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. μαλακός translates to English as "gentle" or "soft". 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. This first practice book is centered primarily around melodic composition, with the harmonic considerations not being featured until the following book.

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).

The majority of the book, however, is spent 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	Natural Tone	Powerful and tense	Lax	64/63 "is not discernible in singing, but in the tuning of instruments their difference is indispensable."
6	Major 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	Notably distinct despite being separated by 64/63
11	Supermajor Third	Extremely tense	Extremely sad and lax
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

On Practice II

In the second book on musical practice, Vicentino discusses the three methods of writing effective music. The first is the usage of melodic and harmonic intervals to mimic the character of sung lyrics; the second is the usage of melodic and harmonic intervals to create clear senses of tension and release; and the third is to balance different types of characteristics to create a clear sense of motion from start to finish. The bulk of the second book focuses on the principles of writing melodies and harmonies that play into these methods.

Vicentino applies the principles of counterpoint regardless of the method: all voices must begin and end a melodic line on the tonic pitch, contrary motion is preferred between voices, parallel perfect consonances are dispreferred between voices, and resolutions must be approached through stepwise motion.

In the following chapters, the natures of harmonic consonances are discussed, much the same as the melodic natures in the preceding book. Vicentino advocates specifically for the usage of syncopation, whereby two lines have the same rhythm offset by some consistent amount until the resolution; this syncopation will create dissonances between voices that would otherwise have been consonant, which allows for these dissonances to resolve

Intervals of the 31-form

Step	Name	Harmonic Function	Comments
1	Diesis	N/A	Does not occur between voices
2	Chromatic Semitone	Resolves to minor third or unison	Vicentino prefers semitone suspensions over wholetones.
3	Diatonic Semitone
4	Minor Tone	Resolves to third or unison
5	Natural Tone
6	Major Tone
7	Minimal Third	Imperfect consonance approached by seconds
8	Minor Third
9	Supraminor Third
10	Major Third	Imperfect consonance approached by fourths
11	Supermajor Third
12	N/A	N/A	Vicentino skips this interval in his analysis
13	Perfect Fourth	Resolves to major third or perfect fifth
14	Superfourth
15	Augmented Fourth	Resolves by contrary motion to third or sixth
16	Diminished Fifth	Fudging of either an augmented fourth or imperfect fifth
17	Imperfect Fifth	Half-resolves to perfect fourth or superfourth; or resolves to perfect fifth or minimal sixth
18	Perfect Fifth	Perfect consonance approached by fourths
19	Superfifth	N/A	Does not occur between voices
20	Minimal Sixth	Imperfect consonance approached by diminished fifth
21	Minor Sixth	Imperfect consonances leading away from fifths
22	Supraminor Sixth
23	Major Sixth	Imperfect consonances approached by sevenths
24	Supermajor Sixth
25	Minimal Seventh	Resolves to sixth
26	Minor Seventh
27	Supraminor Seventh
28	Major Seventh	Resolves to octave
29	Supermajor Seventh
30	N/A	N/A	Octave complement of the diesis; not mentioned.
31	Octave	Perfect consonance approached by ninths or sevenths

Vicentino notes that the ear can hear dissonant intervals such as tritones as more concordant when approached via small steps such as dieses and semitones that create a more dolce melody.

Todo: finish summarizing Practice II, document rest of books in treatise