Friday, September 28, 2007

The amazing Golden Ratio

The amazing Golden Ratio
Assem Deif
Al-Ahram Weekly
27 September - 3 October 2007

Issue No. 864


Artists reckon that the "Golden Ratio", also called the "Golden Section Phi" and nature's most astonishing number, is the ratio that controls the proportions of all beautiful objects, writes Assem Deif*

Historians trace the Golden Ratio back to Euclid, yet even before him it was governing the dimensions of monuments in ancient Egypt. The most pronounced of these is the Great Pyramid. The Great Pyramid is not the only structure from ancient Egypt that complies with constants like Pi or Phi; the Egyptians used the Golden Ratio in many ways both in the architecture of their temples and in their drawings. So whereas, the discovery of the "golden rule" was generally credited to the Greeks, the findings of such Egyptologists as De Lubicz and Fliders Petrie produced irrefutable proof that the Egyptians had a mathematical understanding of these constants, the ratios, not the symbol, 1000 years earlier.

There was much cross-culture between the Egyptian and Greek civilisations during the Hellenistic era, particularly in Alexandria where Egyptian and Greek scientists studied together at the Mouseion. Among them was Euclid. Historians call him Euclid of Alexandria without precluding the possibility he might have been Egyptian. It was in Alexandria that Euclid wrote The Elements.

Greek scholars were visiting Egypt even before the Mouseion was founded, including Thales, Socrates, Plato and Aristotle, and Pythagoras, who spent 22 years in Egypt and announced his theory only after leaving. Egyptians were aware of the triangle 3:4:5 which Pythagoras himself called the "Holy Triangle". Eight pyramids from the fourth and fifth dynasties have their inner triangle conforming to these ratios.


Giza Pyramids

leaf arrangements around a stem and plant branching in a fibonacci formation;

golden spiral

pascal triangle; panel of Khesi-Re

Monday, September 17, 2007

The Well Tempered Keyboard

The Well Tempered Keyboard

Bevin Chu

September 18, 2007

The Well Tempered Keyboard

You just bought yourself a midi keyboard controller, as a cheap alternative to an expensive electric piano, or an even more expensive regular piano.

Not a synthesizer. A midi keyboard controller. No sound. No speakers.

You didn't want either built-in sound or built-in speakers because you wanted to spend money only on the keyboard. Not on dedicated electronics and speakers good for nothing else. You wanted your PC to generate the audio signal, and your speakers to transform those audio signals into piano sounds.

You wanted semi-weighted key action that emulated, but did not necessarily duplicate piano key action.

Semi-weighted Midi Keyboard Controller vs. Fully-weighted Electric Piano

Q: Will keyboard playing skills spoil the ability to play the piano, because of the difference in touch?

A: It is a myth that beginners MUST start with the piano in order to correctly develop a piano playing apparatus. This myth originated from the elitism and conservatism of modern piano education that focused only on raising of a few concert performers. In reality, playing on any other musical instrument, including the piano keyboard, can only improve the piano performance of your child.

More over, we recommend that children start learning the piano with the piano keyboard. The regular piano is very physically challenging for beginners, because it requires physical strength along with advanced coordination and perfect orientation on the piano keys. The majority of problems with piano techniques start with the lack of confidence in beginners. When the student has built his eye-hand-fingers coordination by playing on the piano keyboard, the task of mastering the "hard touch" of the real piano is much easier to handle. Freedom and flexibility of the apparatus appear gradually with the confidence of the student.

Being a 3-year-old child, Mozart started with the harpsichord (with the touch of a modern keyboard). It didn't spoil his apparatus at all!

We recommend a keyboard with at least 61 keys. Very soon you will find that a keyboard with less than 61 keys is just a toy, and you will be able to play only simplest songs.

- Hellene Hiner, Russian American Piano Instructor

Novation ReMOTE LE 61 - 5-octave Light Edition USB MIDI controller. Unsurpassed MIDI controlling technology is now available in its most compact format to date. With its funky Touchpad and cool 4-way joystick, the lightweight ReMOTE LE is the only choice for the musician on a budget wanting to trigger samples, lay down basslines or control a sequencer with true style.

Review of Novation ReMOTE LE

The ReMOTE LE is undoubtedly a cut above most portable keyboards we’ve seen. Its plastic casing feels durable and the weighted keys are good to play. The likes of Edirol’s PCR-M1 and M-Audio’s 02 are slightly more portable, but thanks to an above average feature set and impressive ease of use, the ReMOTE LE shines. Novation understand the needs of today’s computer musicians, and this understanding is reflected in their well-designed range of keyboards. If the SL isn’t for you, there’s a good chance that the LE will be. A lightweight SL it may be, but the ReMOTE LE is still one of the finest MIDI keyboards in its class. You’ll struggle to find better at this price. Verdict – 8/10

- Computer Music – Summer 06

Major Sticker Shock!

The salesman at the musical instrument store tried to sell you an electric piano.

They cost three times as much as your midi keyboard controller. Over one grand, instead of a few hundred.

Major sticker shock!

The salesman at the musical instrument store tried to sell you one of the well known commercial VST host, MIDI recorder/sequencer and audio recorder software packages.

