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, so called because notated without any alteration sign, plus 5 altered ones; the distance between each of 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

Now that we know the note names and alterations, we can move to the theory of intervals. Given the twelve sounds of our tempered system, through the theory of intervals we understand how these sounds relate to each other, which is essential to understand scales, arpeggios, chords, melodies, counterpoint and more. 

First of all, 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. 

As for all the other intervals, not belonging 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. 

At this point you might wonder why, besides the major and perfect intervals belonging to the diatonic notes of the major scale, some of the minor, augmented and diminished intervals are left empty. The answer is: in theory, all those empty spaces can be filled, but the resulting note would be simply a duplicate of the intervals previously seen. For completeness, in the following table you will find all the intervals not used because of enharmonic relation. Consider that, for 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, 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 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, an interval was chromatic if belonging to one of the seven chromatic scales, and same can be said for the enharmonic ones.

 

The question is, how to transfer these concept to our actual music system, and how all this relates to the actual meaning of diatonic and chromatic interval? If the Greek diatonic modes clearly match the actual major scale modes, can we just say that diatonic intervals are such if belonging to the major scale modes? And what about the Greek chromatic scales, so different from our single chromatic scale?    

 

Starting from this last question, we can say that the double semitone of the Greek chromatic tetrachord offers us a hint to consider it as a distant relative of the actual chromatic scale. Therefore, in contemporary terms, we can simply say that an interval is chromatic when belonging to the chromatic, i.e. dodecafonic scale. Curiously enough from an etymological standpoint, the Greek word chromatikos (χρωματικόζ), musically referred to the chromatic species, could also mean, more generally, flourished, 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, are we allowed to transfer that idea to our music system, and say that diatonic is any interval belonging only to the major scale modes, leaving out all the other minors, pentatonics and more? We cannot be further from the truth. Despite the similarities, music has evolved through the Centuries, and the two systems are so different that analogies ad litteram can be misleading, and bring to incoherent conclusions. An interval in Ancient Greece was diatonic because belonging to the diatonic species, i.e. all the scales used 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 sound belonging to the chromatic scale, or better said, any sound non diatonic to a specific given scale.

 

By contrast, if we decide to keep the Greek definition of diatonic ad litteram, what would we call the intervals among all the other scales? Does 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?  

Few more words on the etymology of diatonic: some sources mention dia tonikon (διά τòνικον) as the original Greek expression, meaning literally “through the tones”. Considering our conclusions on the definition of diatonic intervals, it’s self evident that this etymology doesn’t provide a satisfying answer. On the other side, if we relate diatonic to dia tonon (δια τóνον), we have a more clear answer to our question, since tonos (τóνοζ), among its other meanings, was used to denote in general the Greek scales. 

To wrap up this brief inquiry, we can say that, based on the Greek music system and  etymologies, given any scale in a specific key, diatonic is any interval between two or more notes belonging to that scale. All the other intervals, not belonging to that given scale, will be called chromatic. 

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

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