Heptatonia

The foundation of the Western musical tradition is the diatonic scale, known best by its "major" and "minor" modes, though there are five other modes of this scale used somewhat less often. The diatonic scale is a specific pattern of intervals, called whole- and half-steps (or more formally, tones and semitones), arranged in a circle. Any of the seven degrees of this circle can be used as a starting position, becoming the tonic of a particular mode, the pattern of which is formed by going around the circle until returning to the tonic.

On a piano, starting on a particular white key and playing up along the next seven white keys yields one of the modes, with a "whole-step" being whenever a black key is skipped and a "half-step" being wherever there is no black key. However, the pattern itself is what defines a mode, and the pattern could be started from any key, skipping or landing on both white and black keys as the pattern dictates; the "white keys only" method simply provides one convenient example of each mode to understand and remember.

PATTERN	2367	MODE	WHITE KEY
WWHWWWH	MMMM	Ionian (major scale)	C
WHWWWHW	MmMm	Dorian	D
HWWWHWW	mmmm	Phrygian	E
WWWHWWH	MMMM+#4	Lydian	F
WWHWWHW	MMMm	Mixolydian	G
WHWWHWW	Mmmm	Aeolian (natural minor scale)	A
HWWHWWW	mmmm+b5	Locrian	B

In this table, the "2367" column gives the patterns of major (M) and minor (m) seconds, thirds, sixths, and sevenths for each mode; the fourth and fifth degrees are assumed perfect, though the Lydian mode has an augmented fourth and the Locrian mode has a diminished fifth, as noted. This view provides an easy way to construct the modes from any starting key, and to directly compare their properties.

Notice that each sequence in the "Pattern" column features the same sequence as its neighbors above and below, but with the interval at one end (either a Whole- or Half-step) moved to the other end; the sequences at the top and bottom of the list are likewise related. This reflects the circulating nature of the diatonic scale.

While the "major" and "natural minor" modes have been most commonly used, all seven modes of the diatonic scale have been employed throughout history and are still in use today. There are, however, two other circulating seven-tone scales that can be built out of the standard twelve-tone system using only whole- and half-steps, and these scales remain considerably more obscure. In this context, the diatonic scale is known as Heptatonia Prima, in contrast to Heptatonia Secunda and Heptatonia Tertia.

HEPTATONIA SECUNDA

PATTERN	2367
WWHWHWW	MMmm
WHWHWWW	Mmmm+b5
HWHWWWW	mmmm+b4+b5
WHWWWWH	MmMM
HWWWWHW	mmMm
WWWWHWH	MMMM+#4+#5
WWWHWHW	MMMm+#4

HEPTATONIA TERTIA

PATTERN	2367
HWWWWWH	mmMM
WWWWWHH	MM#M+#4+#5
WWWWHHW	MMMm+#4+#5
WWWHHWW	MMmm+#4
WWHHWWW	MMmm+b5
WHHWWWW	Mmmm+b4+b5
HHWWWWW	mbmm+b4+b5

A quick glance at these tables can give a good idea why these patterns haven't often been explored: they exhibit many more augmented and diminished intervals (and resulting chords) than Heptatonia Prima, which makes working with them harmonically considerably more difficult. Tertia even has an augmented sixth in one mode, and (even worse for the tonic chord) a diminished third in its inversion! These are certainly awkward in comparison to Prima.

However, there are clearly a few modes that are relatively straightforward. For example, the MmMM mode of Secunda is also known as the "melodic minor" scale, and has been used regularly. Its inversion, the mmMm mode, is equally stable, though both these modes do feature some augmented and diminished chords, and therefore some skill is required to handle them well. Similarly, the mmMM mode of Tertia features both augmented and diminished chords, but has seen use as the "Neapolitan major" scale.

An exploration of even the most complicated modes could yield interesting results in the hands of an adventurous composer. It is a challenge not often undertaken, and many distinctive works may yet be produced!

Classic Rock: The Great Stalacpipe Organ

Today, I'd like to take a look at what I consider the most incredible musical instrument in the world: the Great Stalacpipe Organ of Luray Caverns.

