L'Antica Musica
L'Antica Musica was a treatise published in 1555 by Nicola Vicentino, which explores how Renaissance-era advancements in musical tuning could be used to adapt the lost traditions of Ancient Greek musicians in such a way that blends them with the sensibilities of the 16th century. It is perhaps most revered in xenharmonic communities for its attestation and argument for 31 equal divisions of the octave†, a tuning for which Vicentino had designed his own custom instruments.
†Vicentino's suggestion was likely not an equal temperament as we think of it today, but rather a well temperament or MOS scale based on meantone temperament.
On Music Theory
The first book of L'Antica Musica, On Music Theory, is intended as a sort of "recap" of the principles of Ancient Greek music theory, and the means by which those principles arose.
According to Greek musical tradition, just intonation was discovered by the mathematician Pythagoras when he noticed that the hammers used by blacksmiths would produce more consonant sounds with one another if the sound that they displaced created certain frequency ratios; notable was the 3/2 ratio, which was considered the most consonant of all. Ancient Greek musicians considered the usage of low-complexity just intonation intervals as the primary way of tuning music
According to Vicentino, Pythagoras also went on to construct the first tetrachord, by stacking two concordant whole tones within the span of a perfect fourth. This construction, Vicentino asserts, would pave the way for more such tetrachords to be devised, and they were split into three "genera" based on the step sizes. Vicentino provides diagrams to display the forms of these genera, with their steps arranged from the largest to the smallest.
| Genus | Step Sizes | Comments | ||
|---|---|---|---|---|
| L | M | s | ||
| Diatonic | Tone | Tone | Limma | Vicentino seems to consider the two "tones" necessarily equal. |
| Chromatic | Minor Third | Apotome | Limma | |
| Enharmonic | Major Third | Diesis | Diesis | The diesis is said by Vicentino to divide the limma into two equal parts. |
Vicentino additionally sorts the genera by their "sweet" (Italian: dolce) quality of sound. This appears to be an attempt to translate the Greek term μαλακός, which was used by Boethius to describe scales; however, most other Romance scholars used the word mollis (Italian molle) for this. As Boethius used it, the term specifically describes melodies and scale forms that are said to create a sense of intimacy and resolution by the inclusion of exceedingly small intervals in specific places. Vicentino gives little elaboration on what precisely is meant by dolce, but the term is always used alongside a note of a genus's smaller available step sizes.
Vicentino goes on to discuss the various permutations of these tetrachords that can be constructed by putting the same step sizes in a different order; these permutations constitute the "species" of tetrachords. These permutations can be used to construct eight church modes, which Vicentino enumerates as follows:
| Mode | Pattern | Comments |
|---|---|---|
| Dorian | | LMs sLM | |
| Hypodorian | sLM | LMs | |
| Phrygian | | MsL MsL | In diatonic genus, resembles modern Mixolydian mode |
| Hypophrygian | MsL | MsL | In diatonic genus, resembles modern Dorian mode |
| Lydian | | sLM LMs | In diatonic genus, resembles modern Melodic Minor scale |
| Hypolydian | LMs | sLM | |
| Mixolydian | sLM | sLM | In diatonic genus, resembles modern Phrygian mode |
| Hypermixolydian | sLM sLM | | In diatonic genus, resembles modern Locrian mode |
The | symbol is here used to represent a step of precisely 9/8, which separates the two tetrachords from one another.
Note that these modes are constructed by Vicentino's enumeration of the tetrachords, and do not represent rotations of a single scale pattern. Some of these modes are thus rather odd, such as Dorian Diatonic having two consecutive semitones, or Lydian Diatonic having four consecutive whole tones.
Todo: document rest of books in treatise
