the square __ the hypotenuse

One of the choirs I sing in started practicing the chorus of the Major-General’s song from Gilbert and Sullivan’s The Pirates of Penzance, very slowly, starting with 

with many cheerful facts about the square of the hypotenuse.

Hang on, shouldn’t that be on the hypotenuse?  At least, that’s what I’ve always thought it was.

Apparently not. The two books on Gilbert and Sullivan’s operas I have both give of, and the video I linked above has it. But, in general, of and on seem to be interchangeable, with a recent preference for of

There doesn’t seem to be an original Greek form of the theorem, whether formulated by Pythagoras or someone else. If there is a difference, it’s that the square on the hypotenuse is an actual square on an actual side of an actual triangle, and the square of the hypotenuse is a mathematical function of the length of that side. To the ancient Greeks, γεωμετρία (geometria) was literally about measuring the earth.

If you are a singer, use what you conductor provides or tells you. If you are a maths teacher, use what’s in your textbook. If you are anyone else, choose one and don’t worry about it.


Ceiling wax

One song I remember from my childhood is Puff, the magic dragon, sung by Peter, Paul and Mary and written by Peter Yarrow and Leonard Lipton. For some time I wondered what

ceiling wax

is. I don’t know how I found out that it is, in fact

sealing wax.

I obviously knew about ceilings before I knew about sealings.

Ceiling is a strange word. It ends with -ing, but it’s not related to a verb; we don’t usually ceil ceilings like we build buildings. (Someone has flippantly suggested that we should call them builts.) In fact we do, or buildingers do, whether they call it that or not. records the verb ceil, meaning

1. to overlay (the ceiling of a building or room) with wood, plaster, etc.
2. to provide with a ceiling 

dating from 1400–50, from late Middle English celen to cover, to panel, followed by a rather vague < ? 

Seal is ultimately from Latin signum and is related to sign. The animal seal is from Old English with cognates in Old Norse and Old High German. There is a story that one holder of the British government office of Lord Privy Seal objected to being addressed as such because he wasn’t a lord, a privy or a seal.  

While I was researching for this post, I found a blog called of ceiling wax, which is about “reading YA, graphic novels and the spaces in between”. Its not-immediately-named author quotes Lewis Carroll’s The walrus and the carpenter (text, Wikipedia), which I’m not as familiar with and didn’t think of. She/he also originally mistook this for ceiling wax.

“The time has come,” the Walrus said,
“To talk of many things:
Of shoes–and ships–and sealing-wax–
Of cabbages–and kings–
And why the sea is boiling hot–
And whether pigs have wings.” 

Some of Carroll’s poems are direct parodies of the poems Alice Liddell would have been familiar with, but this seems to be totally original. 

PS 3 Oct: information about the poems Carroll parodied.

A new unit of hearing loss – the Jagger

In my last post, I mentioned that a colleague had mentioned the Rolling Stones song 2000 light years from home. I’m not a Stones fan and didn’t know it, so I searched for it and found the video and lyrics, started the video and … couldn’t hear any lyrics. Maybe it was an instrumental piece, or an instrumental version of a song, but the video said “Official”. I finally thought to flip my headphones, and there was Mick. 

I have been significantly deaf in one ear since contracting measles at an early age. I wasn’t sure if I’d mentioned that here; a quick search doesn’t show that I have. I’ve had some problems with headphones before, but this was just another level. 

That evening, I realised that despite several listens, I had no clear memory of what the song actually sounded like, except that it had a prominent keyboard part. The next morning I listened again and … could’t hear any keyboard. It seems that the vocal is entirely on one track, the keyboard (Brian Jones) is on another and the the guitars and drums are on both. When I flipped the headphones again, I could just sense … something in that ear, but wouldn’t have known that it was a voice, or Mick, or what the words actually are. The only way I can get the full effect is to to listen without headphones. But with one or two people in the house all day, I use the headphones. 

