Monday, January 9, 2012

A post for both halves of your brain to start the week off right


It’s not a foreign word. It isn’t even a word at all, so don’t try to pronounce it. (How many of you remember the time on Sesame Street when Big Bird saw ABCDEFGHIJKLMNOPQRSTUVWXYZ and sang “Ab-keddef-gajihkel-monop-quristuv-wixyz, it’s the most remarkable word I’ve ever seen, Ab-keddef-gajihkel-monop-quristuv-wixyz, I wish I knew exactly what I mean”?)

Singers everywhere will recognize the conglomeration of consonants BDFLMNPTV-V-V as a vocal exercise sung on the following musical syllables:


The accompanist then modulates a half-step upward, and the singers commence their BDFLMNPTV-V-Ving again in the new key, and so on and so forth, until only first sopranos who can hit the high notes without busting a gut are left. I’m kidding, but only slightly. Most choir directors seem to be either sopranos or tenors who refuse to accept the vocal limitations of altos and basses. Altos and basses do not become choir directors.

Of course, there is the ever-popular old standby “Mee-May-Mah-Mo-Mu” and its many variations (“Nee-Nay-Nah-No-Nu” and “Bee-Bay-Bah-Bo-Bu” and, well, you get the idea) using the pentatonic scale.

If you don’t know what the pentatonic scale is, go to the back of the line.

Another popular warmup vocal exercise for singers hereabouts is “Who washed Washington’s white woolen underwear when Washington's washer woman went west?” in which all the words except one are sung on the same tone. The penultimate word is sung a half-step lower than the others. Repeat in the next higher key, following modulation by the accompanist. Again. Again. About thirteen times in all.

If you don’t know what penultimate means, go to somewhere near the back of the line.

Last of all, you mustn’t forget to limber up your body, sort of like this, with less bouncing.

We would begin practicing the anthem for Sunday now, but the rehearsal time has expired.

If you are more interested in math and physics than music, you can use the following formula to determine the frequency of a tuning fork (the frequency of a tuning fork depends on its dimensions and the material from which it is made):


f is the frequency the fork vibrates at in Hertz,
1.875 is the smallest positive solution of cos(x)cosh(x) = -1,
l is the length of the prongs in meters,
E is the Young’s modulus of the material the fork is made from in pascals,
I is the second moment of area of the cross-section in meters to the fourth power,
ρ is the density of the material the fork is made from in kilograms per cubic meter, and
A is the cross-sectional area of the prongs (tines) in square meters.

If you don’t know what Young’s modulus and pascals are, or that cross-sections even have moments, go to somewhere near the back of the line.

For those who simply must know, Young’s modulus, also known as the tensile modulus, is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke’s Law holds.

For your own good, I would discourage you from thinking too much about either the length of the prongs in meters or the cross-sectional area of the prongs in square meters, especially in connection with the stiffness of an elastic material.

And the pascal? Well, the pascal (symbol: Pa) is the SI derived unit of pressure, internal pressure, stress, Young’s modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square meter. In everyday life, the pascal is perhaps best known from meteorological barometric pressure reports, where it occurs in the form of hectopascals (1 hPa ≡ 100 Pa) or kilopascals (1 kPa ≡ 1000 Pa). In other contexts, the kilopascal is commonly used, for example on bicycle tire labels. One hectopascal corresponds to about 0.1% of atmospheric pressure slightly above sea level; one kilopascal is about 1% of atmospheric pressure. One hectopascal is equivalent to one millibar; one standard atmosphere is exactly equal to 101.325 kPa or 1013.25 hPa or 101325 Pa. The correspondent Imperial unit is pounds per square inch (psi).

The pascal can be expressed using SI derived units, or alternatively solely SI base units, as:

where N is the newton, m is the meter, kg is the kilogram, and s is the second.

Happy now? I do hope both sides of your brain have had a good workout.

Now go take on the world.


  1. I have to work on church financials today and this post has totally blown both halves of my brain. Thanks!:)

  2. I've given up thinking entirely.

  3. The word "penultimate" is one of my favorite words, but after reading that post, I still think I belong towards the back of the line...

  4. I'm now so far at the back of the class, I doubt if you can even see me.

  5. I actually did a lab on tuning fork frequency in college physics...which is pretty impressive considering I was a high school music major. My grade however, was less impressive.

  6. Pat, glad to be of service!

    Carolina, was that before or after you read this post?

    LightExpectations, penultimate is my second-favorite word. My favorite word is antepenultimate.

    Shooting Parrots (Ian), methinks Yorkshire Pudding's Blogger of the Year for 2011 doth protest too much!

    Jewels, I'm still pretty impressed.

  7. From back at the end of the line I say, "Excellent post, rhymsie!" In high school chorus, we warmed up with "me-may-ma-mo-mu". Thanks for the memory.

  8. I'm going to forward your blog post to my Dad (he always said he was an athiest, so I don't know whether to use the heaven or hell email address)...BTW I love/loved him and respected his decision to believe or not believe! Anyway I'm sending this on to him since he was the family mathematics whiz! I'm sure he will understand exactly what all this means!

    It's funny I was in chorus for two years while in school and I don't remember ever warming up my vocal cords with any exercise ;-) What were the teachers thinking!?

    Even with a high powered telescope you'd never even find me in the line...perhaps I'm not even in the line!

  9. Jeannelle and Theanne, it's getting rather crowded with all of my readers at the back of the line!

    Methinks you all protest too much! I mean, really, just the fact that you continue to read my blog each day speaks volumes about your vast intelligence and your excellent ability in making choices. That's my story and I'm sticking to it.

  10. Splendid post. My favourite word is ubiquitous. When it's not indubitably. Or one of the words in this: