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.

Trigonometry – the Flame of the Rudiment Rock-it

June 25th, 2014

trigonometry needed

This week I have been thankful that I paid attention and did well in my high school trigonometry class. Sine, Cosine, and Tangent really came in handy when the flames of my rocket in Rudiment Rock-it wanted to do detach themselves and do their own thing.

A Trigonometry Story Problem

It had been a very long time since I used trigonometry for anything. This problem presented itself whilst I was innocently developing a game for drummers who are looking for a fun way to learn some of their basic rudiments. In the game, the player taps each side of their mobile device in the pattern specified. The goal is to perform the pattern correctly and evenly as quickly as possible. If its not even, the rocket will tip and the flames on the side of the inaccurate hand will get smaller. Or if the player is going too slowly the flames will go out altogether and the rocket will not go higher. This gives the player feedback on what they need to fix in order to do better. The problem happened when the rocket rotated and the flames would not come with it.

The flames needed to be programmed separately from the rocket. They needed to act independently of each other to give correct and good looking feedback. Yes, I could have asked my animator to graciously draw 50 versions of a rocket with flames. But that would have been a waste of memory (mobile app) and not an efficient use of his time either. The better solution was to tie the separate flames to the rocket and get better results with less strain on the device. I hesitated when I realized that the answer to tying a rotating image to a part of another rotating image required some very difficult trigonometry. “I know some people who could do this faster,” I thought. But no, I wanted the challenge all to myself.

The Solution

superhuman-trigonometryIf you’re not into actually doing trigonometry with me, now would be the time to check out and go play Rudiment Rock-it. Have fun, we’ll join you in a minute!

The rotation of the flame was easy: flame.rotation = rocket.rotation. If the rocket always stood up straight, the rest would be easy too:

flame.x = rocket.x and flame.y = rocket.y

Oh, but the flame changes length so we need to make an adjustment: flame.y = rocket.y – (flame.length/2)

This ties the top of the flame instead of the middle. But now we need to actually tie the flame to the engine of the rocket (we’ll just do the left one for now):

flame.y = (rocket.y – 26) – (flame.height/2)

flame.x = rocket.x – 7

But what about when the rocket tips? The flame will detach and look silly. And that’s where the trigonometry comes in. First we need to figure out how far away the flame is (the hypotenuse) because this number will not change. x and y will be changing every frame! So x and y need to be based upon the total distance:

7^2 + 26^2 = 26.93

So now we can use a combination of the hypotenuse and the angle of the rocket’s rotation to determine either x or y first. I think it’s easier to think horizontally, so we’ll do x first. We want “flame.x” to equal “-7” when the rocket is straight since the flame should be directly left of the rocket (we’re ignoring y for now). We have to use cosine because x will the adjacent side once the rocket rotates. So since “cos(-90) = 0” and “cosine = adjacent/hypotenuse” we can do this (assuming that flame.x is -7 and rotation is 0):

flame.x/26.93 + 7 = cos(rocket.rotation-90)

flame.x = (cos(rocket.rotation-90) * 26.93) – 7

But we also need flame.x to be “+7” when the rocket is up-side-down. To fix that we need to modify that “-7” in our equation by finding a way to switch it to a positive number when the angle is 180 degrees.  I found this easier to do while thinking of the rotation in 90 degree increments:

flame.x = (cos(rocket.rotation-90) *26.93) + (cos(rocket.rotation)*7)

This way, when the rotation is at 180 degrees, the 7 becomes positive and it’s still negative when the rocket is right-side-up! But now when it on its sides, x should be +/-26 and not the length of the hypotenuse like it is right now. But I really don’t care because it’s not even a whole pixel of difference. Moving on!

We have one more major problem to solve: we still have to compensate for the changing height of the flame. So we modify our hypotenuse because that is the flame’s distance from the rocket. Currently, the middle of the flame is touching the engine. To change that to be the end of the flame, all we do it add half of the length of the flame to the distance from the center of the rocket.

flame.x = ((cos( rocket.rotation -90)*(26.93+( flame.height /2))) – (cos( rocket.rotation )*7))

And of course we should probably add in rocket.x

flame.x = ((cos( rocket.rotation -90)*(26.93+( flame.height /2))) – (cos( rocket.rotation )*7)) + rocket.x

Now for flame.y. Just use sine instead of cosine to find the other axis. Simple as that:

flame.y = ((sin( rocket.rotation -90)*(26.93+( flame.height /2))) – (sin(rocket.rotation)*7)) + rocket.y

Now for the right engine. Just add instead of subtract:trigonometry-flame

flame.x = ((cos( rocket.rotation -90)*(26.93+( flame.height /2))) + (cos( rocket.rotation )*7)) + rocket.x

flame.y = ((sin( rocket.rotation -90)*(26.93+( flame.height /2))) + (sin(rocket.rotation)*7)) + rocket.y

Simple trigonometry, right?

