— 2013 — Jun 23

Random Roots

by Anton Schwartz

NEWS: I have created a practice-aid app for iPhone/iPad that implements all the concepts in this post! To learn more and try it for free, visit randomroots.app

As jazz musicians, we all know how important it is to practice things in every key. It is, indeed, useful to play passages written out in every key. But it is of far greater benefit to internalize a passage and practice executing it in all twelve keys without reading.

Here’s a tool to help you do that. A printed sheet. I’ll go into details below, but the concept is very simple: take an idea (a scale, a chord voicing, etc.) and go across the rows of the sheet playing the idea in each key you see.

The pdf file (click to view):

Click to Download

And separate versions for B and E instruments:

Bb VersionEb Version

Why do we need this? Why not go through every key chromatically, or through the circle of fifths?

There are four simple ways to go through every key: chromatically upward, chromatically downward, up fourths (down fifths), and down fourths (up fifths).

If what you’re practicing is an entire song or a long passage, then any of these ways is fine; you can ignore this post.

But for practicing shorter things—which is especially important for beginning and intermediate players—there’s an interesting predicament: when you move through the keys either chromatically or in the circle of fifths it’s difficult not to “game the system,” and that interferes with learning the task at hand. Let me explain:

Suppose your aim is to learn a piano voicing in all twelve keys. If you move chromatically upward then each note of a chord you play is simply a half step above the corresponding note of the previous chord. This allows each finger to simply “crawl up” the keyboard from one chord to the next, to the next. Each previous chord provides a huge hint for the next, and all those hints hamper learning. The same is true for chromatically downward.

Likewise, moving through the keys according to the circle of fifths has its own problems. Here the process of moving from one chord to the next is artificially simplified by the fact that the black-key/white-key patterns that the chord voicings make change very slowly as you move in fourths or fifths: often they are identical from one chord to the next; when they differ, rarely is it by more than one note. It becomes possible to keep your hands in more or less the same position and just move your arms back and forth from one chord to the next, with occasional adjustments. This shortcut is harmful, because it is not available when you’re actually playing a song.

If your aim is, say, to learn scale degrees in the different keys (see below), then the situation is even worse. Consider the task of playing the major sixth in each key. If the keys you test yourself on are moving chromatically, then the exercise requires only starting on the right note and playing the chromatic scale. Apart from that first note, it requires no knowledge at all of major sixths! Likewise, if the roots move in fifths then the exercise requires only playing the circle of fifths.

These random root sheets eliminate all of the above problems. If there is no rhyme or reason to the sequence of roots, then there will be no rhyme or reason to the sequence of answers, which is just what we want. We’ll have to construct each answer afresh, without “cheating” based on our previous answer.

Why do I need a separate version pitched in B or E?
Why can’t everyone use the original version?

You’re right—any of the sheets could work just fine for any instrument!
I’ve included the transposed parts so that players with transposing instruments (B trumpet, E alto sax, etc.) can play exercises together in unison.
Playing with others can be good for motivation… and it also provides a self-check feature that you don’t get when you play alone: If you play an exercise with others then you should all be playing the same things in unison. If you hear anything else, then you know one of you has made a mistake.

Should I start at the top and go through all the roots until I get to the bottom?

I suggest a row at a time, doing however many rows you feel you need. You can start at any row. In theory, if you practiced just the first row over and over you might memorize it. In practice, that’s not likely to happen for a long time, but by mixing up the rows you get to practice the roots in different sequences, with different intervalic jumps, which is good for the ears and a good way to make sure you know all the answers “from every angle.”

What’s with the stripes and stuff?

The rows alternate shades to make it easier to track which row you’re on.
Likewise, each row of 12 is separated into three groups of four to make it easier to keep your place.

Why does the sheet have D and G, never C and F?

We have to write B, E and A anyhow, so we write all accidentals as flats for the sake of consistency. If D and G are unfamiliar to you, I’m sorry. Or perhaps “you’re welcome” since maybe it’s time you became familiar with them! :)

Are these root sequences really random?

Actually they are not. A sheet of randomly chosen roots would contain lots of repeated roots (who needs to see one A chord immediately following another?!), and some roots would occur more frequently than others. These sheets are special in the following regards:

  • Every row contains each of the 12 roots exactly once.
  • Each row begins a half-step higher than the previous row.
  • The last note in a row is never the same as the first note of the next.
  • The intervalic leaps between notes are equally distributed.
    (A note is followed by a note a major third higher just as often as it is followed by a note a minor seventh higher, etc.)

Ok, so what should I practice using this sheet?

