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Improvised, Free Ornamentation in Violin Music of the 18th Century

️Yuki Horiuchi️ and ️Akira Takaoka




Ornaments for Corelli's Violin Sonatas, op.5, V/1, mm.1-6 (see Example 1.1 below) in a manuscript by Johan Helmich Roman (1694-1758)
Shelfmark: Ro 97:57, Musik- och teaterbiblioteket, Stockholm, Sweden (courtesy of librarian Sebastian)

Our research aims to identify guiding principles for the ornamentation of 18th-century music, which will also serve as a rule system for algorithmic composition. What follows is an outline of our ongoing joint research.

This webpage, co-authored by Yuki Horiuchi️ and Akira Takaoka, started as supplementary reference material for our paper presentation at the 23rd Annual Meeting of the Japan Music Expression Society (日本音楽表現学会 第23回大会) in Sendai, Japan, on June 21 and 22, 2025 (The handout in Japanese (学会発表の日本語ハンドアウト) is available here). Yuki Horiuchi is the first author of the paper (発表論文の筆頭著者). This page now outlines our ongoing joint research into the ornamentation of 18th-century music.

Dr. Yuki Horiuchi️ 堀内由紀️ is a distinguished Baroque violinist and musicologist, currently a lecturer of music at J.F. Oberlin University in Tokyo, Japan, and a member of Bach Collegium Japan (BCJ). She leads this joint research project (この共同研究の筆頭研究者).
Akira Takaoka 高岡 明 is a composer and music theorist. In addition to the performance practice of the 18th century, he specializes in atonal theory, compositional algorithms, and methodological issues such as the roles of metaphor in music theory. He is currently a professor of music at J.F. Oberlin University and Tokyo College of Music and a lecturer of music theory at Tokyo University of the Arts in Tokyo, Japan.

This joint research is supported by the Rohm Music Foundation.

1. Improvised, Free Ornamentation in Violin Music of the 18th Century and its Sources that Have Survived to Date

(We use Scientific Pitch Notation (SPN) to denote pitches.)

1.0. Introduction: The Purpose and Outline

The art of ornamentation is always a balancing-act between the performer's intuition and the composer's specification; all that can be demonstrated from historical sources is a series of such reconciliations as proved acceptable to (some) 18th-century tastes. (Hogwood 2013a, IX)
In Corelli's time, performers customarily improvised ornamentation. Due to its improvisational nature, however, such free ornamentation was rarely notated. This study aims to identify the rules that govern the patterns of free ornamentation found in Corelli's Violin Sonatas, Op. 5. Zaslaw (1996, 95) points out that "Following their [the sonatas'] publication they attained the status of classics, and by 1800 had been republished more than 50 times, in Amsterdam, Bologna, Florence, London, Madrid, Milan, Naples, Paris, Rome, Rouen and Venice. No other set of works enjoyed a comparable reception in the 18th century." We expect, therefore, that if the rules are identified, they will serve as guiding principles for today's performers of the 18th-century music to improvise their own ornaments. With respect to the patterns of ornamentation, we have classified all surviving notated ornaments from the Amsterdam edition (Corelli 1710) all the way through Johan Helmich Roman (c. 1715–21), Michael Christian Festing (c. 1733-36), Francesco Geminiani (1776), Giuseppe Tartini (n.d.), to Francesco Galeazzi (1817). Through the analysis of the relationships among those ornamental patterns, we have found that a relatively small set of rules governs the patterns. In other words, those various patterns of ornamentation can be derived from the set of rules, and any ornaments derived in this way do not entirely deviate from the 18th-century Italian style of free ornamentation. To test the plausibility of this finding, we have written a computer program that implements the set of rules and generates ornaments, and found that it can generate all the surviving notated ornaments. Consequently, observing the set of rules, today's performers will be able to improvise their own ornaments without entirely deviating from the stylistic framework of the 18th-century Italian free ornamentation. Just as 18th-century performers experimented with a variety of ornamental patterns, today's performers can try out new combinations of the rules to test various new, original ornamental patterns that will be "acceptable to (some) 21st-century tastes" without entirely deviating from the stylistic framework of the 18th-century Italian free ornamentation. Having finished the "lexicology" of 18th-century ornamentation, our next goal will be to find its pragmatics and its implementation in a computer program.

