3 is 1.259*.784 = .988m. Alternately, since 1.259 is similar to 5/4 = 1.25, it is reasonable to tune F3 as (5/4)*.784 = .980m. I’ll speculate that he split the difference: .984m. F, A, and C combine to make a good harmony called the F major chord. The most popular pieces in F major sound woozy and not-quite settled in my opinion, perhaps because of the oddness of the F tuning. See, e.g. the Jeopardy theme song, “My Sweet Lord,Come together (Beetles)Beethoven’s Pastoral symphony (Movement 1, “Awakening of cheerful feelings upon arrival in the country”). Scriabin saw F-major as bright blue.

We’ve only one more white note to go in this octave: B4, the other tension note to A4. Since the wavelengths for G3 was 9/8 as long as for A4, we can expect the wavelength for B4 will be 8/9 as long. This will be dissonant to A4, but it will go well with E3 and E4 as these were 2/3 and 4/3 of A4 respectively. Tuned this way, B4 vibrates a column 1.40 m. When B, in any octave, is combined with E it’s called an E chord (E major or E minor); it’s typically combined with a black key, G-sharp (G#). The notes B, E vibrate at a ratio of 4 to 3. J.S. Bach called the G#, “H” allowing him to spell out his name in his music. When he played the sequence BACH, he found B to A created tension; moving to C created harmony with A, but not B, while the final note, G# (H) provided harmony for C and the original B. Here’s how it works on cello; it’s not bad, but there is no grand resolution. The Promenade from “Pictures at an Exhibition” is in E.

The black notes go somewhere between the larger gaps of the white notes, and there is a traditional confusion in how to tune them. One can tune the black notes by equal temper  (multiples of 21/12), or set them exactly in the spaces between the white notes, or tune them to any alternate set of ratios. A popular set of ratios is found in “Just temper.” The black note 6 from A4 (D#) will have wavelength of 0.784*26/12= √2 *0.784 m =1.109m. Since √2 =1.414, and that this is about 1.4= 7/5, the “Just temper” method is to tune D# to 1.4*.784m =1.098m. If one takes this route, other black notes (F#3 and C#3) will be tuned to ratios of 6/5, and 8/5 times 0.784m respectively. It’s possible that J.S. Bach tuned his notes by Just temper, but I suspect not. I suspect that Bach tuned these notes to fall in-between Just Temper and Equal temper, as I’ve shown below. I suspect that his D#3 might vibrated at about 1.104 m, half way between Just and Equal temper. I would not be surprised if Jazz musicians tuned their black notes more closely to the fifths of Just temper: 5/5 6/5, 7/5, 8/5 (and 9/5?) because jazz uses the black notes more, and you generally want your main chords to sound in tune. Then again, maybe not. Jimmy Hendrix picked the harmony D#3 with A (“Diabolus”, the devil harmony) for his Purple Haze; it’s also used for European police sirens.

To my ear, the modified equal temper is more beautiful and interesting than the equal temperament of todays electronic keyboards. In either temper music plays in all keys, but with an un-equal temper each key is distinct and beautiful in its own way. Tuning is engineering, I think, rather than math or art. In math things have to be perfect; in art they have to be interesting, and in engineering they have to work. Engineering tends to be beautiful its way. Generally, though, engineering is not perfect.

Summary of air column wave-lengths, measured in meters, and as a ratio to that for A4. Just Tempering, Equal Tempering, and my best guess of J.S. Bach's Well Tempered scale.

Summary of air column wave-lengths, measured in meters, and as a ratio to that for A4. Just Tempering, Equal Tempering, and my best guess of J.S. Bach’s Well Tempered scale.

R.E. Buxbaum, May 20 2013 (edited Sept 23, 2013) — I’m not very musical, but my children are.