The diatonic and chromatic intervals between the twelve sounds of our music system.

In music, an interval is the distance between two sounds, measured in terms of tones and semitones. In our tempered system, perfected by Johann Sebastian Bach in the XVII° century, there are 7 “natural” sounds, notated without any alteration sign, plus 5 altered ones, and the smallest interval between these twelve sounds is called semitone.

A) NOMENCLATURE AND ALTERATIONS

For the 7 natural sounds we use the alphabet letters C, D, E, F, G, A, B, respectively DO, RE, MI, FA, SOL, LA, SI in Italian nomenclature.

The 5 altered sounds correspond to the semitone found between the notes C-D, D-E, F-G, G-A and A-B, while there’s no semitone between E-F and B-C, as shown below here.

Every altered sound can be notated in two different ways, with a sharp (#) or a flat (b) sign, for a total of ten additional notes on the music staff. The sharp sign is used to raise a natural note up a semitone, while the flat lowers a natural note of a semitone. Two notes belonging to the same altered sound are called enharmonic, meaning “one sound” from Greek (έιζ αρμονία).

 

B) THEORY OF INTERVALS

Given the twelve sounds of our tempered system, the theory of intervals explains how these sounds relate to each other, which is essential to understand scales, arpeggios, chords, melodies, counterpoint and more. 

There are two types of intervals: chromatic, based on the 12 sounds of the chromatic scale, and diatonic, based on any other scale (more on the exact difference between chromatic and diatonic later in this article).

In Western music, the distance among the seven sounds of the major scale is used as a reference to establish the distance among any two notes. Being the major scale a heptatonic one, its intervals are enumerated from one to seven. The 2nd, 3rd, 6th and 7th intervals are called major, while the relation of 4th and 5th is called perfect. 

For all the other intervals that don't belong to the diatonic major scale, three different terms are used: minor, diminished and augmented. In the following synoptic table the five species of intervals have been outlined with regard to the seven degrees of the major scale. 

As you can see, some of the minor, augmented and diminished intervals from the previous table are left empty. Theoretically, all those empty spaces can be filled, but the resulting note would be simply a duplicate of another interval. In the following table you will find all the intervals not used because of enharmonic relation. Consider that, for the practical purpose of an easier sight read, double flats or sharps are normally replaced by their corresponding natural note.

Keep in mind that all intervals belonging to the major scale pattern are diatonic (to the major scale), while all the other ones can be classified as chromatic. 

 

This introduces us to the last part of this article: the definition of diatonic and chromatic intervals. 

 

C) AN INQUIRY ON CHROMATIC AND DIATONIC INTERVALS.

 

Unfortunately, music theory is not unanimous on the definition of diatonic and chromatic intervals, and very different answers can be found on multiple sites. Some recognize as diatonic any scale with the seven “natural” notes, some just the heptatonic major scale in any key, and there are even more answers than this out there. 

 

To clear this debated matter, we need to understand what was the original meaning of diatonic and chromatic, and then adapt those concepts to our actual music system. In Ancient Greece, scales were a succession of sounds at specific intervals of tones, semitones and quarter tones, and the foundational block was represented by the tetrachord, i.e. four notes. Each scale had three distinct species, or genera, called diatonic, chromatic and enharmonic, and each one with a different intervallic distance among its pitches. 

The following is a synopsis of the seven Greek modes in all the species. 

From The Harmonics of Aristoxenus, with introduction by Professor H. S. Macran

Besides the enharmonic species, involving quarter tones no more in use in Western contemporary music, the tetrachord of a diatonic scale was always based on the tone-tone-semitone pattern, variously disposed because of the different root note, while semitone-semitone-tone and a half belonged to the chromatic ones. Same idea as our scale modes. 

Based on all this, we can say that diatonic, for the Ancient Greeks, was any interval belonging to one of the seven diatonic scales. On the other side, a chromatic or enharmonic interval belonged respectively to one of the seven chromatic or enharmonic scales.

The question is, how to transfer these concepts to our current music system, and how to relate them to the actual meaning of diatonic and chromatic? Since the Greek diatonic modes match the actual major scale modes, can we just say that diatonic intervals are such when belonging to the major scale modes? But then, what about the Greek chromatic scale modes, so different from our single chromatic scale?    

 

Starting from this last question, we can say that the actual chromatic scale can be traced to the double semitone pattern found in the Greek chromatic scales. Therefore, in contemporary terms we can simply say that an interval is chromatic when belonging to the chromatic scale. Curiously enough from an etymological standpoint, the Greek word chromatikos (χρωματικόζ), musically referred to the chromatic species, could also mean, more generally, flourished or artistic: another hint that might tell us something about the “ornamental”, quasi unorthodox quality of the chromatic scales, even if having their independent life as a species of the Greek scale system. 

And now we come to the diatonic interval. If diatonic was, for the Ancient Greeks,  any interval belonging to the diatonic scales, can we transfer that same idea to our music system, inferring that diatonic is any interval belonging only to the major scale modes, leaving out all the other minor and pentatonic scales? I don't think so. Despite the similarities, music has evolved through the Centuries, and the two systems are so different that analogies ad litteram can be misleading, and cause incoherent conclusions. An interval in Ancient Greece was diatonic because belonged to the diatonic species, i.e. all the scales employed at that time, at least in the Diatonic species. 

Applying this same idea to the present music system, we can say that diatonic is any interval belonging to any given scale, be it major, minor, pentatonic and more, with the only exception of the chromatic scale. By contrast, chromatic is any interval belonging to the chromatic scale, or better said, any interval non diatonic to a specific given scale.

Otherwise, keeping the Greek definition of diatonic ad litteram, what would we call the intervals among all the other non major scales? Would that mean that Ab is not diatonic to Gb minor melodic only because we are not in the major scale realm? Or F# not diatonic to B minor harmonic, and so on? Should we call all these “chromatic intervals” only because not belonging to a major scale mode? Certainly not, they are all diatonic to a specific given scale!  

To wrap up this brief inquiry, we can say that, given any scale in a specific key, diatonic is any interval between two or more notes belonging to that scale, while all the other intervals, unrelated to that given scale, will be called chromatic. 

Thank you for reading and see you in the next one!

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