Production Information “Prime”
Produced by Andy Suzuki & Nick Manson
Recorded by Dave Marks at Justplainmusic Studio
Mixed & Mastered by Nick Manson
Graphic Design by Michael Uhlenkott
All compositions by Andy Suzuki (Onymous Music/ASCAP)
2. Machine Language (8:13)
3. Good Things … (10:21)
5. Four Fingers and a Thumb (7:47)
7. Lady Luck (6:55)
11. One Broken (8:04)
13. Triskaidekology (6:06)
17. Tombstone (8:11)
Total time (56:17)
Andy Suzuki – Tenor, Alto , Soprano Saxes, Flute
Steve Huffsteter – Trumpet, Flugel horn
Nick Manson – Rhodes electric piano
Dean Taba – Acoustic bass
Kendall Kay – Drums
I wanted to combine my interest in composition and my fascination with numbers. The process began with the decision to only use prime numbers (I’ll explain what they are later). Each tune would represent a different prime number. I decided on the general shape of the CD very early on, where the up-tempo tunes should be, where things need to cool out with a ballad, etc. I chose to work with the numbers; 2,3,5,7,11,13, and 17, also being a prime number of songs total. I used these numbers as building blocks for many of the structures in my tunes, both in common and in some unexpected ways. The idea was to come up with a number-based structure to work from. With all the pegs in place the final step was to actually compose the individual pieces. In the past, I’ve written tunes one at a time and assembled them together for an album. This time I took a reverse approach, starting with the blueprints, constructing each structure based on the given prime number, and finally filling in the musical details, like interior decorating. The hardest part was keeping an eye on the big picture and trying to compose all seven tunes sort of at the same time.
About Prime Numbers
All the numbers from one to infinity can be grouped into two categories; Prime and Composite. Before defining these let’s look at some numbers and their factors. 1=(1×1), 2=(2×1), 3=(3×1), 4=(4×1 and 2×2), 5=(5×1), 6=(6×1 and 3×2), 7=(7×1), 8=(8×1 and 4×2 and 2x2x2), 9=(9×1 and 3×3), 10=(10×1 and 5×2). 11=(11×1). Do you notice that some are only divisible by the original number and 1, while others can be represented in more than one way?
A number is Prime if there is only one way to factor it, namely by itself and 1; so 2,3,5,7, and 11 are prime. A number is Composite if there are other ways to factor it, like 4,6,8,9, and 10. Prime numbers are the building blocks of the rest of the number line, the composite numbers. Composites are all made up of smaller prime numbers.
Technically, 1 is not considered a prime, due to its special honor as a multiplicative ‘identity’; in other words, when you multiply any number by 1 it remains unchanged. Thereby, eliminating the redundant cases of factorization, like (2x1x1) and (5x1x1x1). A list of the first few primes looks like this: 2,3,5,7,11,13,17,19,23,29,31,…etc.
It was proven by Euclid in a simple proof that the primes go on forever. Notice how difficult it is to predict the next number in the above sequence. Is there a formula that will show us that the next number should be ’37’? A mystery to me is how such twisted and irregular scaffolding could possibly be the building blocks of such an orderly universe as the whole numbers. Combining prime factors in all possible ways, fills in the rest of the number line exactly!
Compositions can come about in many ways. When inspiration hits, the music just pours forth almost in its entirety. A three-note melodic fragment may blossom into a full composition. Sometimes I start with a chord progression first and add a melody later, other times I may have a specific groove in mind and build upon that. The thing that all these ways have in common is that they are ‘additive’. You begin with a small piece and add to it until you’ve built up your final structure.
In contrast, all the compositions on this CD were created ‘top-down’. Structure came first. I used prime numbers and mapped them (gave them a one-to-one correspondence) onto various countable aspects of music. I’ve found, choosing carefully how this ‘mapping’ is done makes the difference between beautiful music and an unlistenable math project. There are so many ways to enumerate music; you are only limited by your imagination.
Let’s look at some of the aspects of music that can be counted.
Please note: I use the words ‘bars’ and ‘measures’ interchangeably.
You can count the number of: notes in a fragment of melody, notes in longer phrases, notes in the whole melody, the duration of individual notes, and most importantly, given some arbitrary starting point (say middle C) you could assign a number to any note based on which scale you start with. For example, (middle C = 0, C# = 1, D = 2, D# =3, etc.), so 5 would be equivalent to the note F. If a diatonic scale is used instead, C-major scale would be (C = 0, D = 1, E = 2, F = 3), so 5 would now be the note A.
