Detectar los factores de riesgo determinantes en la evolución de la DM2

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The main currents of musical theory and composition of this century have he two streams of music - harmonic and tempered - had now wandered along

quite distinct paths. Not only keyboards, but guitars had become popular.

The C.F. Martin company, founded in 1833, and Gibson Guitar Company, founded in 1896, were turning out high quality acoustic guitars, and the

instruments were popular. Keyboards and frets sent the tempered stream along its own path. Certain a cappella choirs and chamber groups continued to perform harmonic music, but from the perspective of 1900, the future of music, at least in the west, looked like equal temperament.

By 1937 the Encyclopedia of Music and Musicians confirmed the current paradigm by claiming that tuning by pure intervals was “strictly impossible,” that

“the mechanical obstacles to pure tuning in keyed instruments are insurmountable, and the question of some compromise is hence necessary.”56 In 1950, Llewellyn Lloyd wrote in Intervals, Scales, and Temperaments that “the present supremacy of equal temperament will remain unassailable until someone invents a really practicable means of playing ... alternative notes ... by a single key.”57

accepted the compromise deemed inevitable. The parallel chords, wholetone scales, and serial techniques of composers like Debussy, Ravel, Stravinsky, and Schönberg carried Beethoven's instrumental music into ever new subtleties of expression. The chords of Schönberg and Scriabin built on fourths, took advantage of equal temperament, and moved music toward an atonal aesthetic.

These composers fully embraced tempered harmony, in part because their music was a rejection of traditional harmony and tonality all together, but equally so because that was the intonation available on modern instruments. In much modern music dissonance is featured, and a sense of tonal center is obliterated.

In Problems of Harmony Schönberg introduced twelve-tone and serial techniques. His “emancipation of the dissonance,” was a movement to put all intervals of the chromatic scale on equal aesthetic footing. Schönberg was well aware of pure harmonics, and saw the major scale as the addition of the tones of the tonic, dominant and subdominant major triads. He wrote that “we actually to some extent hear and to some extent feel this relationship in every sounding tone.”

He equated the other chromatic tones also with higher harmonics, saying “if we note the more distant overtones (up to the 13th) ... we find the chromatic scale.”⁵⁸ In fact, as Henry Cowell later pointed out, this is not exactly correct. For example, Schönberg states that the 13th overtone of G is Eb, but the 13th overtone is a 13/8 interval that is almost a quartertone sharp of Eb, a “neutral sixth” that has been used in certain Arabic and other scales. This tone has no western chromatic counterpart.

Paul Hindemith faced the same contradiction. He attempted to explain the western chromatic scale by the overtone series that did not entirely support it, yet he understood that tonality itself was a natural phenomenon. He wrote in A

Cowell knew this, and felt that the natural evolution of chord development was not 12-tone chromatic, but rather would follow the harmonic series, “from the seventh overtone upwards.” He adds that “there seems to be need of such a system to further the understanding of contemporary material, which has had no adequate theoretical coordination.”59

The aleatory (chance) music of John Cage and Karlheinz Stockhausen took this revolution against tonality to ever further limits. Cage’s experiments with random sound, prepared piano, and even complete silence in 4’33” had nothing at all to do with harmonic proportions. It was sound Dada. He was not only

liberating dissonance, but liberating noise and even silence, as musical elements.

Blues and jazz forms were developed in the U.S., from the early 19th century, and although this music evolved within the equal tempered stream, it produced some interesting intonation experiments. Equal temperament gave jazz players the freedom to roam unrestricted among tonal centers, and the music tended toward chord sequences with a widening definition of chromatic chordal resources. Musicians like Louis Armstrong, Charlie Parker, Sarah Vaughan, and others were delivering music into new realms of sound, speed, and rhythm. Later Miles Davis, John Coltrane, and a new generation of jazz musicians advanced the form, playing up and down through fast chordal cycles, leaving the melody for spontaneous inspiration, integrating Afro-Caribbean polyrhythms and Latin- Oriental off-beat melody lines. All of this was helped along by the ease of equal temperament. Horn players like Davis and Coltrane, however, instinctively shaped the intonation to fit the mood of a passage. Later, in the 1970s, flutist Paul Horn recorded over his own echo inside the Pyramids and the Taj Mahal, working Composer’s World that “in music we cannot escape ... tonality. The intervals which constitute the building material of melodies and harmonies fall into tonal groupments, necessitated by their own physical structure and without our consent.” He calls tonality “a very subtle form of gravitation,” and adds that

“some composers who have the ambition to eliminate tonality, succeed to a certain degree in depriving the listener of the benefits of gravitation. To be sure they do not, contrary to their conviction, eliminate tonality.”60 Hindemith may have come up with the best definition of equal temperament: “a compromise which is presented to us by the keyboard as an aid in mastering the tonal world, and then pretends to be that world itself.”61

with the natural resonances of these sites as well as the natural harmonics of the flute tones.

