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What is The Intonation Tutor?

    The Intonation Tutor is a two-part set consisting of an audio compact disc and a printed manual.  The CD contains audio files that can be played on any common CD player.  These files correspond to the printed music in the manual and, when combined, form the basis of the intonation ear-training exercises of The Intonation Tutor.

    The manual contains instructions in the use of the tutorial, background information about musical sound and intonation, and printed music for use with the CD.

Jump to:

The audio CD: The printed Manual  How to Use

Hearing the Beats: The Essence of the Tutorial

By-products

The audio CD:

    The Intonation Tutor CD consists of sixty (60) tracks of audio.  The audio was recorded by using the combination of computer-controlled MIDI (Musical Instrument Digital Interface) files and a tunable MIDI tone generator.  This enables The Intonation Tutor to present just, pure intervals that emulate the sounds that instrumental and vocal musicians strive to produce in their ensemble performances.  The MIDI voice chosen for the audio files is rich in harmonic content and straight in tone (NO vibrato or wavering of pitch), making it quite suitable for the purposes of the tutorial.

CD Tracks 1 through 8:

    Tracks one through eight of the sixty tracks play tuning (reference) notes and examples of the equal-tempered and just-tuned intervals.   The tracks are as follows:

  1. Bb (tuning note), 

  2. A (tuning note),

  3. Equal-tempered and just major 3rd,

  4. Equal-tempered and just major 6th,

  5. Equal-temepered and just minor 6th,

  6. Equal-temepered and just minor 3rd,

  7. Equal-temepered and just perfect 4th, and

  8. Equal-temepered and just perfect 5th.

    These interval examples not only point out the differences between intervals in the equal-tempered and just-tuned schemes, but also lay the groundwork for training the ear to hear differences in just and non-just intervals.

    The remainder of the CD holds the interval studies in the form of scales, duets, trios, and quartets.

CD Tracks 9 through 20:

    Tracks 9 through 20 play the major scales.  These scales are the only CD play-along tracks recorded in equal temperament and are used to assist the player in recognizing differences in the CD pitches and the pitches performed on the instrument or by the voice. 

    In addition to practicing the major scales and establishing good pitch relationships, these scale tracks can be used to practice intervals above and below the recorded scales.  For example, one can practice tuning perfect fourths by listening to the C-major scale track (CD track 9) while playing an F-major scale above it.  This will produce the interval of the perfect 4th above each note of the scale played from the CD.  One can practice other intervals in a similar manner.

CD Tracks 21 through 40:

    Tracks 21 through 40 contain the duet interval studies.   These studies are recorded in movable-comma just intonation and make it possible for the player to adjustment along with the audio on the CD. In other words, part of the adjustment necessary to make pure intervals has been recorded on the CD, leaving the remainder of the adjustment up to the user. The result is similar to what is experienced when working with other players.

    Each audio track contains one of the duet lines and the player has opportunities to play each line with the accompanying CD audio sounding the other line. There are a total of ten duet interval studies and twenty duet CD audio tracks.

CD Tracks 41 through 52:

   CD tracks 41 through 52 contain the trio interval studies.  Again, the audio is recorded in movable-comma just intonation and all the parts compromise in pitch adjustment.   There are four trios that make up the twelve trio audio tracks so the player has opportunities to play all of the trio lines with the CD.

CD Tracks 53 through 60:

   The final group of CD tracks, numbers 53 through 60, are the quartet interval studies.  These quartet studies are taken from Nicolai's harmonization of Wachet auf, ruft uns die stimme, and follow the format of the preceding CD groups. 

    As one progresses through the interval studies and ear-training exercises new challenges are presented, with the most challenging being in the quartets.  The duets and trios are purely interval studies, however, the quartet tracks are taken from actual music.

    Taken as a whole, these studies help players improve intonation perception and shorten intonation reaction and adjustment time.

