The chromatic genus is a genus of divisions of the tetrachord characterized by an upper interval of a minor third. The remainder of the tetrachord (the pyknon) is divided into two adjacent semitones (hence this genus is the origin of the modern term, chromatic). In ancient Greek music there were three genera (singular: genus) for classifying musical scales: diatonic chromatic enharmonic, diatonic being the simplest and enharmonic the most complex. ... The tetrachord is a concept of music theory borrowed from ancient Greece. ... A minor third is the smaller of two commonly occurring musical intervals that span three diatonic scale degrees. ... The musical interval of a half step, semitone, or minor second is the relationship between the leading tone and the first note (the root or tonic) in a major scale. ... The chromatic scale is any musical scale that contains more than one consecutive half-step (in other words two adjacent pairs of scale degrees or members which are separated by a semitone). ...

Note that the scale generated by the chromatic genus is not the modern chromatic scale. The modern chromatic scale has 12 pitches to the octave, and consists only of semitones. In contrast, the ancient Greek chromatic scale had seven tones to the octave (assuming alternating conjunct and disjunct tetrachords), and had undivided minor thirds as well as semitones. The chromatic scale is any musical scale that contains more than one consecutive half-step (in other words two adjacent pairs of scale degrees or members which are separated by a semitone). ...

 Scale generated from the chromatic genus D Eb E G A Bb B D Eb E G A... 

 Modern chromatic scale D Eb E F F# G Ab A Bb B C C# D Eb E... 

Tunings of the chromatic

Thrasyllus of Mendes gave the traditional Pythagorean tuning of the chromatic genus: Thrasyllus of Mendes was an Egyptian astrologer, astronomer and mathematician who lived during the reign of the Emperor Tiberius, whom he served. ... Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. ...

 hypate parhypate lichanos mese 4/3 81/64 32/27 1/1 | 256/243 | 2187/2048 | 32/27 | -498 -408 -294 0 cents 

Archytas replaced the 81/64 with the simpler and more consonant 9/7, which he used in all three of his genera: The cent is a logarithmic unit of measure used for musical intervals. ... Archytas (428 BC - 347 BC), was a Greek philosopher, mathematician, astronomer, statesman, strategist and commander-in-chief. ...

 hypate parhypate lichanos mese 4/3 9/7 32/27 1/1 | 28/27 | 243/224 | 32/27 | -498 -435 -294 0 cents 

Didymus's chromatic has only 5-limit intervals, with the smallest possible numerators and denominators. Also note that the successive intervals are all superparticular numbers: The cent is a logarithmic unit of measure used for musical intervals. ... Didymus the Musician was a music theorist in Alexandria of the 1st century AD who combined elements of earlier theoretical approaches with an appreciation of the aspect of performance. ... Just intonation tunings and scales can be described by giving an upper bound on the complexity of the harmonies admitted by the tuning or scale. ... Superparticular numbers, also called epimoric ratios, are improper rational fractions of the form Superparticular numbers were written about by Nicomachus in his treatise Introduction to Arithmetic. They are useful in the study of harmony: many musical intervals can be expressed as a superparticular ratio. ...

 hypate parhypate lichanos mese 4/3 5/4 6/5 1/1 | 16/15 | 25/24 | 6/5 | -498 -386 -316 0 cents