My mother told me that I had moderate hearing loss in one ear. Later, I realised that she was probably understating that. On the scale of mild, moderate, moderate-severe, severe and profound hearing loss, I am at least severe – the audiogram I found shows me going off the bottom end of the scale at 80 dB. In one ear. Fortunately, I have normal enough hearing in my other ear. Some years ago, I asked my father what he knew, and he said very little; my mother had taken me to audiologists all those years ago. 

This hasn’t stopped me studying classical music (specifically piano) and singing in choirs, but has had a number of other consequences, especially easily becoming overwhelmed in enclosed, noisy spaces. Also, if I can’t hear Mick directly in my bad ear, it makes me wonder what else I’ve missed out on along the way. The fact that I am now working as a legal editor, either in a mostly-quiet office or at home, isn’t coincidental. 

Meanwhile, how far is 2000 light years? This page gives the approximate thickness of the plane of the Milky Way galaxy at the Sun’s location as 1500 light years, and the distance to Deneb as 3200 light years, if that helps. Certainly, we’e talking on a galactic scale. But the song mentions Aldebaran between mentioning 1000 light years and 2000 light years. But Aldebaran is (only) 65 million light years away.

Trail mix tape

Several years ago I posted about the distance 10,000 miles, which occurs in several songs. I suggested that it’s the archetypal long distance because it is the furthest away (in nautical miles) one can travel on Earth. (Presumably it came into use after long-distance sailing became common.) I mentioned that A space oddity has the distance 100,000 miles, which is less than half-way to the moon.

This morning a colleague mentioned that today is Trail Mix Day. I said in a group email that I was going to make a selection of songs and call it a trail mix tape (not an original joke), and suggested These boots are made for walking, Over hill, over dale, Climb every mountain, I’m gonna be (500 miles), 500 miles away from home and 10,000 miles. I pondered what longer distances are mentioned in songs. After I sent that email, I also thought about Fly me to the moon and The final countdown (“We’re heading for Venus”). Then a colleague replied with 2000 light years from home, which I topped with Across the universe, Stairway to heaven and Highway to hell (though those don’t mention actual distances). 

Apropos the last two, there are several cartoons with two men wearing a Led Zeppelin and AC/DC t-shirt respectively. One version has the Led Zep fan saying “We split ways here”.


I woke up in the middle of the night with the “word”


in my head.

I have sometimes got up in the middle of night to do linguistic research, but on this occasion I was determined to go do back to sleep as soon as possible. A few obvious preliminary questions: is this actually a word? if so, what does it mean and where did I encounter it? if not, why did my brain think of that combination of letters rather than any others?

If it is a word, it’s not a standard English word, because all the standard English words starting with pn– are technical and relate to air or breathing, and most of the standard English words ending with –au are French (with a few German and Welsh). 

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my guide

Speaking of bachs: In December 1933 the German composer Richard Strauss wrote a song titled Das Bächlein, (originally for voice and piano but the first recording that came up is for voice and orchestra), in which a wanderer asks a mountain stream where it came from and where it is going. It answers “I come from the womb of dark rocks. A merry childlike spirit drives me onward, I know not whither. He who called me forth from the rock, He, I think, shall be my guide.”

Strauss set the words for my guide rhapsodically. There can be no doubt that he realised the double meaning of mein führer (leader/guide). There is still debate about his interactions with the Nazi regime, even though he was cleared by a denazification tribunal in 1948. In the early days he might have seen it as the (or a) solution to the chaos of the previous 20 years, but after he reluctantly accepted the position of president of the Reichsmusikkammer he quickly lost whatever illusions he had and fell from favour, especially because of his professional relationship with author Stefan Zweig and personal relationship with his daughter-in-law and her family. The song wasn’t published until after his death. 

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Bach and ch in general

One of my first piano learner’s books had a piece called Air from Bach, which I first pronounced as /bætʃ/ (batch). When one of my older sisters told me it was /bak/ (bark) (non-rhotic in Australia), I didn’t believe her until someone else (maybe our piano teacher or grandmother, assured me that it was. Except it’s not. The sound at the end is /x/, a voiceless velar fricative, the sound at the end of Scottish loch, or /χ/ a voiceless uvular fricative. Most English speakers don’t bother, either with Bach or loch or any other relevant word, but I vaguely remember hearing a monologue by Garrison Keillor on how he first started in radio. He volunteered for a student radio program (?to impress a girl), and when he needed to study, he’d put on the complete and uninterrupted recording of the Mass in B minor by Johann Sebastian Bacchh (in the days of LP records?). I can’t find that online. If anyone can help me, I’d be grateful. 

