Some stuff » post

kendall band still broken

admin — Wed, 12 Sep 2012 22:12:02 +0000

After more than 1 year — judging by this post — the Alewife bound part of Pythagoras is still broken. Up till a few months ago the graffiti stayed off. But finally somebody caught on that they aren’t actually going to fix this a second time. Blame it on shoddy mechanics — the poor handle broke after only a month in use the first time they fixed it.

continuous chord progression

admin — Sun, 22 Feb 2009 22:21:16 +0000

Following up on a side note from this post, it is possible to construct continuous changes from one chord to the other by linear interpolation of their frequency envelopes (i.e., chord interpolation).

Here is an example in Mathematica.
A[f_] := Sin[2*Pi*t*f*220];

For example, one of the major triads is 4:5:6, and the harmonic minor triad is 6:7:9.

First, the two chords:

Play[{A[1260/1260] + A[1575/1260] + A[1890/1260]}, {t, 0, 1}]

Play[{A[1260/1260] + A[1470/1260] + A[1890/1260]}, {t, 0, 1}]

Normally, if you were to move from one to the other (e.g. on an intrument), you might bend the middle note from a major 3rd until it becomes a septimal minor 3rd with respect to the low note. However, this (inner) interpolation produces dissonant beats during the entire process:

Play[{A[1260/1260] + A[(t*1470 + (1 - t)*1575)/1260] + A[1890/1260]}, {t, 0, 1}]

On the other hand, by frequency blending instead (and keeping the implied harmonic structure), the (outer) interpolation produces a very agreeable progression*:

Play[{A[1260/1260] + t*A[1470/1260] + (1 - t)*A[1575/1260] + A[1890/1260]}, {t, 0, 1}]

This was just one simple example.

*Indeed, this may very well be the implicit aim in many works with multiple voices.

Now this is very interesting. No, not the isomorphic keyboard, which is old, but the odd harmonic based scale and compositions. I’m not entirely convinced of the merits of odd harmonics (on grounds of psychoacoustics), but in my opinion, this is a much more productive direction to take than say, mechanical serialism and aleatoricism.

ridiculously antiquated banking system

admin — Sun, 05 Oct 2008 07:36:54 +0000

For an advanced economy with advanced electronic banking systems, it is embarassing that there is no bank that has branches in all parts of the country and no electronic funds clearing other than on “business days”. Computers don’t have geographic boundaries nor do they take breaks. Why can’t money be available everywhere (without resorting to a middle-man cash machine network) and be freely transferable 24/7?

For that matter, what is the fear of a central bank? In some countries, banks are like utilities and post offices — public services provided by the government. The First and Second National Banks were killed because people did not trust the government with their money. Well, it seems like big commercial banks can be trusted even less. Also, it’s not like anything would function with just community banks. It’s not a country of farmers any more…

I mean, capital allocation decisions can still be locally made and subject to market forces, as they should, but banking infrastructural issues like described here (and regulatory ones, some say) should have no reason not to be national, am I wrong?

V I Fabrikant

admin — Thu, 26 Apr 2007 07:50:58 +0000

Note: There has been some confusion about this post. Let me make it very clear — I am NOT Fabrikant, nor do I have any relation to him, or even know of him in any way. I just came across this hilarious correspondence address on the internet. I have NO idea who this guy is, or whether the people commenting below are who they claim to be.

Look at the correspondence address of this Journal of Applied Math article

Utilization of divergent integrals and a new symbolism in contact and crack analysis
VI Fabrikant
Prisoner #167932D, Archambault Jail, Ste-Anne-des-Plaines, Quebec, Canada J0N 1H0

Correspondence: Email: valery_fabrikant@hotmail.com

Received for publication 15 June 2006. Revision received 1 December 2006.

Abstract
The main potential function, used for the complete solution of the contact and crack problems for elliptical domains, is presentable as an integral of an expression comprising a logarithm of a distance between two points. These integrals were considered to be impossible to compute, though various derivatives of these integrals were computed in the past. The new symbolism, introduced here, combined with utilization of divergent integrals, allows us to compute these integrals exactly and in a closed form. It also introduces a dramatic simplification in the final expressions and restores some mathematical symmetry and elegance.

You can look up this guy on Wikipedia.

What is this “blog”

admin — Tue, 24 Oct 2006 16:23:51 +0000

…you speak of… what, do I write to myself? I only have 100MB.

First post and already TeX can be rendered. I stole the idea from fakalin.

\( \int_{0}^{1}\frac{x^{4}\left( 1-x\right) ^{4}}{1+x^{2}}dx = \frac{22}{7}-\pi \)

Dom sovetov

admin — Mon, 03 Jul 2006 11:33:40 +0000

Note: This is an anti-causal post, because the writing existed before this blog thing here.

Well, well, well, so Konigsberg of East Prussia became Kalinigrad of the USSR after World War II. Konigsberg was famous for the 7 bridges problem often assoicated with Euler, of course.

According to Wikipedia,

In the Soviet part of the region (note: i.e. former East Prussia) a policy of eliminating all remnants of German history was pursued. In 1967 this resulted in the demolition of the remains of Königsberg Castle by order of Leonid Brezhnev to make way on the site for the new “House of Soviets”.

In other words, Brezhnev dynamited this

Konigsberg Castle

To make room for this

House of Soviets (Dom Sovetov)

Was the architect of the House of Soviets a robot, who modeled the building after its own face? Dom sovetov indeed. Har har.