So glad you asked! Here are some suggestions…

Exercises using Random Roots
for All Instruments

Learning Scale Degrees

Learn to be able to play, in tempo, any scale degree relative to any key.
For instance, be able to play the answers to: “What is the major third of E?… the major second of A?… the minor sixth of B?”
The random root sheet will supply all the keys, so quiz yourself on one scale degree at a time, using the sheet.
Here is what you do:

  • Decide on a scale degree. Say, the major third.
  • If you’re not sure that you know all your major thirds, check yourself on the top row, playing major third of each key. E, A, B, F, etc. Learn any ones you find that you don’t know.
  • Set a metronome to a slow tempo, perhaps 60.
  • Start at the beginning of the top row.
  • Play the major third of each successive root, switching roots every half note. E, A, B, F, etc…
  • At the end of each row, go straight to the next row without pausing.
  • If you’re able to do it easily with no mistakes, increase the tempo.
  • If you’re making mistakes, decrease the tempo.

Here’s a good sequence for testing yourself:

  • root (ok, this one should be easy—just play the note you see written!)
  • major third
  • perfect fifth
  • minor third
  • minor seventh
  • major second
  • major sixth
  • perfect fourth
  • tritone (diminished fifth)
  • minor second
  • major seventh
  • minor sixth

Variations on Scale Degrees

  • if you’re not in a place where you can play, speak the answer to each question instead. Or imagine fingering the note.
  • play two notes over each root: first the root itself, then the target scale degree. You may find it easier this way! It also gives you the opportunity to check your answer by listening for the correct interval; if you’re quizzing yourself on major thirds and you play root-minor third, then you ought to be able to hear the minorness of the sound you play and know that you’ve made a mistake.

Arpeggiation & Scales

  • Arpeggiate a chord upward from the root. Start with major triads. Then minor, diminished, augmented triads. Then seventh chords of all sorts…
  • Arpeggiate a chord downward from the root.
  • Arpeggiate an inverted chord, starting on a non-root chord tone.
  • Play a given scale starting on each successive root. Go through this for all the modes of the major & melodic minor scales, plus diminished, whole tone, bebop, major & minor pentatonic, blues scale…


Choose a phrase you wish to integrate into your improvisation vocabulary and practice it in each key using the same techniques described above.
It could be a simple major phrase:
Simple Major Phrase

or a more complex one:
Major Phrase

or a ii-V-I phrase:
Phrase over a ii-V-I

For a ii-V-I, I suggest you play the phrase in each key that you see written rather than starting on the chord that you see written. In other words, you would play the above phrase when you see C on the sheet, not when you see D.


  • Choose a tempo, as well as the duration that will apply to every chord (two beats; one measure; two measures…)
  • The sheet specifies only the root, so you need to decide in advance the quality of each of the chords you will play. (e.g., all altered chords… or alternating major and minor chords)
  • Improvise, in time, over each successive chord. The sheet lets you practice connecting phrases across chords in an unusual/unpredictable order.

Practice sight-transposition

This is especially useful if you play sax, trumpet, clarinet, or any instrument not pitched in C… but could also be good for, say, accompanists.

  • Choose a transposition interval. Play each root you see, transposed.
    (At first blush, this seems the same as the scale degree exercise. For instance, playing each root transposed down a minor third, as a saxophone pitched in Eb must, is very similar to playing the major sixth of each root. Indeed, the resulting notes are identical. The difference is mental: In the first case, you are conceiving of the transposed note you play as the root of a chord, whereas in the second, you are imaging the written note as the root and thinking of the note you are playing as the major sixth.)
  • Choose a transposition interval and play any exercise listed above.

For Chordal Instruments

Putting the Above Exercises in Context

You can supplement any of the exercises listed above by playing the root simultaneously, pitched low on your instrument. That lets you hear the relationship between the root and the note or notes you’re practicing, and lets you use your ears to verify the accuracy of what you’re playing—especially for one-note exercises such as scale degrees.

Practicing Chords

  • Play a root position major triad in every key. Repeat the exercise for minor, diminished, augmented. Then for inversions.
  • Play a particular voicing in every key. (e.g. dominant chord as third-seventh-ninth.)
  • Play a each chord voiced in a particular range of the instrument (piano) or neck position (guitar).
  • Piano: Play root in left hand and a simple rootless voicing in right hand
  • Piano: walk a bass line with left hand; play a rootless voicing with right hand.
  • Extra points for guitarists who walk a bass line with the low strings and play chords with the upper strings.
  • Practice a sequence for each root, such as:
      • V → I
      • iimV → I
      • I → III → VI13Valt → I.

For Bassists

Walking Bass Lines

  • Choose a duration that will apply to every chord (two beats; one measure; two measures…)
  • The sheet specifies only the root, so you need to decide in advance the quality of each of the chords you will play. (e.g., all altered chords… or alternating major and minor chords)
  • Walk a bass line, in time, over each successive chord. The sheet lets you practice connecting phrases across chords in an unusual/unpredictable order.

Let me know if you have any questions. Enjoy!

NEWS: I have created a practice-aid app for iPhone/iPad that implements all the concepts in this post! To learn more and try it for free, visit randomroots.app

16 Responses

  1. Wow, thanks for this practice tool and the suggestions! I’ll start using these with myself and with my students right away.

