CatSynth pic: Video on a Wurlitzer Electric Piano


“Video” the Cat takes a stroll on a Wurlitzer 200e electric piano. Submitted by The Wiggly Tendrils via our facebook page.

One may argue that a Wurlitzer electric piano isn’t a “synthesizer” per se. But electromechanical pianos (Wurlitzer and Rhodes) are among my favorite instruments and feline pictures with them are always welcome here!

Me too. I bought this one in Oshkosh Wisconsin years ago at the music store that time forgot. The guy was renting them out to piano students who didn’t have pianos at home. (their original purpose) I eventually talked him into selling me one. I love it. I also briefly had a Yamaha CP-70 but had to sell it when I moved from Philly to Berkeley.

Weekend Cat Blogging: Play with Me!

On sporadic mornings, I have been taking Instagram photos of Luna like the one above. She is often basking in the sunshine on one of the dining-area chairs, but on this occasion she was rolling on the floor with one message: “Play with Me!”

And it was a good message for her to give. Like many mornings, it was a bit frenzied with things pulling me in multiple directions. Luna made it clear what I should be doing, which was to drop everything and come play with her, even if only for a few minutes before work. And so this is a very roundabout way of interpreting this week’s Photo Hunt theme of DROP. Weak, perhaps, but it means something to us.

Weekend Cat Blogging #352 is hosted by Pam at Sidewalk Shoes.

The Weekly Photo Hunt theme is DROP.

The Carnival of the Cats will be hosted this Sunday by Nikita and Elivra at Meowsings of an Opinionated Pussycat. We also wish Nikita and his dad a Happy Birthday this coming week!

And the Friday Ark is at the modulator.

Fun with the Arithmetic Derivative and Twin Primes

Anyone who has stayed in math classes long enough to reach calculus quickly comes to believe that calculus is more advanced and complex than arithmetic. And while that may be true for the most intuitive aspects of arithmetic that we learn in grade school, the seemingly innocent discipline quickly becomes more mysterious as one advances into it.

Consider the most basic operation in calculus, the derivative. The derivative of the a function is said to describe the instantaneous rate of change of function (how fast it is going up or down in any given direction), or alternatively the slope of a function at any given point. However, there is a related operation on integers is called the arithmetic derivative, defined as follows:

  1. p’ = 1 for any prime number p
  2. (ab)’ = a’b + ab’ for any a,b ∈ &#8469
  3. 1′ = 0
  4. 0′ = 0

While there is an intuitive and even “visual” nature to the calculus derivative, the arithmetic derivative seems more abstract and opaque. Additionally, the former is about continuous functions, while the latter is about discrete entities such as integers or rational numbers. The main thing the two concepts have in common is that they obey the Liebniz Rule governing the products of derivatives, as described on line 2 above.

So can the arithmetic derivative tell us anything useful about integers? It is intimately tied to prime numbers and prime factorization, so it is in that sense an additional tool for examining fundamental properties of numbers as they relate to primes and patterns of primes. The article Deriving the Structure of Numbers quotes Linda Westrick, who has studied the arithmetic derivative and says that it “provides a different context from which to view many topics of number theory, especially those concerning prime numbers. The complex patterns which arise from its simple definition make it interesting and worthy of study.” To see such patterns, one can apply the derivative repeatedly, n’, (n’)’, etc., just as one would in calculus, to chart the variations even among the first few natural numbers.

n
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
n‘
0
1
1
4
1
5
1
12
6
7
1
16
1
9
8
32
1
21
n"
0
0
0
4
0
1
0
16
5
1
0
32
0
6
12
80
0
10
n"’
0
0
0
4
0
0
0
32
1
0
0
80
0
5
16
176
0
7

Indeed the interesting patterns include the fact that some numbers quickly go to zero as one repeatedly applies the arithmetic derivative, as on the case of 6′ = 5, 6” = 1, 6”’ = 0. Other numbers, seem to increase without bound. In the above chart, for example, powers of 2 appear to grow quite quickly. Yet others bounce around unpredictably somewhere in between. In many ways, this reminds me a bit of the Collatz Conjecture which have discussed on CatSynth in the past.

