Mendelssohn – “Elegy” from Songs Without Words, Op. 85 #4

One of my students wants to learn the Brahms Intermezzo Op. 118 #2, which scares me to death because I’ve never played it.  I’m reminded of the time when I tackled the Alban Berg Piano Sonata, and my teacher Sementovsky (who had never heard the work before) said to me, with supreme confidence, “You teach it to me; then I will teach it back to you!”

It occurred to me that before my student pounces on the Brahms Intermezzo, she should build up to it with a work that is easier but stylistically similar, with long, legato phrases and undulating rhythm.  I thought of this piece by Mendelssohn.

Here is my recording of it.  It came out much more sentimental than I thought it would.  I wanted to play the piece with classical restraint, but that didn’t happen. Oh well.

Meter Test (1st Revised Version)

In this blogpost, you’ll find the audio files of the Meter Test – 1st revised version, along with this answer sheet (page 1 and page 2).  I’m proud to announce that I shaved a whopping 10 minutes off the test!  From start to finish, it now takes 20 minutes to administer, even with the new recorded directions.

When I administered the original version, I gave students directions off the cuff.  For this revised version, I put together (and recorded) standardized test directions that you can hear in the audio files below.  (Those of you who are Gordon savvy will notice that these test directions sound suspiciously like the instructions Gordon wrote in his PMMA, IMMA, and ITML test manuals.  Why reinvent the wheel?  And hell, it’s the highest form of flattery!)  Here are the test directions in written form:

 

You will hear some short pieces of music. Listen carefully, because you will be asked to indicate whether each passage is in duple or triple meter. If the piece of music you hear is in duple meter, circle the word duple. If the piece of music you hear is in triple meter, circle the word triple. Look at your answer sheet and find Example #1. Now listen to Example #1.

(Play Example #1)

There is a circle drawn around the word Triple because the piece of music you just heard is in triple meter. Now listen to Example #2, and then circle your answer.

(Play Example #2)

You should have circled the word Duple because the music is in duple meter. We will now begin question number 1. The number of each piece of music will be announced before the music is played. Each piece of music will be performed only once. Listen to the entire piece before circling your answer.

 

After the audio files, you’ll find brief explanations of how I constructed—or rather, reconstructed—the test.

(A) Directions for administering Meter Test – 1st Revision

EXAMPLE #1:  Simon & Garfunkel – “America”

(B) Directions for administering Meter Test – 1st Revision

EXAMPLE #2: Haydn – Symphony #100 – “Military”, 2nd mvmt

(C) Directions for administering Meter Test – 1st Revision

 

ONE

Bizet – Carmen – Overture

 

TWO

Schubert – German Dance in B-flat, D. 783 #7

 

THREE

The Beatles – “Norwegian Wood”

 

FOUR

Scarlatti – Sonata in G Major, K. 455 (synthesizer)

 

FIVE

Bernstein – West Side Story – “I Feel Pretty”

 

SIX

Prokofiev – “Classical” Symphony, 3rd mvmt

 

SEVEN

Seal – “Kiss from a Rose”

 

EIGHT

Beethoven – Symphony #9, 4th mvmt

 

NINE

The Del-Vikings – “Come Go with Me”

 

TEN

Johann Strauss – Tales from the Vienna Woods

 

ELEVEN

Verdi – Rigoletto: “La donna è mobile”

 

TWELVE

Mozart – “Eine Kleine Nachtmusik” 1st mvmt

 

THIRTEEN

James Taylor – “Sweet Baby James”

 

FOURTEEN

Johann Strauss – Blue Danube Waltz

 

FIFTEEN

Handel – Parnasso In Festa – Chorus

 

SIXTEEN

Haydn – Symphony #103, “Drumroll”- III. Menuet

 

SEVENTEEN

Verdi – Il Trovatore – Anvil Chorus

 

EIGHTEEN

Bach – Toccata In D, BWV 912

 

NINETEEN

Billy Joel – “Piano Man”

 

TWENTY

Banjo solo – Cherokee Shuffle

 

TWENTY-ONE

Handel – Brockes Passion – “Gott selbst der Brunnquell”

 

TWENTY-TWO

Bizet – Carmen – Suite No. 2- Habanera

 

TWENTY-THREE

Smetana – Bartered Bride – Act 1, Scene 1

 

TWENTY-FOUR

Molly Mason & Jay Ungar – “The Mountain House”

 

TWENTY-FIVE

Bizet – Carmen Suite No. 1- IV. Seguidilla

 

