This page will cover brief explanations of tetrachords and the three genera: diatonic, chromatic, and enharmonic. In addition, it will explain basic information on octaves, fifths, fourths, whole tones, and how these are used to construct the full Ancient Greek scale according to Boethius.

The tetrachord is a fundamental building block of the Ancient Greek tuning system. According to Boethius, a full scale consists of the lowest tone (the proslambanomenos), the hypaton tetrachord which begins a whole tone up from the proslambanomenos, a conjunct (i.e., sharing a note) tetrachord called the meson, either a conjunct tetrachord called the synemmenon or a disjunct one called the diezeugmenon, which begins a whole tone up from the mese on a note called the paramese, and finally the hyperboleon tetrachord, which is either a wholetone up from the synemmenon tetrachord or conjunct with the diezeugmenon tetrachord.

Every tetrachord in the scale will be tuned such that the intervals are proportionate to each other. The intervals in one tetrachord will sound identical to the intervals within another.

diatonic

The diatonic genus is one of three genera typically used in Ancient Greek music. The diatonic is characterized by having a relatively small interval between the 3rd to 4th note in the tetrachord, especially when compared to chromatic or enharmonic tuning. In modern musical terms, a diatonic tetrachord might sound approximate to a half step followed by two whole steps. A full diatonic scale, using the diezeugmenon, sounds similar to a modern minor scale.

Aristoxenus further divides the diatonic into two sub-genera, the sharp diatonic and the soft diatonic. The sharp diatonic sounds most similar to the diatonic put forth by Archytas and Boethius, while the soft diatonic flattens the 3rd note.

The chromatic genus is one of three genera typically used in Ancient Greek music. The chromatic is characterized by having a moderately sized interval between the 3rd to 4th note in the tetrachord, with the interval being larger than the one found in the diatonic and smaller than the one found in the enharmonic. In modern musical terms, a chromatic tetrachord might sound approximate to two half steps followed by a minor third.

Aristoxenus further divides the chromatic into two sub-genera, the tonic chromatic, the hemiolic chromatic, and the soft chromatic. The hemiolic chromatic has a flatter 2nd and 3rd note than the tonic chromatic, and the soft chromatic has a flatter 2nd and 3rd note than the hemiolic.

enharmonic

The enharmonic genus is one of three genera typically used in Ancient Greek music. The enharmonic is characterized by having a large interval between the 3rd to 4th note in the tetrachord, especially when compared to the diatonic or chromatic. In modern musical terms, an enharmonic tetrachord might sound approximate to two quarter steps followed by a major third. Because of its reliance on quarter tones, the enharmonic scale does not have a close approximate in common Western music theory.

conjunct

The term conjunct refers to two tetrachords stacked on top of each other such that the top note of the lower tetrachord is the same note as the bottom note of the higher tetrachord.

disjunct

The term disjunct refers to two tetrachords stacked on top of each other such that the top note of the lower tetrachord is a whole tone lower than the bottom note of the higher tetrachord.

The octave is one of the fundamental intervals of the Ancient Greek musical tuning system. It is a consonance and can be heard by plucking two strings, one of which is double the length of the other. The octave is so related to the ratio of 1:2. Accordingly, a note that is one octave up from a previous one will be twice the frequency, and a note that is an octave down from the previous one will be half the frequency (i.e., an A one octave up from an one tuned to 432 Hz would have a frequency of 864 Hz, or an A one octave down from 432 would have a frequency of 216 Hz).

fifth

the diapente

The fifth is another consonance in Ancient Greek music. It can be heard to plucking two strings with lengths in a ratio of 2:3 (i.e., one is 50% longer than the other). The frequencies of two notes heard as a fifth apart will likewise adhere to this ratio: a fifth up from an A at 432 Hz would be a note at 648 Hz, approximately an E in modern tuning.

The fourth is also a consonance in Ancient Greek music. A harmonic fourth can be created by plucking two strings, one of which is longer than the other by a ratio of 3:4. Ergo, if the first string is 9 centimeters long, the second would be 12 centimeters long. The frequencies of two notes heard as a fourth apart will likewise adhere to this ratio: a fourth up from an A at 432 Hz would be a note at 576 Hz, approximately a D in modern tuning.

whole tone

The whole tone, which can be represented by the ratio of 9:8, can be derived through several means in Ancient Greek tuning. First, if a base note is taken, and then a fourth and a fifth up from that base note is played, the distance between those two notes will be a whole tone. A whole tone, moreover, will be the remainder of an octave if two fourths are stacked on top of each other–i.e., the top note of the first fourth is the bottom note of the second fourth. An example of a whole tone occurs at the bottom of each full scale.