装飾法は、作曲家が記した演奏に関する指示と演奏家の直感の間のバランスを取る行為である。18世紀において、当時の嗜好を反映しながら、そのバランスを取る試みが絶えることなく継続していたことは、歴史的資料が証明している。 (Hogwood 2013a, IX)
コレッリの時代には、演奏者は即興的に装飾を演奏するが習慣がありました。しかし、その即興性ゆえに、そうした自由装飾は稀にしか記譜されていません。本研究では、アムステルダム版（1710）からジェミニアーニ（1776）、タルティーニ（n.d.）、ルーマン（c. 1715–21）、フェスティング（n.d.）、ガレアッツィ (1817) に至るまで、コレッリの《ヴァイオリン・ソナタ》作品５ (1700) の緩徐楽章に適用された現在入手し得るすべての記譜された自由装飾のパターンを分類し、それらのパターンが従う原則の特定を試みました。コレッリの作品５は、ザスロー (Zaslaw 1996, 95) やタラスキン (Taruskin 2010, 524–525) が指摘するように、18世紀全般を通じて比類ない影響力を持った作品であったため、そうした原則は、18世紀の音楽を演奏する際の有用な指針になると思われます。そうした装飾パターン間の関係性を分析した結果、それらの装飾パターンは、比較的少数の原則の組合せによって規定されていることが判明しました。つまり、コレッリの作品５に付されたあらゆる自由装飾のパターンは、それら比較的少数の規則を適用することによって導出可能であると思われます。そこで、それらの原則を装飾生成のアルゴリズムとするコンピュータ・プログラムを作成し、その導出可能性を検証しました。それらの原則によって生成された装飾は、いかに多様であっても18世紀イタリアの自由装飾の様式から完全に逸脱することはありません。従って、そうした原則が判明した結果、現代の演奏家は、18世紀イタリアの自由装飾の語彙を習得することが可能となり、18世紀の演奏家が様々な装飾パターンを試みたように、現代の演奏家も原則の新たな組み合わせを試し、18世紀イタリアの自由装飾の様式的枠組みから完全に逸脱することなく、「21世紀の嗜好を反映した」様々な新しい独創的な装飾パターンの探求が可能になると期待されます。装飾法の語彙論がある程度判明しましたので、次の研究目標としては、そうした装飾語彙の用法 usage を規定する装飾法の「語用論 Pragmatics」とそのコンピュータ・プログラムへの実装になります。

1.1. Notated examples of ornamentation

Not many notated ornaments of 18th-century violin music have survived to date. Some of the rare exceptions are those written for Corelli's Violin Sonatas, op.5, which was published in 1700, reprinted more than fifty times even during Corelli's lifetime, and remained the most influential violin piece throughout the 18th century.

For example, the following is the first five measures from Corelli's Violin Sonata, op.5, V/1:


Example 1.1: Mm. 1-5 from Corelli's Violin Sonata, op.5, V/1 (Corelli 1700)


The video below (courtesy of Tokyo University of the Arts) shows that Yuki Horiuchi improvises her own ornaments for those five measures:



Copyright (C) 2023 Tokyo Geidai (Tokyo University of the Arts)

Example 1.2: The ornaments for the five measures above played by Horiuchi (2018), transcribed by Takaoka.


The following are the ornaments applied to Corelli's op. 5, V/1, mm. 1-2 by Horiuchi (2018a, 2018b) and violinists of the 18th century (Scroll down):



Copyright (C) 2024 Yuki Horiuchi

Example 1.3: Free ornamentation by Yuki Horiuchi, transcribed by Akira Takaoka, and violinists from the 18th century (Scroll down)

  1.2. Sources ("*" indicates the locations of anonymous manuscript sources.)

Some examples of ornamentation applied to Corelli's op. 5 are available in Zaslaw (1996), Hogwood and Mark (2013a, 2013b), and so on We have also assembled, edited, and typeset all the extant notated ornaments in the manner of Ex. 1 from Zaslaw (1996, 100-4) so that performers, researchers, composers, and music lovers can compare all of them at once on the same pages.

