Approaches to Violin/Viola Pedagogy

TTSTTTS ? or 221 (2) 221 ?
Reformulating the Basics of Theory
in a String-Friendly Fashion (Part 1)

 

By Dr. Charles Heiden
July 17, 2009

From primer to college textbook, a violin student is apt to encounter the theory of music framed from a keyboard bias. This is understandable, even desirable, perhaps. On the piano keyboard, the structure of Western music is displayed in a black and white format relevant for all musicians. The keyboard approach begins from the Perfect octave [P8 – first in the overtone series] spanned in the pianist’s hand between first and fifth finger, and “filled” scale-wise by the player with the pitches of the major mode.

But students who study an instrument of the violin family need a perspective adjusted to their experience – two neighboring strings tuned at the Perfect fifth [P5 – derived from the second overtone] and “filled” by a major tetrachord that relates to the fingerboard distances between four fingers..

 

 

 

 

 

 

 

 

Playing instruments tuned in P5ths, string players can experience for themselves the fecundity of this interval. For by projecting or stacking P5ths, ALL twelve pitch classes [assuming modern equal temperament] are generated!

The following exercise demonstrates this 12-stack [starting, for violas and cellos, on open C, then joined by violins from open G. [When the ascent threatens to go “stratospheric”, the player drops down to the lowest available pitch of that class-name, as indicated below.]

 

 

 

 

 

 

 

Theory books are prone to present the major scale as TTSTTTS [T = tone, or whole step. S = semitone, or half-step].2 This pattern – 2, then 3 T’s -- corresponds to the geometry of the black keys of the piano. But for the string player, the major scale structure is better formulated 221 (2) 221 [1 = a semitone or half-step. 2 = 2 semitones or whole-step]. Thus, the major scale is a matter of playing the major tetrachord twice, with 2 semitones as the link between the units. In a heterogeneous string class, the beginner learns to mount the major tetrachord on the open D, next on the open A, and then combines the two tetrachords to make the D-major scale.3 Below and above this D-string centering, the scales mounted on G- or A-strings begin an education about key signatures and about interlocking key structure [What served as the lower tetrachord of the D-scale becomes the upper tetrachord of the G-scale. What served as the upper tetrachord of the D-scale becomes the lower tetrachord of the A-scale, etc. around the circle of 5ths].This notion of interlocking tetrachords [the relatedness of keys] – will it become, perhaps years later, the foundation for understanding modulation and key-architecture in a concerto by Mozart?

The chart above shows how sharps and flats become necessary in order to construct the major scale from a given starting pitch according to the 221 (2) 221 formula: the sharps or flats are employed so that the “landmarks-for-the- ear” [those 1’s or semitones in the formula] will occur at the end of each major tetrachord. At the beginning of each staff in our notational system, these sharps or flats needed for the desired key are listed in a zig-zag format called the “key signature”. Derived from the stack of 5ths, the two patterns [7 sharps, 7 flats] can be learned mechanically: for sharps, starting from F#, down 4, up 5 – zig-zagging in order to stay on the staff [beware at A!]; for flats, starting at Bb, it’s the opposite direction, up 4, down 5.

 

 

 

 

 

 

 

 

 

For the signatures of specific keys, apply the “rules” [they all trace back to the stack of 5ths]. The last flat in a signature is scale step 4 – count down to 1. The second-last flat is 1, the key itself. The last sharp is 7, the leading tone – count up to 8 [=1]. To write a given signature in sharps, write the proper zig-zag, stopping at the pitch just below the desired keynote. For example, the B-major signature is F# - C# - G# - D# - A#. Or, for an example in flats, consider Gb. Write the proper zig-zag until reaching the desired keynote, Gb – then go one more step [the key must be the 2nd-last flat] Thus, Bb – Eb – Ab – Db – Gb – Cb.

Minor mode, in a string-friendly presentation of theory, also can be approached in terms of P5ths on the key circle, but now the tetrachord finger-patterns that “fill” the 5ths will be minor plus Phrygian.4

 

 

 

 

 

Above, the minor scale starting from d is the relative minor of the major scale on F. Human blood relatives share common family traits. F major/d minor [“doh-ti-la” or 8-7-6 expresses the relation] share the same key signature, the same set of pitches. But d-minor starts on d not F, and in other ways behaves differently. Why this upstart individuality? To a considerable degree, it is because the two keys have different dominants. The V of F is C-E-G. The V of d is A-C#-E [yes, C-sharp! There must be a leading tone – that’s what makes the dominant chord dominate!] Notice d-minor’s upstart individuality! Not only does this mode don new clothing [C#] not found in F- major, but it is this precise rebellion that denies C [V of F], the old family identity!