You can just as easily use numbers to form harmonic shapes. By the numerical scheme mentioned, you could now take every, say, 3rd-note of a chromatic-scale and end up with the group of notes (chord), C, E-flat, F-sharp, and A (a diminished chord-shape). Every 3rd note of a C-major-scale will run through all the notes of the scale once, C-E-G-B-D-F-A.
It is an interesting exercise to take the 12-note chromatic-scale and divide it by all the numbers less than 12. You’ll find that dividing by 1, taking every next note just gives you the original unchanged. Dividing by 2 (in other words, taking every other note) leaves a whole-tone scale, C-D-E-F#-G#-A#. As we saw earlier, 3 gives us a diminished-shape, 4 yields an augmented-shape, 5 skips in fourths exhausting all 12 notes once before returning back to C. 6 splits the octave exactly in half with the tri-tone-shape, C-F#-C. Now it turns out that 7 thru 11 are just like 1 thru 5, but in reverse. 7 cycles thru every note, 8 leads to augmented, 9 to diminished, 10 to whole-tone, and taking every 11th note gives you the chromatic-scale in reverse. One key observation is that dividing 12 by 1, 5, 7, or 11, gives you the full chromatic scale back with just a difference in order. Dividing 12 by the remaining 2, 3, 4, 6, 8, 9, 10 always leaves a few missing notes. The reason for this difference has to do with shared factors. 12 can be factored into 2x2x3, all the numbers 2,3,4,6,8,9,10 can be shown to have a factor of 2 and/or 3. As for, 1, 5, 7, and 11 they share no factors with 12 and are called, ‘relatively prime’.
Numbers can be assigned to many aspects of rhythm. The number of beats per measure, the number of measures in a phrase, the number of times the phrase is repeated. Some of the tunes on this record use this ‘nested’ approach. Note durations, spaces between notes, note-groupings, just about every aspect of rhythm is countable. If you are getting to the point where you are counting the number of musicians in the band, or the number of letters in the title of the song, you should take a break.
2. Machine Language: Two is the first and only even, prime number. Duality is a theme that has its roots in the distant philosophical past. With time, meditations on good/evil or being/non-being have been replaced with the modern mantras, on/off or 1/0. Computers use a system of numbers called, binary (base-2), unlike our everyday decimal system of base-10. Instead of using the digits 0 to 9, only the 0 and the 1 are used.
The core of this piece is a two-octave mode. It was derived by dividing the chromatic-scale by 2, but since 12 and 2 share the common factor of 2, it only gives you a whole-tone scale (a six-note scale built out of consecutive whole-steps). I wanted the two numbers to be relatively prime (sharing no common factors); I expanded my initial scale from a 12 to a 13-note chromatic scale (starting from C# up to and including the C# an octave above). This small change means we’re now dealing with the numbers 2 and 13, these are relatively prime. This resulted in something much more interesting, the scale is: C#-D#-F-G-A-B-C# (next octave) D-E-F#-G#-A#-B#-(C#). It’s interesting depending on which part you look at, it can have a C# whole-tone on the bottom-octave and D whole-tone on the top-octave. In the middle area are B-melodic-minor, and others, to be found. These two whole-tone-scales playing against each other were used quite a bit.
In the intro there are two big fermata sections, the tenor played one of the whole-tones and the trumpet blew over the other whole-tone. After the main groove is established, the whole-tone ostinado bass-line comes in; the electric piano joins in with perfect-5ths. The main head-in continues with this sound, the trumpet and tenor (two voices) play in two different colors, one in unison, and the other in octaves.
The next section ‘doubles’ up the tempo, for an exploration of this two-octave mode. We all used 2’s and multiples (4,6,8, etc.) for solo motifs. The head-out now combines the two tonalities for a poly-tonal experience. Drums are featured on the end, a slow boil with the horns doubling the bass and piano motif, now in a four-voice spread of perfect-5ths.
Considered as a whole, this dual whole-tone mode could be nicely represented by perfect 5ths. As long as the root (bottom note) stayed in its respective whole-tone mode, the perfect-5th above will always be in the opposite mode. Due to the structure of a whole-tone scale (consecutive whole-steps), no matter which note you choose, its perfect-5th will lie outside that scale. In other words, in a whole-tone structure you can only combine whole notes to form the intervals; major 2nd, major 3rd, augmented 4th, augmented 5th (skipped the perfect 5th!), augmented 6th, etc.
