Diatonic scale

See also: Scale

The diatonic scale is the scale Fréquence S used in tonal Western music -, that in others standard of music, connected thus besides or not with this one.

The diatonic scale is heptatonic , i.e. it is made up of seven degrees, separated by seven joint spaces - by joint space , we will hear the distance between two close degrees.

Seven joint spaces of the diatonic scale are unequal : largest are called tons diatonic, smallest, semitones diatonic.

It is possible, by means of deteriorations, to add on a diatonic scale a certain number of intermediate notes, placed about in the middle of each diatonic ton. In this case, the scale thus amplified , takes the chromatic name of scale. The exact frequency of these intermediate notes can pose problems of agreement: the system known as “of the equal temperament” makes it possible to simplify the chromatic scale of reference.

Terminology and etymology

While anticipating on what is explained after, the methods of division of the octave in intervals for a very long time gave rise to the range known as heptatonic, i.e. including/understanding seven intervals in an octave, that is to say eight notes.

The GROUND is the “fifth” of C i.e. the fifth starting from C (counted like first) C is the octave of C, i.e. the eighth starting from C. One sees that C is the “quad” of GROUND, i.e. the fourth starting from GROUND. In the same way, F is the “quad” of C or, which returns to same, C is the “fifth” of F.

It is also seen that a major tone separates F (quad of C) and GROUND (fifth of C).

One also speaks about “diatonic” range, that where the successive notes have distinct names - the chromatic range being that where certain notes take the same names with Dièse or Bémol and come to be intercalated between the sounds of the diatonic range.

In fact, no range is free from disadvantages of various natures: a Tempérament is a way of modifying it slightly to attenuate some of them, sometimes while amplifying some of others.

Structure

The diatonic scale takes the form of a “ succession of isolated semitones diatonic, forming between them alternate groups of two and three let us tons ”.

In the natural diatonic scale - i.e., in the absence of all deterioration -, the two semitones are located, one between semi and F , the other between if and C .

One can represent this one in a vertical way, or, in cyclic form:

Various categories of joint spaces

One classifies the joint spaces constituting the diatonic scale in two principal categories: the diatonic spaces and the color spaces .

The diatonic space is the joint space ranging between two notes close but of different names . All joint spaces of the not amplified diatonic scale are thus diatonic spaces. The your diatonic and the semitone diatonic are the two only types of diatonic spaces.

The color space is the joint space ranging between two close notes, of identical names but different heights . One of the two notes delimiting the color space - the intermediate note - is a sound of which the initial height was slightly faded. The sign indicating the modification height of the note concerned is called deterioration. The color space is thus obtained artificially , contrary to the space diatonic, which him, exists in a native state in the not amplified diatonic scale. There exists one type of color space: the chromatic semitone .

Your

The your diatonic is more joint big space of the diatonic scale.

Reduced to extended from only one octave, the diatonic scale contains five tons diatonic (example: gilded, Remi, F-ground, ground it and the-if , for the natural diatonic scale).
In practice, the diatonic ton is simply called your - without more precision. When one speaks about tone, indeed, it is obvious that one hears your diatonic , considering it does not exist any other species of tone. On the other hand, when one speaks about semitone, it is advisable not to omit the qualifier in order to distinguish “ semitone well diatonic ” and “ chromatic semitone ”, these two intervals not having neither same nature, neither the same extent, nor the same function.

Semitone diatonic

The Demi-ton diatonic is the smallest joint space of the diatonic scale. It is called thus because it is practically equal to half of the diatonic ton.

Reduced to extended from only one octave, the diatonic scale contains two semitones diatonic (example: semi-F and if-C , for the natural diatonic scale).

Chromatic semitone

The chromatic Demi-ton is a joint space pertaining on an amplified diatonic scale, i.e., with the chromatic scale (example: C-do♯). It is called thus because, just like the semitone diatonic, it is practically equal to half of the tone.

Reduced to extended from only one octave, the chromatic scale contains five chromatic semitones and seven semitones diatonic.

The chromatic semitone is defined as the joint space which, added to the semitone diatonic, transforms this last into your, that is to say, as the joint space which, cut off with the tone, transforms this last into semitone diatonic.

The diatonic ton is thus not equal to the sum of two semitones diatonic - as one could have supposed it - but with the sum of a semitone diatonic and a chromatic semitone . One can thus write: “ YOUR = semitone diatonic + chromatic semitone ”.

