Reading: Arithmetic

So I mentioned a while back that I was reading Arithmetic.  I did pretty well with it for a while; Lockhart has an engaging writing style, and his was by far the best explanation of thinking in anything other than base 10 that I’ve come across.

…But, yes, there’s a but.  I’m nearing the end now–I’ve just gotten to the bit about fractions–and I’m flagging.  I’m no longer wowed by the different perspectives you can take on how all of this works, and I’m starting to think he’s annoyingly glib at times.

I’ve spent some time as I read Arithmetic trying to decide who I would recommend this book to.  It’s not really for children, for all that I think children are the ones who could benefit most from the different takes on how arithmetic works, and interesting points of view as those takes are explained.  Adults can just use a calculator if they don’t enjoy doing the arithmetic themselves, as Lockhart points out every few pages.  Kids, though–kids are stuck in school math classes where they’re graded on this stuff, and not tracked into the actually interesting math until/unless they master arithmetic.  But this isn’t really a book for kids.

Maybe it would be good for the parent or tutor of a kid struggling with math?  Or anyone who teaches math to elementary schoolers, I suppose.

Anyway, I’m not 100% sure whether or not I’ll finish this one.  I might.  But then again, I’ve already stumbled across Music and the Making of Modern Science while trying to find stuff to buy for collection development.  I’m not sure I can justify buying it for the library… but I can certainly justify ILLing it for myself!  Maybe this one will be the bedtime reading I’ve been waiting for.  It could be, right?

In other news, I think I saw a house finch yesterday, and I’ve definitely seen crocuses in bloom in two different places.  It’s spring!  And See You Around has been on repeat in my office and apartment for the past couple days.  That has nothing to do with spring, but it’s always nice to have new music as you usher in a new season.

So you think you can read music

Once upon a time I became kind of obsessed with Palestrina.  Not only did he write fabulous music for listening to on your headphones when you need to block out conversations from your office suite, he also wrote… well, fabulous music.  Everything I read says he’s most famous for Missa Papae Marcelli, so here you go:

(Incidentally, yes, the Tallis Scholars are also pretty fantastic.)

Being the geektastic, musical-when-I-bother-to-practice librarian that I am, I decided a few weeks back that I really needed to own sheet music or a score or something for some Palestrina music.  Surely, my reasoning went, if I had something that sounds like *that* to practice, I would carve out the time.  Wouldn’t Missa Papae Marcelli sound fantastic as a horn choir?  I could record myself on all the parts and edit them together, and improve my Audacity skills as well as my French horn chops!

So I bought myself the music using the power of the internet.  (How did people live before you could just order absolutely everything online?)  I waited in eager anticipation for my book to come, and then it did, and I looked at the music inside, and–

Beginning of sheet music for a Palestrina motet

I couldn’t read it.  I mean, I could sort of read it, but was I reading it correctly?  A decade of piano lessons definitely taught me treble and bass clefs, and I’ve heard of alto clef, but… I mean, *is* that alto clef?  And what are those funny arms sticking out of some of the treble clefs?  And why do some lines have a maybe-alto-clef PLUS also a treble clef with arms?  And if that’s alto clef, why is it moving around on the staff so much?

So it was time for some research, and boy did I learn stuff I wasn’t aware of.  Was I just not paying attention in all those music lessons?

Familiar old treble clef has another name: G clef.  And that name is because the position of this clef tells you where G is on the staff.  Who knew?  When you’re writing/drawing your own treble clef, you need to get the open part inside the swirly bit centered on G.  Otherwise you’re doing it wrong.

Better still, there used to be *other* G clefs, because you could move the clef around, center it on a different line, and thus declare that *that* line is a G.  Here’s the relevant part of the Wikipedia article on clefs.

But that still doesn’t tell me what’s going on with this Palestrina music.  Right.  So, it turns out that what I thought might be alto clef is a C clef, and it moves because it’s telling us a different position for C on the staff.  Ok so far, but why is it on a line that also goes on to have a treble clef?  And what’s going on with those funny arms on the treble clef?

Some more Googling brought me to this page on “chiavette” which is “a system of standard combinations of clefs used in polyphonic music of the 16th–18th century.”  So, that’s great–that *is* the right time period for Palestrina–but it doesn’t tell me anything about why all the lines in my book have treble clefs (and why some of those treble clefs have arms).

Pro tip: At this point in your research, don’t Google “treble clef arms” or “arms on treble clef” unless you want to look at lots and lots and lots of pictures of people who tattooed treble clef on their arms.  I don’t want to look at your tattoos of treble clef!  I just want to know what’s going on with the music in my book!

Moving on through several other search terms, eventually I made my way from “combination of clefs” to “hybrid clefs.”  And this–I think this is actually what I was looking for: “As for tenor singers, the strange custom has grown up in recent years for them to pretend that they are reading in treble clef, like sopranos, but actually to produce the sounds an octave lower! Sometimes, to show that the tenor’s treble clef is not a real one, it is printed as a double clef, the second one actually looks like the notation I'm trying to figure out!” (Learn to Read Music by Howard Shanet, 1956).

That… by golly, I think that’s it!

In short, I’ve spent several hours of my life searching the library stacks and Google, just to try to understand what octave these notes are meant to be played in.  But hey, the more you know.

Now I can get on with my plans to actually play this music!