[Author’s Note: A tradition owing to Dr. Stu Forster during his many years as President and Editor, the Syracuse Astronomical Society (www.syracuse-astro.org) features (at least) one Constellation in each edition of its near-monthly newsletter, the Astronomical Chronicle.]
The Constellation discussion for this year is going to take a bit of a turn.
As part of the 2011 Syracuse Astronomical Society (SAS) lectures presented at Liverpool Public Library and Beaver Lake Nature Center, I spent a few minutes covering (briefly) how to navigate the Night Sky. By way of introduction, I described how one of my graduate advisors, Dr. Bruce Hudson, began scribbling furiously a long string of quantum mechanical equations about something-or-other that devoured the lion’s share of a whiteboard. Upon mentioning that I had no idea how he kept such information at the ready in his noggin, he replied “Try doing it 50 years.”
It is, in my humble opinion, useless to present the 88 Constellations to a general, new-to-observing audience in an hour and expect anyone to remember information that I, as el presidente, am still trying to digest after several years (a problem made all the more infuriating by the fact that this information hasn’t changed in several millennia). The problem that I and others at this latitude have is that the vast majority of the Night Sky changes throughout the year and, given that weather conditions often result in short spells of clear sky and long patches of overcast conditions, there is often little opportunity for “mental reinforcement” to help commit the lesser (well, at least smaller or dimmer) Constellations to memory.
The solution I discussed in the lectures was to play the “observability odds” and focus on learning those Constellations that you can, given clear skies, see all year long from Central New York (CNY). This group of Constellations are defined as “circumpolar” and, by their location about the axis of rotation of the Earth, never dip below the West/Northwest Horizon (or, at least, they do not entirely disappear over the course of a long evening of observing unless you’re surrounded by considerable foliage).
The set of images at the end of this article will show you how to kill six birds with one long, clear turn of the stone we call Earth. The small family of six Constellations I’ve included in this discussion are (1) Ursa Major (although, here, I’m only including the Big Dipper asterism for ease of identification. This is obviously a better target for new observers), (2) Draco the Dragon (a long and winding Constellation that is curled around the Little Dipper), (3) Cepheus, the late-late-late King of Ethiopia (as much as I dislike the use of simple geometric objects to identify groups of stars (because, well, they’re all points on imaginary polygons), the odd pentagon does stand out at night), (4) Cassiopeia (Jonathan Winters’ Big “W” and, thanks to Earth’s rotation axis, also sometimes a “3,” or an “M,” or an “E,” but obvious upon first being pointed out), and (5) Camelopardalis the giraffe (one of the last Constellations you might otherwise learn. Also one of the last Northern Constellations marked as such, in this case in 1612 by Petrus Plancius. You might even have a little trouble picking this one out. The Greeks (for instance, and in their infinite wisdom (I note with a 100% Greek heritage)) did not even bother to identify anything in this part of the sky as being of significance given how relatively dim the stars are). This list leaves number six, Ursa Minor, which I denote in the images as “0” as your celestial clock face base of operations.
Ursa Minor, or the Little Dipper (below, shown at its approximate orientation at 10:00 p.m. on March 23rd), is a nondescript Constellation that requires a bit of searching to find in the Night Sky. Polaris, its last handle star (2.0 mag.), is made easier to find by the fact that it is in a very dark, very nondescript piece of sky (it is identifiable simply by being where it is). Its cup-edge stars Pherkad (3.0 mag.) and Kochab (2.1 mag.) are a bit brighter and also in a dull region of the sky. The four remaining stars are the ones that become more visible as you mark their location with your scanning eyes. These four are made a bit more difficult to find from Darling Hill Observatory (home of the SAS) because of the bright light bulb directly at our Northern Horizon that is downtown Syracuse.
A possible trick to finding Polaris for the new-at-observing is to use the two most prominent Constellations in the North, Ursa Major (again, using the Big Dipper asterism here) and Cassiopeia. Finding the bowl of the Big Dipper and imagining a clock face, find Cassiopeia at nearly 7 o’clock to the edge-most bowl stars, then aim for the location where you’d expect those hands to be riveted (as shown below). Again, you’ll find a single bright-ish (“eh”) star at this location.
Having sufficiently talked down the significance of Polaris as a celestial observable, this otherwise nondescript star has something other nondescript stars have. To quote “Glorious John” Dryden:
Rude as their ships were navigated then;
No useful compass, no meridian known;
Coasting they kept the land within their ken;
And knew no North but when the Pole star shown.