Perhaps the most intriguing property of the arithmetic derivative is its relation to twin primes, pairs of prime numbers whose difference is 2, like 11 and 13 or 29 and 31. It is conjectured that there are infinitely many such pairs of twin primes, but no one has ever proven this. However, it turns out that twin primes are related to the second derivative of a number n”. So if there are infinitely many numbers n for which n” = 1, then there are infinitely many twin primes. As described in this paper by Victor Ufnarovsk, one can derive this from the following theorem:

Let p be a prime and a = p+2. Then 2p is a solution for the equation n’ = a

The proof is relatively straightforward:
(2p)’ = 2’p + 2p’ = p + 2

So if 2p’ = p + 2 and p + 2 is also prime, as would be the case for twin primes, then 2p” = (p + 2)’ = 1.

Unfortunately, this does not answer the question of whether there are infinitely many such pairs. So the famous problem remains open.

Fun with Highways: Michigan

Today we continue our “primary highways” tour with a virtual visit to Michigan, and in particular to Detroit.

My most significant visit to the state took my to Ann Arbor and the University of Michigan for a music technology conference. The conference was a great experience, of course. The campus what quite interesting as well. As with many traditional college campuses, it has an iconic bell tower, Burton Tower. But it has a second one as well on the modernist North Campus. Our conference required going back and forth between the two where we could easily see the contrast between the traditional collegiate architecture and the modernist, which I quite liked but my colleagues derided.

If instead of going west from airport to Ann Arbor on I-94 we had instead gone east, we would have arrived in Detroit. I have yet to visit Detroit, and as such the city has taken on a mythical quality. I-94 enters the city as the Edsel Ford Freeway, mostly staying to the north of the city center. We can turn south onto I-75, the Chrysler Freeway to head downtown. One would expect the “motor city” to have an impressive network of freeways. I-75 runs along the edge of downtown as the Fisher Freeway, and together with I-375 and Michigan Highway M-10 form a loop around downtown, anchored by some large interchanges on either end.

As one can see in this map, the loop frames the downtown and Grand Park Circus. The famous People Mover is primarily located within the boundaries of the loop as well. But us now turn our attention to the surface level, beginning with this view from the connection between M-10 and I-75.


[Photo by ifmuth on flickr. (CC BY-NC-ND 2.0)]

That large building behind the highways is Michigan Central Station (or sometimes Michigan Central Depot, perhaps someone can tell us which is the correct name actually is).


[Albert duce [CC-BY-SA-3.0 or GFDL], via Wikimedia Commons]

The massive and once upon a time grand train station now sits alone and abandoned. It symbolizes much about the city and its history, both rise and decline; and people have very strong opinions about it. It’s “heartbreaking” to some who love Detroit. Some see potential for it to have new uses in the future, perhaps as green revitalization project. Others simply see it as an “eyesore” that needs to be removed. For me, it is quite captivating as a quintessentially American form of “ruin.” We tend not have ruins, preferring to remove that which offends us in favor of bigger, faster, newer, etc. And ruins from the 20th century seem even more vulnerable to our need to remove and remake. But perhaps more than most large cities, Detroit stands out for its ruins that remain. This in part because the city was the center of our iconic automobile industry, and quite prosperous with grand buildings and streets. The decline and decay are quite dramatic, but happened in such a way that many of the places are still there in their decayed state. I first became fascinated with this through the website The Fabulous Ruins of Detroit, which is a loving tribute to the city and its ruins, albeit a melancholy one. And for me, these ruins can be as much a source of creative inspiration as the landscape of Arizona that we explored yesterday. Indeed some of the basic elements of color, shape, texture and sound have things in common, although the human factor is quite different. There is definitely more that Dystopian feel here. I could certainly see music and image inspired by visiting the ruins of the abandoned Packard Automobile Factory.


