Following up (at long last) on Musical Pi, Part 1, we present the remaining nine pieces (plus bonus tracks!) in the suite of music based on π, composed by Jon Turner, professor of musical composition at Nazareth. (see also part 1 and part 3)
The nine pieces and their specs:
- 1. Circle of the Great Spirit 1
- MM=72 54mm 3/4 3:00
- Melodic theme is first 19 digits of π in base 12.
- 3.14159 = 3.18480 in base 12.
- 3.184809493B91866457 = π to nineteen digits in base 12.
- 3.18480 (etc) = E♭ D♭ A♭ E A♭ C A E A E♭ B A D♭ A♭ F# F# E F G (etc).
- The opening setting of the π theme is in gospel 3/4, making it the “triplet” variation not included in CGS2 (below).
- 2. Quest 4 Pi 1
- MM=288 175mm 2:26
- 1400 digits assigned to 12 respective percussion sounds, with the occurrence of the digit “0″ a bass drum/crash cymbal combination that coincides with the irregular slower sequence 85 digits, sounded in the bass with parallel mixolydian harmony. A freely composed continuous guitar solo is overlayed.
- The 85-digit π sequence is framed and punctuated by the harmony of the leading zero (with 0 = C, the harmonic form is 0. 318480…0…0…etc…0).
- 3. Arc Tango 1
- MM=85 129mm 4/4 6:04
- Follows 48 digits of arctangent (π/4), repeat, 49-64, 1-7. The arctangent sequence begins with the duodecimal digits .95120, which maps to the augmented triad A-F-C# at the beginning. This is used as the main melodic motive, and other similar melodic contours and intervals are derived from this opening shape.
- 4. Mock Apple Pi
- MM=100 296mm 5/8 7:20
- Mock = fake, 355/113 gives 112 repeating digits. Melody in same first six digits. The first twelve digits, which diverge from true π after six digits, are repeated to form a 5/8 bluesy chord progression, repeated a half dozen times to symbolize the repeating character of the fractional part of 355/113 in base 12, that is, the sequence starts over (.18480) but then continues for a hundred measures. For now, the repeating 112-digit fractional part is left bare for improvisational practice (1x only).
- 5. Pi Counter Pi
- MM=160 451mm 11:16
- Several thousand π digits percussion, fewer thousand continuous in bass, with canonic bassoon and flute entries at major thirds. The varying rhythm was generated by an HMSL program which varied the duration of each digit according to the pitch value of its neighboring digit in π’s duodecimal sequence. Thus, the bass (ever accompanied by bass drum and cymbal) follows the π sequence exactly and continuously, but the notes form unexpected ever-changing rhythm patterns of two, three, four, or five eighth notes. Two other voices, flute and bassoon, are deployed in a series of fugal entries, passages, and cadences. Cadences (and the beginnings of new points of imitation) occur at selected points where all three voices arrive together. These cadences are articulated by a crash cymbal. Then the bass plows ahead, and the other voices follow at an organizing interval of 16 pulses, exactly canonic, by transposed up and down major thirds, to provide chromatic complementarity.
- 6. dSnTSM
- MM=200 76mm 4/4 swing 1:30
- Π as walking bass, 144 digits=36mmx2+tag.
- Bass follows π sequence in quarter notes. For every 4 quarters, a piano chord and bebop riff are overlayed (same 4 tones), for 8+12+8=36 measure progression.
- “dSnTSM” means da Sphere n Thelonious Sphere Monk. As straight up as it can get, plausible avant-garde bebop riffs with crunchy Monk overtones based strictly on π.
- 7. Arc Tango 2 4/4
- MM=170 194mm 4:33
- Thematics follow 1, but 160 digits are continuous, repeat 160-4 coda.
- In this version, the entire melodic structure of AT1 is applied to the continuous arctangent sequence (π/4, which begins .95120…). AT1 set up a strophic phrase structure over the first 48 digits as a repeated progression, but AT2 continues for 160 digits before a coda. But the strophic phrase structures always seem inevitable, in spite of the completely unpredictable chord progression on the arctangent sequence.
Tracks 8 and 9 and the bonus tracks – Coming Soon!