Or, as William Tyler Olcott sums more quickly in his book “Star Lore,” Polaris is “the most practically useful star in the heavens.” Modern civilizations know Polaris as the star around which the Earth appears to spin, making it the most stably-placed object in the Night Sky over any reasonable span of human existence (a qualification I use in this article to avoid a discussion of the fascinating but “not relevant to learning the Night Sky right now” Precession of the Equinoxes).
The apparent constancy of all of the star positions (and Constellations) in the Night Sky relative to one another is, of course, due to stellar parallax, the celestial equivalent of the more familiar terrestrial parallax. If you’ve ever been the passenger on a long drive, you’ve borne witness to the trees along the road moving at a tremendous clip while the distant trees slide far more slowly through your field of view (that is, stay in your field of view while the trees along the road fall far behind you over the same amount of time). Polaris provides an ideal example of this same phenomenon on a celestial scale by its apparent immovability in the Night Sky despite the best efforts of Earth as it reaches nearly 300,000,000 kilometers of physical separation from its starting point every six months. The two images below demonstrate the phenomenon…
Your Green Laser Along Earth’s Rotation Axis (Pointing UP From The North Pole), One Beam Every Three Months, Separated By (At Best) 2 Astronomical Units (a.u.), Looking At A “Close Object” With A Large Apparent Motion Against The “Background”
Your Green Laser Along Earth’s Rotation Axis (Pointing UP From The North Pole), One Beam Every Three Months, Marking A Position 431 Light Years Away (Looking At A “Distant Object”) And A Small Apparent Motion Against The “Background” (All NOT To Scale)
At above-left you see a small slightly-sideways model of Earth’s motion around the Sun (at points being marked about every three months), with the left-most and right-most positions separated by two astronomical units, the astronomical unit being the mean distance between the Sun and Earth (bearing in mind Kepler‘s Elliptical description of our orbits), a value of about 150 million kilometers. To objects in our own Solar System or even a few nearby stars, this large change in position is enough to clearly see those objects that are nearby move more than the “background” of more distant objects (you could do this at home with a decent scope and excellent note-taking skills, possibly reproducing the 1838 work of Friedrich Bessel in his measurement of the parallax of 61 Cygni). In our case, the more distant objects are the stars far from our vantage point (think of “stars” as “trees” and the same driving analogy works, although now you’re driving around a circular track and paying your passenger to always look North). Polaris, as measured by the Hipparcos satellite (using parallax to exacting detail), determined that Polaris is 431 light years away, a distance of 27.5 million a.u.! And this is a CLOSE star considering the 100,000 light year diameter of the Milky Way. At this distance, if the four green laser pointer beams were a meter long, their separation in Earth’s orbit would be a small enough measuring distance to map out the contents of a single-celled organism in exacting detail. My ability to draw a proper parallax-like image to show this is limited by the pixels on my screen being gigantic compared to the apparent change in position in this crude image (so the above image is decidedly NOT to scale).
All of this discussion above is basically to convince you that, when you look up in the Night Sky, Polaris will effectively NOT move to the best of your ability to observe it, making it a best starting point for your Constellation memorization adventure.
Well, Polaris will NOT move provided you always observe from the same latitude on the Earth’s Surface. The last piece of the puzzle to put ourselves into proper perspective comes from a zoom-in of our Earth, shown below. You’ll see that our North Pole, appropriately placed at 90o North Latitude, is aligned nearly exactly with Polaris (again, for our purposes, this approximation is fine). What does that mean? It means that, with the right low Horizon (or high hill), nearly ALL of the Northern Constellations are circumpolar at the North Pole! Think of the memorization mess! Alternatively, at the equator (0o), the Night Sky is, effectively, constantly in motion (this should make you truly appreciate the navigational and astronomical skills of the Polynesians in their spread across the South Pacific islands).
As you walk from the Equator to the North Pole, moving from 0o to 90o North Latitude, the North Star appears to get higher and higher in the Night Sky. By this, the angle of Polaris above the Horizon (its altitude) is equal to our latitude (so when you know one (say, by getting your latitude and longitude from google maps or the like), you know the other. This is one of the great “then explain this, dummy!” rhetorical smack-downs to members of the Flat Earth Society). In our case, Polaris is about 40o above our horizon. Personally, I think 40o North Latitude is a perfectly reasonable place to begin Constellation memorization. Not too many, not to few. And, as is the common theme we’ll explore this year, once you have a reliable base of celestial operations, learning the remaining Constellations becomes a significantly easier (but still Herculean) task.