[By Albert duce (Own work) [CC-BY-SA-3.0 or GFDL], via Wikimedia Commons]

I hope to have the opportunity to visit the city and explore creativity and meet people in the local community there, and make something to share. I hope perhaps the city can find a way to live with its ruins and draw from them without it having to be “blight”, and that vital communities, perhaps greener communities, can grow up within them. Some of the old towers around Grand Circus Park are being redeveloped at this time. And this is all the context of positive news from “Detroit” the automobile industry.


[By Andrew Jameson (Own work) [CC-BY-SA-3.0 or GFDL], via Wikimedia Commons]

In the meantime, there certainly are plenty of cultural opportunities. The Detroit Institute of Arts and the Museum of Contemporary Art Detroit (MOCAD). We have been shadowing the artist Mark Di Suvero throughout this series, and the DIA has two of his works, including an older piece Tom made primarily from wood. Music of Detroit is of course legendary. I have a fondness for quite a lot of classic Motown, much of which was done before they moved – I tend to think it works best in minor keys or when the overall sound is a bit more melancholy than when it is at its most bouncy and upbeat, but that is perhaps just me. Detroit also has a place in the history of popular electronic music. To me, these are not as disparate as others might think, particularly when one considers the harmony. (On this note, I would also enjoy hearing suggestions of music in the comments.)

But it is time to get back on the road. We can head northwest from Detroit on I-96 to Lansing, the state capital. For those like me who are amused by highway trivia, in Lansing, I-96 and I-69 meet, and even run concurrently for a brief period of time. I think this only place where there is such a mirror-image concurrency (as I-87 and I-78 in New York actually never meet). A spur I-496 turns off into the center of Lansing, with the state capital building to one side.


[Criticalthinker at the English language Wikipedia [GFDL or CC-BY-SA-3.0], via Wikimedia Commons]

If from Detroit we head north on I-75, we pass through Flint (of Michael Moore fame) and then further away from the Great Lakes that define the state’s geography and into the center of the lower peninsula. But I-75 is also the main highway connection to the Upper Peninsula over the Mackinac Bridge.


[By Jeffness at en.wikipedia. Later version(s) were uploaded by Sam at en.wikipedia. (Transferred from en.wikipedia) [CC-BY-SA-2.5], from Wikimedia Commons]

North of the bridge, we can switch to US 2 which hugs the shore of Lake Michigan on the southern side of the peninsula. But we can also head inward on M-28, from which we can approach the northern shore along Lake Superior, traveling by many picturesque parks such as Tahquamenon Falls and Pictured Rocks.


[By Attila Nagy (anagy) (Own work) [GFDL, CC-BY-SA-3.0 or CC-BY-2.5], via Wikimedia Commons]


[By MJCdetroit [CC-BY-SA-3.0], via Wikimedia Commons]

M-28 continues on to Marquette, the largest city in the Upper Peninsula even though its population is around 21,000. It is home to Northern Michigan University and the Superior Dome, the largest wooden dome in the world.


[By Bobak Ha’Eri (Own work) [GFDL, CC-BY-SA-3.0 or CC-BY-2.5], via Wikimedia Commons]

In researching this article, I came across the blog Michigan Architecture. This site’s author is a gradulate of Northern Michigan University and is still based in Marquette. I recommend checking out her blog and seeing some of her interesting photograph of unexpected places around the state.

We conclude in the northernmost part of Michigan, Isle Royal. It is far north within Lake Superior, and indeed closer to Minnesota and Canada than it is to the rest of Michigan. It has an odd geography, basically a series of parallel ridges sticking up from the lake.

The middle of the island is a lake, Siskiwit Lake. It is trippy to have a large lake in a large island in a larger lake.

But it gets better. When nearby Moose Flats pond is full, Moose Boulder becomes the largest island in the largest lake in the largest island in the largest lake in the world! I will leave readers to ponder this…

Fun with Highways: Arizona

This week the primary season brings us to two very different states, each of which are a source of creative inspiration but in very different ways. The first of these states we will visit is Arizona.

