Smart Guns. Well, well, well, well. What's going on here?

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[Added later: 2014/5/29]  There has been a shooting in California, where a young man has gone on a shooting spree.  He wanted to kill some young woman who was not cooperating with either his plans for romance or for sex, and didn’t cooperate with his plans for doing violence on her either, so he shot a half-dozen people who happened to be available.

Gun advocates never see the connection between the ready availability of firearms with the incidence of shooting sprees.  [For a look at the objective data, see here in Wikipedia, for a list of countries and their deaths per 100,000 by firearms.  You can sort the table by clicking on little arrows at the top of each column.]   This is one sort of phenomenon that is not open to examining with a controlled statistical study that will convince anyone who refuses to be convinced.  [The US ranks below Peru, Chile and Montenegro for Homicides, while it ranks above (more deaths than) Chile, Peru, Serbia, Switzerland for Total Deaths.  This is probably where the data can be manipulated; taking shooting sprees, are they intentional or unintentional?  I suppose they're classed as homicides.]  The difficulty is that gun advocates —by which I mean those who refuse to allow controls on the purchase and ownership of guns, and they must bear with my using this misnomer to identify them— are generally unreasonable about any sort of gun control.  This is a large class of people, and include at least two people whom I greatly respect, so we must not regard them all as maniacs.  On the other hand, the few people who go on shooting sprees are most certainly unreasonable, and the question that seems to face us is whether we must live our lives in a maner that is dictated by their insanity.  Non-gun users generally feel that we must, and that the rules that govern gun purchases by the vast majority must be designed to prevent the tiny minority of people with mental deficiencies who might decide to go on rampages from doing so.  (We also feel that a lot of accidental shootings will also be prevented.)  The question is confused by the quite significant number of criminals who own guns illegally, and we can expect that if guns were to be made safer by technological means, that the older weapons owned by aggressors will have an advantage in convenience over the newer, safer weapons (see below) in any sort of a shootout.  I have actually witnessed a shootout from my home when I lived elsewhere, but for most readers, an actual shootout would be only an academic possibility!  Families of those in law enforcement or the military probably think that a shootout or an armed altercation is a very real thing, so there are some people on one hand who think of shoulder holsters and concealed weapons and that sort of thing as very real, everyday pieces of equipment, and people like myself on the other hand, who think of this sort of equipment as entirely outside our world.  Gun owners probably think of us as sheep, for whom they have to be responsible.  Well, that’s fine by me; I’m entirely incapable of defending myself except with my bare hands and feet, and I don’t plan to change things.

[Original post: 2014/5/23]
Obviously, we non gun-owners are not usually up on the latest developments in gun technology, gun regulation, and the opinions of the gun lobby on them.  It is trickling in to our attention, firstly, that for more than a decade gun manufacturers (hereinafter “manufacturers”) have been working on developing types on guns that can only be used by authorized owners (hereinafter “Smart Guns”).  In other words, the gun cannot be fired except by the owner of the weapon (hereinafter, “owner”).  Something similar is already available for automobiles (hereinafter “cars”), where a certain wireless device must be carried by the driver of the vehicle, or at the very least, somewhere in the car.

Secondly, this innovation so pleased a New Jersey state representative that she sponsored, and succeeded in getting passed, a state law that required all registered gun retailers (hereinafter “retailers”) to sell only these smart guns, as soon as the technology was widely available.  (In other words, sales of regular dumb guns would be outlawed.)  The law was passed back in 2002, when smart guns were only a glimmer on the horizon.

Meanwhile, thirdly, down at the OK corral, the National Rifle Association (“the NRA”) expressed its opposition to the New Jersey law.  It also expressed its opposition to the concept of smart guns (at least from a practical standpoint.  In principle, though, representatives of the NRA have said that they do not oppose smart technology per se).  So, fourthly, the sponsor of the New Jersey law offered to have the law repealed if the NRA would only stop opposing smart guns.

Why are smart guns so relatively nice (from the point of view of us sissy bleeding hearts)?  You can’t just steal these guns.  You also have to steal the safety device, or you can’t shoot the stolen gun.  Secondly, it raises the possibility that a stolen gun can be traced, just as smart phones can.  It also makes it difficult for little kids to get hold of a gun and shoot if off, a major problem with guns in homes with children.  It also makes it impossible, during a fight between the owner of a gun and an intruder, or anyone, for the gun to be wrested from the one holding it, and to be used against him or her.  These were, ostensibly, the reasons the New Jersey gun law was passed.  All you needed was to buy the smart gun, have a little chip embedded in your skull, or whatever, and nobody could shoot your gun, except you.  (But, as we speak, secret factories on the dark side of the moon are manufacturing universal chips that will allow anyone to shoot off any gun by just concentrating real hard.  Haha, just kidding.)