The Counterclockwise Circumpolar Map
Your Northern Horizon from CNY will, clear skies permitting, ALWAYS look something like the following, with the Constellation closest to the N/NW Horizon labeled as follows (0 = Ursa Minor, the Little Dipper. * = Polaris, which appears to not move (to a coarse approximation)):
A. Big Dipper (1, technically, Ursa Major, but the Big Dipper is smaller and more obvious)
B. Draco (2, aim for the dragon’s head. If the Big Dipper is N/NE, an easy find)
C. Cepheus – 3, a crazy house standing upright, just right of a bright “E”
D. Cassiopeia – 4, the big “W,” at the horizon an “E” (or its canonical chair)
E. Camelopardalis (?!) – 5, the back-end of a giraffe(with Cassiopeia as a “Big W,” the giraffe is drinking from the tipped bowl of the Big Dipper).
NOTE: The Earth’s rotation makes 1-to-5 move counterclockwise! Fresh Constellations over your Eastern Horizon, stale ones disappear at your West.
On October 4, a concert is planned with “The Excelsior Cornet Band”. “The Excelsior Cornet Band” is New York State’s only authentic Civil War brass band. Founded in 2001, the band consists of a group of upstate New York musicians who are dedicated to the performance of original Civil War music on actual antique brass band instruments of the 1860’s period. They will be performing their Abraham Lincoln Program on Sun., Oct 4 at 2 pm on the second floor of the Library.
With my trusty Olympus LS-10 (Linear PCM) Recorder set to PCM (44.1kHz/16bit) mode (additional settings: Low Cut OFF, Mic Sensitivity HIGH, recorder placed on the drums side of the band 20 feet away from any instruments) and my Canon Powershot SD780 IS (digital ELPH) set to HD video mode (the only canon in attendance), I managed to capture an official bootleg of a Civil War Band in performance, certainly one of the few in history. Regretfully, the video is only of the first 25 minutes of the performance.
Our fearless leader Jeff Stockham provided a considerable amount of text about the occasion and the music of the occasion (as 2009 is, now was, the bicentennial year of President Abraham Lincoln’s birth) that I decided was best retained in the full recording. As this was too much to type out (and it is quite clear in the recordings anyway), I have included brief comments on the pieces in the concert below with relevant links to web content about pieces, original performers, and significant historical figures.
The set list is below. The full MP3 album (320 kpbs) of the performance is available for download at the link “1” below (all song and album data should appear with an import to iTunes or related). In .tar.gz format. Most modern operating systems will open this file automatically to provide the .mp3 files. If not, I suspect you’re running an older version of Windows and should, therefore, download 7-Zip, Winzip, or related. Link “2” contains the unseperated MP3 audio of the concert (the talk between music is hard to hear. The .tar.gz file has the spoken sections amplified). Link “3” is of the .mov file of the first 25 minutes of the performance (much faster if you download to desktop). For both the MP3 and MOV files, please save to your own machine instead of streaming from my website (right-click over the link and “Save As,” “Save Link As,” etc.).
Henry Clay Whitney‘s recollection of a comment from Abraham Lincoln – all other pleasures had a utility, but that music was simply a pleasure and nothing more, and that he fancied that the creator, after providing all the mechanism for carrying on the world, made music as a simple, unalloyed pleasure…. This text is copied from www.abrahamlincolnsclassroom.org.
“I am loath to close. We are not enemies, but friends. We must not be enemies. Though passion may have strained it must not break our bonds of affection. The mystic chords of memory, stretching from every battlefield and patriot grave to every living heart and hearthstone all over this broad land, will yet swell the chorus of the Union, when again touched, as surely they will be, by the better angels of our nature.” – Abraham Lincoln‘s close of his first inaugural address.
03. Introduction to “Old Joe Hooker Quickstep” – 2:37
The Wide Awake Quickstep, possibly performed on 11 September 1860 for a meeting of “The Wide Awakes,” is from Schreiber’s Albany Cornet Band, which was organized 12 June 1860. Information about the Wide Awakes is available at wikipedia.
An engraving of a Wide Awake’s 1860 rally.
A Wide Awakes website also exists for an organization that claims to be of the order of the original movement (someone can confirm or deny this accordingly). This can be found at www.wideawakes.net.
