Microtonal Ukulele

Here's a great video of a young musician playing a ukulele tuned to thirteen tone equal temperament. This is often thought of as a dissonant and unpleasant tuning, but I think he makes it sound wonderful.

Thirteen Tone Uke


Nose Music

It's marvelous that a simple piece of plastic can employ the nose to produce a continuous microtonal range of pitches. The infamous nose whistle (sometimes called a nose flute) owes its success to using the nose as a source of wind, freeing the mouth to serve as a flexible resonating chamber that can adjust to produce the required notes. If that sounds confusing, this video should help clear things up.

Nose Whistle Demonstration

Other kinds of nose flutes are used throughout the world, as shown in the following video.

Vietnamese Nose Flutes

It should be pointed out that the nose has other musical uses besides the mere blowing of air. Notice the subtle and delicate use of the nose as a temporary substitute for the fingers while they are employed elsewhere.

Shnozzage (Etude # 23 by David Rakowski)


Microtonal Speedlinking

Xenharmonic Wikispaces has a new equal temperaments section devoted to organising compositions and theory by individual temperaments. This is the first online attempt that I'm aware of to organise compositions in this manner. I hope this idea takes off. I think this could be a great resource for studying the repertoire of specific temperaments.

Neil Haverstick, the prolific microtonal guitarist, author and composer, was recently interviewed at Tokafi. The interview is well worth reading. It's nice to see one of the "Forgotten Greats and Unsung Heroes" (explained in the interview) get some well deserved recognition. (see also this article.)

The hang drum is a recently invented pitched percussion instrument that has been receiving a lot of attention lately. Some of them feature microtonal tunings. You can learn more about them at this page at Odd Music

How about a xenharmonic ukulele tuned to thirteen tone equal temperament and played by a thirteen year old? You can listen to it here. (I wish I had one of those.)


Tagged! (The Mutation Meme)

Mr. Startling Moniker just tagged me with a meme. I've never done one of these before. Apparently, a meme is like a self-replicating virus that uses a host (like me) to propagate itself throughout the blogosphere at an exponential rate. Like a virus, a meme comes with a set of instructions that presumably replicates with a high rate of precision:

1. We have to post these rules before we give you the facts.
2. Players start with eight random facts/habits about themselves.
3. People who are tagged need to write their own blog about their eight things and post these rules.
4. At the end of your blog, you need to choose eight people to get tagged and list their names.
5. Don’t forget to leave them a comment telling them they’re tagged, and to read your blog.

Well, every once in a while, the genetic material of a virus will mutate, perhaps resulting in a new strain that terrorises millions. I don't see why this can't also happen with a meme. I will make some small changes to the meme and then everyone I tag can ignore or change one or more of the rules (including the new rule to ignore or change one or more of the rules).

Here are nine statements about me. One of them is false. If you want, you can guess which one it is.

1. I recently started learning to play the erhu (a type of Chinese fiddle).

2. I once owned a windshield repair business.

3. I have lived in the Upper Peninsula of Michigan, Wisconsin and South Dakota. I currently reside in Saint Paul, Minnesota.

4. I dislike clowns, centipedes, and chicken salad sandwiches.

5. I used to have a job building barbed wire fences. One time, a tractor malfunctioned and pinned me against a fence.

6. One of my hobbies is boomerang throwing.

7. I have an unusual fascination with countries that begin with I, Iceland, Italy, India, and Indonesia.

8. I once held my breath for 2 minutes and twenty seconds.

9. I lied in statement number 8.

Now, I get to tag the following blogs: (I decided on six. If you want to be seven or eight just claim the honor in the comments section.)

Infinitely Crazy
My Lounge
Notes Become Thee
Skittles' Place


A Scream from Lebanon

Here is a cool video that uses a microtonal variation of the C minor scale where the A and D notes are each thirty cents flat.

A Scream from Lebanon


Unusual Microtonal Instruments, Part 5

Bells often work very well with microtonal tunings. Many of the instruments we are familiar with (pianos, violins, guitars, most wind and brass instruments, etc.) have a harmonic spectrum that tends to work best with more traditional tunings. They can also work well with some very exotic or dissonant tunings, but the inharmonic spectrum of bells often provides a better match. I am fascinated by bells and the possibilities they represent.

As an example, Tony Salinas performs on a microtonal bellophone that uses a tuning of 96 equally spaced tones to the octave. The conic bells that are used can be arranged in various ways.

Here is a picture of a single conic bell.

