Dissonance Dissonance means without sonic alignment or to "beat against". Our first reactions to dissonance, whether in music or life, are to label them undesirable and something to be avoided. According to John Beaulieu “During the Middle Ages the Catholic Church determined what musical tones and intervals were spiritual. New musical sounds were usually introduced through heresy and thought to be the work of the devil. As hard as it is to believe, many people were executed and tortured for playing the "wrong note.” (John Beaulieu - Dissonance) When Igor Stravinsky premiered 'The Rite of Spring' in 1913 many listeners rioted. The complex music and violent dance steps depicting fertility rites first drew catcalls and whistles from the crowd. At the start, the audience began to boo loudly. There were loud arguments in the audience between supporters and opponents of the work. These were soon followed by shouts and fistfights in the aisles. The unrest in the audience eventually degenerated into a riot. The Paris police arrived by intermission, but they restored only limited order. Chaos reigned for the remainder of the performance. “A commonly used word for dissonance is stress. Dr. Hans Selye defines stress as adaptation to change. Those that resist change will perceive stress as distress. Those that accept change may experience the same stress as euphoria. In other words what is distress for one person may be euphoria for another. This may explain from a scientific perspective why the dissonance of a music composition like Stravinsky's 'Rite of Spring' may be terrible for one person and beautiful for another." (John Beaulieu - Dissonance) "The Nobel Prize winning physicist, Dr. Ilya Prigogine discovered the importance of dissonance while investigating chemical systems. He termed his discoveries "order from chaos". Prigogine proved that for a system to change and go into a higher state of functioning it must first pass through a state of disruption or chaos. The sonic term for chaos is dissonance." "Prigogine points out the crucial role dissonance plays in living systems evolving into higher levels of order or resonance. He discovered that all living systems dissipate more and more energy over time caused by fluctuations or dissonances inherent within the system. As time passes these dissonances increase in intensity causing the system to move further and further from equilibrium. Soon everything begins to wobble. The wobbling increases until all pre-existing order within the system shatters causing the system to leap into chaos." "Prigogine terms the precise moment a system goes from order to chaos a bifurcation point. As a system approaches bifurcation it only takes a very small and seemingly inconsequential event to create chaos. From chaos the system reorganises itself into a new system functioning at a higher level resonance." “The process of moving into higher states of being begins with dissonance. During dissonance our life becomes challenged. The more we deny our challenge the greater our dissonance becomes. There are no solutions on our current rung of the ladder. We must seek change and seek resolutions from a higher perspective”. Dissonance by John Beaulieu, N.D., Ph.D. From web site - http://www.biosonicenterprises.com 55 Well Tempered or Equal Tempered Scale In the fifteenth century Andreas Werkmeister devised the equal tempered tuning system for the piano. The octave was divided into twelve equal semitones in order to make it possible for the keyboard to play the polyphonic music that was coming into vogue. Prior to this the keyboard or piano would need to be re-tuned every time music in a different key was to be played. The well tempered scale is the one that we are familiar with today: - Note C C sharp D E flat E F F sharp G A flat A B flat B Freq. 1 1.059 1.122 1.189 1.260 1.335 1.414 1.498 1.587 1.682 1.782 Since the semitones (a gap of half a note) are all the same size in the well-tempered scale it follows that all the intervals between each note will be the same, 1.05946 of the fundamental frequency. Comparing the well-tempered scale with the just scale we can see that the intervals of the sixth (A/C) and the seventh (B/C) diverge most from the whole number harmonic ratios. Notes Harmonic Ratio Just Scale Well-Tempered Scale D/C 9/8 = 1.125 1.222 E/C 5/4 = 1.250 1.260 F/C 4/3 = 1.333 1.335 G/C 3/2 = 1.500 1.498 A/C 5/3 = 1.666 1.682 B/C 15/8 = 1.875 1.888 C/C 2/1 = 2.000 2.000 E flat/C 6/5 = 1.2 1.189 (The minor third) A flat/C 8/5 = 1.6 1.587 (The minor sixth) John Backus says that these differences are 'not negligible', they are responsible for the continued assertion that the tempered scale is 'out of tune'. (Backus, J.1977) From this we can see that the scale now used in most Western music is out of step with the whole number ratios found in nature. The closest intervals to the harmonic intervals in the well-tempered scale are the intervals D/C, F/C, and G/C. The great Indian singer Pandit Patekar found that he was unable to sing the classical Indian raga 'Bhairavi' when accompanied by a recently tuned grand piano. "They are not in tune," he kept saying. (Hamel, 1978, p120) The just scale is the closest to the harmonic series as long as we only use intervals based on the fundamental note. As soon as we use notes above the fundamental to form intervals the sound produced may depart from the whole number ratios found in nature. This has important implications when music is used for healing. Every note we think is a single note actually produces overtones, which can be heard, but not as different notes, but as a change in quality for example, allowing us to tell the difference between a piano and a trumpet even though each plays the same note. This is mostly due to the different strengths of the overtones of that note in the instrument. A "natural 5th" is based on the first different overtone of any given note. For example, C's first different overtone is G, which when lowered one octave, is the natural "5th" of C. 56 You can produce a series of such 5ths, or a "cycle of 5ths" as it has been called in music, such as C to G, then D (based on the preceding G), then A, based on the preceding D, etc. Such a series or cycle looks like this: C-G-D-A-E, etc. Simply put, starting on C, if you produce this series of perfect 5ths, eventually you come round again to the original note, but in the form of B#. This B# differs from the original C by an amount called a "Pythagorean comma." In music we can correct this anomaly by re-tuning the notes slightly off "natural." The way this is done on fixed-key instruments (like the harpsichord or piano) is to divide the octave into 12 equal semitones or half-tones. This process is called "Temperament," and as a result, the notes are no longer perfect or "natural" in relation to others. C to G is no longer a natural or perfect 5th, but very slightly out of tune. Also as a result, B# and Cb no longer appear to exist as separate notes in this tempered system. So you won't find music written in these "keys," as the enharmonic version of them (B instead of Cb, E instead of Fb, etc) is used. As a result two notes become one note, for example a Db becomes the same as C#, a B# becomes a C, a Cb becomes a B. Each of these are really two different notes which are playable as different notes on violin fingerings or as sung by singers. The motivation for tempering notes comes also from transposing music. In the past with fixed-key instruments if you tuned the scale of C to perfect steps, then the scale, while sounding perfect in C, when transposed to other keys, would sound seriously out of tune because of the Pythagorean "error," or natural flaw. These other keys, for example, those requiring a Db, and NOT a C#, would be the cause of the mistuned sound. But when the 12 tones are tempered or equalised by dividing the "error" equally among all the 12 notes, then ALL the keys are equally "out of tune" by a very small amount, none of them so badly as to sound like a serious mistuning to most or average ears. Many singers still sing the true intervals despite what a piano plays as accompaniment. Indeed, some singers hate the piano because they find its temperament annoying to their sense of pitch. Harvey Reid wrote: "Our ears actually prefer the Pythagorean intervals, and part of learning to be a musician is learning to accept the slightly sour tuning of well-tempered music. Tests that have been done on singers and players of instruments that can vary the pitch (such as violin and flute) show that the players and singers tend to sing the Pythagorean or sweeter notes whenever they can. More primitive ethnic music from around the world generally do not use the well-tempered scale, and musicians run into intonation problems trying to play even Blues and Celtic music on modern instruments." (Fink, R.