TWENTY-SIX

The Marcels – “Blue Moon”

 

TWENTY-SEVEN

Handel- Water Music, Suite #2 – Minuet

 

TWENTY-EIGHT

Gotye – Somebody That I Used to Know

 

TWENTY-NINE

Saint-Saëns – Carnival of the Animals – Fossils

 

THIRTY

Kelly Clarkson – “Breakaway”

 

THIRTY-ONE

Saint-Saëns- Samson et Dalila – Bacchanale

 

THIRTY-TWO

Rankin Family – “Mo Shall al dhekh”

 

Please take a look at this spread sheet.  You’ll see that I retained most of the items from the original meter test, and re-ordered them with 4 factors in mind: meter, genre, item difficulty, and item discrimination.  Let me go into this in greater detail.

—In its revised form, the meter test consists of 32 items, 16 in duple meter and 16 in triple meter.  There are no new items; each item came from the original test.  I threw out 8 test items (4 in duple meter and 4 in triple meter) from the original test because of their poor discrimination values.  Incidentally, I changed my mind about the Bach Gloria; I decided to drop it and replace it with Kelly Clarkson’s “Break Away.”  The Bach and the Kelly Clarkson examples are each in triple meter, and they each have low discrimination values, but “Break Away” is a slightly easier item.

—I shortened the test items.  They are now between 28 and 33 seconds long.  Most are exactly 30 seconds long.  (You’ll notice in the spread sheet that the timings in column G are new, but the item difficulty levels and discrimination values are “old”—that is, they are data from the original test.  I have no way of knowing, yet, if shortening the items will have any effect on how students respond to them.)

—From the original test, I chose the Haydn “Military” Symphony and the Simon and Garfunkel song “America,” as preliminary examples (shown in purple font).  They seemed ideal for such a purpose because they’re easy items with low discrimination values.  My hope is that most students—high scorers and low scorers—will understand, after listening to each excerpt, why duple or triple is the correct answer.  In a nutshell, these easy items should provide the “aha” moment students need, at the outset, to understand 1) the nature of the test, and 2) what their task will be when they take it.

—No more than 2 duple examples appear consecutively, and no more than 2 triple examples appear consecutively.  If students circle duple or triple only, or if they consistently alternate their responses, they will receive a chance score of 16.

—The revised test has 15 vocal items (shown in bold print) and 17 instrumental items.  In the last blogpost, I said that the test items, taken together, make up a variety of styles and genres. This is true for the revised version as well.  You’ll notice that pieces similar in style and genre are not lumped together.  No two vocal items appear consecutively; in a few instances, two instrumental items appear consecutively (#1 and #2; #24 and #25).  This was inevitable.  Still, I made sure the back-to-back instrumental items are stylistically different from each other.

—The 4 very difficult items (shown in green font) are those with difficulty levels at 60% or lower).  I deliberately spaced them apart, so that students would not face the daunting task of answering many difficult items in a row.

—The 3 very easy items (shown in red font) are those with a difficulty level of 90%.  I deliberately spaced them apart to ensure that kids, while taking the test, got a periodic breather.

— Half the revised test items have difficulty levels at or above 75%, while half have difficulty levels below 75%.  If you look at the item difficulty levels in column C, you may think that the items were randomly scattered, so that the varied difficulty levels happened by chance.  Not true!  To make sure that items varied in difficulty level throughout the test, I arranged them by following this procedure: I divided the 32 items into four 8-item groups. I then made sure that each 8-item group had 4 above-average items and 4 below-average items. These groups then became items 1-8, 9-16, 17-24, and 25-32.

—All 32 items are positively discriminating, and only 3 have discrimination values lower than .2.

I just listened to the whole test all the way through, and I’m happy with the sum of its parts.  I got rid of some of the gentler items, so the revised test is a bit more raucous than the original version was; and because the items are shorter, the whole test moves at a faster pace.  But I’m glad it still has moments of humor, like the “Blue Moon” example that kids love, and Glenn Gould’s positively goofy performance of the Bach Toccata.

And now, we come to the hard part: waiting.  Next year, perhaps midway through the year in January, I’ll administer the revised test to a new group of 4th grade students, and we’ll see… Will the items retain their varied difficulty levels and their high discrimination values?  And what about the reliability of the test?  Will students’ scores be relatively stable over time?  And will the test show a high degree of internal consistency?  By next January, I should have the answers.  As Willy Wonka said, “The suspense is terrible.  I hope it’ll last.”