Of course, this is all very interesting, but you probably want to know how it sounds and see it in action. Click here to see a video demonstration. The bellophone has already been used in concert and I hope to hear more about in the future.

Well, this concludes the first batch of unusual microtonal instruments that I wanted to share with you. I hope you enjoyed reviewing just some of the fascinating approaches to exploring pitch with instruments. This series will take a break for a while, but I hope to discuss more microtonal instruments in the future, including some of my own.

See also:
Part 1
Part 2
Part 3
Part 4


Unusual Microtonal Instruments, Part 4

So far, we have examined a large variety of microtonal instruments. We have yet to discuss the keyboard and its role in producing microtonal music. In some ways the piano style keyboard is the victim of its own success. Its twelve keys per octave arrangement has become so common that many have forgotten that there are other alternatives, but imagine what you could do with this alternative keyboard controller from H-Pi Instruments.

Tonal Plexus

This keyboard features an impressive 211 keys per octave. I can't imagine a situation where this wouldn't be sufficient. This same company also sells the Tuning Box, the world's first microtonal midi converter. You can use it to retune electronic keyboards or software synthesizers. It can store over 500 tunings. This is a great idea. This could save a person a lot of time and money shopping for equipment with microtonal capabilities.

If this all sounds new and unusual, you might enjoy visiting their instrument galleries that feature a long history of keyboards capable of playing more than 12 notes per octave. For example, here is a modern reconstruction of a sixteenth century harpsichord that has 36 keys per octave split between two manuals.


Here is a 31 tone to the octave pipe organ.

Fokker organ

Here is a closeup of a 22 tone just intonation harpsichord keyboard with unusual split keys.

Just Intonation harpsichord

See also:
Part 1
Part 2
Part 3
Part 5


Quarter Tone Piano

Normally, a piano has notes that are a half tone apart. If you take two pianos and tune one of them a quarter tone sharp, you can use them to play 24 tone equal temperament. These videos demonstrate 3 quarter tone piano pieces by Charles Ives.

24 tone equal temperament is a somewhat controversial tuning. It's similarity to 12 tone equal temperament makes it an obvious choice for study, but many people don't like it. They point out that the in between notes tend to be rather dissonant. This tuning is regarded by some as one of the least interesting. Well, I haven't formed any strong opinions about it myself. I have had very little success with it, so far, but I recently had some ideas that may be productive. I can say that I like these pieces and hope you will enjoy them, too.

Charles Ives-3 Quarter Tone Pieces-Largo

Charles Ives-3 Quarter Tone Pieces-Allegro

Charles Ives-3 Quarter Tone Pieces-Chorale

Many thanks to Daniel Stearns for bringing these to my attention. See this page for more information on these pieces.


Unusual Microtonal Instruments, Part 3

I have already discussed several microtonal guitars in this series. This next guitar is one of the most unusual. Dave Keenan is the inventor of the Choob, a tubular (choobular?) electric guitar.

Microtonal Choob

This picture is of the first microtonal choob. It has eight strings and is tuned to a seven limit schismatic temperament. One of the chief advantages of this design appears to be the ease with which you can setup a microtonal fret layout or even change it if you aren't satisfied. The frets are monofilament that are threaded through drilled holes. You can drill new holes if you want to change the fret layout.

The use of a light weight tube requires some wet sand for ballast and an internal truss wire system to counteract the tension of the strings. There are also plans to include a neon tube to light up the frets at night.

It looks like the curved fretboard would make it difficult to play, but the reports I've heard indicate that it's much easier than it looks. The curved design also makes it possible to use a bow. I don't really need a microtonal guitar at the moment, but if I ever decide to get one, I will definitely consider this new design.

Another recently invented microtonal instrument is the udderbot. The invention of the instrument was a collaborative effort that took place in the vicinity of Jacob Barton. I don't know much about it since it's new and the web site is still under construction. I could describe it, but I thought it might be more fun for you to try to guess its general appearance based on the name, udderbot. You can then check the website for pictures and further information.

The udderbot was used at the 17 tone piano project, phase 3. Recordings of the concert are archived here.

See also:
Part 1
Part 2
Part 4
Part 5


15 Tone Gamelan (a new version of an old piece)

Jon Lyle Smith suggested that my Study for Bells might work well with gamelan sounds. He was also nice enough to render the midi file for me. Here is the new version. I'm impressed with how it turned out. It sounds very different than the original.