We begin where we left of in Colorado. From Four Corners, we head west on US 160 through the Navajo Nation. The dry landscape is punctuated by red rock formations such as Baby Rocks, which can be seen along the highway.


[By Reinhard Schön (original photograph) and Andreas F. Borchert (postprocessing) [CC-BY-SA-3.0], via Wikimedia Commons]

The shapes and textures of the rock formations and the sparseness of the landscape are what attract me to the southwest. The unique combinations of climate, water and rock composition lead to this landscape, and individual varieties of rock (many of which are different types of sandstone) lead to the distinctive shapes in different locations. Sometimes the most interesting can simply be found on the side of the road. But that does not detract from the many iconic parks in this state. Indeed, if we continue on US 160 west to its terminus at US 89, and then further west along State Highway 64, we come to the most iconic of all, the Grand Canyon.


[By Tobias Alt (Own work) [GFDL or CC-BY-SA-3.0-2.5-2.0-1.0], via Wikimedia Commons]

It’s quite hard to summarize the Grand Canyon in such a brief article, but to say that it is most defined by its vast size. One is not simply looking at a large rock formation, but an entire carved landscape that extends in all directions. The space left by the canyon is big enough to support the same atmospheric effects as the sky itself, such as the refraction that leads to a blue tint in the space. Sadly, this also makes it a magnet for air pollution. The scale also means that from a distance one sees the rough surface and curved lines of the overall topography, but not as many distinctive formations like the Baby Rocks described above. To see such details of the Grand Canyon, one must travel to the far sections of the rim or descend into the depths.


[Photo by Al_HikesAZ on flickr. (CC BY-NC 2.0)]


[Photo by Al_HikesAZ on flickr. (CC BY-NC 2.0)]

For many, places such as this are as much about recreation (rafting, hiking, climbing), but for me the interest in going back sometime soon is primarily about the visual landscape, touching feeling and breathing the desert air, and hearing both the sounds and the silences.

We head south from the Grand Canyon on US 180 to I-40 near Flagstaff. We take I-40 east to another of Arizona’s iconic locations, the Petrified Forest National Park. The eponymous petrified trees were created by combination of trees and minerals that were deposited over long periods of time and the gradual replacement of the organic matter with minerals. The relatively soft and easily eroded sandstone have left a surprisingly large number of these artifacts in one location. The extreme erosion patterns of the area also gave rise to the colorful formations of the Painted Desert.


[By User:Moondigger (Own work) [CC-BY-SA-2.5], via Wikimedia Commons]


By Finetooth (Own work) [CC-BY-SA-3.0 or GFDL], via Wikimedia Commons

Leaving the park, we turn back west on I-40 to Flagstaff, and then head southward on I-17 towards the Phoenix metropolitan area and a very different Arizona. But along the way, we pass by Arcosanti, an experimental town and “urban laboratory” that began construction is 1970. It was started by architect Paolo Soleri to experiment with ways of developing urban environments that minimized the impact on the natural environment. The architecture of Arcosanti is quite unique.


[By Cody from Phoenix, AZ (arcosanti western half) [CC-BY-2.0], via Wikimedia Commons]

In addition to being an experimental project itself, it hosts a variety of events (including the annual Different Skies Music Festival).


[By Cody from Phoenix, AZ (arcosanti apse) [CC-BY-2.0], via Wikimedia Commons]

And it’s on to Phoenix. It’s hard to conceptualize that in the middle of the desert is one of the largest and fastest-growing metropolitan areas in the United States. Yet there it is. The recent rapid growth of Phoenix and the entire “Valley of the Sun” and the relatively flat terrain have led to some rather impressive highway interchanges.

The rather complex tangle above is the interchange of I-10 (the Papago Freeway coming from downtown Phoenix), Arizona Loop 202 and Arizona State Highway 51, which is supposedly the busiest interchange in the state. A more elegant one (which I have in fact seen in a museum piece) can be found further east where AZ 202 meets US 60.