Meter Test (Original Version)

Here is a meter test I put together many years ago, but never got around to administering.  I forgot all about it until recently when I was going through some old files and found the test and this blank answer sheet.  Each musical example is in either duple or triple meter.  Students are instructed to listen to each example once and then circle the correct word: Duple or Triple.

Here are the audio files of the test items.

Haydn – Symphony #100 – “Military”, 2nd mvmt

Johann Strauss – Tales from the Vienna Woods

The Beatles – “Norwegian Wood”

Bizet – Carmen Suite – Habanera

Bernstein – West Side Story – “I Feel Pretty”

Bach – Toccata In D, BWV 912

Kelly Clarkson – “Breakaway”

Beethoven – Symphony #9, 4th mvmt

The Marcels – “Blue Moon”

Haydn – Symphony #103, “Drumroll”- III. Menuet

Verdi- Rigoletto – “La Donna È Mobile”

Mozart – “Eine Kleine Nachtmusik” 1st mvmt

James Taylor – “Sweet Baby James”

Mahler – Symphony #1, 2nd mvmt

Handel – Parnasso In Festa – Chorus

Schubert – German Dance in B-flat, D. 783 #7

Bizet – Carmen – Overture

Verdi – Il Trovatore – Anvil Chorus

Handel- Water Music, Suite #2 – Minuet

Banjo solo – Cherokee Shuffle

Seal – “Kiss from a Rose”

Bach – Goldberg Variations – Variation 18 (woodwind transcription)

Saint-Saëns – Carnival of the Animals – Fossils

Bach- Mass In B minor – Gloria In Excelsis Deo

Prokofiev – “Classical” Symphony, 3rd mvmt

Billy Joel – “Piano Man”

Schubert – Moment Musical #3 in f minor

Rankin Family – “Mo Shall al dhekh”

Stravinsky – Suite for Chamber Orchestra, # 2- Waltz

The Del-Vikings – “Come Go with Me”

Haydn – Symphony #101 “The Clock”, 2nd mvmt

Handel – Brockes Passion – “Gott selbst der Brunnquell”

Saint-Saëns – Samson et Dalila – Bacchanale

Smetana – Bartered Bride – Act 1, Scene 1

Molly Mason & Jay Ungar – “The Mountain House”

Gotye – “Somebody That I Used to Know”

Bizet – Carmen Suite No. 1- IV. Seguidilla

Simon & Garfunkel – “America”

Scarlatti – Sonata in G Major, K. 455 (synthesizer)

Johann Strauss – Blue Danube Waltz

I called the test the “original version” because I planned to write at least a few revisions, depending on the numbers it generated.  My intent was to give it to my older students (4th grade and up), as soon as they were exposed to division patterns in duple and triple meters.  But I got bogged down in other things, and this test stayed buried in my computer hard drive.  During the past week, just on a whim, I administered the test to 75 students in 4th grade.  The results were fascinating!  But before I talk about the results, let me talk about the test for just a minute.

Because it’s a 40-item test, and each item has two options (duple or triple), the chance score is 20, the theoretical mean is 30, and the theoretical standard deviation of 3.33.  If you look closely at the way I ordered the test items, you’ll see that no more than 2 duple items (or 2 triple items) appear in a row.  I also rigged it so that if students tried to be sneaky by pattern-marking with alternate responses (duple-triple-duple-triple-duple, etc, or triple-duple-triple-duple-triple, etc,) they would get a chance score of 20.

Here are some of the preliminary results:  The raw scores range from 20 to 38.  (Two students out of 77 scored below the chance score, but I removed these outliers from the results, leaving N=75.) The mean is 28.91 (slightly lower than the theoretical mean) and the standard deviation is 4.38, (greater than its theoretical counterpart), which basically means that the test is slightly more difficult than it ought to be, and there’s too much variability around the mean; in simple terms, too many kids scored too close to the chance score of 20.

The test could stand some tweaking, but still, it’s pretty damn fine as it is.  The items, taken together, represent a great variety of styles and genres; and each item has its own shape, so to speak.  Most of the musical excerpts end on a cadence; only rarely did I end an item in the middle of a phrase.  Although most of the musical excerpts are instrumental, I was careful to avoid putting two instrumental items of the same timbre and time period together.  To avoid placing two vocal items back-to-back, I deliberately interspersed the vocal items with the instrumental.  Most of the vocal items ended up being in triple meter.  I tried to find pop music examples in triple, because they’re so rare, and maybe I got carried away.  This didn’t pose a problem.  The item difficulty levels (which I’ll discuss in greater detail later) reveal that some vocal items were easy while others were difficult.  In other words, students were not able to guess the meter by the genre.

