Counterclockwise – Circle of Fifths or Fourths?

July 20th, 2014

counterclockwise-2048-infinite2048 Infinite – The Circle of Fifths is soon going to have a counterclockwise mode if the Kickstarter is funded. It’s going to sound very different, and here is why:

Going up a fifth repeatedly yields the clockwise circle of fifths. But what about down a fifth? Counterclockwise, of course, but can we really call it the circle of fifths at that point? It really depends on how you look at it. Taking cognition into account really messes the whole thing up.

Whenever we’re working with the raw materials of sounds, music theory should be looked at with a blank slate. No style in mind. Just air reverberating at certain frequencies. Get past all of your personal bias and look at sound the same way a machine would. Pure and cold objectivity (hey, that’s a great description of Stockhausen!).

This is sound we’re talking about! So, let’s listen to the circle of fifths counterclockwise:

Like I said before, I know that an inverted fifth is a fourth, and that there are fourths in the example. But remember; pure and cold objectivity. This means interval classes, not intervals. No tonicization means no hierarchy.

Just because it’s pretty sweet, here’s the tone row in fifths straight down in literal fifths:

Since I’m on a tangent anyway, serialism (the logical conclusion to 12-tone music) is the attempt at eliminating the hierarchy of pitches in music. It is to balance the sonic spectrum. The previous example does not do this. It makes the C at the end the most important note and the note we remember. This does not give us an accurate impression of what the circle of fifths sounds like.

Back to the circle of fifths! Compare the counterclockwise circle of fifths to the clockwise circle of fifths:

Presented in this pure and unbiased form, they sound very similar. Comparable harmonic material results. For all practical theoretical purposes, the counterclockwise circle of fifths is still the same circle of fifths. Just in retrograde.

But then we make music out of it and everything changes. Particularly the bass…which it why everything changes. Here is the Berg style tone row from last time…backwards!  And I mean really really backwards; I forgot to save the MIDI and only had the mp3 file to work with:

Here it is forwards for comparison:

Hear how the middle is a lot crunchier than it is when it’s backwards?

The Counterclockwise Circle of Fifths and Perceived Bass

The bass is quite literally the harmonic foundation and context for everything else you hear in a musical texture. So, the dissonance made out of a counterclockwise circle is welcome because the perceived bass is constantly changing to meet the new sounds. We don’t have to change the bass because our ears do the work or us.

Why do our ears do this? The ratio of the frequencies caused by the notes that make a fifth are 2:3. In other words, the sound waves line up every three oscillations of the higher note. This ratio is easier to understand than the 3:4 ratio of the fourth. Since the fifth’s ratio is simpler, our brains are more drawn to that sound and automatically rearrange any fourth they hear into the simplest ratio. This is possible because the octave above any given note is actually present in the sound via the harmonic series. Our brains reorchestrate sounds into their simplest ratio, and this changes the perceived bass as we go backwards in the circle.

We can also approach it from tonal theory when we are thinking melodically. An ascending melodic fifth (clockwise) ends on the note the ear perceives as least important. This means it sounds unresolved as opposed to the descending fifth (counterclockwise) which ends on the important sounding note (tonic). Here it as ascending:

And now descending, which is the one that sounds resolved and therefore less dissonant (Isn’t the Xylophone sweet):

CounterclockwiseSo counterclockwise fifths are persistently resolving to each other. It puts the music in a state of perpetual resolution. As opposed to clockwise which puts the music in a state of perpetual tension.

Basically, fifths are actually fourths because of some crazy cognition stuff, and going backwards in the circle fixes all dissonance.

So, is it fifths or fourths? If you take cognition into account, it’s fifths. In fact, it’s even more fifths than clockwise. Clockwise is really the awkward direction.

Here is that cool improvisation from last time–backwards! And therefore more resolved:

If all of this stuff sounds jazzy, you are correct. Now listen to Bill Evans.

Tone Row – The Circle of Fifths

July 8th, 2014

tonal-tone-rowThe Circle of Fifths can be considered a tone row. Cool, huh? One of the defining concepts of the tonal system when written in a score turns out to be atonal. It’s an oxymoron, really. A tonal tone row. Atonal tonality. Consonant dissonance. A never-ending resolution. The beauty of the paradox is unending.

Two Sides of the Tonal Tone Row Spectrum

The amount of tonality you hear really depends on the rate at which you hear the notes and how many are played at a time. To start out the audio examples, listen to a clear presentation of the circle of fifths as a tone row:

Now, before anyone decides to be a Smart Aleck, yes I know that when you invert a fifth it turns into a fourth and that my example has fourths. But since this is atonal music, we are dealing in pitch classes, not in intervals. 🙂 I win.

Since the first example is played rapidly, it is perceived as sounding random. Yet at the same time it is symmetrical; perfectly ordered and balanced. That’s the touch of tonality leaking into the sound. We just can’t fully get away from it!

Let’s try a bunch of notes together without using orchestration to change how it’s heard.

Pretty much the same effect. Now lets try changing the orchestration and the number of notes we hear at one time. We can trick the ear into hearing tonality.

