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. 1990)

Schneider writes, "When the same song is performed simultaneously by voices and instruments, the melody proceeds in two different tunings. The instruments on their own scale, the voices in theirs..."

He says we must suppose "that the vocal tone-system has been evolved in a natural and specifically musical fashion, whereas in the tuning of instruments quite different principles were applied such as, for example, the breadth of the thumb as the standard for the space between flute holes,"

When a need on the same instrument arises to transpose melodies into higher or lower keys, the notes are adjusted toward greater equality (tempered) so that each key will remain tolerable, if not perfect. Thus we have developed from this kind of typical behaviour an expectation NOT to find perfect pitch tunings on an instrument. (Schneider, M. 1957 p.14-15)

57 “The operative word here, relative to criteria for what is "acceptable" is that these instruments are tolerated, but when perfect pitch is available (voice, strings) then musicians choose the perfect intervals. In practical terms of instrument-making, the tolerable amounts have been in the neighbourhood of up to a Pythagorean comma.” (Fink, R. 1990).

The overall consequences of the equal temperament scale are a mixed bag. On the positive side, an instrument may be played in any key with no change in tonal relationships, and flats and sharps become truly equivalent (e.g. Ab = G#).

On the negative side, every single note in the scale (except for the octaves) is out of tune to some extent, with the result that the intrinsically harmonious ratios of 4:5:6 are never heard exactly in modern performances. There are a few recorded examples of performances on keyboard instruments with Pythagorean tuning, with results that are said by reviewers to be a "revelation".

58 How did the Musical Scale Develop?

Robert Fink in his book „The Origins of Music‟ says, “historically, the ear has preferred simple ratios as harmonious, and complex ratios have been avoided or considered noisy or dissonant”. (Fink, R. 1970)

He says that the two notes on the piano right next to each other have a complex ratio and these kind of ratios cause "beats", a kind of repetitive "wow-wow" effect, which is unpleasant to the ear.

As we have seen in the last chapter whenever a single note, like "C," is played, we actually hear several notes at once, called overtones. The most audible overtones of any one note add up to its major chord, Tonic, Fifth & Third e.g. C,E,G.

Harmonic Series – C Fundamental

11th Harmonic G Perfect Fifth 3,072Hz Ratio 12/1 10th Harmonic F # (flatter) Augmented Fourth 2,816Hz Ratio 11/1 9th Harmonic E Major Third 2,560Hz Ratio 10/1 8th Harmonic D Major Second 2,304Hz Ratio 9/1 7th Harmonic C Octave 2,048Hz Ratio 8/1 6th Harmonic B flat (flatter) Minor seventh 1,792Hz Ratio 7/1 5th Harmonic G Perfect Fifth 1,536Hz Ratio 6/1 4th Harmonic E Major Third 1280Hz Ratio 5/1 3rd Harmonic C Octave 1,024Hz Ratio 4/1 2nd Harmonic G Perfect Fifth 768Hz Ratio 3/1 1st Harmonic C Octave 512Hz Ratio 2/1 Fundamental C Octave 256Hz Ratio 1/1

The most audible overtones of a tonic or keynote all have simple ratios: -

2:1 (e.g. C/C above) (octave) 3:2 (e.g. C/G) (fifth note of scale) 4:3 (e.g. C/F) (4th note of the scale)

Robert Fink says, “In fact these three notes are present in virtually every musical scale known on earth. If you write out the overtones of these three notes and pick out the three most audible ones of each within the span of an octave, you will get the major scale.” (Fink, R. 1970)

Tonic C: Overtones are: C, G, E and Bb Fifth G: Overtones are G, D, B, and F Fourth F: Overtones are F, C, A, and Eb.

If you substitute the three weakest notes, the 3rd, 6th and 7th notes of the scale with another three notes, (which includes the even weaker next overtones), and which are flatter, you get the minor scale. The 6th note is strongest of the three because it forms no complex ratios with adjacent notes in the scale. (Fink, R. 1970)

If you leave the 3rd and 7th notes out altogether, you get the pentatonic five-note scale.

Fink says that because these overtones are very weak, they were the last to come into the scale. How people tuned them is uncertain. Many people tuned them somewhere between minor and major (in the 'cracks' on the piano), producing what are known as 'blue' or neutral notes.