The lines and curves complement the desert terrain (disregarding the subdivisions for the moment). Indeed, the structures themselves have a reddish color reminiscent of the desert landscape.

Traveling up Arizona Loop 101 to Scottsdale in the northeast corner of the metropolitan are, one finds Taliesin West, the winter home and school of Frank Lloyd Wright. Wright designed this home to reflect “Arizona’s long, low, sweeping lines, uptilting planes”, aspects of the natural landscape which we have explored in this article.


[I, Gobeirne [GFDL, CC-BY-SA-3.0 or CC-BY-2.5], via Wikimedia Commons]

In ways, his goals predate and inform the work that continues at Arcosonti, although the latter has more of an urban focus.

Heading south and east on I-10, we come to Tucson and a very different but still quintessentially “Arizonan” landscape. Here the most distinctive features are not the rocks but the vegetation, especially the saguaro cactus. Like the Grand Canyon, the saguaro is a symbol of the state, and of the best preserved tracts of these and other cacti can be found in Saguaro National Park west of Tucson.


[By Saguaro Pictures (Own work) [CC-BY-3.0], via Wikimedia Commons]

Heading back west on I-10, we switch to I-8 through the southwest corner of this southwestern state. We turn south on State Highway 85 through relatively empty but rocky landscape. Highway 85 intersects with 86 at the small town of Why, named for the “Y” shape of the original intersection of the two highways. Because Arizona law required location names to have at least three letters, the name “Why” was used instead of “Y”. Continuing south on 85, we eventually reach Organ Pipe Cactus National Monument.


[By Pretzelpaws at en.wikipedia [GFDL], from Wikimedia Commons]

Although this park is named for the organ pipe cactus (shown above), it contains many of the other varieties found in southern Arizona, such as the saguaro. However, the converse is not true. The organ pipe cactus only grows wild here. I visited in the winter of 2004-2005 and found this park to be quite sparse and peaceful. The landscape does not really have many of the monumental rock formations further north, but it does have interesting hillsides covered with rough crumbling stone and frequently punctuated by the cacti.

And I think the final desert sunset is an appropriate way to conclude this article. I of course know there is much more to consider in Arizona, and welcome thoughts and ideas from others as comments.

CatSynth Video: Arp Odyssey Strange noises and drones, using sample and Hold modulations

From our friends at polynominal.com, another video featuring images of Mimi. The modulated sounds are quite interesting as well – lots of rich noisy timbres.

“For more info, longer demo and more, please visit the arp odyssey page at this URL:
http://www.polynominal.com/site/studio/gear/synth/Arp_odyssey/index.html”

Weekend Cat Blogging: Luna encounters the Skatchbox

Those who read yesterday’s review of Music of Invention concert encountered Tom Nunn’s musical invention, the Skatchbox. Today, Luna discovered this instrument for herself:

I chose this model of the limited-edition mini-Skatchboxes made specifically for the concert because of its visual aesthetics. It reminds me a bit of paintings of Kandinsky. As for the sound, it can make a variety of loud noisy timbrally rich sounds. They were a bit new to Luna’s ears:

I literally just scratched the surface (no pun intended). I wouldn’t yet play this in a formal musical setting. But it is loud, and a somewhat sneaky way to participate in this week’s Saturday Photo Hunt on the theme LOUD. Here is another image of Luna with the Skatchbox using the new America pack in the Hipstamatic app.

Those who have regularly seen my photos know I tend to prefer crisp images with high contrast, whether from the Hisptamatic or the DSLR. But this one seemed to work best blurred. And Luna was not going to cooperate for another take.

Weekend Cat Blogging #351 is hosted by The Bengal Business.

The Saturday Photo Hunt is up with the theme of LOUD.

The Carnival of the Cats will be hosted this Sunday by When Cats Attack!

And the Friday Ark is at the modulator.