I had also thought that gamelan sounds might work well with this piece. The tuning of 15 tone equal temperament contains a subset of five tone equal temperament which resembles the Indonesian slendro scale. This makes gamelan sounds a logical choice, although the particular scale I used also has some striking differences from traditional gamelan scales. This piece doesn't sound much like authentic gamelan music, but it does provide an interesting study of the pairing of an unusual tuning with the beloved gamelan sound. I'm grateful to Mr. Smith for providing this audio file. Click here to listen.

See also:
Two Gamelan Transcriptions for Piano
Wikipedia article on gamelan music
Study for Bells in 15 Tone Equal Temperament


Unusual Microtonal Instruments, Part 2

Neil Haverstick is a well known guitarist whose compositions include explorations of exotic microtonal realms. He uses a large variety of microtonal guitars including 19, 31 and 34 tone equal temperaments and fretless guitars tuned to the harmonic series. Here is a collection of his 34 tone guitars. Notice how close the frets are to each other.

You can visit him at his website or My Space page. You may also enjoy visiting microtones.com for more information on microtonal guitars.

Dante Rosati uses a just intonation guitar, a harmonic guitar and a very unusual prime guitar that uses ratios of purely tuned prime numbers up to 199. You can also hear some of his music at his Zebox page.

Doctor Oakroot plays a rough edged type of blues on homemade guitar-like instruments. Some of the instruments are based on Pythagorean tuning and one uses 17 tone equal temperament. Here's a video of him playing a homemade guitar.

Doctor Oakroot-Snake in the Grass

If you are interested in making homemade instruments, you might like to read his article on how to make a diddley bow (a cool, but simple, instrument with microtonal capabilities).

See also:
Part 1
Part 3
Part 4
Part 5


Unusual Microtonal Instruments, Part 1

A few weeks ago, I received a surprising email. It was from a TV show in Britain. I was asked if I would be willing to be consulted about an upcoming segment on unusual musical instruments. Apparently, a researcher discovered my ancient instrument blog through an Internet search and concluded that I was some sort of expert on the subject. (I'm just an amateur collector and connoisseur of musical instruments.)

I replied that I would be delighted to share whatever knowledge I had. I then waited to be contacted. I began to think about some of my favorite unusual instruments like the bazantar, stalacpipe organ, sarrusophone, LEGO harpsichord and even the Vienna Vegetable Orchestra.

I thought I should also do some more research on instruments that are specifically designed to make microtonal music. Of course, many unusual instruments are microtonal, but this isn't always intentional. I posted a request for assistance at a few microtonal music groups. I received a good number of emails describing some great instruments, many of which I wasn't familiar with. I never was contacted again by the TV show, but I am pleased to offer these microtonal instruments some modest publicity here.

Kraig Grady is a well known microtonal composer who has found it necessary to make his own microtonal instruments.

His Lake Aloe is a vibraphone-like instrument that is tuned to a type of extended just intonation. It has a dreamy otherworldly sound. You have to hear it. See this page for an mp3 sample and for more detailed information on his instruments and tunings.

There are several varieties of microtonal guitars. The following picture compares the fret layout of a normal guitar with a guitar that uses Lucytuning, a tuning system based on pi.

This fret layout allows for slightly different tunings of sharp and flat notes. See this site for more information on Lucytuning.

Ethan Tripp, the author of one of my favorite blogs, Of Sound Mind frequently chronicles sonic experiments that sometimes involves homemade instruments.

This instrument is loosely modeled on a Thai phin. It also represents the beginnings of his microtonal explorations. The frets are made from "zip-ties". This simple, but elegant, solution allows him to easily move the frets and thereby change the tuning. This project is described here.

See also:
Part 2
Part 3
Part 4
Part 5

Changes at this Blog

Perhaps you didn't realise that this blog has, or rather had, a sibling. This blog and another blog, Resources for the Microtonal Composer, were started at the same time. This was a result of my compulsive urge to organise and classify. It seemed that the term microtonal was just too vague. I wanted a general microtonal blog where I could share my music and discuss theory. I also wanted a different microtonal blog where I could discuss specific aspects of making microtonal music. I had big plans. I thought I would regularly try demo versions of software with microtonal capabilities and write reviews. I wanted to warn people about the mistakes I had made. I even began making some simple microtonal software. I figured that blog would make a great launching platform.

I should have been able to predict the results of all this. I ended up lavishing time and attention on this blog and couldn't seem to find the time to properly maintain the other one. This blog grew strong while the other grew weak. And then the unthinkable happened...

While I was distracted and preoccupied, a barbaric act of cannibalism occurred. This blog engulfed the best content of its smaller sibling, leaving only a few pitiful scraps to wither in the digital sun.