By-products:

   In addition to the stated goal of improved intonation perception and adjustment, playing with the CD audio also requires the performer to produce unwavering notes with a good sound.   This is achieved by using good air movement (support) and a solid embouchure.  If one allows the airflow to diminish or increase any point of a note, the pitch and sound changes are immediately noticeable against the CD's consistency of tone production.  This will aid the player in all performing circumstances, and result in better tone quality and uniform tone production. 

The printed Manual:

    The Intonation Tutor manual opens with an introduction that explains why the tutorial was developed, what is included in the manual, and how to use the tutorial.  The manual is in two parts:

    • How to Use The Intonation Tutor

       In order to use The Intonation Tutor one must only have a conventional CD player on which to play the CD.  The tutorial can be used with either loud speakers or headphones.  It is necessary to adjust the output volume of the CD player to balance the volume of the instrument or voice.  When the balance is correct, the beats on a mis-tuned interval will be heard and indicate a need for adjustment of pitch.

    Hearing the Beats:

    The Essence of the Tutorial

        The manifestation of mis-tuned intervals is exhibited by pulses or beats that can be heard along with the pitches of the intervals.  These beats are the result of the out-of-phase sound waves that travel through the air to our ears. 

        An excerpt from the Manual might help make this clear:

        Musical sounds are complex and consist of the fundamental (the note being played) and overtones.1  Collectively, the fundamental and its overtones are known as the harmonic series.  Because the sounds of human voices also include parts of the harmonic series, other sounds that are similarly constructed are generally interpreted in the human auditory system as being relatively harmonious or consonant.2

       For clarity in this tutorial the overtones will be referred to as partials and the fundamental will be considered to be the first partial.  The partials of the BB-flat fundamental through the twelfth partial3 are as follows: 4   

                              Figure 2. The Harmonic Series: partials 1 through 12.

        When two players are performing an interval, a unison for example,both notes of the interval sound their individual partials that combine to make the whole sound of the interval.  Unisons, with the ratio of 1:1, have common or coincident partials throughout the harmonic series of the notes.  It could be stated that the unison is an interval with the ratios of 1:1, 2:2, 3:3, 4:4, and so forth, and the upper partial ratios can all be reduced mathematically to 1:1.

                                                  Figure 3. The Unison.

    Notes:

    1. David Doty, The Just Intonation Primer (San Francisco: The Just Intonation Network, 1994) 13-14.

    2. Doty, 15.

    3. The musical depictions of the harmonic series include whole notes that symbolize fundamentals and stemless quarter notes that symbolize the overtones.

    4. “Acoustics IV. Harmonics.” Harvard Dictionary of Music. 1966.

       In addition to the influences of the fundamental notes of an interval, the overtones, or partials also come into play on the intonation of the interval.

        The notes of any interval will have common, or coincident partials.  If the fundamental notes of the interval do not interact, the coincident partials will, and it will be possible to hear beats at the point(s) of the coincident partials. Elimination of the beats will bring the interval in tune.  This is possible only by adjusting the notes of the interval so the coincident partials match in pitch and become harmonious.  An in-tune interval will have no beats present over the sound of the notes of the interval.

        For more information about the elimination of beats in intervals and the principles used in this tutorial go to the

    Tutorial Examples page:

     

    The Intonation Tutor

       

                

                                  

                         

    Part I: Musical Intonation and the Principles Employed in this Tutorial begins with a discussion of musical intonation and includes information about how to use the tutorial.  Chapters in Part I include:

    Musical Sound and Intonation

    Musical Temperament

    The Intonation Exercises

        Tuning the Instrument to the Pitch Sources

         Some words about Electronic Tuning Devices

         Hearing the Beats

         Practicing Beat Perception and Note Adjustment

         The Major Scales

         Duets

         Trios

         Quartets

         Compact Disc Tracks

         Beyond Playing with the CD
    Part II: Printed Music for Use with the Compact Disc consists of the music to be played with the CD.  In the trombone-tessitura version, all music is printed in bass clef with options for reading tenor clef in the quartets.  In addition the entire printed music set is repeated in Bb treble clef.