The analogy of family relationship helps to explain the three forms of the minor scale. Natural minor? That’s according to the family crest, the key-signature of F major. Harmonic minor? That’s with scale-step 7 raised [as an accidental] so that the V harmony will have the leading-tone [semitone-to-the-tonic] that it needs in order to do its job. Melodic minor? That’s to smooth out the “bump” [2+] in the harmonic form. For in fig. 5, if C is raised to C#, then to play melodically from Bb to C# is to play a skip of 3-semitones, the enharmonic equivalent of a minor 3rd. Therefore, as an accidental, raise scale-step 6 [B] to smooth this gap. The need arises on the ascent; when descending -- moving away from the tonic -- no leading tone is required, and therefore no “bump” occurs. Descending melodic minor reverts to the natural, key-signature form. In practice, composers often mix the natural, harmonic, and melodic forms of minor.

Intervals is another fundamental area of theory from which the string player can benefit greatly if the presentation is translated into string-friendly terms based on the P5 and four fingers. Below, the “Chart of Fingerboard Equivalents” enables a lesson in fingerboard geography. This is a chart of relationships that can start at any pitch. When the player has reached the tritone [4+/5o], 1-4, then the next moves will repeatedly cross to the next higher string [always retaining the guiding finger as foundation]… P5, m6, M6. etc. In this way, the player learns, for instance, that the P4 on one string, and the P8 to the next string is the same 1-4 hand-span!

This figure [learn to write it] is a convenient way to remember the 2 classes of intervals: those above come in 3 sizes, those below come in 4 sizes. The intervals of the major scale [bold type on the chart] are either P or M; regard these intervals as “standard”. Then for the upper group [3 sizes], 1S [semitone] smaller than standard is diminished [ o ], while 1S larger is augmented [+ ]. For the lower group [4 sizes], 1S smaller than “standard” is m, and 1S smaller than that is diminished [ o ]. While 1S larger than “standard” is augmented [ + ].

ROUTINES FOR PRACTICE/DRILL
Route #1 going left to right
   The high road: short (Major scale – bold italics), or long (chromatic scale), starting string, then to next higher.
   The low road: starting string, then to the next lower string.
Route # 2 “Navaho rug zig-zag”-- i.e., crenelated.
    Upper road: P1, up to P5, right to m6, down to m2, right to M2, etc..
    Lower road: P1, down to P5, right to 4+/5o, etc.

The basics of music theory -- reformulated in string-friendly terms and applied to every playing task -- need not be compartmentalized in college level courses. From the beginning, the basics ought to contribute to a string student’s progress. Pragmatic and applied, a string-friendly presentation can turn dull, intellectual theory into jubilation. “Allelujah,” the string student can say – with pride! “Those 88 keys of the piano – every pitch in the musical universe – all is generated from the P5 of violin family tuning, by the tetrachord patterns made by my 4 fingers, and the geography that they explore on the fingerboard!”

Charles Heiden, 2009


Bibliography

1. See “Harmonics,” The new Harvard dictionary of music, Don Michael Randel, ed., 1986

2. Ibid., article “Scale”.

3. For example, see Michael Allen, et alia, Essential Elements 2000 Plus for Strings: A comprehensive String Method, Hal Leonard Corp, 2001, Violin Book 1: p 6, D String Notes; p.10, A String Notes; p.11, Down the D Scale; p.26, G String Notes; p.27, G Major Scale. Absent here is any recognition that it is the same 221 tetrachord pattern of whole and half steps that is being mounted from these open strings, or that learning the new G major scale involves applying a pattern of structure that the student has already experienced.

4. Charles Heiden, Franz Wohlfahrt, Op. 38 / Easiest Elementary Method / for Violin / Revised for D-major Beginners, Heiden Music Publications, 2008. See “The Three Tetrachords,” Bk. 1, p.17. And for string-friendly concepts about minor mode patterns, see Bk. 2, pp. 22 -24 in the same C-to-D major rapprochement.

5. Ibid.Bk. 2, p.34
 

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