Words and music by Transfer Point

Draw a unit circle around my heart
Trace out 2 Pi radians,
And we’ll never be apart
I’ll be sine and you’ll be cosine
Weaving to infinity
Draw a unit circle around my heart

A compass planted on a plane
You pinned my heart
And I will never be the same
With every angle subtended
I can feel my loneliness is ended
Draw a unit circle around my heart

Draw a unit circle around my heart
It may seem irrational,
But it’s the perfect place to start
I can see the digits of Pi
When I trace the circles in your eye
Draw a unit circle around my heart

Here’s the point we start and never end
Our course will always around us bend
What we don’t know
We can always solve together, if we stay together
Draw a unit circle around my heart

Draw a unit circle around my heart
Every revolution is a brand new start
Our limit is the sky
I’ll meet you there at a quarter Pi
Draw a unit circle around my heart

Alan Sanderson: vocals, vocoders, synthesizers, mixing, mastering
Tom Sanderson: synthesizers, drum programming

Alan’s Notes

Last year we wrote a song called “Chemistry Class (Look My Way!),” which tells the true story of how I met my wife in a university general chemistry class. An early draft of that song mentioned a trigonometry class that we also had together that semester. I scrapped that line to keep the chemistry song more focused, but I liked the idea of using a mathematics analogy for our romance.

One day around that time I was out on a long trail run, and a fantastic line popped into my head: “Draw a unit circle around my heart.” By the time I reached the summit of the trail I had worked out the first verse, and I paused to record it on my phone. I had a second verse composed by the time the run was over, and later that day I worked out the chords on guitar and sent a sketch to Tom. Tom quickly sent back a great sequence for this song, which was essentially similar to the final version. I had limited creative bandwidth for a lot of 2022, and I didn’t feel like the composition was totally complete, so I left this project on the back burner for a few months until the muse struck me again last fall with some new verses and an alternate chord progression.

Some time last year I learned about an interesting old labor-intensive studio technique developed by 10CC for the song “I’m Not in Love,” and later used by Billy Joel in “Just the Way You Are.” Basically, you sing every note in the musical scale on a different track, and then loop each track individually so that it plays indefinitely without breaks. These tracks then become an “instrument” that is played by moving the volume sliders up and down on the mixing console to play only those notes from the scale that you want at a given point on the timeline of the song. The result is an eerie, half mechanized, half organic sound that makes for a really smooth backing vocal track but also sounds like a warm pad synth. I thought a sound like this would fit well in the unit circle song, so I spent a few hours making looped vocal tracks to use. Each note is a mixdown of three voices, looped out to 4 minutes in length, and the performance was done using automation of the fader levels on each track. This was perhaps not quite as labor-intensive as the original analog technique, but still more trouble than I normally go through for a recording. That made it really satisfying.

Another fun thing for me in this recording is a little melody based on the digits of Pi. To derive the melody I used the scale position for each note in the key of F, like this:

0 = E5
1 = F5 (root)
2 = G5
3 = A5
4 = Bb5
5 = C6
6 = D6
7 = E6
8 = F6 (octave)
9 = G6

The melody is made from the first 35 digits of Pi: 3.1415926535897932384626433832795028

Truncated versions of this melody appear in two other places in the song. To make this sound I used amsynth, a simple software synthesizer, with a tone made up of pure sine waves. I was surprised at how musical this melody turned out to be, and how well it tracked the chords in that part of the song.

Tom’s contribution to the soundscape of this piece has been enormous. I especially like the interesting chord progression of bridge he added. Almost all of the synthesizers you hear in this recording were done by him, and his input during the mixing and mastering phase was invaluable.

Tom’s Notes

I believe that Alan started the idea of “Unit Circle” late in 2021. I liked Alan’s concept and demo and could picture a simple synthpop arrangement. I submitted some music and a couple lines of lyric but the composition is primarily Alan’s and I think it’s a clever metaphor. Alan was really deliberate about the shaping of the song and I think it is well balanced because of his refinements.

The initial sequence I made in early January 2022 was not very fancy. Perhaps because it was missing character and embellishments, it was put on the back burner for quite a few months. In October, Alan proposed reordering the chords and I agreed this would make the song more interesting. I had to learn more about the editing features of the Roland FA-06 but I was able to re-perform and paste over the old performances and also cut out a repeat of the second instrumental segment to decrease monotony. After this, I added a moog bass and a pad patch.

In early November, Alan decided that the current key did match the normal “sweet spot” of his voice, so he suggested transposing up three semitones which I did and re-rendered the sequence and changing the bass patch. Alan soon got to work assembling the vocal loops that comprise the backing vocals which was a laborious but fruitful project.

In the home stretch (January 2023) as Alan’s technical labors were wrapping up (including adding some great beat delay to the TR percussion), I submitted a few more elements, among those a couple of lead synths for instrumental sections. I think we both intended for a smaller production initially but there were so many things we wanted to throw in.

Overall, I like what Alan stated in his comments about how the labor in this song’s creation won him some personal satisfaction in the end product. Similarly, I think there was ample opportunity to abandon the project in at least a few junctures. But I am glad we continued to shape it until it took on a pleasing form as it was an idea worth the effort.

Info and Stats

• Production Dates: November 2021 — February 2023
• Equipment:
  • Interface: Behringer Xenyx 1204USB, Behringer Ultra-DI DI400P
  • Hardware synths: Roland FA-06, Yamaha Reface CS
  • Microphones: DIY condenser by Michael Willis
• Software:
  • Linux Mint 20.2
  • Ardour 7.1.0
  • amsynth
  • Dragonfly Reverb: Hall, Room, Plate
  • x42-plugins: parametric equalizer, dynamic compressor, digital peak limiter
  • Calf Studio Gear: vintage delay, multi-spread, flanger, phaser, vocoder
  • TAP-PLugins: tremolo
  • ACE: Delay
  • Guitarix: Gx Studio Preamp Stereo
• Total Tracks: 44
  • Vocal: 24 (including the 20-track vocal loop choir and 2 vocoders, which take up 2 tracks each)
  • Synths: 15
  • Drums: 5