About that Requiem... (enter the "3D fugue")

I just discovered a level of fugal polyphony that, as far as I know, not even Bach attempted. (But Mozart did, or was beginning to at least.)

This is a variation of the multiple fugue (double, triple etc.). However, instead of developing the first subject, than the second later, and so on, this is a fugue with the subjects being developed at the same time. In other words, a "three-dimensional fugue", with fugues layered on top of fugues. If the fugue is the musical equivalent of chess, than this is the music equivalent of 3D chess.

It just so happens that a two-by-two fugue has been written: the Kyrie from Mozart's Requiem. Here it is again; start at 4:46:

I'm writing a three-by-three example in the Second Symphony, fourth movement (Massachusetts), and the final reprise of the Ouverture in the First Symphony has a two-by-four-voice fugue.

(It's not quite the same as the twelve-part "group fugue" in the sixth movement of my First Symphony--that's a four-voice fugue, with each voice harmonized in three parts, but it is another example of a 3D fugue.)

Also, what I'm talking about would be an example of what could be called "hyperpolyphony". The best established example, from the Renaissance, would be Thomas Tallis' Spem in alium:

This isn't a fugue, but it's still 40-voice polyphony.

But does this mean that someday I have to write a 40-part fugue?

What if he had lived longer?

I am convinced that Mozart, had he not died so tragically young, could've done for music what Beethoven did later.

Anyway, one more post: his unfinished Requiem. Specifically, the Kyrie.

A couple things to notice:

• the use of basset horn (marked by the gold diamonds) in the introduction; the basset horn is an alto/tenor clarinet in F with a low range extended to C (in modern instruments)--and remember, Mozart was the first major composer to write extensively for clarinets in general
• the double fugue in the Kyrie--I told you he was getting good at this counterpoint thing

I am planning on writing a Mass someday, maybe a Requiem. So I'll be studying this tonight, another thing I wish I had done when I was much younger.

The "Jupiter" Symphony: when Mozart challenged the musical gods

Wolfgang Amadeus Mozart was born in Salzburg, Austria on this day in 1756.

I have had an obsession with the finale of his 41st and final Symphony for many years now.

This is when the composer triumphantly goes all out with all of his techniques. It's almost a fugue worthy of Bach himself, working five different themes together. He had used Baroque counterpoint in other works late in life: the Requiem, the Magic Flute (especially the Overture) and of course the Adagio and Fugue, K.546.

His music was also becoming heavily dramatic, especially in his unfinished Requiem. Had he not have died much too soon, he would've started the Romantic era of music decades before Beethoven did. (He already was part of the Sturm und Drang movement since the 25th Symphony, in G minor.)

Also, the chromatic stuff that began the development in the final movement of the 40th symphony? (See Leonard Berstein's commentary, beginning at 7:48.) He uses note of the chromatic scale except G, since it was a symphony in G minor and he had used the note enough. Almost a tone row à la fellow Austrians Arnold Schoenberg and company, but with a few repeated notes. And he had done it at other times.

I mean it; Mozart was really getting good near the end.

The Rite again, and what it did to me

The beginning of the still-unfinished First Symphony was 35 years ago, when I first heard The Rite of Spring on vinyl in my bedroom. It was part of a compilation (one of those boxed "best-of" classical compilations); I don't remember what orchestra recorded it, or what year.

I consider that event when and where I, the composer, was born. I had heard Bach, Mozart, Beethoven, Chopin, Tchaikovsky, the rest, but it was Stravinsky that made me decide I wanted to be like them all, and innovate in my own way. The first ideas of the First Symphony came to me around that time. The ideas came to me in little pieces, from movies, television, video games, everything I was exposed to.

I didn't start writing and recording any of it until about ten years ago. I wasn't ready until then. I would have rather been a bassist for a metal band somewhere. This was even long after I went to college to study musical composition and theory, but dropped out my freshman year due to illness. (I'm entirely self-taught after that.)

Doktoro Esperanto--an opera

After debating with myself over whether I should do this, I've decided to write an opera. It'll be about L. L. Zamenhof, the creator of the Esperanto language.

The libretto, of course, would be in Esperanto, though there may be lines in Yiddish, Polish and Russian. (I may let someone else write the libretto.)

I would be using 72 equal temperament, of course. I do plan on finishing my Second Symphony first, though.

"Virtual pitches" on timpani rolls

Very high pitches, higher than what humans can hear, are called ultrasound. A famous example is a dog whistle, and good quality headphones can reproduce sound considerably higher than 20 kHz.

At the other extreme is infrasound. Anything below 20 Hz is more likely felt, not heard. (That applies to the fundamental, not harmonics.) Few acoustic musical instruments can play pitches that low--the first is E flat octave 0, at 19.45 Hz. 32-foot organ stops can play in that range. The low C is 16.35 Hz in standard tuning.

The Sydney Town Hall Grand Organ has a 64-foot stop, so it can play pitches in the negative-first octave, the low C being 8.18 Hz. With audible overtones, pitches this low are heard as beats rather than tones, and have been described as sounding like timpani rolls.

Which led me to another experiment...

This might require some considerable skill by percussionists, and certainly a metronome. If a roll on timpani, or bass or snare drum, could be an exact number of strokes per second, it would simulate an extremely low pitch. A double-stroke roll at 16.35 Hz would be a similated C0, which would go well with a timpano tuned to concert C2 (65.41 Hz). The drum should be tuned an octave, two octaves or a perfect twelfth above the virtual pitch.

So far, I have timpani rolls with specified frequencies in two movements of my Second Symphony: XXXVI. Montana and XXXIX. Nebraska.

Also, if an organ is being used, one still can produce resultant tones, by playing parallel fifths to simulate lower registers. (In Symphony No. 1, ninth movement, I used a resultant B-2, or about 7.72 Hz.)

Symphony No. 1: The Cipher, the Devil's Ball

Though there are many protagonists in DIES IRÆ, there is one chief antagonist: an inanimate object that somehow gains power and threatens to conquer or destroy the world.

This object, called the Cipher (from Arabic صفر şifr "zero; empty"; see cipher), may not even be real. It just exists somehow, but only as an illusion. It is a shadow in Plato's cave, but it is a shadow of nothing.

It is an object of pure lies and deception. It promises great magical powers and knowledge, and may grant such powers, but ultimately it steals power. It survives and grows on evil deeds, but usually thrives on ignorance and folly.

It seems to have fallen to Earth from space many thousands of years ago, in the form of a marble-like sphere of black glass, one centimeter in diameter. It often shines with multi-colored light which swirls around it, like a tiny black hole.

Its influence on the world was greatest around 10,000 BC, but after the collapse of the city-state of Hriya, which possessed it, it disappeared, only to turn up again around the year AD 2000. Many leaders of the world, political, business and religious, who learned of the object and its powers, began to seek it, but before any of them even found it, they were already corrupted.