We were certainly able to drive that F to resolve to the E. Not very tonal, but we were able to get enough emphasis on a single pitch the make some of the original serialists not approve (Webern, anyway). Let’s see if we can sound like Berg by using rhythm to reach into tonality.

Still Serialism, but we are certainly getting dangerously close to tonality! Now let’s do a little repetition and break from the serial idea entirely.

I could listen to stuff like that all day! All 12 pitches were used many times using the contour of the circle of fifths, but we were definitely in C. The reason it sounds so different is that the pitches are separated into musical ideas over time instead of just thrown at the ear all at once. It’s also why we can’t call it serialism, but it’s still the circle of fifths! And now for a little hop to the total opposite side of the style spectrum.

And that’s how to serialize tonality. I hope you enjoyed my little tone row based compositions!


To hear the circle of fifths paradox over a very long period of time, try 2048 Infinite – The Circle of Fifths. It’s as fun as it sounds.

Pick-A-Mode – Bonus Features in Upbeat Bird

June 14th, 2014

I wanted to avoid redundancy in the music produced by Upbeat Bird. On the other hand, I also wanted the music to repeat itself to an extent. When first being introduced to new sounds, the listener needs some time to adjust the idea. But it has to do something eventually. The solution was to change the mode in which the music was being played. But not until the player starts to get the idea of how to play the game well. Since there are seven primary modes to work with, that also leaves plenty of opportunity to give the player goals to aim for as their timing becomes more accurate. Rewards and checkpoints are important parts of good games! Here’s the breakdown of the rewards in Upbeat Bird:


Yeah, I rock at this.

  • A high score from 0 to 199 = Ionian (major)
  • 200 to 599 = Mixolydian
  • 600 to 1199 = Lydian
  • 1200 to 1999 = Dorian
  • 2000 to 2999 = Aeolian
  • 3000 to 4199 = Phrygian
  • 4200 to 5599 = Locrian

So what happens when the player exceeds 5599? This opened up another opportunity. After the player has earned every mode, why not let them pick the mode their next game is in? So, at 5,600 points the player gets to have a say in what they’re hearing! Or if the player doesn’t care, the can just pick random.

Programming mode selection

Many people understand modes as scales and stop there. But it’s both simpler and much more complicated at the same time. In short, all I had to do was transpose the base line without changing the bird sounds. Change the lowest note in a song, and you change the mode. And just like that, we magically have seven times the music which develops slowly over time! In reality, it’s much more complicated than that, but you get the idea.

Just like a good piece of music, Upbeat Bird always has something new to offer the listener.

Improvisation in Upbeat Bird – Musical Gaming

June 13th, 2014

Click here to learn a little about how pitches in Upbeat Bird are selected. In short, the game uses an improvisation algorithm through limited random selections. The limits for the bass are determined using the notes that came before and after. The limitations for the bird sounds are generated using the direction of the bass line.


This perfect upbeat probably yielded a leap (pun intended).

What is most compelling about the music is that the bird sounds are completely based on user input. A sound occurs whenever the player taps to jump. Then the pitch is based on a combination of what the bass is about to do, and on when the player jumps. If the player succeeds in performing a perfect upbeat, the bird’s melodic line leaps. The line will also leap if it has to change direction due to range limitation. Otherwise the melodic motion goes only by step.

So then, rapid tapping will usually result in stepwise motion. Since rapid stepwise motion is more desirable to listen to than rapid leaps, the result is good melodic content during dense clusters of notes. Accurate upbeats, on the other hand, yield leaps. Since this requires slower rhythm, it makes sense that these notes would be where leaps occur. This keeps the line interesting during sparse passages of improvisation.

Small Steps Toward Good Improvisation

These rules have exciting possibilities both inside and outside of Upbeat Bird. It yields a form of guided improvisation. While eliminating pitch selection, it gives total control of rhythm to the player. This will lead to other games and tools to guide people efficiently towards logical improvisation.

Ear Training Game – It's Really That Easy

June 11th, 2014

Why the Ear Train-A-Tizer Is My Favorite Ear Training Game.

The problem with ear training games is that they’re just not gamey enough. Throughout my first two years or so at Cornerstone, I enjoyed using an ear training game for my basic musical development. But it just seemed too academic. More like homework and less like the game it seemed like it was trying to be. It also wasn’t free…


My favorite ear training game to date.

Music Interactive’s first attempt at making an ear training game was the Ear Train-A-Tizer. I like it because it gets straight to the point of what an ear training game should be. It has a score, levels, time limits, and teaches the user how select the correct answers. It gets progressively harder and even has bonus levels! But It lacks graphics and hand to eye coordination. It’s fun, but it could be more fun. It needs lasers and jumping. Something sweet.

But for now, it’s what we’ve got and it’s great! Here at Music Interactive our goal is to make your musical abilities develop as quickly and effortlessly as possible. The Ear Train-A-Tizer is a great way to help you learn how to identify sounds. To the best of my knowledge, it’s the best ear training game out there to date. It’s currently only browser based and works best in Google Chrome…But it’s also free!

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