The sources we have examined for our research are the following (click on the "sources" button below):


   


  Corelli, Arcangelo. 1700. Sonate a Violino e Violone o Cimbalo, op.5. 1st ed. Rome: Gasparo Pietra Santa.

  _______. 1710. Sonate a Violino e Violone o Cimbalo di Arcangelo Corelli Da Fusignano Opera Quinta Parte Prima Troisième Edition ou l’on a joint les agréemens des Adagio de cet ouvrage, composez par Mr. A. Corelli comme il les joue. Amsterdam: Estienne Roger. RISM ID no. sources/990011197.

  Dubourg, Matthew. c.1725. Corelli’s Solos Grac’d by Dobourg [sic], versioni ornate delle Sonate op. 5 di Corelli. Microfilms A1494 M and A2337. Jean Gray Hargrove Music Library, University of California, Berkeley (US-BEm).

  Festing, Michael Christian. c.1733-36. Manuscript. Add MS 71244, The British Library (GB-Ll).

  Hogwood, Christopher and Ryan Mark ed. 2013a. Sonatas for Violin and Basso continuo, With Contemporary Embellishments, and a Keyboard Realisation by Antonio Tonelli (1686-1765), vol. 1. Kassel: Bärenreiter.

  Hogwood, Christopher and Ryan Mark ed. 2013b. Sonatas for Violin and Basso continuo, With Contemporary Embellishments, and a Keyboard Realisation by Antonio Tonelli (1686-1765), vol. 2. Kassel: Bärenreiter.

  Lund* n.d. Manuscript. Saml Wenster L: 61, Lund Universitetsbiblioteket, Lund (S-L).

  Manchester*. c. 1750. Manuscript. Newman Flower Collection: MS. 130 HD 4 v. 313, Henry Watson Music Library, Manchester, (GB-Mp).

  McGibbon/McLean. c. 1740. Manuscript. MS 957, Jean Gray Hargrove Music Library, University of California, Berkeley (US-BEm).

  Roman, Johan Helmich. c. 1715-1721. Ornamentikförslag till Corellis, op.5. Manuscript. Ro 61:3 and 4, and Ro 97:57, 58, and 60, Musik- och teaterbiblioteket, Stockholm. Also available under "Romansamlingen" at ALVIN: Platform for digital collections and digitized cultural heritage, www.alvin-portal.org/

  Tartini, Giuseppe. n.d. Tartini Miscellanea Parti incomplete. Manuscript. D.VI. 1896, Biblioteca Antoniana, Padua (I-Pca). RISM ID no. 850731001.

  Tonelli, Antonio. n.d. Realizzazione del basso continuo dell’opera quinta di Arcangelo Corelli. Manuscript. Mus.F. 1174, Biblioteca estense universitaria, Modena.


We are grateful to the following librarians for kindly providing us with the PDF copies of those manuscripts in the list above and allowing us to post them on this Web page:

Mr. Sebastian at Musik- och teaterbiblioteket, Stockholm
Ms. Fiona McHenry at Rare Books & Music Reference Team, The British Library, London
Mr. John Shepard at Jean Gray Hargrove Music Library University of California, Berkeley
Ms. Åsa Sjöblom at Department of Collections, Lund University Library, Lund


      Example 1.4: List of Sources (PDF copies of these sources will soon be posted here with permission.)

  1.3. Corelli. Violin Sonatas, op.5: Notated Examples of Ornamentation

Hogwood and Mark (2013a, 2013b) come with solo parts with ornaments notated by various 18th-century violinists, copied from the manuscripts listed in Example 1.4. Although they are useful, since each of them does not align with the B.C. part, it's rather inconvenient for us to examine the onsets of those ornaments with respect to harmonies. So, we have prepared scores in the manner of Zaslaw (1996, 100-4) that allow us to examine the solo parts alongside the B.C. parts on the same pages.

Click on the following buttons to see examples of ornaments applied by 18th-century violinists to Corelli's Violin Sonatas, op.5 (Scroll down to see the entire score.):


   

   


   

   


   

   


   

   


   

   


   

   


   

   


   

   


   

   


   

   


   

   



      Example 1.5: Ornamental passages found in manuscripts in Example 1.4.


