L'Antica Musica

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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.

Tetrachord Genera

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. On the rest of this page, the term will be left untranslated to avoid the ambiguity with English senses of "sweet."

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:

Eight Modes

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.

On Practice I

Following the book on ancient theory is the first book on contemporary practice of the Renaissance era when the treatise it was published. The first several chapters summarize musical notation; to accommodate for the microtones of Vicentino's proposed tuning, he suggests a circular accidental which represents raising a note by the interval of a diesis (one step of the 31-form).

Chapters XV through XL enumerate the intervals of the 31-form, gives each a name, and describes their unique nature and usage; Vicentino specifically uses properties such as consonance potential, subjective emotional content, and dolce qualities to describe the nature of the intervals used as steps or leaps in a melody.

Intervals of the 31-form

Step	Name	Melodic Quality		Comments
		Ascending	Descending
0	Comma	N/A (tempered out)		Of note because the archicembalo was well-tempered
1	Diesis	Concordant, lax, and dolce		To be used in alternating succession
2	Chromatic Semitone	Tense, yet cheerful	Lax and sad
3	Diatonic Semitone
4	Minor Tone	Lax or tense		Assimilates tension to nearby intervals
5	Major Tone	Powerful and tense	Lax	64/63 "is not discernible in singing, but in the tuning of instruments their difference is indispensable."
6	Chromatic Tone
7	Minimal Third	Lax	Somewhat tense and very sad
8	Minor Third
9	Supraminor Third			Also known as "proximate" third; "neutral" had not yet been coined
10	Major Third	Tense and imperious	Somewhat tense; sad if accidental
11	Supermajor Third	Extremely tense	Extremely sad and lax	Notably distinct from the major third despite being separated by 64/63
12	N/A	N/A		Vicentino skips this interval in his analysis
13	Perfect Fourth	Tense; points to the thirds	Lax	Level of tension when ascending depends on type of tetrachord used
14	Superfourth	Lively	Sad and lax	Also known as "proximate" fourth
15	Augmented Fourth	Vivacious and forceful	Funereal and sad	Vicentino advocates for liberal usage of tritones for "marvelous effect"
16+	Octave Inversions	Inverse qualities of their inversions

Todo: document rest of books in treatise