Well, I try to remain philosophical about this. This will allow me to better maintain this blog. I will still write about issues of microtonal music production, I just won't have to worry about doing so on a regular basis. I may even finish that microtonal software. If I do, I'll release it here.

Still, the precedent worries me. This blog also has a cousin, Lutes, Viols and Other Ancient Instruments. It was actually more popular than this blog until recently. Now, strengthened by its recent conquest, I see this blog looking in that direction with hungry and envious eyes.

Who knows what the future will hold?

The following is a list of the new articles added to the archives. I kept the publication dates the same.

What is Xenharmonic Music?
Embrace the Controversy
L'il Miss' Scale Oven™
Take advantage of Free Music Software
Tonescape Tuning Software Now Available
Two Gamelan Transcriptions for Piano
Wendy Carlos Discusses Microtonality


The Seventeen Tone Piano Project

The seventeen tone piano project is an ambitious undertaking that involves tuning two pianos to share the notes of seventeen tone equal temperament (seventeen equally spaced notes to the octave instead of twelve). This is an unique and exotic tuning. It is characterised by fifths that are somewhat sharper than purely tuned fifths. (Twelve tone equal temperament and mean-tone tunings have somewhat flat fifths.) It also has a neutral third in addition to versions of major and minor thirds.

That's enough theory, it's better to listen to it, so I have included this video of phase two of the project.

Seventeen Tone Piano Project, Phase Two

Phase three is scheduled to be performed this coming Monday. I'm excited because I have submitted one of my own pieces for the concert. It's a gentle nocturne. I tried to write a piece that contrasts with the reputation of 17ET as being somewhat rough sounding. Time will tell if I succeeded or not.

Update: Recordings of phase 3 are archived here.


A New Recording of Organ Study #1

Jon Lyle Smith graciously offered to produce a new recording of my Organ Study #1 in 26 tone equal temperament. He used contrasting pipe organ sounds to accent different sections of the piece. He also employed his audio production skills to make further enhancements. I think it is a great improvement over the previous version. I intended this piece as a study in the combination of an interesting tuning with the powerful sound of the pipe organ. I think this new recording does a great job of further exploring these sonic effects.

See also:
Jon Lyle Smith's Zebox page
The original Organ Study #1


Slow Dance in Thirteen Tone Equal Temperament

What happens if you add an extra note to the common twelve tone scale? Well, if you space these thirteen notes equally within the octave, you get a tuning that is very dissonant and very unlike anything you may be familiar with.

Some have even concluded that this infamous thirteen tone equal temperament is the worst possible tuning! This kind of assertion just makes me want to explore this tuning even more. I really don't believe it's the worst. I actually consider it to be one of my favorites, although I'm willing to admit it can be difficult to work with at times.

Slow Dance in thirteen tone equal temperament is one of the first microtonal pieces I have worked on. I have tried to make a soft and gentle piece that contrasts with the ideas that many people have about this tuning.

I played this once for a friend. It was actually a version played with a different sound, so it sounded more dissonant than this one. He claimed he could hear it with his deaf ear. We were both pretty shocked by this. We tried several other microtonal pieces, but none of them had this same effect.

I have spent a ridiculous amount of time working on this piece. It's still not how I want it. I find the strange dissonances to be compelling, but they make for difficulties with production. I would like to add extra parts, but they always seem to clash with what is already there. Maybe, after I've gained more experience, I'll be able to return to it and expand upon it.

In the meantime, I hope you will enjoy this little glimpse into a very exotic tuning. Click here to listen.

X.J. Scott has written some excellent pieces in thirteen tone equal temperament. You can find them near the bottom of this page.


Experimental Music on the Radio

Well, this is a first for me. My Organ Study #1 in 26 edo was included on an experimental music radio show this past weekend. I always thought it would be cool to be heard on the radio, but realised that there aren't many opportunities for experimental microtonal music.

I'm glad that the airwaves aren't entirely dominated by the more popular and commercially successful types of music. This particular show airs in Southern Illinois, but regardless of where you live, you can download an mp3 version of the show at the excellent Startling Moniker blog. This is great place to learn about and hear a wide variety of experimental music. I am a big believer in exploring the frontiers of music and listening to things that may be somewhat difficult to understand, but can broaden your horizons. If you feel the same way, there's enough there to keep you busy for a long time.


Wendy Carlos Discusses Microtonality

New Music Box has posted a fascinating video interview with Wendy Carlos, one of the great pioneers of electronic and microtonal music.