Some notes on the part by Roman are in order here. In all of the scores in Example 1.5, we added footnotes on the differences between Hogwood and Mark (2013a, 2013b) and manuscripts. We gave no footnotes on the differences in No. 11, Movement 1, however. There are too many to mention. For example, m. 4 in Roman's manuscript (Ro 97:60, Roman c. 1715-1721) looks like the following:



Example 1.6: M. 4 from No. 11, Movement 1 in a manuscript by Johan Helmich Roman
Ro 97:60, Musik- och teaterbiblioteket, Stockholm, posted with permission

And the following is the same measure from Hogwood and Mark (2013b):



Example 1.7: The same measure from Hogwood and Mark (2013b), posted with permission

Roman's handwriting seems to indicate that those manuscript parts were jotted down as quick notes to himself. It seems to be the case especially for No. 11, Movement 1. The following are the manuscripts of the violin part of No. 11, Movement 1 by Roman (Ro 97:60, fol. 2v and Ro 97:58, Musik- och teaterbiblioteket, Stockholm. Posted with permission).


   


   


Example 1.8: Manuscripts of No. 11, Movement 1 by Johan Helmich Roman. Posted with permission from Musik- och teaterbiblioteket, Stockholm.


Concerning Roman's manuscripts and their edition, Hogwood and Mark (2013b, 66) observe that
[manuscript Ro 97:60 has] no title, notated imprecisely, and presented here in an editorial realisation where full-sized notes provide a metrical skeleton largely derived from those passages with exact rhythms (but often in double-length note-values) and from those unbeamed notes singled out with dots (removed editorially); the remaining unbeamed notes are treated here as grace-notes and all trills are editorial.
Reiter (2020b) also points out that
The fact that Roman's ornaments for both this [1st movement from Corelli's Violin Sonata, V/1 (Corelli 1700)] and the other Adagio from the same sonata are written out on the same page without any corrections indicates that he had worked out his "improvisations" either to perform them himself or for didactic reasons... (Lesson 30)
Therefore, although we also believe that most performers would play, for example, the two dotted notes of E5 and F#5 (in Example 1.6) with trills, due to the too many possibilities of interpretation and the improvisational nature of those ornaments, we would rather refrain from presenting our own interpretations here and rely solely on those presented in Hogwood and Mark (2013a, 2013b) as possible ones.

2. Patterns of Ornamentation in Violin Music of the 18th Century: Lexicology of Ornamentation

Horiuchi (2018a, 2018b) examines all the surviving scores and manuscripts of Corelli's op. 5 from the 18th century listed as columns B to L of the table in Example 2.1 below, and classifies them into 18 patterns listed as P1 to P18 in column A of the table:


Example 2.1: Ornamentation patterns of the 18th century identified by Horiuchi (2018)


In what follows, P1, P2,..., and P18 shown in Example 2.1 are used to denote the names of the patterns as well as the rules that govern or generate the patterns. Example 2.2 below shows some examples of those patterns (Scroll down):




Example 2.2: A list of the patterns of free ornamentation by violinists of the 18th century (Scroll down)


Now, it seems that some patterns, P4 in row Q and those in rows R and S, namely, P7 to P13, can be derived from {P1, P2, P3} as basic patterns (BPs) in row P through the following three derivation rules D1, D2, and D3:
D1: Increase in the number of notes, "diminution"
D2: Wider rhythmic variety
D3: Wider registers and intervals

Example 2.3: Three derivation rules, D1, D2, D3

All those "derivative" ornamentation patterns in rows R and S, that is, P7 to P13, can be derived from BPs and {D1, D2, D3}. For example, P7 and P8 are derived in the following ways:

Example 2.4: Derivations of the ornaments in rows R and S (P7 and P8)


Similarly, P9 to P13 can be derived in the following ways:

Example 2.5: Derivations of the ornaments in rows R and S (P9 to P13)


Some ornaments in Corelli (1710), the Amsterdam edition, and in Roman (c. 1715-1721) are derived from the original melody by Corelli (1700) in the ways shown in Examples 11 and 12 below:


Example 2.6: Ornaments in Corelli (1710) and in Roman (c. 1715-1721) derived from the 1st edition of Corelli's Violin Sonata, op.5, V (1700)



Example 2.7: Ornaments derived by Corelli (1710) and Dubourg (c. 1725) from the 1st edition of Corelli's Violin Sonata, op.5, V (1700)


In this way, all the ornaments found in the manuscripts listed in Example 1.4 can be derived using the set of rules, {P1, P2,..., P18, D1, D2, D3}. In other words, what we have so far discussed amounts to the lexicology of the ornamentation of the 18th-century Italian violin music.