Why does the NRA oppose the New Jersey law?  Well, obviously, the NRA does not like any restriction on gun ownership whatsoever.  When the government wants to restrict ownership of assault weapons (a type of machine-gun that can fire multiple rounds in quick succession, which would be reasonable for use only in the context of a wartime action, or a police action, or a gang action: you know, breaking down a door and shooting up a complete meeting of an enemy gang, or a prayer meeting, or whatever), the NRA opposes it, because it believes that it would lead to additional proscriptions, and eventually to the complete emasculation of the Freedom to Bear Arms (hereinafter “The Second Amendment”), which is what the NRA practically exists to defend (hereinafter Raison d'etre).

Ironically, the NRA finds itself in the position of opposing the very invention that just might pave the way to the vast majority of those opposed to gun ownership beginning to accept, however grudgingly, the sale and the ownership of guns.  The reasons people like me hate firearms of all kinds are that (1) they’re often used carelessly, (2) they fall into the hands of children, (3) they’re too conveniently accessible when tempers are high, (4) they too easily stolen and used by criminals, and (5) they symbolize the escalating violence in society and in the world.

Of course, nothing can be done about (5); outlawing guns because they symbolize violence is silly, and not something we can impose on people.  Nothing can be done about (1) either.  If we were to forbid the use of cars because people drive carelessly, we would remove a resource that American depend on, however wrong-headedly.  Similarly with (3).  Gun owners are notorious perceived to have uncontrollable tempers, but that is most likely merely a matter of unequal reporting.  But all the other objections —and they’re good objections— are at least significantly addressed by smart gun technology.

But looking at the issue from the point of view of the NRA and the Second Amendment, are they justified in their hostility to smart guns?  Remember that their objection is that when the technology becomes available, government legislation will begin to appear, requiring the smart technology.  Are they justified?  Yes, as illustrated by the New Jersey action.  Quite honestly, the hearts of gun owners and gun advocates have been hardened by a century of (what they perceive as) creeping gun control, so that they are no longer impressed by any instances of careless use or storage of guns, or of preventable massacres, or violent crime statistics.  On the other hand, the hearts of legislators are acutely sensitive to every instance of a gun-related crime which might have been prevented by some measure of gun-control.

I believe that the Second Amendment really has no place in the constitution.  What did it benefit the citizens of the emerging free nation to be guaranteed gun ownership rights?  That they could overthrow a second oppressive foreign power, or their own government, if it were to become oppressive, by sheer force of arms?  On one hand, it is hardly necessary to have force of arms to overthrow the government; all you need is cash.  (It would have made greater sense for the second Amendment to guarantee that every citizen had the right to a personal fortune of the size of that of the Koch brothers, in order to lobby the heck out of the legally constituted government.)  On the other hand, we seem to have a history of overthrowing, or voting out, good government, and replacing it with a terrible government.  For close to 250 years, guns have never been a factor in restoring liberty.  That is not to say that it never will be.  (Heaven knows that votes are getting less and less a factor in determining which sort of government wins power.  See graph at above right.)

Look at automobile safety.  The minute a safety feature is widely available, it becomes law, for instance air-bags.  What about gun safeties?  There have been many groups opposed to requiring gun safety mechanisms, and they continue to be not required.  The only folks objecting to gun safeties on their own merits are those who imagine themselves at a shootout.  Damn, if not for that pesky safety catch, I might be alive right now.  The rest of them object to gun-safety catches simply because: you got it.  If their use was widespread, the damn government would make them mandatory.

If the right of the Second Amendment were to be treated like all other rights: e.g. the right to clean air, or the right to water, or the right to marry whomever you please, or the right to equal protection under the law, then it can be reasonably regulated, and we could require safety catches on all guns, and that guns should be stored safely out of the reach of infants, and that individuals who have a history of violent crime, or those with a history of mental impairment should be denied the right to purchase or own or use firearms.  But since we have the second amendment, the NRA can view any control, no matter how reasonable, as an attempt to abridge the Second A.

The history of this battle has been the history of attempting to persuade the NRA to treat the right to bear arms as any other reasonable right.  Until the air and the water are so polluted that the right to clean air and the right to clean water become more important, the Right to Bear Arms will be fanatically defended in such a way that guns will be a danger to everyone, including their owners.