07. Introduction to “Meditation: 20 Years Ago” – 2:54
08. Meditation: 20 Years Ago – 3:07
“That tune is enough to make an E-flat cornet player dizzy.” – Jeff Stockham
This medley was arranged by George Holton Goodwin. “20 Years Ago” is reported by Ward Hill Lamon to be Lincoln’s favorite piece of music. The piece “20 Years Ago” was written by William Willing in 1856. “Ever Of Thee” was written by Foley Hall and George Linley in 1852. A link to sheet music (and a snippet of audio) can be found at the National Library of Australia website at catalogue.nla.gov.au/Record/1683158. A copy of the cover is shown below.
The quickstep version performed here is attributed to the Manchester Massachusetts Cornet Band (there also exists a Manchester New Hampshire Cornet Band if you google around. Accept no Manchester imitations! That said, there is a complete history of the Manchester New Hampshire Cornet Band from 1890 available in PDF format (as well as the usual browser-friendly format) at google books: books.google.com/books?id=5PBYAAAAMAAJ&printsec=frontcover#v=onepage&q=&f=false).
Another piece by George Holton Goodwin titled “Door Latch Quickstep” can be found at www.digitalhistory.uh.edu/audio/music2.cfm. The tune is near the bottom of the top-fifth of the website. A copy of the provided MP3 from the Library of Congress is provided locally HERE.
10. The Irish Medley: The Sprig of Shillelagh, Rakes of Mallow, and Lament of the Irish Immigrant – 2:43
The alternate name for “Lament of the Irish Immigrant” is “I’m Sitting On The Stile, Mary.” The Irish Medley is from The Squire’s Brass Band Olio. I’ve found precious little online about the music and the band, but direct you to the following few links for some additional information:
Adelina Patti 1843-1919, Spanish Opera Singer. From wikipedia.org.
From the wikipedia entry for Adelina Patti: “In 1862 she sang John Howard Payne’s Home, Sweet Home at the White House for Abraham and Mary Lincoln, who were mourning for their son Willie, who had died of typhoid. The Lincolns were moved to tears and requested an encore. This song would became associated with Adelina Patti. She performed it many times as an encore by popular request.”
It probably was in this room that singer Madame Patti came to visit with and sing for the Lincolns. She said later that “we were received by Mrs. Lincoln in one of the big parlors. The President’s wife was a handsome woman, almost regal in her deep black and expansive crinoline, only an outline of white at throat and wrists. Her manner was most gracious without a particle of reserve or stiffness. ‘My dear, it is very kind of you to come to see us,’ she said. Taking both my hands in hers and smiling in my face, she added,’I have wanted to see you… to see the young girl who has done so much, who has set the whole world talking of her wonderful singing.'” After several songs, Madame Patti accompanied herself on the piano while singing, ‘The Last Rose of Summer.’ She realized afterwards that she had “made an awkward choice.’ Mary has “risen from her seat and was standing at a window in the back part of the room with her back toward me. I could not see her face but I knew she was weeping.” Mr. Lincoln then requested ‘Home Sweet Home.”
Historian David Rankin Barbee wrote that her accompanist “did not know the air, and Patti, who knew it, did not know the words, and had never sung them. Seeing her dilemma, ‘the President rose from his seat, went quickly to a small stand at the foot of the piano, took from it a small music book, with a vivid green color, and placed it on the piano rack, opened to the music of Home, Sweet Home. Then he returned to his seat without a word and resumed his former posture. ‘Well, I sang the song the very best I could do it,’ Patti concluded,’and when Mr. Lincoln thanked me his voice was husky and his eyes were full of tears. By that time I was so wrought up over the situation myself that I was actually blubbering when we were taking leave of the recently bereaved parents.'”
All people that on earth do dwell,
Sing to the Lord with cheerful voice.
Him serve with fear, His praise forth tell;
Come ye before Him and rejoice.
In combination with the text from the performance, Lincoln’s Gettysburg Address is provided in its entirety below (using his aptitude for impact and brevity as a metric, Lincoln would have made one helluva blogger). I remember Carlos Moroz memorizing this for our 4th Grade English class (I had picked a section of George Washington’s Farewell Address) and thinking it was pretty good (well, it was 4th Grade).
So brief, the photographer only caught Lincoln as he sat down. From wikipedia.org.
Four score and seven years ago our fathers brought forth on this continent a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal.
