New Music

The score for British composer Cornelius Cardew’s Treatise is 193 pages of abstract and geometric shapes. There’s no indication as to how to interpret these, but Cardew suggested that the players work out a plan in advance.

bussotti

Sylvano Bussotti’s Five Pieces for David Tudor drives conventional notation in the direction of graphics and visual art. “For Bussotti, musical results, whatever they may be, flow directly from the visual,” writes Simon Shaw-Miller in Visible Deeds of Music (2002). “The ear plays no part until the work is performed.”

berberian

Stripsody, by Bussotti’s friend Cathy Berberian, is composed as a cartoon strip, complete with characters (including Tarzan and Superman) and sound effects at approximate pitch (including oink, zzzzzz, pwuitt, bang, uhu, and kerplunk). The instructions explain, “The score should be performed as if [by] a radio sound man, without any props, who must provide all the sound effects with his voice.” Here’s an example:

See Difficult Music.

Solitons

In 1834, engineer John Scott Russell was experimenting with boats in Scotland’s Union Canal when he made a strange discovery:

I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped — not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation.

They’re known today as solitons. He found that such waves can travel over very large distances, at a speed that depends on their size and width and the depth of the water. Remarkably, as shown above, they emerge from a collision unchanged, simply “passing through” one another.

(Thanks, Steve.)

Keyboard Variations

https://commons.wikimedia.org/wiki/File:A_caricature_of_Louis-Bertrand_Castel%27s_%22ocular_organ%22.jpg

Inspired by Isaac Newton’s theory that the seven notes of the diatonic scale were related to the colors of the spectrum, French mathematician Louis Bertrand Castel in 1725 invented an “ocular harpsichord” outfitted with lanterns so that “the pressing of the keys would bring out the colours with their combinations and their chords; in one word, with all their harmony, which would correspond exactly to that of any kind of music.” Voltaire devoted Chapter 14 of his Eléments de la philosophie de Newton to the the theory and to Castel’s instrument, and Telemann composed several pieces for it.

The Great Stalacpipe Organ in Luray Caverns, Virginia, produces its tones by striking stalactites with rubber mallets. Leland W. Sprinkle spent three years in the 1950s identifying promising stalactites, shaving them to pitch, and wiring solenoids to trigger the mallets. The tones can be heard throughout the cavern even without amplification, but a loudspeaker system is normallly used.

https://commons.wikimedia.org/wiki/File:Katzenkavalier.jpg

I think I’ve written elsewhere about the Katzenklavier, a thankfully imaginary instrument first described by Athanasius Kircher in 1650. In the words of one writer, “if a key was pressed on the keyboard, the corresponding tail would be pulled hard, and it would produce each time a lamentable meow.”

https://commons.wikimedia.org/wiki/File:La_Piganino.jpg

Allegedly Louis XI of France challenged Abbé de Baigne to do the same thing with pigs to produce a “piganino”:

That brutal monarch, Louis XI of France, is said to have constructed, with the assistance of the Abbé de Baigne, an instrument designated a ‘pig organ,’ for the production of natural sounds. The master of the royal music, having made a very large and varied assortment of swine, embracing specimens of all breeds and ages, these were carefully voiced, and placed in order, according to their several tones and semitones, and so arranged that a key-board communicated with them, severally and individually, by means of rods ending in sharp spikes. In this way a player, by touching any note, could instantly sound a corresponding note in nature, and was enabled to produce at will either natural melody or harmony!

“The result is said to have been striking, but not very grateful to human ears.”

After our civilization has destroyed itself, the Adriatic will still be playing harmonies on the “sea organ” in Zadar, Croatia. Wind and waves interact with a system of polyethylene tubes to produce sound in a resonating cavity. In 2006 architect Nikola Bašic received the European Prize for Urban Public Space for the project, voted the best among 207 candidate projects from across Europe.

12/17/2016 UPDATE: I completely forgot the mouse organ! (Thanks, Gavin.)

The More the Airier?

https://commons.wikimedia.org/wiki/File:The_Caproni_Ca.60_on_Lake_Maggiore,_1921.png

In 1921 aeronautical engineer Giovanni Caproni designed a 100-seat transatlantic airliner with nine wings. With an empty weight of 14,000 kg, the Caproni Ca.60 Transaereo did tolerably well on its first test flight on Lake Maggiore, but it crashed on the second and never flew again. Caproni said, “So the fruit of years of work, an aircraft that was to form the basis of future aviation, all is lost in a moment. But one must not be shocked if one wants to progress. The path of progress is strewn with suffering.”

Nine wings isn’t even the record — that might belong to the “clever but somewhat dogmatic” Victorian engineer Horatio Phillips, who devised aircraft with up to 200 airfoils, basing them on a multi-vaned marine hydrofoil that he had designed. “But air and water do not behave similarly,” notes James Gilbert in The World’s Worst Aircraft (1976). “Air is compressible, while water, as you will know if you have ever belly-flopped into a swimming pool, hardly is. Multiple vanes lift well in water, poorly if at all in air.” Phillips spent £4,000 and gave up.

https://commons.wikimedia.org/wiki/File:Horatio_Phillips_1904_Multiplane.png

Growth Potential

Suppose you’re working on an algebraic expression that involves variables, addition, multiplication, and parentheses. You try repeatedly to expand it using the distributive law. How do you know that the expression won’t continue to expand forever?

For example, expanding

(x + y)(s(u + v) + t)

gives

x(s(u + v) + t) + y(s(u + v) + t),

which has more parentheses than the original expression.

Click for Answer

Black and White

hochberg puzzle

To kill some time before a meeting of chess grandmasters, Burt Hochberg offered this anonymous puzzle from the 15th century. White must place four white rooks on the board, one at a time, giving check with each one. After each placement the black king can respond with any normal legal move. How can White plan his moves so that the fourth rook reliably gives checkmate?

There’s no trick, and in fact there are several solutions, but Hochberg says the grandmasters studied the position for several minutes before Paul Keres came up with an answer. What was it?

Click for Answer

Last Business

http://news.usask.ca/archived_ocn/09-jan-23/see_what_we_found.php

Working alone in his fields on June 8, 1948, Saskatchewan farmer Cecil George Harris accidentally put his tractor into reverse. It rolled backward, pinning his left leg under the rear wheel. His wife didn’t find him until 10:30 that night, and he died at the hospital.

Days later, surveying the scene of the accident, neighbors noticed that Harris had scratched an inscription into the tractor’s fender using his pocketknife:

In case I die in this mess, I leave all to the wife. Cecil Geo Harris.

The courts determined this to be a valid will. The fender was kept at the Kerrobert Courthouse until 1996; today it and the knife are displayed at the University of Saskatchewan law library.

8 Is Enough

8 Is Enough - problem

This is said to have been the most popular problem presented in the American Mathematical Monthly. It was proposed by P.L. Chessin of Westinghouse in the April 1954 issue. Each of the digits in this long division problem has been replaced with an x — except for a single 8 in the quotient. Can you reconstruct the problem?

Click for Answer

Podcast Episode 133: Notes and Queries

https://commons.wikimedia.org/wiki/File:Samuel_L_Clemens,_1909.jpg

In this week’s episode of the Futility Closet podcast we’ll explore some more curiosities and unanswered questions from Greg’s research, including a pilot who saved Buckingham Palace, a ghost who confronted Arthur Conan Doyle, what Mark Twain learned from a palm reader, and a bedeviling superfluity of Norwegians.

We’ll also discover a language used only by women and puzzle over a gift that’s best given sparingly.

See full show notes …