[Added Later: 2014/5/29]
Just this morning, someone posted a complaint quoting the TV personality, comedian and guest host on Comedy Central, John Oliver, who asks why after 31 school shooting since Columbine, there is still no change in the gun laws.

This resulted in such an enormous volume of responses, both for and against gun regulation that I am simply overwhelmed with the foolishness of typical posts of Facebook.  Is it that those who shoot their mouths off (obviously more acceptable than shooting guns off) are a particularly silly subset of the population, or is the population getting sillier every year?  It might be something to do with the food, or education, or popular entertainment.  There are a million possible hypotheses as to why people are becoming increasingly weak-minded, or that we're more aware of weak-minded folks, simply because they're weak-minded in our faces.  But no way to actually prove anything.

Arch

Archimedes on the Radio: The World Is Not Ready

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I have grievously neglected this blog; let’s see: the last post was more than a month ago.

At least, boys and girls, you have to admit that I don’t keep yammering at you if I don’t have anything to say!  In fact, this is the first time that I’m making a post just because I have been away too long.

Here is a brief report on Arch and his not-so-busy life.  The end of term brought with it the usual desperate scramble to get semester grades calculated and entered.  (It’s interesting: the grades I assign are calculated using an incredibly complicated formula that uses a combination of (A) several semester tests, usually 3, but with the option of using 4; (B) numerous homework assignments, usually about 35; (C) at least one or two so-called ‘extra-credit’ opportunities, which means that if there is a really terrible test, where a large number of my students in a given class reveal that they haven’t a clue about a portion of their curriculum —remember, this is mathematics— they get to work the very same problems on the blackboard sometime when the whole class can meet outside the scheduled period, one at a time, and embarrass themselves for not following the simple procedures that have been taught at such length, to no apparent avail, and get half the points they lost.  Each student is only allowed to make up half the points between his or her score, and the next higher score.  This is a logistical nightmare, and I rub their faces in how painful it is; (D) a score for in-class participation, a score for (E) attendance, and (F) the Final Examination.  I can get the exact same final average by using just (A) and (F), but the remaining test items are effectively nothing but psychological aids.  If I stop using them, the grades would plummet, just because motivation would plummet.  If you did not know already, college kids have to be treated like elementary school kids, and urged and encouraged along.  I do not hand out M&Ms, but a colleague of ours does have one day a week devoted to games, a depth to which I refuse to sink, though I have been known to use a quiz-show format for review sessions.  (It did not work.  Kids do not like routine questions during these Quiz Show games, so they have to be tricky.  But kids are too complacent when someone on a team gets a tricky question right, and the entire class is on the lookout for tricky questions, and completely miss the straightforward questions which are the bread and butter of tests.

This is one of the things that grind my gears, as the man said.  Being accommodated and indulged in college simply postpones the moment at which a young person takes responsibility for his learning and his obligations.  There is a sort of wall that they hit when they get their first job.  Pretty soon, I suppose, special jobs will have to be created in what has heretofore been termed the Real World, little starter jobs, where for a year or two, new hires are given lollipops for everything they do correctly, and gently spanked with a rolled-up newspaper for dropping the ball.  (A fake little starter ball.)

It turned out that the local independent radio station was hurting for spots on its schedule, and my wife and I volunteered.  It took me three weeks to put together something that looks like a program, so that they can see whether they want to put me on the air.  It is called “Music From All Over”, and they’re still getting their heads around the fact that it is not all over the globe, but all over the world of musical styles; eclectic, in other words.

You might not have noticed, but when you hear music on the radio of your car, for instance, it has a sort of marquee that gives a fair degree of text information about the music.  This is packed into the music file itself, part of the mp3 file standard, which allows for non-sound information to be placed at the top of the file, in the so-called file header area.  In the case of sound files, such as a piece of music, this is called meta-data, or just metadata.

[Most modern file types, such as music files, picture files, spreadsheets, documents, web pages, have invisible (for the most part) header areas, in which you can pack in information that used to be considered “extra”, such as author, owner, genre, date of original creation, album cover, composer, and so on.  Even this post, for instance, could contain invisible junk, such as that it was created by Microsoft Word, which is not the case.  I create it right on the Web in an environment called Blogger, which is the blog-creator interface put together by Google themselves, and is a pretty nice HTML editor.  Can you believe that sound files can contain a picture of the album cover?  That is amazing.  And a waste of space, in my humble opinion.]

So, the radio station was pretty keen that all the extra metadata was carefully inserted into each tune that I used, so that each record company and recording artist got credit for being played on the air, since they’re not getting money, or very much, anyway.  Record companies forgo their royalties for small public radio stations.

Apparently many radio show hosts do not do their show on the air, but put their mp3's together at home, at their convenience, and then upload their tracks to the Station’s computer via the Internet, and the computer software, called SAM Broadcaster (one option; apparently there are a few alternative broadcasting softwares, but SAM is the one favored by our station) plays the tracks for you.  The order would be random, which meant that if I also put in some explanation about the music as a separate track, it would be randomized too.

In addition, the station wants either four minutes at the middle of the hour for station identification, or two minutes at the midpoint, and two minutes at the end.  (My wife thinks it is the former, while I believe it is the latter.  We just don’t know yet.  All I have to do is just listen to this station, I suppose.)

A significant number of the tracks I wanted to feature were created by me, as you can guess, and I had to insert the metadata right into the file myself.  The software I use can do this, and I also got free software off the Web that enables anyone to edit the metadata on their own mp3's obtained from anywhere, because metadata is being taken more seriously today, whereas about 10 years ago, record companies just couldn’t be bothered.  Also, sometimes the operating system would strip out the metadata when moving files from your hard disk into a floppy.  I still don’t understand this; do they filter it out, or does Windows maintain the metadata in some other location than the header area, like inside the bowels of, what, MediaPlayer, or something?  What is with all this metadata stripping?  It does not compute.

Anyway, with great difficulty I actually created new mp3's which contained an introduction, the music, and a closing, which sometimes had the performers’ names. (My voice is a lot less clear and attractive than my writing, which tells you something; but no matter how clearly I try to speak, I seem to my own ears to be mumbling.  I need to get a hearing aid---seriously; I can’t hear some of the things my students say, which is a problem, but in my line of work, I can do all the talking first, and then go around the classroom trying to understand what the questions are.  If I were a receptionist, or something, obviously a hearing aid would be a major priority.  A decent hearing aid, the top of the line, is between $3000 and $5000, at time of going to press.)

But now, we have a problem.  I can arrange for the first set of tracks to be exactly 28 minutes, as the engineer wanted, and the second set to be another 28 minutes, so that they had the whole program in the format they wanted for station breaks.  But obviously this does not permit randomization, because if they reorder the tracks so that a track from the second half got into the first half, the 28-minute structure would be screwed.

“I guess you’re going to have to do a 28-minute podcast, or actually, two 28-minute podcasts, then,” said brother engineer.  I pointed out that this meant sacrificing the metadata, because a podcast was just a single mp3, with a whole bunch of “songs”.  (The radio world, as it exists for people outside classical music, is focused on the model of the song, and the album, and the performer.  A performer is a collection of albums, and an album is a collection of songs.  And a genre is a collection of performers.  This is the silliest thing I have yet had to deal with.  As a hierarchical structure it is brilliant, except that it does not reflect the real world.  What about performers who perform in different genres?  Hah.  They create two symbolic performers, one for each genre.  That way they can have the cake and eat it too.  So there’s Linda Ronstadt I, who is a country-western singer, and Linda Ronstadt II, who is a rock singer, or whatever.)

Anyway, I went in with all the songs on a CD, because I was too lazy to pick up a flashdrive to dedicate to the radio program.  I did take in an SD card also with the same songs on that.  (SD cards are the things you use in a phone, or a digital camera.)

Well, they had to ‘rip’ the CD, and they promptly lost all the metadata.  (It is possible to rip the CD and preserve the metadata, but brother engineer (who, to be fair, had been laboring under a personal tragedy at the time) had either not figured how to do this, or was under the impression that my CD had been created without metadata.  But we listened to the tracks anyway, and he liked it.  It was a crazy collection, with my own MIDI stuff, and some classical pieces, some Beatles, some Peter Paul and Mary, some chamber music, some opera, and even a track from my daughter’s first group, Episodes.  It would have satisfied anyone with the attention span of a demented fruit fly, but there was such a variety that, by the same token, it would have antagonized anyone who was any sort of purist.  I also put in a track by Tom Lehrer, namely Alma, which describes a lady who was married to three famous musicians.  (The theme was Three: trios, counterpoint with three themes, etc etc.)

SD card reader

I offered the SD card, with exactly the same material.  But they did not have a SD card reader.  This is a really shoe-string operation.  I offered to donate one of my own SD readers, because I have two.  This way, I contribute to public broadcasting.

