See
User Interface
for more about the
other selectors above. To learn more about the etude patterns, see
Patterns.
If you're new to your
instrument or to ear training, see
For
Beginners.
Browser Compatibility
This app doesn't work correctly on the Brave Browser for reasons
I've not yet determined. I use it mostly with Chrome on Android and Mac
OS and test it occasionally with Safari and Firefox. So far no problems
with any of those.
For the curious
Infinite Etudes generates ear/finger training exercises for
instrumentalists. The emphasis is on improving your ability to play what
you hear by thoroughly exploring combinations of 2, 3 and 4 pitches over
the full range of your instrument.
Infinite Etudes doesn't try to teach music theory, melodic
structure or how to read and write notation and it's not necessary to
know these things to use the program, though it certainly doesn't hurt.
The exercises follow a simple form: a sequence of different
notes is played on beats 1, 2, and 3 and a rest on beat 4. By default,
each bar is played four times before moving on -- so you have 3 chances
to play the sequence after the first hearing. You can control the number
of repeats. You can also choose to silence one or more of the repeated
measures.
The program is called 'Infinite Etudes' because the number of
possible orderings of the sequences is so large that you'll never play
the same exercise twice. That's an important part of the design. It prevents
you from relying on the muscle memory that develops if you play the same
etude repeatedly.
Here are brief descriptions of the patterns currently supported by
Infinite Etudes accompanied by notated examples. For brevity, the score
examples shown here are captured with a repeat count of zero.
All of the score examples were created by importing MIDI files downloaded
from Infinite Etudes into MuseScore.
One Interval
One Interval presents 12 instances of the same
interval pair, i.e. 3 notes, in random order. Each instance begins on a
different pitch so that all 12 pitches are covered.
One Interval Example
Tonic Intervals
Tonic Intervals presents 13 different intervals,
i.e., all possible pitches relative to the chosen tonic pitch. Use this
pattern as a self-test to gauge your progress at distinguishing the
between the intervals.
Tonic Intervals Example
Two Intervals
Two Intervals is, as you might expect, a series
of three pitches specified by the interval1 and interval2 selectors. The
score example shows a typical etude produced by choosing 4 half steps (a
major third) for the lower interval and 3 half steps (a minor third) for
the upper interval, i.e. a a major triad in root position. It's useful
to be able to recognize and play the notes of any interval pattern in any
order. For 3 notes, there are 6 possible orderings. The program
arranges for each ordering to occur twice among the 12 sequences
presented.
Two Interval Example
Two Intervals Up/Down offers an easier
alternative containing only notes in ascending or descending order, e.g.
either "C E G" or "G E C" but not "C G E", "E C G" etc.
Two Interval Up/Down Example
Three Intervals
Three Intervals is similar to the Two Interval
pattern but uses 3 intervals to produce 4-note sequence. There are 24
examples in etudes produced with this pattern because you can play 4
notes in 24 different orders. The example shows a typical etude
constructed with a 2-2-1 pattern of half steps, corresponding to the
first 4 notes of a major scale.
Three Interval Example
Three Intervals Up/Down offers an
easier alternative containing only notes in ascending or descending order,
e.g. either "C E G B" or "B G E C" but not "C G B E", "E C B G" etc.
Three Interval Up/Down Example
Instrument Ranges
Each instrument has an associated pitch range. Generally, the range
goes from with the lowest note playable on the instrument up to the highest.
Infinite Etudes starts the first pattern example in an etude on a random
pitch within the range and then moves to the each subsequent pattern in a
random walk that keeps the first note of the pattern within a fifth of the
prior one.
The program tries to keep all the patterns completely within the
instrument's range but it can fail if you specify a large pattern for an
instrument with a small range. In that case, the lowest notes of each
pattern are guaranteed to be placed within the instrument's lowest octave
but the higher notes may exceed the highest playable note. The image below
illustrates the situation for a 3 octave pattern on an instrument with a 3
octave range (from F3 to F6). The red note heads indicate the out-of-range
notes.
First the bad news: Playing by ear has a lot in common with
learning to a speak a language fluently: you need to learn a lot of
vocabulary (among other things). For a language the vocabulary elements
are words, for music the elements are short sequences of pitches —
and there are a lot of them.
If you include unisons and octaves in the set of intervals to be
used, there are 13*13 = 169 possible ways to put two intervals together
to form a sequence of 3 pitches. For sequences of 4 pitches, there are
13*13*13 = 2197 combinations of 3 intervals.