Wendy Carlos has explored many historical, ethnic and experimental tunings. You may also want to visit this page where she discusses microtonality in greater detail.


A Microtonal Interview

Xenharmonic Wikispaces is having a discussion where microtonalists are invited to answer a series of questions. Here is my submission.

What was your path to discovering alternate tunings?

When I was about five years old, I would "play" on the family's piano and wonder who gave the piano tuner the right to decide which notes I could play. I wanted to know about the other notes that were between the keys. I tried playing adjacent notes at the same time, but decided that it didn't sound very good and wasn't really the same thing as playing the in between notes.

Years later I read about purely tuned intervals and how our modern tuning system deviates from these intervals and is actually based on the twelfth root of two, an irrational number!

This seemed scandalous to me. I felt like I discovered a great historical secret. I would tell others about this, but they never seemed to care that much. I felt that I needed to try out different tunings. I wanted to play with purely tuned intervals. I also wanted to try scales based on other irrational numbers and find out if this was a valid approach to making interesting music.

My first experiments involved acoustic instruments. I had a little harp that I would tune to just intonation. I experimented with using a slide on a guitar to play microtones. I even made a primitive clarinet like instrument that played septimal intervals like 7/6 and 7/4.

I eventually got an electronic keyboard that could be retuned. This is when my interest really took off.

What are your current/ past/ future particular interests?

I enjoy just intonation, but have decided that I prefer to focus on equal temperaments, especially ones that contain interesting dissonances. I am working on several projects in 26 tone equal temperament as well as some in 13, 19, 28 and 29 tone equal temperaments. I plan on also doing some experimenting in nonoctave tunings.

What instruments or means have you had/do you have now/do you want
for the making of microtonal music?

I frequently use a Triton Extreme keyboard. It has pretty decent microtuning abilities, but it has some limitations, especially for tunings that require a mapping of more than twelve keys to the octave. I also have a Yamaha TX81Z sound module and some older Emu sound modules that allow for microtunings. On my computer, I enjoy using a combination of Cubase SL3, Kontact 2, Scala and the Scala 2 Kontakt Microtuner. This gives me a lot of tuning flexibility.

I would also enjoy having some kind of microtonal guitar in the future.

Any good microtonal anecdotes?

I once played a little piece in thirteen tone equal temperament for a friend. A shocked expression came upon his face. He was deaf in one ear and could actually hear it pretty well in his deaf ear. We tried several songs and tunings, but it only worked for that particular piece and tuning.

If you would like to take part in this exchange of microtonal information or would like to read other answers to these questions, please see this page.

Two Gamelan Transcriptions for Piano

It can be pretty difficult, at times, to perform microtonal music on certain acoustic instruments. This video results from an ambitious yet rewarding process of retuning a piano to a gamelan scale. I love this pairing of tuning and timbre. It might not be authentic, but it sure is interesting.

Two Gamelan Transcriptions

See also Microtonal Music Videos


Microtonal Podcasts

There's a lot of microtonal music on the Internet. This doesn't mean that it's always easy to find or of consistently high quality. If only there was a place where you could go to get a good selection of microtonal music along with insightful commentary.

Well, there is such a place. It is called Podcast 1024's Podcast. This is a great place to get your feet wet with microtonal music. Each podcast contains music from a variety of composers and styles. Microtonal music is very diverse, so this gives you a chance to decide where you want to go for further exploration.

I especially enjoyed the Neo-Medieval podcast. It is fascinating to consider what early music might have been like if the history of tuning took a different path. This podcast gives you a chance to hear some of these possibilities.

Many of you may be new to microtonal music. I would love to hear your comments and thoughts about microtonal music.


Organ Study #1 in 26 Tone Equal Temperament

Here is another experiment in microtonality. This tuning features 26 equally spaced tones to the octave instead of the more traditional 12. This is not a very common tuning, even among experimental microtonalists. Its intervals tend to be a little more dissonant than we are used to. It is, however, one of my favorite tunings. (The term temperament is a little more accurate in this case, but less known.)

This study is fairly simple. I have avoided complex harmonies and modulations. It uses a simple seven note diatonic scale. You could easily "translate" this piece into a similar piece tuned to twelve tone equal temperament. (The common scale in use today.) I don't find the translation to be effective. This tuning has its own peculiarities and suggests different ways of organising the notes. My ears find this tuning to be somewhat darker and more mysterious. I have tried to take advantage of this by using the majestic sound of a pipe organ.