They cost twice as much as your midi keyboard controller.

Major sticker shock!

Worst of all, they are far more powerful, hence far more complicated, than anything you are ever likely to need. They force you to waste time learning to use unfamiliar software before letting you play a single note of music.

The salesman at the musical instrument store tried to sell you one of the well known commercial piano plug-ins.

They cost as much as your midi keyboard controller.

Major sticker shock!

Your sticker shock. His bottom line.

So What Do You Do?

So what do you do?

Well, if you're like me, you go to websites such as Tobybear Productions, ASIO4ALL, Don't Crack Software, and KVR Audio.

You download the following VST hosts and VSTi plugins. All of these are freeware, except Tobybear Minihost, which is donationware.

Begin by installing Tobybear MiniHost.

Tobybear MiniHost

MiniHost is a powerful and full-fledged ASIO host that loads a VST plugin (instrument or effect) and processes it in realtime. MiniHost has been voted by the members of the KVR audio community as the best free host of the year 2004! Send MIDI data to VST plugins from external MIDI inputs, a resizable virtual MIDI keyboard, the computer keyboard or MIDI files, process live ASIO audio input or a WAV file, record audio output to WAV (16 and 32 bit), support for VST MIDI plugins that generate MIDI data. Donating $20 or more will make the daily donationware remainder disappear and put your name in the about box

Next, install ASIO4ALL.

ASIO4ALL - Universal ASIO Driver For WDM Audio

What's the difference between ASIO and DirectSound audio drivers? ASIO is a standard developed by Steinberg and designed specifically real-time audio processing. DirectSound is a Microsoft audio technology designed primarily for games. In general ASIO is the preferred type of driver for use with Cantabile. DirectSound support is provided for cases where no ASIO driver is installed or available.

ASIO4ALL seems to be most beneficial for AC97 based sound cards. And it does work well with SoundBlaster Live cards. It gives people with basic systems a boost. If you don't have a proprietary ASIO driver available, it can help a lot.

- RobertB

Do not neglect this! The latency using DirectSound is simply unacceptable. ASIO bypasses Windows' slower audio engine, offering much lower latency (audible sound delays).


Finally, install these VSTi piano modules.

4Front Piano Module

A small and versatile piano module with unique sound. This piano module is neither a sample player, nor synthesized. It's a hybrid technology that combines both methods. This results in greatly reduced module size and light CPU usage. Unlike many other piano modules (like those gigabyte pianos), this module will never overload your CPU. It will never stick notes, and never break the sound or click during live performances.

mda Piano

The mda Piano VSTi is modelled around 31 carefully sampled and mastered Piano samples. Its Width Control not only controls panning of notes across the keyboard but at high settings adds a psychoacoustic widening effect adding a touch of room ambiance and spaciousness to the sound. The polyphony is up to 32 voices.

Woodstock tickling the ivories, as Snoopy listens

Well, that about does it.

You now have a compact, portable, realistic sounding piano. All for the price of a cheap midi keyboard controller.

Now start playing.

Friday, July 13, 2007

Introduction to Proporzione Divina

Proporzione Divina features commentary on art and music by architect and author Bevin Chu.

Proporzione Divina is Italian for "Divine Proportion." The Divine Proportion is also known as the golden ratio, the golden section (Latin: sectio aurea), golden mean, golden number, divine section (Latin: sectio divina), or golden proportion, and is represented by the Greek letter phi (φ).

The Golden Section

From Wikipedia, the free encyclopedia

The golden section is a line segment sectioned into two according to the golden ratio. The total length a+b is to the longer segment a as a is to the shorter segment b.

In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is approximately 1.6180339887.

φ = (square root of 5 – 1)/2 = approximately 1.6

The Golden Rectangle

Many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing.

The Fibonacci Series

The irrational numbers of the golden section closely correspond to the whole numbers of the Fibonacci series, in which each number is the sum of the two preceding numbers.

The numbers of the Fibonacci series are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ... ad infinitum

This makes the Fibonacci series highly useful for architects and designers who wish to make their buildings and designs approximate the golden section, but must as a practical matter use whole number units.

Divine Immanence

The Golden Rectangle shows up in the most unexpected places.

For example, it shows up in the 16:10 aspect ratio of the newest, most advanced LCD monitors, which provide more comfortable viewing than older, now obsolescent LCD monitors with 4:3 aspect ratios.

The newer 16:10 aspect ratio is more ergonomic because it more closely matches the human being's natural field of view, formed by the two overlapping fields of view of two side by side human eyes.

Vesica Piscis: Latin for "bladder of the fish," two circles of the same radius whose centers lie on each others' circumference, aspect ratio of 3:2 corresponds to the fifth and fourth numbers in the Fibonacci series

The older 4:3 aspect ratio, by contrast, is noticeably less ergonomic because it chops off the left and right margins of that natural field of view.

ViewSonic Home Page (Traditional Chinese): "ViewSonic VG2230wm 22 inch multimedia liquid-crystal display, 16:10 golden ratio display ... high resolution golden ratio display 1680x1050"

The 16:10 aspect ratio of the newest LCD monitors reduces to 8:5, the seventh and sixth numbers in the Fibonacci series.