Extended from the spaces united in comas

The usual diatonic scale, is called cyclic scale , or scale pythagorician, in remembering that which defined it. Its various joint spaces were measured in Comma S by Holder at the end of the 17th century.

the cyclic name of scale comes owing to the fact that the degrees are obtained by the cycle (approximate) of seven fifths: F, C, ground, D, the, semi one, if, etc, and by reduction of the octaves - cf the article Equivalence of the octaves. Pythagore would have been the first to make of it the demonstration on a tended cord, the monocorde. Thus, if the cord into two is divided, this one doubles its frequency and produces the octave; if one makes vibrate the cord on his 3/2, this one produced the fifth; the new note thus obtained produces in its turn its own fifth, etc

  • the coma is theoretically the smallest difference which an exerted human ear can tolerate concerning a given height. For example, so instead of playing a semi one plays the height between halfway semi and F , i.e., two comas higher than the semi normal, the listener will test a faintness: “Is this semi , or F ? ”. On the contrary, if one plays the height higher of one coma than the note semi , the listener will not hesitate any more between semi and F : he will perceive well a semi , but simply, a semi a little high. This concept of tolerance is capital to include/understand the system of the temperament. In conclusion, beyond the coma, any difference in height, becomes unacceptable, because the degrees as well as the intervals which separate them, are not perceived any more with precision by the listener.

It is wrongly that the coma is regarded as the smallest difference in frequency which a human ear can perceive between two sounds: actually, a human ear, even not exerted, can distinguish quite lower differences: about one 1/100 of tone, and sometimes more. Moreover, a very weak interval between two notes emitted simultaneously produced a phenomenon of “very perceptible Beat” and which is made profitable besides to grant the instruments.

It is appropriate always to specify coma holdérien , because the word coma has only one general direction of “distance lower than the semitone” which can in theory indicate different extents. There exists also the coma zarlinien or syntonic coma - derived from the scale of Zarlino -, the coma of Sauveur , etc

  • One can thus write: “ 9 = 4 + 5 ” or, “ 9 = 5 + 4 ”.

  • Recapitulation on joint spaces:

In the table above, the accodances indicate tons them. The semitones diatonic are left blank. The intermediate notes appearing between brackets, are faded notes.

Simplification operated by the equal temperament

The temperament is a conventional simplification of the Western musical scale , consistent, in the case of very close notes but nevertheless different - theoretically separated by a coma -, to preserve only one note out of two for reasons of convenience. The temperament is thus an attempt at compromise enters, on the one hand, the auditive requirements, and on the other hand, the practical needs for certain instruments.

We know, for example, that between C and D , two intermediate notes are: ré♭ , and, a higher coma, do♯ . But on a moderated instrument, one will find between C and D “ only one intermediate note ”, which could be, according to the type of temperament, either ré♭ , or do♯ , or still, a height fulfilling at the same time the function of ré♭ and do♯ . Starting from the Rebirth, the temperament, by saving a note on two, thus allowed the development of the technique and instrumental virtuosity , in particular with regard to the keyboard instruments.

The equal temperament is a variety of temperament which spread during the 18th century, and which consists with to divide the octave into 12 Demi-ton S rigorously equal . Thus in this system, the semitone is worth 4,416 comas - instead of 4, for the semitone diatonic, and of 5, for the chromatic semitone -, and the tone, 8,833 comas - instead of 9. All the notes are thus false except one - generally, the the , starting point of the agreement -, but the ear is culturally accustomed to this type of agreement and tolerates the scale with the equal temperament, as if this one were the scale right. The advantage of the equal temperament is that, nonglad to save a note on two on the instrument concerned, it makes it possible moreover to play all possible deteriorations - until the doubles Dièse S and with the doubles Bémol S -, in the same piece, without having to modify the agreement of the instrument. With this system, it is from now on possible to modulate or to transpose in any from the 12 twelve Tonalité S of the chromatic scale.

The musical instruments concerned with the temperament are the instruments with its fixed , also called moderate instruments . The other instruments are called natural instruments .

1. Some examples of natural instruments : the voice, some string instruments rubbed, without Hoop S - Violin, viola, Violoncello, etc -, some instruments wind - Bagpipe, bombards, slide trombone, etc

2. Some examples of moderate instruments : instruments with keyboard - Piano, Organ, Harpsichord, Harmonium, Accordion, Celesta, etc -, some string instruments - Guitar, Mandoline, Lute, Toothing-stone, Viol, etc -, wind instruments with keys or pistons - trumpet, tuba, Clarinet, Oboe, Uilleann pipe, etc

  • Two notes theoretically separated by a coma - for example, ré♭ and (a higher coma) do♯ , or, F and (a higher coma) mi♯ - are called enharmonic notes or, synonymous notes . The interval which separates them is a decreased second.

  • the equal moderate scale gradually became the standard musical scale . When moderate instruments play with natural instruments, it is the system of the temperament which carries it: in a Sonata for Piano and Violin for example, the Violoniste goes from instinct, to agree on the piano, and will play in moderate fact . However, from the point of view of the notation, one continues to respect the orthography of a note, and one takes guard not to confuse the nomenclature of the enharmonic notes. For example, do♯ and ré♭ have same the height in vain on an instrument with fixed sounds, it is appropriate carefully to distinguish them, because it do not have the same function.

  • Thus, from a theoretical point of view, it is the range pythagorician , divided into 53 comas holdériens, which must remain the “ range of reference ”, because it justifies at the same time the theory of the deteriorations and the generation of the Tonalité S - cf the article Cycle of the fifths.

See too

Internal bonds

External bonds

  • Summarized major diatonic range

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