    All the best,

  2. saxy1 says:


  3. Thiago says:

    Really nice tool, thank you so much, Anton!

  4. Serge says:

    That’s a good idea but I wouldn’t discard the cycles training, especially for the beginners/learners. In the beginning it’s important to get everything under your fingers and the easier the method is the better because there are too many things to struggle with for a student. Cycles help ear traning as well because most of the standard progressions are cycled.
    But, once you can easily move through the cycle(s) while reading a book (a signal you should move on) why not to make the task a little more challenging? Then move on to random keys! (you’ll have to put the book down)
    In other words, one needs to know WHEN he wants to make his task o learning more difficult.

    • Thanks, Serge. I agree that practicing in cycles is wonderful for certain things – especially dominant chords and phrases, where the harmonic progression is logical and great for the ears. Where cycles don’t work well at all but this sheet does is for the super basic exercises such as playing scale degrees (e.g. playing the minor 6th of every key). If you move the root in fifths then your answers will always be moving in fifths too, just starting on a different note.

  5. David BV says:

    Very helpful, thank you so much for this concept. Oh and thanks for the transcription article which is the most practical and accessible approach I’ve found. Now I just have to continue to do it and “face the dragon” of my harmonic and aurual challenges.

    • Those dragons look scary but they’re our friends. By telling us what we’re not good at they hand us the key to getting better! :) Thanks for dropping a line, David.

  6. willIam Goldwyn says:

    Wow….great stuff..thanks–I am looking for every educational tactic I can find to help me get to where I am trying to go on the sax.

  7. Daniel says:

    Hi Anton

    Can’t wait to get the Random Roots app. I keep checking the App Store daily.

    • I submitted it to Apple for approval in mid October, and they still haven’t reviewed it – frustrating! Thanks for your interest, Daniel. FYI I’ll be keeping people posted about it via twitter (@randomrootsapp) and my educational mailing list.

      • Daniel says:

        Hi Anton

        I just downloaded the RandomRoots app. Nice work. You know what would, IMO, make it even better? How about giving us the option (on the settings page) to choose the maximum interval between each randomly selected note?

      • Daniel says:

        I purchased a yearly subscription. It was easy peasy! Was I the first?

      • Glad to hear you had an easy experience with it, Daniel!
        What would be the advantage of having a maximum interval?

      • Daniel says:

        The request for a maximum interval setting has to do with one of the ways I am using your app. In addition to using the app in the ways you have suggested I am also using it for fundamental ear training.

        Specifically I am working on strengthening the automatic connection between pitch heard and pitch played on my instrument. I use your app to play a randomly selected pitch and then I try to play it automatically without think about anything besides what I am hearing. The larger the interval is between any of the randomly selected pitches the more difficulty I have in achieving the automatic response I am developing. So I would like to be able to limit the interval between successive pitches so that I can incrementally tackle larger intervals. Right now I have almost 100% accuracy with any interval up to a 4th when the pitches are being played at a rate of 1/second. I am pushing onward! My goal is 100% accuracy for intervals up to one octave at that rate or even faster.

        By using the app in its present state I can do something similar to what I want. I can simply select pitches that are within a chosen interval by using the key selection settings. The problem with this (although still very useful) is that the pitches are confined to that small set. I would instead like the app to play random pitches over an octave or two but with no interval between any two pitches greater than a user-selected maximum. This way I would be testing and developing this skill over the range of my instrument.

        This brings me to another point. I think you should develop and market this app as an ear training tool as well as a tool to get comfortable playing in all keys. IMO there is a big overlap between these two ostensibly different tools.

        I hope this is of help to you. I wish you great success with this app. It’s a simple app. But that’s it’s and your genius. As with all things it’s the clever emphasis of the fundamentals through simple tasks that most effectively accelerates and deepens learning.

  8. Daniel says:

    Hi Anton

    I noticed that the randomly selected keys aren’t confined to one octave when played. It would be very nice to have that option (Essential for my use).

  9. […] I created a sequences of exercises designed to help you make approach notes automatic, and posted them at RandomRoots.app. They’re meant to be practiced in all keys, and to do that you’ll need use some unpredictable system. (Going through keys chromatically or in the circle of fifths will be too easy to “game” and you won’t get the desired benefit.) The Random Roots app works great for that, or you can use flash cards or this pdf sheet. […]

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ScaleMate App


ScaleMate is the interactive app for visualizing scales. It shows you scales in ways that make their harmonic qualities apparent, while playing you the sounds you see. Choose from its library of scales or use it as a playground to create on your own.

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Watch the short video… or visit ScaleMate.app.


Random Roots App


Random Roots is a groundbreaking practice app I've created for players looking to deepen their musicianship and increase the efficiency and effectiveness of their practice. Guaranteed that you've never experienced anything like it.

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