Most harmony in folk melodies uses the three chords of the tonic, dominant (5th) and subdominant (4th) to harmonise all the 7 scale notes. This further underscores that these three notes and their overtones were fundamental influences in the formation of the scale's notes. (Fink, R. 1970)

59 There is confirming evidence in the 'babies experiment' by Sandra Trehub (see Babies Prefer Harmony p62).

Pentatonic Scale While the diatonic scale predominates in Europe the Pentatonic scale predominates in a huge part of the non-European world. People raised on the music built by different scales become used to them and the scales are entwined in the culture.

In early music of Scotland, Ireland and the Orient one can often find the missing 3rd and 7th notes of the scale being used not as part of the official scale, but as passing notes or leading tones. That is, they are notes in the gaps that 'lead' 'to the fourth or 'pass over into' the octave. In different cultures the names for this are different, but have similar meaning. The Pien tones in Chinese pentatonic scales mean 'becoming' that is, a 7th 'becoming' the octave, in a sequence of melody or scale notes. The words are different, the concept and usage is similar. This is widely reported among musicologists and anthropologists.

Scales Come from Melodies Robert Fink says “It's my belief that melodies first existed vocally, and then instruments, like flutes, were made to produce the most commonly used notes in a favoured melody or melodies. This would produce, in effect, a general "scale" on an instrument [even before a concept of "scale" existed], but it wouldn't necessarily play all other favoured melodies containing intervals sung differently.” (Fink, R. 1970)

“As a result, many flutes would be needed with slightly different intervals which we still have in modern times, by using valves, or making flutes with different keys. In the case of the piano, we temper the whole twelve notes and scale, rather than making different pianos tuned for playing in different keys.” (Fink, R. 1970)

“While many flutes have unequally spaced holes, which usually produce perfect acoustic intervals, the common equally-spaced-holes flutes were made not only to suit the convenience of finger-width and spread but likely also as a rudimentary attempt at "temperament". This allowed all melodies to be played almost in tune, all holes being just slightly "off-key" or containing non-acoustic or complex-ratio intervals.” (Fink, R. 1970).

“Musicology and ethnomusicology observers over the years have repeatedly reported that singers in various cultures and times would rarely match the tempered flutes that accompanied their singing, preferring to sing perfect acoustic intervals despite the instrument. This shows that a concept of "in tune" existed vocally.” (Fink, R. 1970.

The "tonic" (for lack of a better term), and its fourth and fifth, are almost everywhere used in scales, and their overtones are most frequently heard, although were not necessarily heard consciously as different notes.

In the course of making scales, Helmholtz has noted that most peoples have avoided notes in their scale which produce melodically dissonant semitones. Semitones are admitted only apparently when justified by being melodic "leading tones" whether moving melodically upward or downward to one of the strongest notes (tonic, dominant or subdominant). (Helmholtz, H. 1954, p.255)

Why the Minor Key is "Sad"?

“In brief, the third note of the major scale (Mi) is the note which, if made flatter, will essentially create the minor scale.” (Fink, R. 1970)

“The minor third is sad simply because the major third is more harmonious than the minor third, which has a more complex ratio of vibrations. In other words the minor is more on the edge of discord than is the major. If you accept psychologist/musical test conclusions, which I do, then

60 discord or dissonance creates a sense of physical pain in the ear, very mild pain of course. It is avoided, or repels the listener.”(Fink, R. 1970)

“Harmony without the fetters of any discord at all, is like contentment, it has an "everything fits nicely" feeling; no loose ends, little or no ambiguity. These "happy" emotions are also simpler (like driving on a smooth road) or are more physically integrated in our bodies than stressful or "sad" ones (like driving on a rough surface). It is basically a matching of emotional roughness to the degree of roughness of the sound.” (Fink, R. 1970)

“If a fast bouncy rhythm is coupled with the minor key, any feeling of "sadness" would be greatly lessened or eliminated. If the rhythm is slow, it would often be enhanced. This might be true for other cultures as well, because of the physiological aspects of rhythm and discord being common to all humans, although as mentioned, these reactions might be modified by cultural conditioning.” (Fink, R. 1970)

61 Babies Prefer Harmony

Glenn Schellenberg of the University of Windsor and Sandra Trehub of the University of Toronto have done research into how children respond to the pure tone changes.

The researchers observed parents singing to their babies and watched how the babies responded to those songs. They found that a mothers' singing mesmerised babies, and lullabies sound the same the world over. They also documented that a mother's singing decreased stress hormones in her child.

The researchers found that babies seem to have an innate appreciation for music. The experiment was repeated successfully using non-western musical scales as well.

The consonant tones, sounds generally associated with the words "in tune" and prevalent in Western music ranging as far afield as Beethoven and Motown were able to readily attract the attention of the infants being held on the parents' laps.