Now consider that
each sequence can be started on any pitch. If your instrument has a 3
octave range, you're looking at (approximately) 6000 ways to play 3 notes
and 79,000 ways to play 4. And, remember, each 3 note sequence can be
played in 6 different orders and each 4 note sequence in 24 orders.
Now the good news: while it's probably true that if you
searched all the music ever written or recorded you'd find at least one
instance of each of those combinations, it's also certainly true that
most music uses a much smaller subset most of the time. In fact, getting
fluent on the 12 intervals plus 18 interval pairs (3 notes) and 35 sets
of three intervals (4 notes) will take you a very long way. It's still a
lot of work but you can get there if you're willing to devote five to ten
minutes of your practice time every day.
Your first goal should be to master recognising and playing single
intervals at a brisk tempo over the full range of your instrument. The
One Interval and Tonic Intervals patterns are your friends. Use the
former to get solid on each of the 12 intervals and the latter to relate
all the intervals to specific pitches.
Two Intervals (3 notes)
The next step is patterns of three notes created with the Two
Intervals pattern. Here's a list of 18 common patterns that cover scale
fragments and simple chords. Important: The patterns in
the list below are in half-steps, e.g. "4-3" rather than "Major Third,
Minor Third" to indicate a root position major triad.
Scalar Diatonic and Pentatonic: 1-2, 2-1, 2-2, 2-3, 3-2
Scalar Chromatic: 1-1, 1-3, 3-1
Root Position Triads: 4-3, 3-4, 3-3, 4-4
First Inversion Triads: 3-5, 4-5, 3-6
Second Inversion Triads: 5-4, 5-3, 6-3
Three Intervals (4 notes)
Once the three note patterns start to feel easy, start working on
the following four-note combinations with the Three Intervals pattern.
These 35 patterns cover all the common scale fragments and chords,
including dominant, minor, diminished and augmented 7ths.
If you're just starting out with your instrument, please make
sure you've had at least some basic instruction in how to hold your
instrument comfortably with good posture and hand position and how to
play individual notes cleanly over the full range of your instrument.
The only real prerequisite is being able hear when a note you play
on your instrument matches the one being played by Infinite Etudes.
If your instrument is tunable, make sure it's correctly tuned to
standard pitch (A4=440). You'll also want to adjust the play volume to a level
that's about the same volume as your instrument. If you play Bass or any other
low-pitched instrument make sure to use good speakers or a headset for the output
from your computer or mobile device.
If you're not sure about your readiness, test yourself with the
with the simplest pattern and interval (One Interval, Unison) at the
slowest tempo (60 BPM) with 3 repeats. Each measure will contain a single
pitch and the entire measure will repeat 3 times after the first hearing.
At 60 BPM, you'll have 16 seconds to locate and play the right pitch
before the etude moves on to a new pitch. If you're not finding the pitch
at least half the time, you may want to wait until you've become more
familiar with your instrument.
Using Infinite Etudes for five minutes every day will serve you
better than an hour once a week. Your brain and neuromuscular system
consolidate learning during sleep and, truthfully, the amount of new
information we can absorb each day is limited. So be patient, please.
Start with the One Interval pattern working from the smallest intervals
(Minor2, Major2) up to the largest (Octave). Test yourself regularly with
the Tonic Intervals pattern and a random Tonal Center. Try to wait until
you're getting most of the intervals right on the first repeat before moving
to the Two Intervals pattern.
I conceived Infinite Etudes as an aid for instrumentalists. I've since
found it's also quite useful as a daily vocal workout for intonation. The
instrument selection menu has choir ahh sounds for soprano, alto, tenor and bass ranges.
The Pattern selector allows you to choose one of the patterns
described above. Your choice affects the visibility of the interval and
tonal center selectors. The interval selectors, (Interval1, Interval2 and
Interval3), appear according to the number intervals in the chosen
pattern. The interval choices are labeled by the number of semitones
(half steps) and the corresponding musical name, e.g. "4 (Minor Third)".
The Tonal Center selector appears only when the Tonic Intervals pattern
is selected.
Instrument
The Instrument selector provides a choice of common instrument sounds. Your choice also
determines the range of pitches that can occur within an etude.
Each etude starts on a randomly selected pitch somewhere between
the lowest and highest notes that can commonly be played on your chosen
instrument. The sequence orderings are a random walk constructed to that
the first pitch of each sequence is "close" to the preceding pitch
without wandering outside the playable range of your instrument.
Metronome
By default the metronome is off after an initial 1 measure count-in. You can change this behavior with the
Metronome selector. Choose "downbeat" to have it click only on beat 1 of each measure.