3. Performing Corelli's Violin Sonatas, Op. 5: Applications of the Lexicology of the 18th-Century Ornamentation

We have obtained a set of rules {P1, P2,..., P18, D1, D2, D3} that generate a wide variety of ornaments notated by 18th-century violinists on their manuscripts. Although we know that they generate all the extant examples of ornaments from the 18th century, what we do not know is whether or not they generate only those ornaments in the style of the 18th-century music. In other words, they might generate those ornaments which 18th-century musicians would never have performed and sound totally foreign to the 18th-century music. We will discuss this issue in the next section.

Now, let us present two demos of ornamentation using the set of rules. The video clip in Example 3.3 below is our first example of an application of the rules, which shows Horiuchi playing the last several measures from the first movement of Corelli's Violin Sonata, op.5, XI/1 (1700). The ornaments she plays are all derived from a combination of the patterns found in the Amsterdam edition, that is, only those ornaments that can be derived by P1 to P6 as shown in column M in Example 3.1 below.


Example 3.1: Yuki Horiuchi's ornamentation: Columns M and N


Example 3.2 shows the ornaments she plays in the video. Since the patterns of those ornaments are only those used in the Amsterdam edition (Corelli 1710), they may sound somewhat like the ornamentation by Corelli himself.

Copyright (C) 2024 Yuki Horiuchi

Example 3.2: The ornaments derived from P1 to P6 (the patterns of the Amsterdam edition) by Yuki Horiuchi (2023)


The following video clip shows Horiuchi's performance of the section shown in Example 3.2:



Copyright (C) 2024 Yuki Horiuchi

Example 3.3: Improvised, free ornaments derived from P1 to P6 by Yuki Horiuchi


Let's move on to the next demo. Column N of the table in Example 3.1 above shows a combination of patterns Horiuchi chose. Since the combination was never used by any 18th-century violinists who left those notated ornaments, it's expected to sound like some new ornamentation and yet remain in the framework of the style of the 18th-century ornamentation. Example 3.4 below shows the same section as the previous one, for which only those ornaments that are derived by the combination of the rules are employed.

Copyright (C) 2023 Yuki Horiuchi

Example 3.4: A new combination of patterns by Horiuchi shown in Column N of the table in Example 3.1.


The following is Horiuchi's performance of the section shown in Example 3.4:



Copyright (C) 2024 Yuki Horiuchi

Example 3.5: Free ornamentation for Corelli's Violin Sonata, op.5, No.11, mm.9-16 played by Yuki Horiuchi


Example 3.6 below shows a set of various ornaments applied to the same section, Corelli's op.5, XI, mm. 9-16, by violinists of the 18th century and those played by Horiuchi in the video of Example 3.5 (Scroll down):



Copyright (C) 2024 Yuki Horiuchi

Example 3.6: Free ornamentation for Corelli (1700) by Yuki Horiuchi and others (Scroll down)


In this way, we may be able to obtain, examine, choose, and perform a wide variety of ornaments derived through sets of rules {P1, P2,..., P18} and {D1, D2, D3}. In other words, we have so far attempted to uncover the lexicology of ornamentation in 18th-century Italian violin music. Now it seems that we have access to the entire vocabulary of the ornamentation in the style of that music.

Zaslaw (1996, 95) describes the significance of Corelli's Violin Sonatas op. 5 as follows:
Following their publication [1700] they attained the status of classics, and by 1800 had been republished more than 50 times, in Amsterdam, Bologna, Florence, London, Madrid, Milan, Naples, Paris, Rome, Rouen and Venice. No other set of works enjoyed a comparable reception in the 18th century.
Therefore, considering the unparalleled dominating influence of Corelli's op. 5 throughout the 18th century, the set of rules {P1, P2, P3, P5, P6, D1, D2, D3} together with those in row T, that is, {P14, P15,..., P18} may govern the ornamentation entirely and derive almost any instances of ornaments in the style of 18th-century Italian violin music.