You know, it just struck me that, if SAM considered the program to be two programs, one for 28 minutes, and one for another 28 minutes, the program would tolerate shuffling within each of the two segments.  Hmm.  (I hate it when I get brainwaves while in the middle of a post.)

So, anyway, that is where things stand, and I await their decision.  They’re not in a position to turn me away entirely, because they need locally produced shows, or they become a sort of a robot Clear-Channel type of station that plays exactly the same thing that all other Clear-Channel stations play, which is precisely what they do not want to do.  But they could put my show on at midnight on Sunday, when nobody is listening, and still appease their conscience!  And I’m fine with that.

[Added later:]

The reason I'm hiding this down here is because I'm a little bashful about having any Internet readers hearing my gorgeous voice!  Hee hee.

Anyway, I want to try and embed my second radio show (actually, none of the shows have aired yet.  I don't know whether the Mills of our Radio Station grind exceeding small, but they do grind slowly) right here as a second test of the MP3 player capability in HTML.


If you cannot hear the sound, your computer or browser doesn't support the sound format.
Or, you have your speakers turned off :)

Warning: this code might not work. It DOES not work. Yes, it DOES work. You might be asked whether you want to allow QuickTime to run on this site, and you would answer Yes (or No, as appropriate! Turn the volume down, and allow it, just this once.)

It does not appear to work today (2014/6/30)

Let's try somezing different: click here:  Show 1 part 1

Arch

Little-Known, and Oddball Classical Pieces

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‘Little-known’ is pretty obvious, but what do I mean by ‘Oddball’?  I don’t really know, but there are a few pieces of music that are interesting from the point of view of the circumstances under which they were written, or for some such extra-musical aspect of its existence, at least as much as for its interest simply as a piece of music.

People who are trying to “get into” classical music are usually —and quite understandably— interested in trivia about a piece of music (or at least, a piece of music which is associated with some accessible piece of trivia), just so that they have something to hang their thoughts on!

The music of Haydn is famous for little eccentric things that he put into his pieces.  One little-know instance, I believe, is the opening movement of Creation, or Die Schopfung.  It is intended to represent chaos, and as you can appreciate, music is almost the very antithesis of chaos.



(The clip is conveniently titled, in German: "Introduction: Chaos"), and you can almost guess the meaning of the word Einleitung: Lead-in, or introduction).

Bach is holding one of his
crab canons!

My favorite composer is  —surprise!!!— Johann Sebastian Bach (or just Sebastian Bach, as he was apparently called, in his family, since almost all his uncles and cousins were Johann's).  There are a number of oddities to be found in Bach's music, but one of the most fascinating is also one he was evidently most proud of; in fact, he had his portrait drawn with himself holding a scrap of parchment with this piece drawn on it painfully, in oils.  It is a mirror canon, which is a piece that sounds the same played forwards as well as backwards, as well as upside-down.  It is one of --I believe-- several crab canons he wrote, and actually sounds amazingly good, for a piece that tries to do so much.  Incidentally, the first half of the main tune of the canon is just one of the motifs in another piece from the Musical Offering, namely the Trio Sonata.  That has several themes that are traded around between the three voices of the Sonata of which this is one.  (The mirror canon theme is indicated in purple, because it was also known as The Royal Theme.)

Bach also wrote an aria in one of his church cantatas, which was taken from an aria from a "secular" cantata --pieces written for public celebrations, such as the installation of a new City Council, etc; even civic events had religious observations.  (This particular one was written for someone's birthday.)  Anyway, at the end of the aria (vocal solo) in the church cantata, Bach adds a closing section that is a trio, which goes on for almost a minute and a half!  That is certainly unusual.

Canons are certainly interesting: it is a piece in which a second voice enters with the tune after a delay.  It is the same principle as a round, but the tunes are longer, and typically there are just two voices, each following the other.  Pachelbel's Kanon is an exception: it has three voices: the three violins, and as you know well (especially at Christmastime), the tune is far longer than a typical round.

 [Added Later]

Well, I guess I just couldn't resist.  I hunted down the music for Pachelbel’s famous Kanon (a movement from a sonata), and scored it for as wildly different-sounding instruments as I could think of.  The original, scored for three violins and bass is just too homogeneous-sounding for the canon to emerge; it just sounds like a dance with three masked, identical dancers looks : the dancers are indistinguishable, and you have to take the thing as simply abstract moving patterns.  But I gave the top voice (or at least Voice Number 1) to the violin, the next to the flute, and the third to a bassoon.  That move completely destroys the homogeneity, but guess what: you can actually hear the canon beautifully.  So the delicacy and restfulness of the Canon we hear (usually at Christmas, as I remarked) is gone; this version does sound a little rowdy:



Another unusual use of canon is the last movement of Cesar Franck's famous Sonata in A for violin and piano.  This is beautiful, and the canon is only incidental to the beauty of the piece.