Now we are engaged in a great civil war, testing whether that nation, or any nation, so conceived and so dedicated, can long endure. We are met on a great battle-field of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this.
But, in a larger sense, we can not dedicate…we can not consecrate…we can not hallow this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before usâ€”that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotionâ€”that we here highly resolve that these dead shall not have died in vainâ€”that this nation, under God, shall have a new birth of freedomâ€”and that government: of the people, by the people, for the people, shall not perish from the earth.
Quest for Sound curator Jay Allison unearthed a unique recording: the voice of William V. Rathvon, who as a nine-year-old boy, watched and listened to Abraham Lincoln deliver his address at Gettysburg in November 1863. The story was told in 1938 and recorded on a 78 r.p.m. record.
A family in Pallatine, Illinois shared this recording with us via our Quest for Sound phone line. Rathvon was a distant relative. No other Gettysburg eyewitness is known to have recorded their memories on record.
The historical record reports the following about the most significant performance of this piece, requested by Lincoln upon the surrender of Lee to Grant at Appomattox.
“General Robert E. Lee surrendered to General Ulysses S. Grant on April 9, 1865. The next day, despite rain and mud there were some 3,000 people in the streets celebrating. Crowds serenaded President Lincoln throughout the day. “At length,” wrote a reporter for the Washington paper Daily National Intelligencer, “after persistent effort, the presence of Mr. Lincoln was secured. Three loud and hearty cheers were given, after which the President said:
â€˜FELLOW CITIZENS: I am very greatly rejoiced to find that an occasion has occurred so pleasurable that the people cannot restrain themselves. [Cheers.] I suppose that arrangements are being made for some sort of a formal demonstration, this, or perhaps, to-morrow night. [Cries of `We can’t wait,’ `We want it now,’ &c.] If there should be such a demonstration, I, of course, will be called upon to respond, and I shall have nothing to say if you dribble it all out of me before. [Laughter and applause.] I see you have a band of music with you. [Vocies, `We have two or three.’] I propose closing up this interview by the band performing a particular tune which I will name. Before this is done, however, I wish to mention one or two little circumstances connected with it. I have always thought `Dixie’ one of the best tunes I have ever heard. Our adversaries over the way attempted to appropriate it, but I insisted yesterday that we fairly captured it. [Applause.] I presented the question to the Attorney General, and he gave it as his legal opinion that it is our lawful prize. [Laughter and applause.] I now request the band to favor me with its performance.'”
“In accordance with the request, the band struck up `Dixie,’ and at its conclusion played `Yankee Doodle,’ the President remaining at the window mean-while. The President then said: `Now give three good hearty cheers for General Grant and all under his command.’ These were given with a will, after which Mr. Lincoln requested `three more cheers for our gallant Navy,’ which request was also readily granted. The President then disappeared from the window, amid the cheers of those below. The crowd then moved back to the War Department, and loud calls were again made for Secretary Stanton.”
Less than a week later, Lincoln was dead.”
19. Introduction to “Honor To Our Soldiers” – 3:25
20. Honor To Our Soldiers – 2:35
“When I leave the stage for good, I will be the most famous man in America” – John Wilkes Booth at Taltaval’s Saloon.
The play’s most famous performance came seven years later, at Ford’s Theatre in Washington, D.C. on April 14, 1865. Halfway through Act III, Scene 2, the character Asa Trenchard (the title role), played that night by Harry Hawk, utters a line considered one of the play’s funniest:
“Don’t know the manners of good society, eh? Well, I guess I know enough to turn you inside out, old gal â€” you sockdologizing old man-trap…”
During the laughter that followed this line, John Wilkes Booth, a famous actor who was not in that night’s cast of Our American Cousin, fatally shot President Abraham Lincoln. Familiar with the play, he chose this moment in the hope that the sound of the audience’s laughter would mask the sound of his gunshot. He then leapt from Lincoln’s box to the stage and made his escape through the back of the theater to a horse he had left waiting in the alley.
21. Introduction to “Abraham Lincoln’s Funeral March” – 1:52
22. Abraham Lincoln’s Funeral March – 4:14
Abraham Lincoln’s Funeral March was composed by Christoph H. Bach of Milwaukee, WI. You can read a little more (and see him) at csumc.wisc.edu/exhibit/MusicTour/GAMBands.htm. There is some remarkable photography from this time, with a few selected pieces from google image searches and wikipedia.org below.