The test has its problems.  Not only is it too difficult for its intended population, but it’s too long. With 40 items, it clocks in at exactly 30 minutes.  (I had the kids finish the test in two sessions, so that fatigue would not set in.)

So, how should I go about shortening the test?  One way is to shorten the length of each item. You’ll notice that the items are between 34 and 45 seconds long; in the next version, no test item will exceed 30 seconds.  I suppose I could shorten the test by making the items only 15 or 20 seconds long, but I don’t want to do that (even though I observed most students circle their answers to most test items after roughly 15 seconds).  Students may be able to audiate the meter of a 15-second segment of music.  But I want the test to be a rich, aesthetic experience for them, and not just a test of audiation skill.  In short, I refuse to sacrifice my students’ aesthetic experience for brevity.  Thirty seconds is as brief as I’m willing to go.

Another way to shorten the test is simply to remove test items that are too easy, or too difficult, or those that simple don’t reveal much difference in knowledge between high scorers and low scorers.

In columns B and C, you can see the item difficulty levels (Df) and the item discrimination values (Ds).

First, I scored the papers; then I ordered them from lowest to highest; then I separated the lowest 27 percent and the highest 27 percent, a practice recommended by Robert Ebel in his book Measuring Educational Achievement.  Twenty-seven percent of 75 is 20. In other words, I took 20 of the lowest papers and 20 of the highest papers, 40 papers in all to “play with”.  Then I tallied all the correct answers from each paper.

The procedure for calculating item difficulty is as follows:

Add the number of correct responses from the lowest 27% to the number of correct responses from the highest 27%.  Then divide that sum by the total number of test papers you’re analyzing.

The procedure for calculating item discrimination values is as follows:

Subtract the number of low scorer correct responses from the number of high scorer correct responses.  Then divide that difference by half the number of test papers you’re analyzing.  Keep in mind that you’re still using only the top and bottom 27% of the total number of test papers.

(Some readers may catch that I use formulas that are slightly different from those recommended by Gordon and Walters. They don’t follow the 27% rule.)

Let me use Item #1, Haydn’s Symphony #100, as an example.  From among the low scoring group of 20, 16 kids got Item #1 correct; from among the high scoring group of 20, 18 kids got Item #1 correct.  I added 16 and 18, got 34, then divided 34 by 40, the total number of test papers under investigation.  The result was .85, meaning that Item #1 is a fairly easy item.

I then subtracted the low scorers (16) from the high scorers (18), and then divided that number (2) by half the number of test papers I’m using (20).  The result is .05, which means that Item #1, though it’s a positively discriminating item, doesn’t show a clear distinction between the high and low achievers.

Item discrimination is a bit complex.  If many high-scoring kids get a test item wrong, that’s not a deal breaker; and if many low-scoring kids get a test item right, that item might still be a keeper.  But… if most of the high scoring kids get an item wrong, while most of the low scoring kids get that same item right, that spells trouble: The test item is not doing its job, which is to differentiate between high and low achievers.

If test items fall in the range of difficulty from 60 percent to 90 percent, I will retain them.  If they fall outside that range, I discard them (or at least most of them).  And I want only positively discriminating items with a value of at least .20, with most of the items greater than .40.  If an item has a discrimination value lower than .2, I will, with few exceptions, discard it.

In short, I want a range of item difficulty from .60 to .90, with most items hovering around .75.  And… I want most items to have discrimination values of .2 or greater.  Hooray!  That’s basically what I got!

What’s next for this test?  A revised version with kick-ass items that retain their difficulty levels and high discrimination values.  And then, finally, I will calculate its reliability.  Will improved test items result in high test reliability?  Will shortening the test impact negatively on reliability?  We’ll all have to wait until the next school year to find out!

To finish this long but geekily fascinating blogpost, I’ll discuss a few test items that fell in the extremes, why I’m chucking most of them, and why I’m keeping a few for the next revision.