At the same time, the children hardly responded to the more dissonant combinations for example, C and F sharp played together. These out-of-tune sounding notes are often used by atonal composers such as Schoenberg and Berg and also rap groups such as Public Enemy.

The two researchers noticed the same response to consonant tones in their studies of adults and young people.

The researchers believe that the simplest explanation for their work is that the musical scales that are found in societies around the world are not cultural artefacts but natural apparitions. The infants' responses are "entirely consistent with dominance of musical scales with simple frequency ratios throughout history and across cultures," they write.

The golden note combinations and octaves are everywhere. "I haven't found a musical system which doesn't have a perfect fifth," Prof. Trehub said in an interview. Even something as notoriously dissonant as a bagpipe has perfect fifth tones droning underneath its sounds.

The evolutionary benefit of hearing and liking harmonious notes is unclear. Prof. Schellenberg points out they are tones that underlie human speech and thus paying special attention to them may act as a kind of primer to infants understanding speech.

Perhaps the most contentious issue is what the new findings say about the relationship of atonal to tonal music. Schoenberg contended that when people became familiar with it, his atonal music would eventually become as popular as tonal music.

The researchers say their findings do not mean one musical form is biologically better than another. Consonance does start out with some distinct advantages.

"I would say that atonal music is not inherently pleasing and that you would really have to work to get to appreciate it," Prof. Trehub said. (Psychological Science Vol.7 No.5 September 1996)

In a companion study published in the journal Nature, Harvard University psychologists Jerome Kagan and Marcel Zentner studied the response of 32 infants, some as young as four months old. The Harvard researchers found that the children seemed calmer and more content when harmonious sounds were played.

The out-of-tune sounds produced not just looks of disgust, but the infants would look away, cry, fret and not even look at the speaker, Prof. Kagan told the Reuters News Agency. (Nature 383, p29 5th September 1996)

62 Leonard Bernstein said the diatonic scale is written in our genes. Between the ages of 18 months and 2 ½ years, children from all countries of the world will sing melodic fragments with the Major 2nd/Minor 3rd/Major 3rd intervals. As they get older they go to 4ths and 5ths such as those found in the phrases 'Don-Ald' and 'Old MacDonald'. At the age of 3 the predominant musical style of their culture will take over. (Campbell, D. 1997)

Mark Jude Tramo, Director of Harvard University‟s Institute for Music and Brain Science, devotes his article, “Enhanced: Music of the Hemispheres,” to an analysis of brain structures and experimental evidence. (Tramo, M. J. 2001)

He writes, “By 4 months of age, babies prefer consonant musical intervals (major and minor thirds) to dissonant musical intervals (minor seconds). Even if an infant‟s preference for consonant intervals has been influenced by 6 to 7 months of exposure to music in the womb, it is likely that the human brain enters the world primed to extract the spectral and temporal regularities that characterise popular music.”

63 Musical Roots may lie in Human Voice

Why do tunes in a major key, such as „Singin' in the Rain‟, sound cheerful, while those in minor keys such as Pink Floyd's „Another Brick in the Wall‟, sound gloomy and depressing?

The answer seems to be that the patterns of pitches in major keys mirror those of excited speech, whereas minor keys parallel subdued speech. This suggests that language shaped our musical expression of emotion.

Several factors affect music's sentimental influence, and some are common sense: a fast, loud, jumpy rhythm sounds happy because it reflects the way an excited person behaves, and slow, quiet music with a regular beat mimics a mournful emotional state.

What's less obvious is why do tunes in major keys tend to sound cheerful, whereas those in minor keys sound sad.

"The mysteries of music have a biologically principled explanation," says Dale Purves, at Duke University, North Carolina, lead author of the study. "A reasonable speculation is that we hear these tonal relationships because they are involved in our interpretation of each other's speech."

The Duke researchers randomly extracted over 100,000 speech samples, each 0.1 second long, from recordings of thousands of English sentences. Acoustic analysis of the combined samples revealed 10 frequency peaks in acoustic energy that precisely mirror the distances between important notes in the twelve-tone scale, the system that forms the foundation of almost all music.

Then they compared these musical intervals with those between important tonal frequencies in spoken vowels uttered by American English speakers in either excited or subdued voices. Their speech samples came from ten volunteers who were recorded reading various monologues, including animated accounts of winning the lottery and morose descriptions of failing marriages.

The frequency relationships in excited speech closely matched those of music in major keys, while those of forlorn speech matched minor music.