Devised in 1954 by Leland W. Sprinkle, a mathematician and electronic engineer at the Pentagon and also a talented organist who studied at the Peabody Conservatory of Music, the Great Stalacpipe Organ is the conversion of 3.5 acres of ancient caverns in Luray, Virginia into a single massive musical instrument.

Sprinkle selected 37 stalactites throughout the caverns that, when struck, produced tones that closely matched the Western musical scale, and fine-tuned them to concert pitch by grinding with a sander (though two were found naturally in tune). He then mounted electronic mallets with rubber-tipped plungers and used more than five miles of wire to connect them all to a large console, custom-built with four keyboards and a pedal board. When a key is pressed, it triggers a particular mallet to strike, and the resulting chime rings out through the caverns.

It took Sprinkle three years to complete the initial stage of his project, which he unveiled to the world on June 7, 1957. His dedicatory recital received much attention from the press; the portmanteau "stalacpipe" was coined by music critic Paul Hume of the Washington Post, and the name stuck. Over the course of another 33 years, further development saw this monumental instrument refined to its present state.

Several recordings of Sprinkle's live performances were made. This is an impressive feat of engineering on its own, considering the size of the area involved and the nature of the caverns. Reverberations of dripping water contributed to the natural ambience of these recordings.

The organ can even be controlled automatically by a system of rotating plastic belts full of holes, somewhat like a player piano (or a very large music box). Visitors to the caverns can still hear the organ played this way; the selections of music are changed seasonally.

Although the Great Stalacpipe Organ is certainly expansive, it is not generally considered the largest musical instrument in the world. That distinction is held by the Convention Hall Auditorium Organ in Atlantic City, which will be the subject of an upcoming post.

Circuit Bending

In 1966, Reed Ghazala began experimenting with the musical potential of electronic toys by taking them apart and poking around inside, short-circuiting them in different places and producing all manner of unplanned sounds and effects. He added buttons, switches and knobs to control these sounds, and coined the term "circuit bending" to describe the process. Since then, he has converted many toys into circuit-bent instruments for musicians like The Rolling Stones, Tom Waits, Peter Gabriel and King Crimson. Examples of his work are held by New York City's Museum of Modern Art, The Guggenheim and The Whitney, and other galleries around the world.

While Ghazala is credited with pioneering and championing this unusual art form, he does not claim to have been the first to do it. Serge Tcherepnin, who would go on to design the historic Serge modular synthesizer, experimented in the 1950s with modifying transistor radios. Even as early as 1897, Thaddeus Cahill's Telharmonium reportedly could be influenced by direct contact with its electrical circuits.

Any low-voltage battery-powered device can potentially be "bent" into a useful musical instrument, and such devices are common and inexpensive at secondhand stores. Also, no prior experience or understanding of electronics is necessary, as the low voltages involved (Ghazala recommends 6v or less) are not dangerous; the circuitry can safely be touched by hand, and it can be shorted out and rewired in any configuration. At worst, a device will simply cease to function. For these reasons, circuit bending is very accessible to virtually anyone. There are many excellent tutorial videos and performances on YouTube, as well as written guides, both online and in print.

Interesting connections are usually found by probing different points of a circuit board with either a wet finger or a metal probe, such as the end of a wire held in a clip. Modifications can be made permanent with a soldering iron and the addition of buttons, switches, potentiometers (knobs), resistors, capacitors, and other basic electronic components. Photoresistors can be used to make a circuit light-sensitive, so a performer can wave their hand over the device or cover the photoresistor to achieve a particular musical effect. Even metal objects like nails or studs can be used to provide "body contact" (finger-touching) control points. These additional components can be fastened through new holes drilled in a device's existing case, or the case can be removed and replaced by one custom-built for the project.

I am currently in the process of bending a toy keyboard I bought used, and I also have a voice-changing megaphone I suspect will provide some interesting effects. The plan is to connect them to each other with the addition of a plug to one and a jack to the other; this way, they won't be permanently wired together and the megaphone could also be hooked up to future bent instruments, or any other sound source (like an MP3 player). I might even figure out a way to use the megaphone's microphone to modulate the keyboard. Who knows? Circuit bending is all about experimentation; you never know exactly what you'll find!