I welcome your comments. I neither expect nor hope that my microtonal music will produce any sort of consistent response in my listeners. The varied responses of others are as interesting to me as my own and help me to better understand the effects of harmony, dissonance and novel musical structures.

As the title suggests, I hope that there will be at least one more organ study in this tuning that explores some of its more exotic possibilities. This tuning has enormous untapped potential. Experimentation in it is rare and it doesn't have any established tradition or set of rules to follow. There are ways of handling this tuning that don't seem to have any strong parallels to more conventional tunings. Stay tuned and you may see what I mean.

I hope you will find Organ Study #1 to be enjoyable or at least interesting.


Study in Fifteen Tone Equal Temperament for Bells

I have been working on a lot of microtonal music projects lately. I have been playing and writing music for most of my life, but I am pretty new at producing music with a computer. It sometimes seems that it is easier to write music than produce it. Well, I wanted to start sharing some of my music with you, even if it isn't as professional as I would like. This first piece is a study in fifteen tone equal temperament (fifteen equally spaced notes to the octave instead of the usual twelve) for bells. This tuning has a lot of strange dissonances. I welcome your comments, both positive and negative. I may eventually improve or expand on this piece and your feedback will be helpful to me.

Study in fifteen t...

Note: If you can't see the player or are having problems, try this link.


Tonescape Tuning Software Now Available

A public demo version of Tonescape is now available. I haven't had a chance to try it out yet, but it looks like it has a lot of useful features. You can download it for free at this link.

Tonescape only runs on Windows. Check this page for system requirements. Click here for helpful information and here for tutorials.

Please be advised that this software is new and still has some bugs. I also hear that the help pages aren't complete yet. Understandably, some people may want to try it out right away and others may choose to wait a while. I welcome any comments from those who have tried this software and I may discuss it further when I have had a chance to use it and understand it better. There's also a Yahoo group for discussing Tonescape.

This software is only one feature at the Tonalsoft website. Be sure to visit for a wealth of information on microtonal music.


Why This Blog Exists

I don't have an agenda for this blog. One of the reasons for this blog is to organise my own thoughts on a topic that is important to me and is generally under represented, especially in the blogging community. I have my own opinions. Some of them are pretty strong, but it is not my intention to change the world or coerce others to adopt my viewpoint.

I am pleased to offer my opinions and allow others to think and comment about them. I am delighted if people respond by considering new possibilities or question conventional thinking about music theory.

I try to remain respectful of other people's thoughts and approaches to music. I don't subscribe to the notion that all scales or approaches are equally as good. Neither am I willing to dismiss or severely criticise approaches that seem to me to be less profitable than others.

I draw a distinction between musical practice and the beliefs that surround those practices. If I challenge thoughts or beliefs about a certain musical tradition (such as just intonation), it doesn't mean that I'm suggesting that musical tradition is not valuable. If I point out the advantages of a certain technique, it doesn't mean that I necessarily subscribe to the extramusical doctrine that may be associated with it.

Depending on your perspective and background, you may view the thoughts discussed here as a trivial curiosity or of Earth shaking importance. You probably already enjoy music, even if you have no knowledge of tuning theory. I merely suggest that your appreciation and enjoyment can be improved with a little knowledge and understanding of the processes involved.

There is more to music than sound and the sensory experience it provides, although these are important. Music is the organisation of sound. This organisation, if understood, even dimly, is a key to wonder and excitement that cannot be reached through a mere sensory response to sound waves.

A study of the universe seems empty to me without also considering how the forces of physics combine in music to provoke powerful human emotion.

No study of history is complete without including an examination of the evolution of musical thought, a subject that has provoked passionate debate for centuries. Even more interesting is the inevitable conflict that arises when cherished belief conflicts with observation.

Why study mathematics if you ignore one of the most beautiful demonstrations of mathematical principles?

Can we really understand our fellow man if we don't consider how his cultural background effects how he expresses himself musically or responds to musical expression?

I am more interested in questions than answers. The conclusions I've drawn so far are tentative and an opportunity for further exploration. They are not, nor should they be, the end of the path of inquiry.

I don't want to be just another theoretician who does more to stifle growth than encourage it. I don't wish to indoctrinate anyone. I have no taste for it. If I come across as too forceful or not forceful enough in my presentation of ideas, then you are encouraged to view what I say with a critical eye. Don't let me, or anyone, tell you what to believe.

I do offer encouragement. Please open your eyes and ears to possibilities that you may not have even realised exist.