They also measured the distribution of tones in around 7500 western classical melodies and Finnish folk tunes in both major and minor keys. They found, for instance, that minor thirds made up 15 per cent of tones in minor pieces, but unsurprisingly made up less than 1 per cent of tones in major pieces.

Bowling adds that his team found the same association for Mandarin Chinese speakers, suggesting the link is common to different cultures, if not universal. "This makes a good case that it has biological roots," he says.

(Daniel L. Bowling, Gill Kamraan, Jonathan D. Choi, Joseph Prinz, and Dale Purves - Dept. of Neurobiology and Center for Cognitive Neuroscience, Duke University - Journal of the Acoustical Society of America Volume 127, Issue 1, pp. 491-503 January 2010)

Mandarin and Farsi According to other studies speech in other languages such as Mandarin, Farsi, and Tamil also displayed the same pattern. The frequency peaks are caused when a sound wave from the vocal cords is shaped by the resonance of the throat and mouth.

The researchers say that, aside from animal calls, speech emanating from oscillations of the human vocal cords is virtually the only natural sound that we hear as tones. This fact, combined with the new finding that preferred musical intervals are better predicted by the acoustic quirks of the human vocal tract than by mathematics, leads the scientists to argue that the structure of music is rooted in our long exposure to the human voice over time. (Journal of Neuroscience vol. 23, 2006)

64 What Are Musical Keys?

In music a key is the major or minor scale around which a piece of music revolves. A song in a major key is based on a major scale. A song in a minor key is based on a minor scale.

A song played in the „key of C major‟ revolves around the seven notes of the C major scale – C, D, E, F, G, A, and B. That means the fundamental notes making up the song‟s melody, chords, and bassline are all derived from that group of notes.

A song in the „key of F major‟ uses the notes of the F major scale – F, G, A, Bb, C, D, and E.

A piece of music can be in a minor key and revolve around a natural minor scale. For example, a song in the „key of D minor‟ uses the notes of the D minor scale – D, E, F, G, A, Bb, and C.

Any major scale or minor scale can serve as a key for a piece of music. The centre of It All - The Tonic

The root note of the key acts as the centre of the key. When speaking of keys, the root note of the key is called the tonic.

When you play music, the music is constantly being pulled toward the tonic, or root of the key, wanting to come to a state of rest or completion. The tonic is the most resolved note in a key. The tonic is a key‟s centre.

Moving away from and back to the tonic resting point of the key is partly what makes music interesting and why it has a pleasing effect on us.

Tonality When music has this centred sound to it, it is said to be tonal. Almost all music to which we listen is tonal. When a piece of music lacks a tonal centre it is said to be atonal (pronounced AY-toe-nul). Most people don't like the sound of atonal music. Listen for the Tonic

Most songs finish on the tonic of the key to make the song sound complete or finished. It‟s a very natural sound to expect and it will sound strange when you don‟t hear it.

Can a Piece of Music Only Use Notes within the Key? Notes not in the scale are considered to be outside of the key. Outside notes can be and often are used, but the bulk of the notes will still centre on the notes of the key and the key‟s tonic. If outside notes are used improperly it‟s possible to throw off a song‟s tonality and create an unpleasant effect.

Skilled musicians and composers have learned to use these off key notes without upsetting the tonality of the music. Outside notes occur in most styles of music to some degree. You will hear the use of outside notes heavily in many jazz solos. You also might find them used in heavy metal riffs.

How Many Music Keys Are There? Since there are 12 major scales, there are 12 major keys. Likewise, there are 12 minor scales and 12 minor keys. Hence there are 24 keys all together.

Three of the major keys can be named in two different ways, one way with sharp note names and the other way with flat note names. This results in 15 different major key spellings.

As an example, the keys of Gb major and F# major contain the exact same notes. The former is spelled using flat note names (Gb, Ab, Bb, Cb, Db, Eb, and F), while the latter is spelled with equivalent sharp note names (F#, G#, A#, B, C#, D#, and E#). There will be times when choosing one spelling over another is preferable. (More on that later.)

65

In the same way, there are 15 different minor key spellings. In total, there are 24 keys and 30 ways to spell them.

From the web site - http://www.studybass.com/lessons/harmony/keys-in-music/

Different Keys

In musical circles it is often claimed that the key or pitch of a piece can have a profound bearing on the mood conveyed. For example, if played in the key of E major, the music may be considered bright and powerful but in F major, peaceful or contemplative. This is surprising, given that all keys contain similar intervals when played in equal temperament.