Choose "on" to have it click on every beat.
Tempo
Infinite Etudes generates MIDI files in 4/4 time with the tempo
defaulted to 80 beats per minute. If you need it slower or faster, use
the Tempo selector to choose a value between 40 and 480 beats per
minute.
Repeats
Use the Repeats selector to change the number of repeats for each sequence. The default is
3. You can set it to 2 or 1 to increase the challenge. You can also set it to 0, but that's
not useful unless you want to download an example to import into a score editor.
Muting
The Muting selector allows you silence one or more of the repeated
measures. The cross mark symbol, ✗, indicates a silent measure and
the check mark, ✓, indicates an audible one.
Play, Stop, Download
The Play button tells the server to generate and start playing a
new etude using the settings you've chosen in the the selectors. The Stop
button stops the playback before the end of the etude. The Download
button generates a new etude and allows you to save it as a MIDI file.
If you need something beyond the available tempi and instrument sounds, the easiest solution
is to use the download button to save a local copy of a file and play it with
a program that allows you finer control of the playback. I recommend QMidi for Mac. I don't
know what's good on PC but a little Googling should turn up something appropriate. Downloading
also allows you to play the files through better equipment for more realistic sound.
You might also consider installing MuseScore, the excellent open
source notation editor. Version 3.1 and higher does a very good job
importing Infinite Etudes midi files. Besides controlling tempo, you can
print the etude as sheet music or play it back with real-time
highlighting of each note as it's played.
A third option, if you have software skills, is to install
Infinite Etudes on your computer from the source code on GitHub. and
adapt the program to your needs.
As you progress, some patterns will become easy to recognize and
play before others. When you're nailing a particular pattern correctly and
confidently on first hearing (hooray!), you can either increase the tempo, decrease the
number of repeats, or leave the repeats at 3 and put the remaining two bars
to good use in a variety of ways. Here are a few suggestions, some simple
and some difficult:
Finger it differently.
Change the bowing or picking.
Play it with the other hand (keyboards).
Play it in the same octave on different strings (string instruments).
Play one note up or down an octave.
Play the whole sequence up or down an octave.
Play it in both hands one or more octaves apart.
Play it up or down a fifth (or fourth, third, ...).
Play it as a chord.
Find a bass note or chord that works with the sequence.
Mess with the rhythm, accents, dynamics, timbre, ...
Shred it in sixteenth note cross-rhythm, e.g. 1231 2312 3123
Fill in between the notes.
Invent a counter-melody,
or simply take a deep breath and relax your fingers.
A few good books that influenced the development of Infinite Etudes:
Brown, Peter C. Make It Stick : the Science of Successful
Learning. Cambridge, Massachusetts :The Belknap Press of Harvard University
Press, 2014.
An exceedingly readable and practical summary of what works and doesn't
work for efficient learning. I've attempted to incorporate the core
principles (frequent low stakes testing, interleaving and spaced
repetition) into the design of Infinite Etudes.
Huron, David. Sweet Anticipation: Music and the Psychology of
Expectation. Cambridge, Massachusetts : The MIT Press, 2006
The book's central theme is a theory that a large part of what makes
music enjoyable is a combination of satisfaction from predicting what
comes next and delight when our predictions are occasionally confounded
in interesting ways. Regarding the development of Infinite Etudes,
Chapter 4 "Auditory Learning" and Chapter 10 "Tonality" were quite
useful.
Jazz pianist Kenny Werner's autobiographical take on his own road to
mastery through mindfulness. The title refers the sensation of
effortlessness that accompanies mastery rather than to some magical
method of learning without practicing. I took from it a sense of the
value of patience in allowing musicianship to develop.
Wooten, Victor L. The Music Lesson : a Spiritual Search for
Growth Through Music. New York, New York : The Berkley Publishing
Group, 2008.
Pearls of musical wisdom are threaded throughout Grammy Award winning
bassist Victor Wooten's fanciful tale of adventures with music teachers
who show up unannounced at his home (think Carlos Castaneda without the
hallucinogens.) Read it as a counterpoint to the emphasis on notes
embodied in Infinite Etudes. Good music making is also about
articulation, technique, emotion, dynamics, tempo, tone, phrasing and
space, or as one of Wooten's teachers puts it: "Never lose the groove
in order to find a note!"
I wrote Infinite Etudes for two reasons: First, as a tool for my
own practice on piano, guitar and viola; second as a small project to develop a
complete application in the Go programming language. I'm happy with it on
both counts and I hope you find it useful also. The source code is available
on GitHub.