Bach’s Goldberg Variation 18 and Schubert’s Moment Musical are obvious items to discard (with zero discrimination values, and difficulty levels that make the test tougher than it ought to be).  Same with Mahler’s First Symphony and the Kelly Clarkson song (even though the kids enjoyed it).  Out they go.  The Stravinsky Waltz fascinates me:  it falls in the middle range of difficulty; but, as a negatively discriminating item, it works against the overall test.  More low scorers got it right than high scorers!  With its oom pah pah underlying beat, it makes sense that low scorers got it; but how could so many high scorers miss it?!  We’ll never know.  And Haydn’s “Military” and “Clock” Symphonies?  What could scream duple more than a clock or a military march?!  The low scorers tended to get them.  But high scorers?  Hello?  Where did you disappear to?  At any rate, out go those items. (But not out completely.  Because they’re easy items, I’ll use Simon and Garfunkel’s “America,” and Haydn’s “Military” Symphony as pre-test examples in the next revised version of the test.)

And then there’s the Bach Gloria from the Mass in B minor.  I’m keeping it.  Yes, its discrimination value did not meet my criteria; but it’s a fairly difficult item, and items on the extreme ends of difficulty sometimes have low discrimination values.  It’s a good item.  I’m keeping it.  End of story.  Same with the Del Viking’s “Come go with me.”  It’s an easy item in a test that could benefit from a few more easy items.  It’s staying.  Even though I love the Rankin Family’s “Mo Shall al dhekh,” I can’t really justify keeping it; except that if I cut it, the test will be unbalanced.  I’m getting rid of 8 items—4 duple and 4 triple.  The Rankin Family song stays, at least until I can replace it with a more highly discriminating item in triple meter.

Now let’s look at a few items that are worth their weight in gold.  Mozart’s Eine Kleine Nacht Musik.  Who could have predicted that this piece of Classical Top 40 would make my top 40?  It’s a really difficult item that discriminates so well between those who “get” duple meter and those who don’t.  And the Scarlatti Sonata!  And the Banjo solo! I never would have foreseen their high discrimination values.  And hats off to that Belgian-Australian singer-songwriter Gotye for his song “Somebody that I Used to Know.”  I couldn’t have asked for a better test item.  And it puts a smile on the kids’ faces when they hear it.

Chopin – Mazurka #15 in C major, Op. 24 #2

A few weeks ago, one of my piano students started working on this piece.  My advice, “Pretend you’re Polish,” doesn’t seem to be helping her much.  But this short work is about as far from a Parisian Salon, and as close to a Polish village as Chopin ever got.  The passage in the lydian mode is hauntingly beautiful.  To play this piece, you have to forget everything you know about triple meter, and simply tug and pull at the rhythm until it’s about to break; and yet, it must all come out even, so that you can dance to it without missing a step.  And the coloristic variety that this piece demands!  Don’t get me started!

Sorry Hannah.  Come to think of it, maybe I should have waited before I assigned it to you.

Here is my interpretation of it.  I hope it helps you.  I recorded it this evening on my awful Lester piano.  See what you think.

Beethoven – Sonata in f minor, Op 2 #1, 1st movement.

Happy birthday, Beethoven!

I just finished recording this first movement of Beethoven’s first published sonata.  My performance is a bit rough, but then again, so is this lean-and-mean piece.

It’s the first piece I ever studied with Sementovsky, 35 years ago.  “Do not be afraid to explode,” he used to tell me, referring to the frequent sforzandi.  “When Beethoven explodes, no one dies,” he said with a laugh.  As I was learning this piece, Sementovsky and I battled constantly over tempo.  He wanted me to change tempo radically — for expressive purposes — which went against my restrained nature.  (And you’ll notice, in this performance, I do rush the recapitulation slightly, which he never would have approved of.)  “When Beethoven writes espressivo, he really means ritardando,” he said often. Well, maybe.  But out of respect for Sementovsky, I made a point to slow down the beginning of the closing theme each time it occurred, just a bit.

Prelude Op. 37, No. 1 in B flat minor by Alexander Scriabin

I couldn’t resist playing one more prelude.  This one is an exquisite, soulful piece marked mesto, which means mournful.  This is the sort of piece that George Sementovsky, my teacher, would have reveled in, with his attention to color, shading, blur, and nuance.  I’m sure he would have milked the written-in silences, and he would have played with greater dynamic contrasts than I did.  My performance is more restrained, more intimate than his probably would have been.  Let me know what you think of it.

.

 

Prelude Op. 11, No. 13 by Alexander Scriabin

I just felt like playing this Prelude tonight. It’s been a long day, and I needed this serene piece — except I can’t seem to get a convincing lento tempo out of it.  It came out somewhere between andante and allegretto no matter how hard I tried to slow it down.  See what you think about my up-tempo version.