Hmm.  Let's see now.  (I'm running out of things that I can remember.)  Ah, Dvorak's Harmonium Quartets.

Dvorak wrote some lovely chamber music featuring a harmonium: they were called Bagatelles.  The humble harmonium, of course, is never even heard today as a serious musical instrument.  They're used as accompaniments in poor parish churches that can't afford either a pipe organ, or a Casio keyboard, and heaven knows those cost only about $150.  But a harmonium is a simple thing: it is essentially an enormous harmonica (no, they don't look like harmonicas; they look like tiny organs.  The organ in the Pachelbel's Canon clip is actually a tiny chamber pipe organ.  The pipes are just about 4' long, at the longest) connected to a keyboard, and a foot-operated bellows.  (In the clip, the bellows are operated by hand, which means you can't play with both hands.  This type is not intended for classical music, but for folk music, especially Eastern European and Indian.)  Anyone older than, say, 65 years, is likely to have seen one.  Here is a movement from one of the Bagatelles.  Here is a clip of a rehearsal, showing a harmonium actually being played!

I have to take time out for a brief rant here.  The world is full of countless old things that are extra, we don't need them; they're old, they're marginal, they're on the fringes of modern life.  Should we preserve them?  Will we miss them if they're gone?  If they belong to the distant cultural history of a people with whom I have no direct connection, need I be aware of them, and maintain an interest?  The pieces of paper on which Bob Dylan scribbled the words of his song: Like a Rolling Stone, are being auctioned off at Sotheby's.  They will probably bring millions of dollars.  But I feel it is almost, or more, important to find good harmoniums, and learn to play them, (actually they're easy to play) and perform unusual pieces like Dvorak's Bagatelles on them, and keep them in the public eye.  The wonder of life on Earth is about richness, especially richness that does not imply destroying the environment.  Young people are increasingly difficult to keep entertained; it seems that only something coming out of a video monitor has the ability to keep them engaged.  I suspect that the more balanced individual in tomorrow's society, and the ones on whom we can depend to provide motivation and leadership to solve the enormous problems tomorrow's society will face, will be aware of, and familiar with, a variety of cultures and traditions and cultural artifacts, and at an early age.  We had better work on this; I doubt that my own child knows half the things I'm talking about ...

Talking about unusual instruments, Mozart wrote a few pieces for Glass Harmonica.  The glass harmonica is essentially an instrument that uses an array of things like wineglasses to make a sound.  You may know that it is possible to make a lovely sound by running a wet finger around the rim of a wineglass.  You can even tune the note, by adding liquid to the glass.  In a glass harmonica, the glass pieces are arranged sideways and rotated by a motor, with the lower parts dipped in a container of water, to keep them wet.  Let me try and find you a video clip of one ... Here it is.  (I have been known to disrupt wedding receptions by fooling around with the champagne glasses.  I regret it now.  At a wedding, we should leave the disruption to the couple.)

In popular music, my favorite group is The Beatles.  Over the years, every one of them got a chance to sing in one song or another, but the majority of songs were sung, of course, by John Lennon and Paul McCartney.  Once the group disbanded, arguably it was George Harrison, who played Lead Guitar most of the time, who was best known for his post-Beatles career, certainly among those who were not initially Beatles fans.  But the number of songs in which all three: George Harrison, John Lennon and Paul McCartney sang are relatively few.

One of the best known is Nowhere Man, a song that is sadly neglected nowadays.  (It is a commentary on disengaged individuals, and was probably inspired by someone whose attention John Lennon wanted, and did not get!)  The opening phrases are in 3 vocal parts, after which John takes over, and the other two sing backup.  Another song, even less well known, is You're going to lose that girl, from Help!  This follows a similar pattern, except that most of the song is with a single lead vocal, with backup in harmony by the other two.

While we're on 3-part harmony, here's another favorite: In the early morning rain, written by Gordon Lightfoot, and brilliantly outFooted by Peter, Paul and Mary, arguably the trio that sang the most correctly-written 3-part harmony, that is to say, the most satisfying to the classically-trained ear.

I plan to add a couple of examples here, but that's all for the moment!  Talk to you later,

Arch