Keys used to have distinctive characters, although these died out when the equal temperament tuning system became standard. A key's character is largely determined by the "major third" e.g. C/E, a musical interval between the pitch of two notes which appears in all common chords. Ideally, the frequencies should be in the exact ratio of 4:5. If they are, the pitches blend perfectly to produce a warm, mellow sound, and the interval is called a "natural third".

A major third has a higher frequency and is sharper; this gives the key a bright character. If the major third has a lower frequency, the key sounds dull. It is mathematically impossible to tune the major thirds of all keys to this ideal natural third. On average major thirds are slightly sharp in equal temperament.

Before equal temperament was introduced the commonest keys of C, F and G major have natural thirds and so sound mellifluous; Bb, D, Eb and A are neutral; E and Ab are bright to jangly and the remote keys of B, C# and F# make humans wince and dogs howl. This fits the questioner's descriptions of E and F major. Past composers chose keys to suit the character of the music.

Mozart used Eb major as the Masonic key, because it had three flats and three was the Freemasons' mystical number.

There are a great many factors that influence our perception of musical colour. If we consider the piano, the "shape" of a chord, its distribution of black and white notes and the position of the chord up or down the keyboard can have a considerable effect on the way it sounds. Some composers take advantage of this to achieve a particular tonal colour. Stringed instruments have fixed points in their range when the strings are open.

Certain keys are very much easier to play in than others are and resonance of the open strings plays a part in colouring keys. A further vital factor is the listener's cultural background. If we learn we are about to hear a work in C minor, we think of Beethoven's Third Piano Concerto or the Mozart Piano Concerto in that key all are dark, tragic works. We presuppose that anything else in that key will be similar.

The Sound Quality of Different Keys Because the interval of a tone may be either 8:9 or 9:10, the internal frequency relationships within a scale will depend on the key that is in use. For an example, the key of C starts with a ratio of 8:9, whereas the key of D starts with a ratio of 9:10. Worked out fully for these two keys we find the following frequency ratios: The internal differences between these two keys are fairly subtle, but in every key there is a different pattern, and for some, the differences are so great that the overall effect can be markedly discordant.

Composers have always had views on the subjective emotional quality of different keys. Beethoven, for example, regarded the key of Eb as heroic in sound, and used it for both the Emperor Concerto and the Eroica Symphony, and also, in its equivalent minor mode, for his Fifth Symphony. As we shall see shortly, by the time of Beethoven, such views could not be sustained in terms of internal

66 frequency intervals within individual keys, because the issue of tuning had reached such a critical state that an entirely new system of tuning had come into being.

From the web site - http://www.fortunecity.com/emachines/e11/86/rightnote.html

67 Characteristics of Different Musical Keys

C Major - Completely pure. Its character is innocent, simple, naive and is like children's talk.

C Minor - Declaration of love and at the same time the lament of unhappy love. All languishing, longing, sighing of the lovesick soul lies in this key.

Db Major - A leering key, degenerating into grief and rapture. It cannot laugh, but it can smile; it cannot howl, but it can at least grimace. Consequently only unusual characters and feelings can be brought out in this key.

D Major - The key of triumph, of Hallelujahs, of war cries, of victory rejoicing. Thus, the inviting symphonies, the marches, holiday songs and heaven-rejoicing choruses are set in this key.

D Minor - Melancholy womanliness, the spleen and humours brood.

D# Minor -Feelings of the anxiety of the soul's deepest distress, of brooding despair, of blackest depression, of the most gloomy condition of the soul. Every fear, every hesitation of the shuddering heart, breathes out of horrible D# minor. If ghosts could speak, their speech would approximate this key.

Eb Major - The key of love, of devotion, of intimate conversation with God.

E Major - Noisy shouts of joy, laughing pleasure and not yet complete, full delight lies in E Major.

F Major - Complaisance & calm.

F Minor - Deep depression, funereal lament, groans of misery and longing for the grave.

F# Major - Triumph over difficulty, free sigh of relief uttered when hurdles are surmounted; echo of a soul which has fiercely struggled and finally conquered lies in all uses of this key.

F# Minor - A gloomy key: it tugs at passion as a dog biting a dress. Resentment and discontent are its language.

G Major - Everything rustic, idyllic, lyrical, calm and satisfied passion, tender gratitude for true friendship and faithful love. This key expresses every gentle and peaceful emotion of the heart.

G Minor - Discontent, uneasiness, worry about a failed scheme; bad-tempered gnashing of teeth; in a word: resentment and dislike.