Overall, I wanted this piece to represent duality in its many forms, from the two tonalities to the general use of the block-ish powers of two. Most Western music that doesn’t fall into the category of a Waltz, is usually some power of 2. Really common ones are 4, 8, 16-bar phrases, or the ubiquitous 32-bar tune, with its four sections, AABA, 8-bars each, the melodies often phrasing in 4 and 2-bar phrases.
3. Good Things …: Come in 3’s, or was it three 3’s? Three is the lowest odd prime. I tried to nest as much three-ness at different levels as I could, and still retain the mood of an easy-going jazz-waltz. The main motific shape is a three-bar phrase, three beats per bar, sometimes repeating the whole thing three times. The three chords were chosen based on dividing an octave into three equal parts, which leaves an augmented triad (e.g. E-C-G#). This shape is used throughout the root movement, sometimes in reverse direction.
5. Four Fingers and a Thumb: Similar to the previous tune this uses 5’s throughout. In the intro there are three versions of 5; the drums are playing a pattern in 5/4, each bar is played a total of 10x’s (1×10), the bass line is, with slight variations on every 5th bar, a two measure pattern played 5x’s (2×5), and the keyboard comps a 5-bar phrase, 2x’s (5×2), all repeating itself every 10 bars.
The horns enter with a folky melody, like the minor sounding Finnish folk-songs my mother used to sing, with a 5/8 figures every 5th-bar. Things transition at the solo-section. We go from 5/4 to 4/4 swing, but retain the phrasing of 4 and 1, hence the title of this tune. This 5-bar solo phrase is repeated 10x’s for a total of 50-measures before the form repeats. The horns were arranged throughout the A-sections of the tune to always move in contrary motion. Whenever the trumpet moves down, the tenor moves up, and vise versa. For its symmetry I chose the melodic-rhythm to be (2+1+2). After a visit to the head, tenor solos out on the original riff.
7. Lady Luck: Drums start with 7-bars of 7/8. A series of II-V’s in harmonic phrases of 11/16, 3/16, 13/16, and finally two more bars of 11/16 for a total of 49/16, or 7-bars of 7/16. Then shift to 7/4 latin-feel, and 7/8 divided into 2+3+2. The rest of the arrangement alternates in one of these three meters; 7/4, 7/8, and 7/16.
Looked at two ways, the chromatic-scale can be labeled (C=0, C#=1, D=2, etc.) or (C=1, C#=2, D=3, etc). The only difference being the starting-number. If you learned ‘piano-fingerings’ as a child, you may gravitate toward C=1, but I think the number-theorists out there prefer the inclusion of ‘0’. The number 7 yields, respectively, a perfect-5th or an augmented-4th, so I found as many opportunities as I could to harmonize the horns with these intervals.
“Bonus 7” – near the end the horns play 7-note groupings.
“Double-Bonus 7”- from the keyboard breakdown, the 7 bars of 7/16 repeat exactly 7x’s. Thanks Lil’ Andy Manson for the title.
11. One Broken: For this ballad I wanted the 11 to be subtle. This is very slow, in 4/4, so unless you have patience, you may not notice that the entire tune is a repetition of an 11-bar form. 11th-chords were used…but not harmed.
13. Triskaidekology: Ya, ya, ya, it’s the study-of-13. This absurd bebop-tune begins with 13-bars of drum solo. The form is AABA, the first A-section has an added 2 beats and the B-section is 13-bars (3+3+4+3). The last A-section has a II-V functioning as a pivot to false-cadence into a new key.
If you were to count every single note in the melody (not recommended) you will find there are 195 (15×13).
17. Tombstone: Probably the most obscure title reference. The great mathematician Gauss was so proud of a proof he had come up with in his youth that connected prime-numbers, with geometric-shapes that could be drawn using only a compass and straight-edge. He proved that heptadecagons (17-sided regular polygons) could be constructed, as well as, any other n-sided regular polygon whose number ‘n’ was of a particular form called a ‘Fermat Number’ (2 raised to some power-of-2, plus 1. In our case, 2 raised to the 4th-power plus 1 equals 17), connecting two distinct branches of math. He wanted this 17-gon to appear on his tombstone.
This is a dark and moody tango. Three bars of 4/4 and one bar of 5/4, total 17 beats. I wanted a floaty feel. Drum and bass hold down the 17, while the piano anticipates chord-changes by an 8th-note. Horns start melody phrase in different place every time. After the head out we begin to divide the 17 up differently. Now it’s (7+3+2+2+1+1+1). One final nod, the 17th note of a chromatic-scale is equivalent to a major-3rd or a perfect-4th, so look for those intervals in the horn harmonies.