In this section, we will begin to examine the complex relationship between sounds and music, obviously without any claim of completeness, but rather with the intent to reinforce the many links between physical science, the perception of sound and the composing and playing of music. This page is an introduction and the primary aspects of the following disciplines are dealt with individually on their respective pages:

• Consonance and dissonance;
• Psychoacoustic and musical aspects;
• Physical and mathematical aspects.

Music and intervals

In the playing of music, the ability to associate the correct pitch (or frequency) with a given note is actually of little importance. This ability is called "perfect pitch" and there are very few musicians who can name the corresponding note when they hear an isolated sound in any context. This fact often surprises non-musicians: it would be like saying that a painter cannot recognise the individual colours that they use to create their paintings. Actually, in the playing of music, it is much more important to be able to:

1. recognise the interval formed between two consecutive notes;
2. recognise and use its quality of being "consonant" or "dissonant".

They are directly associated with the way in which sounds are assembled and organised for their transformation into music.

Melody

The perception of the relationship between consecutive sounds corresponds to the perception of melody. When people whistle a tune that they like or cannot get out of their heads, they are usually reproducing the melody. From the Greek mélos (singing), melody is each individual "voice" that makes up a musical composition. From a graphic point of view, we can say that melody is the sequence that we get when horizontally reading an individual line of a score. To each moment in time there corresponds one, and only one, note. In many musical forms, especially almost all of pop music, the melody is the most noticeable part of a song, even for what concerns timbre. It is also what identifies it the most; so much so that when we hear the same song played in various arrangements, we can always recognise it because it has the same melody. From a more objective point of view, we realise that most of the song's sounds have changed with the arrangement variation but the relationships between consecutive sounds executed by the main voice have remained the same.

Harmony

While, the perception of simultaneous sounds corresponds to the sense of 'harmony. Harmony cannot be "whistled" because it does not correspond to an individual "voice" in a composition but rather a blending of all the sounds that are perceived simultaneously moment by moment. Therefore, harmony comes from the fusion of all the "voices". From a graphic point of view, we can say that harmony is determined by the vertical, contemporary reading of all the lines of a score moment by moment. To each moment in time there does not correspond one individual note but rather a blending of notes, which is called a chord. The harmony of a song is not defined by a single chord but comes from a particular succession of chords over time. Historically, the technique of blending voices developed much later than monodic singing (i.e. based only on melody) and that, over the centuries, this compositional technique has undergone many transformations.

While in everyday language the term "harmony" always has a positive connotation and refers to a situation of balance and proportion, in music, due to the presence of the "time factor", the harmony of a song can take on different characters in different times. It employs both chords that are apparently stable and static and chords that seem to introduce elements of instability and contain a tension to be resolved towards more chords. In music jargon, we refer to these two large classes as consonant and dissonant chords.

The theory of harmony is the branch of music theory that regulates the succession of chords present in a song and that possibly indicates the "best practices" of composition.

One or more harmonies?

From a historical point of view, polyphonic music, which needs an harmonic structure, was developed much later than monodic music, which has accompanied us since the dawn of humanity and would appear to be an extension (or an origin?) of language. The general opinion of composers, music theorists and even listeners on which combinations of notes are admissible or inadmissible in a particular context has changed, sometimes through cultural revolutions that are no less inferior to great scientific revolutions.

Music history is filled with anecdotes in which composers introduced an original variation, an extra note or an effect that was welcomed with great success and admiration and recognised as a brilliant innovation; or met with a huge failure or even caused a scandal. A truly innovative music would introduce listeners to a new, unknown and even shocking path. However, over time, the human brain would learn to recognise them and, if they were appreciated, they would be included in the field of what is permitted. Music, like all languages, is not a static entity; it evolves along with the perception and level of recognition of its listeners.

Needless to say, all kinds of cultural factors encourage these types of phenomena; a classic example is the fact that most parents cannot tolerate the music that their children listen to and vice versa. Many artists can still create a "scandal" with their work. Some due to reasons beyond the art itself and some because they dare to move the boundary between what a community considers to be part of that art and what it considers to be external to it.

