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Intonation X - Calibrating the Ear II - John Goldsmith

This is the second part of John Goldsmith's Calibrating the Ear warm-ups. To understand this, you must first read Part I! The singing of chromatic and whole-tone scales will be done every day, along with the earlier exercises. The more advanced exercises can be added later if you wish.
These are great exercises which will vastly improve the ability of your choir to sing accurately and in tune--but only if you do them regularly!
Singing chromatic and whole-tone scales (the ultimate test for accurate chromatic calibration!)
By concentrating on the ear rather than the voice, you accomplish much more than simply warming up!  After the minor melody exercise have your singers ascend the chromatic scale a cappella singing "doo-doo" while you conduct quarter notes in an Andante tempo.  Ask them to sing the octave up and down first (or a 1-3-5-8-1 arpeggio), to establish the aural destination (I suggest the "D-D" or C#-C# octave - relatively comfortable for all voice parts).  
The first time they will over-shoot or under-shoot the octave after those twelve notes! Sing the octave again. Repeat the chromatic scale up in quarters. Work until they can sing an accurate chromatic scale up and down, ending on the same pitch with which they began.
Remind them to sing softly (mp dynamic).
When they can sing the chromatic scale accurately up and down at a steady tempo (all quarter notes) have them sing up with quarter-notes, down the chromatic scale in 8th notes, then back up in triplets, and down again in 16ths.  Don't change the tempo - make the singers do the subdivisions with good ensemble. It's not easy to do the chromatic scale accurately at a rapid tempo, but they will get it.
The most important skill for singers is the ability to sing and hear the difference between half-steps and whole-steps . . . which leads to the next step: the whole-tone scale. This scale has only six tones.  Sing the octave again, then repeat as above . . . up the whole tone scale in quarters, down in 8ths, up in triplets, down in 16ths.  The Whole-tone scale takes a bit longer to learn, but you will be surprised how quickly it sinks in!
Singing minor and major arpeggios:
Conclude with singing minor arpeggios up and a major arpeggio down (start around B, since it's easy for all voice ranges). Remember, you must be able to demonstrate this! Each shift up a half-step must be done without the piano.
If this becomes easy, you can work on arpeggios with all minor thirds (diminished) or major thirds (augmented).
Some Advanced Techniques:
Once your singers can sing the minor melodies shifting down by half-steps accurately, the chromatic and whole-tone scales, and minor/major arpeggios, challenge their tonal memories as follows:  Sing to them a different five-note minor melody, ask them to sing it back . . . then ask them to "audiate" the melody (i.e. hear it silently in your head), then say "OK, sing the 3rd note when I conduct it."  Might not work at first . . . try again.  Then try shifting the five-note down by a whole step, or up by a half-step.  Then "audiate in that tonality, and sing the 4th (or 2nd) note on my cue."  You can also create five-note melodies based on the whole-tone scale using these tonal memory exercises.  Even more advanced: sing a 5-note melody, have them sing it back, then - in silence - ask them to shift down a whole step plus a half-step and audiate in that tonality . . . then "sing the 3rd note when I conduct you!"  If they can do this their tonal memories are STRONG!
Again, my huge thanks to John for sharing with us!
on May 25, 2013 10:07am
Thanks for these great exercises.
on May 26, 2013 12:34pm
Keep up the good work.   And I hope in your list of future topics will be score study, so the conductor can KNOW how tuning should be approached.  In many, many works a choir can't sing in just intonation, so you (the conductor) must decide where and how to compromise.  As an embarassing example, a few years ago I listened to the Philadelphia Orchestra play Bartok's Concerto for Orchestra, tuning their major thirds nicely pure, but resulting in a mess of conflicting harmonic movement that really ruined a great equal tempered work.
on May 26, 2013 12:44pm
One more point:  there are large whole tones (as between tonic and supertonic, 104 cents) and there are small whole tones (between supertonic and mediant, 82 cents).  You sing them naturally in a tonal environment, but the kind of whole tone exercise as above results in approximations to equal temperament, contrary to much of what Richard's posts have been about.  
A just whole tone scale might be, using lwt and swt to mean large and small whole tone respectively:
C-lwt-D-swt-E-lwt-F#-big, wide, not-tuned diminished third-Ab-swt-Bb-lwt-C 
or in cents from equal temperament: C (0) D(+4) E(-14) F#(-12)--total of 126 cents-Ab(+14)Bb(-4)C
William Copper
on May 28, 2013 10:25am
Thanks William! I'll do my best to continue. There will be a break shortly for the summer, but I'll do as much as I can before that.
Tuning always depends on context. There's a passage in one of the Pizzetti Due Corali where the tenors sing the third of the chord, which then becomes the new root, and so one for several times. If one sang a pure third the choir would be flat at the end of that passage. One always has to think whether the composer was thinking in equal temperament or not. Your points are very well taken.
on May 28, 2013 2:19pm
Thanks, Richard, I for one will read your posts eagerly. 
A correction in my earlier comment: all the 'cents' measurements are off by 100 cents (the half tone), so a large whole tone is 204 cents,
a small whole tone 182 cents, the untunable diiminiished third, 226 cents.   Sorrrry.
And, parenthetically,  I think most standard choral conductors should resist barbershop sevenths as an aberration: the 31 cent lower minor (dominant) 7th has been widely publicised but is just wrong, except as a barbershop local color.   4 cents lower minor sevenths give far fewer problems in harmonic movement. 
William Copper