Blues musicians also wandered instinctively from equal temperament. The

“blue notes” heard in some of this music tend toward the seventh harmonic which is obliterated in equal temperament. In “Septimal Harmony for the Blues,” Dudley Duncan analyzes W. C. Handy’s St. Louis Blues, in G, and concludes that “...the singer or horn player uses inflection of the melody or countermelody for color (in ways probably beyond the scope of any simple theory), [but] for simple harmony the blue notes are merely the just intervals 7/6, 7/5, and 7/4.”⁶² These are the blue minor third, augmented fourth, and minor seventh. The blue Eb in the key of G, nominally an augmented fifth, Duncan suggests is, in the blues treatment, the quartertone 14/9 which forms a blues third above the fourth.

String bass players, like singers and horn players have the freedom to place the intonation where they want to because they aren’t limited by frets. However, a bass player with a good natural ear for harmony must be careful not to clash with the lower notes of the piano. This is because the string bass player may

instinctively want to stop the note at the natural harmonic, something the piano cannot do. Jerry Coker, a former saxophonist with Woody Herman, Stan Kenton, and others, mentions this problem in his book on jazz improvisation. “If the pianist’s left-hand base note coincides with the root played by the bass player, there is an intonation problem.” In this case, the bass player either has to stay away from this note, or play the piano intonation. Most modern musicians, of course, learn to play the piano intonation since the piano cannot change.

Guitar players can find the pure seventh harmonic of a guitar string by lightly touching the string about halfway between the second and third frets as the string is sounded. On the bass E string this is a D note. Compare this note to the high octave D at the twelfth fret of the D string tuned two fretted fourths from E.

These two “D’s” are clearly not in tune with each other. The harmonic D is much flatter, and this is the blues seventh. The tempered flat-seven, found with the frets, is the worst of all the tempered intervals when compared to its natural harmonic.

The blues singers and horn players simply used their instinct and good ears to find the pure harmonics that were found by the Harmonists of ancient times.

Guitar players know that when they tune perfect harmonics from the bass E-string to the treble E-string, the two E's are not in tune with each other. By matching the fourth harmonic of the bass E string to the third harmonic of the A string, etc., and by matching the fifth harmonic of the G string to the fourth harmonic of the B string, a guitarist ascends by four pure fourths and a pure third, but this lands flat of two octaves. The interval by which this is flat is the comma of Didymus that the reader may remember from the first five chapters, a

discrepancy that has been known by musicians for two thousand years. It is about 1/5 of a semitone. The ear hears this, and with a flexible instrument, the ear can easily guide the necessary intonation changes. Frets however, demand equal temperament, which disguises these natural discrepancies by spreading them out across the octave and polluting every interval. Noticing the intonation and placement of these harmonics on a guitar is a good way to hear, and even see, the problem with tempered intervals.

The fifth harmonic of the G string is a pure major third of G, a B note.

When you play the B harmonic on the G string, you are dividing the string into five vibrating parts by touching the string at one-fifth its length, just slightly flat of the fourth fret. Play the B harmonic on the G string of a guitar. Now press down and hear the fretted B on the G string. These two B's are noticeably out of tune with each other. You can see how far behind the fret your finger is when you get the ringing B harmonic. On a Martin D-35 the fourth fret is more than 1/8-inch sharp of the harmonic. They say in framing a barn that 1/8 inch tolerance is acceptable. To the delicate art of harmony, it is a problem.

Modern popular music, particularly electric rock guitar playing, is based on fast and colorful chord changes, rather than on the subtleties of pure harmony.

Helmholtz predicted this evolution of instrumental music a century ago when he acknowledged that "in rapid passages ... the evils of tempered intonation are but little apparent," and added, "we might, indeed, raise the question whether

instrumental music had not rather been forced into rapidity of movement by this very tempered intonation, which did not allow us to feel the full harmoniousness of slow chords to the same extent as is possible from well-trained singers, and instruments had consequently been forced to renounce this branch of music."⁶³

Fast, chord-based music is by no means aesthetically inferior, and indeed great music has been created by artists in the blues, jazz, and rock genres. The issue for musicians is one of musical options. The simplicity of equal temperament created new options, but also foreclosed certain other options. As musicians, do we merely accept those limitations, or do we chose to investigate all the musical options that could enhance our ability to make expressive music? The question will have different answers for different artists, but asking the question is the issue, and seeing the options is the opportunity for modern musicians to expand their creative resources.

Composer, producer, and music innovator Brian Eno mentioned this limitation of the 12-tone keyboard in a March, 1995 interview in Keyboard magazine. “The keyboard,” said Eno, “gives you distinct islands rather than a continuous set of pitch possibilities. That's a disadvantage for keyboards.”64 Steve O’Keefe, editor of the Piano newsletter was even more blunt in saying “the piano is one of the most frustrating instruments on God’s green planet. ... If you want to play the piano you are locked into that vision, unable to use anything outside of what is provided.”65 The guitar, of course, has the same problem. “Frets are slightly out of tune,” wrote John Schneider, in Acoustic Guitar magazine in 1994,

“enough to produce a warbling effect on every chord you play and to sabotage you every time you try to tune.”66 These musicians are addressing the aesthetic

limitations of their instruments, a healthy move for any artist.

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