Ab Major - Key of the grave, death, grave, putrefaction, judgement, eternity lie in its radius.

Ab Minor - Grumbler, heart squeezed until it suffocates, wailing lament, difficult struggle. The nature of this key is one of struggling with difficulty.

A Major - This key includes declarations of innocent love, satisfaction with one's state of affairs; hope of seeing one's beloved again when parting; youthful cheerfulness and trust in God.

A Minor - Pious womanliness and tenderness of character.

Bb Major - Cheerful love, clear conscience, hope aspiration for a better world.

Bb Minor - A quaint creature, often dressed in the garment of night. It is somewhat surly and very seldom takes on a pleasant countenance. Mocking God and the world; discontented with itself and with everything; preparation for suicide sounds in this key.

68 B Major - Strongly coloured, announcing wild passions, composed from the most glaring colours. This key expresses anger, rage, jealousy, fury, despair, and burden of the heart.

B Minor - this is as it were the key of patience, of calm awaiting one‟s fate and of submission to divine dispensation.

(From Christian Schubart's Ideen zu einer Aesthetik der Tonkunst (1806) translated by Rita Steblin in A History of Key Characteristics in the 18th and Early 19th Centuries. UMI Research Press 1983)

From the web site - http://www.wmich.edu/mus-theo/courses/keys.html

Key or mode descriptions from Charpentier's Regles de Composition ca. 1682

C major: gay and warlike C minor: obscure and sad D major: joyous and very warlike D minor: serious and pious Eb major: cruel and hard E major: quarrelsome and boisterous E minor: effeminate, amorous, and plaintive F major: furious and quick-tempered subjects F minor: obscure and plaintive G major: serious and magnificent G minor: serious and magnificent A major: joyful and pastoral A minor: tender and plaintive B major: harsh and plaintive B minor: solitary and melancholic Bb major: magnificent and joyful Bb minor: obscure and terrible

From the web site - http://www.wu-wien.ac.at/earlym-l/logfiles/em.2001-03

Key or mode descriptions from the English translation of Helmholtz's Tonempfindungen

C Major - Pure, certain, decisive; expressive of innocence, powerful resolve, manly earnestness and deep religious feeling Db Major - Fullness of tone, sonority and euphony E Major - Joy, magnificence, splendour; brightest and most powerful key E Minor - Grief, mournfulness, restlessness F Major - Peace, joy, light, passing regret, religious sentiment F Minor - Harrowing, melancholy F# Major - Brilliant, very clear Gb Major - Softness, richness

From the web site - http://web.archive.org/web/20050419162711/http://www.win.net/~pelerin/music/science/music5.ht ml

69 Descriptions of Keys from Various Sources

C Major "Completely pure" (Schubart, 1784) "Cheerful and pure" (Knecht, 1792) "State of nature, virginal chastity and purity, lovely innocence of youth" (Heinse, 1795) "Naturalness and nobility" (Gervasoni, 1812) "Cheerful and pure; innocence and simplicity" (Weikert, 1827) "Simple, unadorned" (Schumann, 1835) "Concerning the physical expression of this key, it appears to be completely pure" (Schilling, 1835)

C-sharp Minor "Penitential lamentation, intimate conversation with God" (Schubart, 1784) "Despair" (Knecht, 1792; Schrader, 1827; Weikert, 1827; Ebhardt, 1830)

D Major "Gay things and grandeur" (Rousseau, 1691) "Joyful and very militant" (Charpentier, 1692) "Pleasant, joyful, bright, songs of victory" (Masson, 1697) "Songs of mirth and rejoicing; grandeur and magnificence" (Rameau, 1722) "Martial ardour" (Hawkins, 1776) "The key of triumph, of Hallelujahs, of war-cries, of victory-rejoicing" (Gathy, 1835)

Eb Minor "Horrible, frightful" (Charpentier, 1692) "Feelings of the anxiety of the soul's deepest distress, of brooding despair, of blackest depression, of the most gloomy condition of the soul. Every fear, every hesitation of the shuddering heart, breathes out of horrible Eb minor. If ghosts could speak, their speech would approximate this key" (Schubart, 1784)

E Major "Uplifting" (Junker, 1777) "Bright" (Gretry, 1797)

Bb Minor "Gloomy and terrible" (Charpentier, 1692) "Mournful songs" (Rameau, 1722) "Preparation for suicide sounds in this key" (Schubart, 1784)

(Rita Steblin (2002) A History of Key Characteristics in the Eighteenth and Early Nineteenth Centuries, University of Rochester Press)

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