Fantasia Apocalyptica: Special effects 1) I use the following absolute pitches for Greek letters, to approximate what the Unicode 5.0 manual (section 15.13) says was an ancient system: Α=g♭ Β=f♯ Γ=f Δ=f Ε=e Θ=e♭ Ι=d Κ=c♯ Λ=c Μ=c Ν=b Ο=b Π=b♭ Ρ=a♯ Σ=a Τ=g♯ Υ=g Φ=g Χ=f♯ Ψ=f♯ Ω=f This is used for the names of the seven churches; also for a few other names like ΔΑΥΙΔ, ΙΕΖΕΒΕΛ, ΑΠΟΛΛΥΩΝ, ΣΙΩΝ when the melody happens to sound nice. 2) I also spell some things out by using Morse code. For instance, the rhythm "dash dot dash" in measures 12, 13, 16, 17, etc. of Chapter 1 is Morse code for "invitation to transmit". Hebrew Morse code is used for the twelve tribal identities when groups of 12000 saints march in Chapter 7. For example, the first tribe mentioned (verse 07:05) is "Judah", which in Hebrew is "י ה ו ד ה" (if spelled left to right!); and the Morse code for that is the Morse code for "I O E D O" in the Roman alphabet, namely ".. --- . -.. ---". OK: A dot goes into one beat, a dash goes into two beats, and the space between is a rest. The melody starts at c, then goes up, until resetting back to c after each space. (I actually shortened it to "I O E D".) I also got a nice effect by _repeating_ each tribal theme, on the other manual, with the final letter inverted. We can imagine half of each tribe singing their theme in dialog with the other half, as they go marching in. Greek Morse code is used for the names of precious stones in Chapter 21. Each stone is first encoded by two letters; for example, "sapphire" becomes "ΣΦ". Then the Morse code for Greek "ΣΦ" is the same as for Roman "SF", namely "... ..-.". In verse 21:19 I converted this to c-d-e d-c-b-b-a using the rule that dot means UP in the first letter, DOWN in the second; dash means UP SAME in the first, DOWN SAME in the second. All notes are quarter notes except for the final note of the first letter. (This convention magically makes a decent approximation to plainsong!) 3) The most mathematically complex part of this composition occurs in the changeringing convention of chapter 7. I wanted this part of the music to sound a little strange and to stand out, just as the words of verse 07:05 through 07:08 call attention to themselves by their mathematical structure. I also wanted to suggest 12,000 in some way. Fortunately there's a nice permutation group on 15 letters that has exactly 12,000 elements! Let the 15 "letters" be 00 10 20 30 40 01 11 21 31 41 02 12 22 32 42 and consider the generator permutations a = (00 10 20 30 40), b = (10 11 21 31 41), c = (20 21 22 32 42); a' = (10 20 40 30), b' = (11 21 41 31), c' = (12 22 42 32); u = (00 01 02)(10 11 12)(20 21 22)(30 31 32)(40 41 42). These permutations generate a group of size 24,000; we restrict ourselves to the 12,000 even permutations, namely those in which a', b', c' occur an even number of times. Let ρ = a' b' c u^2 = (00 02 11 20 42 01)(10 22 31)(30 12 21 40 32 41). In 07:04 I begin the changeringing by first forming abc, (abc)^2, (abc)^3, (abc)^4; then I multiply by ρ. In 14:01 I give another example by exhibiting the "Zion permutation" (00 11) a^2 a' a^3. 4) I learned of a medieval custom that was prevalent in some English monasteries of the twelfth century (I think, although I've forgotten the exact reference): In their systematic cycling through the Bible, they would ring the church bells whenever coming to Revelation 04:08. Therefore I've called for ringing the bells in the church tower at this point. Of course I realize that this won't work in all performances.