John Allis – Playing an 1850’s snare drum made by Edward Brown of Albany, NY
Al Thompson – Playing an 1855 o’er-the-shoulder E-flat bass saxhorn tuba made by Charles A. Zobish and Sons of NY
Loyal Mitchell – Playing an over-the-shoulder B-flat baritone horn with Berliner-style piston valves. Imported from Europe by J. Howard Foot of NY (1865-70)
Dickson Rothwell – Playing an over-the-shoulder E-flat alto horn. Imported from Europe
David Driesen – Playing an 1870 rotary valve side-action B-flat cornet made by The Boston musical instrument manufacturer Eldridge G. Wright
Lee Turner – Playing an 1868-1870 side-action E-flat rotary valve cornet made by D.C.Hall and Benjamin F. Quimbey
Jeff Stockham – Playing an 1866 (it’s on the bell) cornet made by Hall and Quimbey of Boston. We know even more about this particular instrument: “Presented by the members of the Brooklyn Cornet Band to Amos H. Bangel, leader, October 11 1866.” That is, for the record, the Brooklyn Cornet Band of Brooklyn, CA.
24. Introduction to “Battle Hymn Quickstep” – 2:29
25. Battle Hymn Quickstep – 2:06
Always end strong. The lyrics to the Battle Hymn of the Republic were written (partly in a dream) by Julia Ward Howe and put to the music of “John Brown’s Body,” who you may remember from the beginning of Ken Burn’s epic The Civil War (I had to fit Ken Burns into the post somewhere). The music for “John Brown’s Body” was originally written/collected by William Steffe in 1856 for a song containing the opening verse “Say, brothers, will you meet us / on Canaan’s happy shore?” A copy of the original first-printing of the poem from the Atlantic Monthly is provided below from wikipedia.org.
While there, McCabe and his fellow prisoners learned of Lee’s defeat at the Battle of Gettysburg. To celebrate, they sang every national song they knew, including Howe’s “Battle Hymn of the Republic.” After a few resounding choruses of “Glory, glory, hallelujah!” the guards put a stop to the singing.
Finally, it would not surprise me that several errors or misrepresentations may have made their way into my text. As I suspect at least a few heavy-duty Civil War nuts will find their way to this page, please do not hesitate to contact me with insights, comments, or lambasting. I’ll be happy to make changes and acknowledge accordingly. Huzzah!
This is the method presented by Terry Bozzio in many of his clinics. Once you can play all 15 measures above against ANY rhythm possible from repeated combinations of the above measures (so-called “ostinatos“), then you’ve played every sixteenth note-based subdivision possible. There are, of course, actually 16 measures, the first being the one with nothing played (the easiest to master for most rhythms). The importance of this null case will be important in later sections. Note that the above is for sixteenth notes in 1/4. The game is played differently for 1/4 with triplets, quintuplets, etc. The mechanism is the same, however. If you feel inclined, the other possible combinations are easy to write down using the Pascal Triangle to keep track.
How to use…
Here’s an easy coordination exercise sure to frustrate. Pick 3 limbs (or 4, if you want to use your voice as another instrument). Assign each of those limbs to a particular measure in the above list. Get that rhythm playing so you have some idea of what it will sound like and to try to internalize it for the next step. Finally, with the unselected limb, play through all 15 measures above (or 16, though you’ll have played the null case to death getting the feel for the rhythm). Don’t try to play through the exercise until you’ve internalized where the notes of every measure fall in the rhythm you’re holding steady with the other limbs. That’s the point of an ostinato. The rhythm over which you solo should be fixed and unwavering and something playable in your sleep. Soloing is secondary to locking down the groove.
Once you’ve played through all 15 (err… 16) measures, either make the “soloing” limb a fixed limb and solo with something else (a killer exercise for getting your hi-hat foot conditioned, for instance) or select another set of measures to hold constant and play the same 15 (err… 16) measures over that new rhythm.
A note to the ambitious: You’ve 16 measures to pick from and 3 (or 4) limbs to make rhythms out of. Therefore, the possible number of rhythms you can generate from the above are, including the null case, (16) x (16) x (16), or 4096. A lot of rhythms to try. Throw in a fifth soloing limb (your voice, for instance), and the number of possible “fixed” combinations to play against goes up to (4096) x (16), or 65536. Granted, some of these are quarter notes and the like and are easy to play, but many are completely uncharted (so to speak).
If you don’t feel like thinking up the combinations yourself, here’s a little script to get you started.