I was reminded of this by the username of my chief commenter of recent times, Batchman. While ch in English can be /k/ (architect), /tʃ/ (bachelor), /ʃ/ (champagne) or /x/ (loch), tch can only be /tʃ/ (unless is is split across two syllables, as in chitchat (which might end up as chi-chat in rapid speech)). Basically, words with /k/ are Greek, words with /tʃ/ are Germanic and words with /ʃ/ are French.

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If ye love me

If ye love me, keep my commandments. And I will pray the Father, and he shall give you another comforter, that he may bide with you forever, even the Spirit of truth.

One staple in the repertoire of the kinds of church or community choirs I sing in is If ye love me, by Thomas Tallis. Note ye and you, will and shall and pray the Father

Some people decry any change in language as the first step to incoherent grunting, but language has always changed and always will. Example 1: ye and you. Until about 400 years ago, (most) English speakers observed the distinction between the subject form ye (ye love me) and the object form you (give you, bide with you), and also the singular and/or intimate thee/thou/thy/thine and the plural and/or polite ye/you/your/yours. These all collapsed onto all-purpose you/your/yours, and almost no-one cared. (Art, wast and wert disappeared around the same time.)

The people who rail against singular they rarely mention singular you, which must have been just as shocking at the time, and the people who use non-standard plural forms such as y’all,* all y’all or yous(e) are railed at for being non-standard. (Note that you started off as plural anyway. If anything, we need a ‘singular you’.) (*I originally included you all, but the more I thought about it, the more I became sure that plural you all is standard: compare “I am very pleased to welcome you all here today” and “I am very pleased to welcome y’all here today”. (Also all of you.))

Because most people encounter thee/thou/thy/thine in Shakespeare, the King James/Authorised version of the bible or the Book of Common Prayer, or musical settings of texts from those sources, they imagine that these are formal/polite, and use them in conscious but often mistaken imitation. Leigh Brackett and/or Lawrence Kasdan, the scriptwriters of The Empire Strikes Back, has/have Darth Vader asking the emperor “What is thy bidding, my master?”. 

(Wikipedia has more about the T-V distinction (from Latin tu and vos).)

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Musicians in the English-speaking often use Italian musical terms instead of the English equivalents. Somehow they sound more musical, or maybe we think they are more musical because we usually encounter them in musical contexts. One of these is ritardando, which I’ll explain more in a moment. Some composers, most famously the Australian-American Percy Grainger, preferred or prefer English, specifically Germanic, terms. In Grainger’s case, unfortunately, this was specifically related to his ideas about racial purity.

A few days ago, one of the choirs I sing in sight-read a work by the American composer Leo Sowerby, whose name I knew but whose music I had never encountered. Scattered throughout is retarding, the direct equivalent of ritardando, but still Latinate. Grainger probably used the undoubtedly Germanic slowing. (I don’t know what Sowerby’s motivation in using the term was.)

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Love’s pure light loves pure light

Six years ago, very soon after started this blog (I can’t quite believe it’s that long), I wrote about Round John Virgin and some other linguistic aspects of the Christmas hymn Silent Night.

Recently, one of the choirs I sing in was invited at short notice to record some items for a Christmas musical entertainment to be streamed into aged care facilities around Australia. (We have just begun to rehearse together again.) One of these was as the backing for a soloist singing a slightly jazzy arrangement of Silent Night. Among other things, there were several extra notes inserted into the melody, which then required extra words (or maybe the arranger decided to insert extra words, which then required extra notes). Small example: in one verse, Silent night, holy night became O silent night, and holy night. Larger example: Son of God, love’s pure light became Son of God, he loves pure light, which is not just adding a word, but changing the grammar and meaning of what follows.

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