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.

Distracted Culture – Entertainment Technology

June 7th, 2014

Distracted by the Eastern shore of lake Michigan

I have recently had the extraordinary opportunity to soar at 500 miles per hour 6 miles off of the ground. Not having flown since I was 14, I was in awe of the engineering capabilities that mankind has achieved. Then I realized that we had this capability long before I was even born! So…why aren’t we flying 60 miles off the ground at 5,000 miles per hour? I’m not complaining, it just seems like we haven’t come very far in the development of our mechanical  capabilities. At least compared to what we did throughout and after the industrial revolution. Then I remembered that our planes are now equipped with wifi, movies, and games. The airlines even allow people to use their smart-phones and laptops. This entertainment technology is far more advanced than the computers that helped us get to the moon.

Computers are fantastic! Infinite knowledge and entertainment at our fingertips. But that’s just it. We’ve developed entertainment technology. In the meantime, other aspects of technological growth have been stunted. We created something capable of incapacitating us with distraction.

Everyone’s a Distracted Entertainer

This is directly related to our current surplus of artists and athletes. Entertainers are the idols of our culture. To many parents there is nothing better than vicariously performing a solo or scoring the winning goal through their child. This carries over into the college years. Becoming a top notch entertainer has become something for which we are willing to spend thousands of dollars. More importantly, we are willing to spend years of our lives training for the endeavor of incapacitating others with our prepared distractions.

As you can see from the rest of this site, I love the arts. But when more people know the name Lorde (I love her work), than Raymond Damadian, Seymour Cray, or Steve Wozniak, there’s a problem. Even Bill Nye is not known for his work for Boeing, but  rather his entertaining style of educating children. We are a distracted culture that aspires to be entertainers rather than innovators.

Distracted into Enrichment

So where does that leave Music Interactive? The arts have value in that (besides beauty) it sharpens the mind and stimulates creative thought. It makes innovators more innovative. Our goal to make music education as efficient as possible so that you can get back to your work refreshed and focused more quickly and without being distracted. We have enough entertainers. Use the arts for inspiration and quickly develop your musical ability for the purpose of enriching your calling.

We’re still very small, but right now we are featuring a game called Upbeat Bird. It is a game designed to deepen your understanding of time and how to accurately dwell in and manipulate it. It is an entertaining way to develop a useful skill both musically and within the world around you.

Manipulate Time – Develop Musical Superpowers!

June 3rd, 2014

Sound happens within time. So making music means you have to manipulate time. It’s not good enough to have your notes happen at any moment that’s convenient. They have to happen exactly when you intend them to. This is a skill that you have to develop. Commanding time to the extent that it is relevant to music is extremely difficult. It may as well be a superpower!

We’re not talking about just staying together. We’re not even talking about changing from an A to a B on the 3rd 16th note of beat 4. We need to manipulate time to the extent that we can make a noise one hundredth of a second before or after another event. This is beyond the capabilities of normal human reaction time. It requires such a deep understanding and mastery over time that you can use the duration of an event the just happened to predict when another event is going to happen. Then you can place your own sound one hundredth of a second sooner to account for the time it took for the other sound to get to you.


Learn to manipulate time using Upbeat Bird.

We recently released a game that produces in a person the ability to manipulate time to the 20th of a second or less. Upbeat bird doesn’t just develop the skill of accurately playing upbeats. It teaches you how to hit every part of the beat and deeply understand what a part of a second is. You can make the bird soar to the top, gradually drift to the bottom, or float indefinitely in the same spot on the screen by tapping at the correct time. A bass line produces downbeats that the player has to use as a reference. The further away in time from a bass hit, the higher the bird jumps. In this game, we have connected an entertaining visual gaming element with aural cognition to enable people to quickly master and manipulate time.

A skill that is useful to everyone.

Don’t think for a second that this skill is reserved for musicians and is only useful in the performing arts. This is a skill that helps a person master their physical world and perform any job better. If it has anything to do with doing the right thing at the right time, Upbeat Bird will help you to do it better.

I work at a coffee shop where I sometimes have to produce one drink every 30 seconds to a minute (usually with assistance from other amazing workers). Timing is key, and understanding the intricacy of time and manipulating time helps me both work faster by myself and more efficiently with other people.

Learning to manipulate time will make you more productive in many aspects of your life. And now you can learn to do it using a fun game on your phone!

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