Such as the famous case of Igor F. Stravinsky, who presented his music for the ballet The Rite of Spring at the Theatre des Champs-Elysées in Paris on 29 May 1913. The newspaper chronicles said that his music caused such indignation that the performance degenerated into a riot that was only partially calmed by the police. Now, this work is acclaimed as one of the masterpieces of modern music.

Stravinskij_sagra.mp3 Stravinskij, from The Rite of Spring

Therefore, we can conclude that, even though it is logical to presuppose that a "natural" basis for the fundamental rules of harmony does exist, we must admit that the enrichment or distortion of the basic rules is an inevitable part of the evolution of the human species. Actually, every new sound and dissonance that is acquired, however shocking it may seem, cannot be meant as an evolution against nature but rather an enlargement of the human brain's ability to recognise harmonic patterns.

Obviously, the role of the natural sciences, with their own methods that preferably go beyond cultural aspects, is to study which objective properties of the sound message and the human perceptual system contribute to determining sense of consonance or dissonance. However, such study cannot be separated from the fact that the human brain does not just receive messages; as recent analysis shows that it plays an active role in constructing perception.

Within the limits of this website, we have tried to deal with this issue from various points of view, in particular, you will find considerations:

• on composition, see the pages Consonance and dissonance and Psychoacoustic and musical aspects;
• on the natural sciences, see the pages Physical and mathematical aspects and Physiology of the auditory system;
• on music theory, see the page From monochords to musical scales and other pages indicated within.

To begin with, below you will find a brief introduction to musical intervals.

Musical intervals

The terms consonance and dissonance seem to introduce elements of subjectivity (which we will see are definitely present) in the judgement of various intervals. However, there also are precise, objective physical and physiological bases that have allowed all civilisations in different times and places to determine privileged intervals to use in their music.

The absolute first for consonance is the interval of the octave. The following four sounds are separated two at a time by an interval of an octave:

Four sounds at intervals of an octave
puro_55_Hz.wav pure tone at 55 Hz	puro_110_Hz.wav pure tone at 110 Hz
puro_220_Hz.wav pure tone at 220 Hz	puro_440_Hz.wav pure tone at 440 Hz

We may ask what type of relationship must occur between the frequencies of two sounds to give rise to an interval of an octave. The following table gives the differences and frequency ratios:

${\displaystyle f_{1}}$	${\displaystyle f_{2}}$	${\displaystyle f_{2}-f_{1}}$	${\displaystyle {f_{2}}/{f_{1}}}$
55	110	55	2
110	220	110	2
220	440	220	2

The results leave no doubts: the perceived interval is an octave if the ratio between the two frequencies is exactly double. In general, to our perceptual system

two intervals are considered equal if the ratio (and not the difference) of the frequencies of the sounds of the interval is identical.

Amongst the perceived intervals, along with the octave, other consonants have been determined including the natural perfect fifth, for which the frequency ratio is 3/2 (instead of 2/1 like the octave), and the natural perfect fourth for which the frequency ratio is 4/3.

The theory of musical intervals quickly leads to the construction of a musical scale. If we want to order sounds in a musical progression (scale) with all "steps" (intervals) being equal, which starts from the lowest note of the octave and ends with the highest, we must use sounds with frequencies in geometric progression and not in arithmetic progression. We observe that in the normal steps of a scale, the difference (and not the ratio) between absolute pitches (with respect to the base of the scale) of two consecutive steps remains constant!

Obviously, this mathematical criterion does not always produce such "consonant" intervals as the octave. Historically, the choosing selection of frequencies (and, therefore, of notes) to insert in an octave that will compose a musical scale has been based on aesthetic criteria related to the consonance of the intervals within the scale itself. The history of how various civilisations produced different divisions of the octave is absolutely fascinating and interwoven with considerations regarding "numerology", aesthetics and the technicality and physicality of constructing musical instruments. The same is true for the study of the evolution of music over time for each individual civilisation.

In-depth study and links

• You will find more detailed information on the pages From monochords to musical scales, Pythagorean scale, Natural scale and Equal temperament.

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