4. Testing the Formal System of Free, Improvised Ornamentation by Computer Simulation

4.1. A Formal System of Free Ornamentation of the 18th Century

The rule system {P1, P2, P3, P5, P6, D1, D2, D3} is a kind of deductive system of rules. More precisely, we have attempted to organize the set of rules that regulate the ornamentation as a deductive system of rules. We do not have to consider P4, and the patterns in rows R and S of the table of Example 3.1, namely, P7, P8,..., P13, here, because they can be derived from {P1, P2, P3, P5, P6, D1, D2, D3}.

Deductive systems such as those of Euclidean geometry and first-order predicate logic derive theorems or true propositions from a set of axioms, postulates, and some other theorems or true propositions and inference rules, or deduction rules. For example, the following is a derivation, or an inference, of a proposition (line 8) from two propositions as premises (lines 1 and 2) in a system of first-order predicate logic (a system of natural deduction developed by Oide (1991, 1999) and discussed in Oide and Takano (2000). This particular example of deductive inference was originally used by Augustus De Morgan (1806-1871) to demonstrate the limitation of Aristotelian syllogism:

where

P: Premise

six rules of inference, or deductive reasoning:

UG: Universal Generalization
EI: Existential Instantiation
UI: Universal Instantiation
EG: Existential Generalization
TF: Truth Function
C: Conditionalization

and line 3, for example, shows that the formula is derived from line 2, or a premise, by means of the deduction rule Existential Instantiation.

Example 4.1: A derivation of a theorem in first-order predicate logic

In this example of a deduction in formal logic, the proposition in line 8 is derived from the two premises, lines 1 and 2, by deduction rules {EI, UI, TF, EG, C, UG}. And when the logical formulas of the premises are interpreted by one-on-one mapping between their symbols and empirical entities, and if the premises are true in the empirical domain, the conclusion on line 8 is also necessarily true. In short, in a deductive system like this one, if the premise(s) are true, the conclusion of an inference is necessarily true.

Just like the example of natural deduction in Example 4.1 above, the rule system {P1, P2, P3, P5, P6, D1, D2, D3} takes any short series of notes as "premises" and "may" derive ornaments in any style of those listed from columns B to L in the table of Example 2.1 or their combinations. In other words, the set could be a deductive rule system of the lexicology of ornamentation, which produces a corpus of the entire vocabulary of ornamentation from the 18th century. Needless to say, however, in a strict sense, the rule system {P1, P2, P3, P5, P6, D1, D2, D3} is not a deductive rule system because, while a deductive system in a strict sense has rules of deduction as its inference rules, those of the rule system we discuss here are not deductive ones. Also, at this point, the rule system only "may seem" to derive all ornaments in the style of the 18th-century Italian violin music because it has to do only with instances of ornaments, or the vocabulary, of the 18th-century free ornamentation. It does not concern itself with their usage, that is, the pragmatics of ornamentation. We will revisit this issue later in the last section.

Nevertheless, for our research, constructing a "pseudo" deductive system of the derivation of ornaments has a significant advantage over other approaches. Since the rule system we have identified can derive all the extant examples of ornaments applied to Corelli's op. 5, it may also generate any ornaments which 18th-century performers did not notate but would have performed. Therefore, when we try to play ornaments in the style of the 18th-century violin music, we can choose any ornaments derived by the rules without recourse to factual, historical evidence or whatever to justify the choice. We no longer have to trace, for example, document-based historical facts concerning, say, teaching instructions on ornamentation from teachers to their pupils. And once such a rule system becomes available, we can assume that, because it derives all the ornaments notated by 18th-century violinists, it's likely that it also derives those ornaments that the violinists might and would have performed. We will discuss whether this argument is sound or not later in the last section.

4.2. Testing the Formal System of Ornamentation by Computer Simulation

So, at this juncture, we need to test our rule system. The rule system can derive all the notated ornaments in sources listed in Example 1.4. Then, the issue we need to discuss is whether or not all ornaments derived from them but not found in the sources are also appropriate in some sense as ornaments for 18th-century music. If they are, the rule system {P1, P2, P3, P5, P6, D1, D2, D3} may serve as a guiding principle for performers to try out their own new ornaments.

Meyer (1967, 281-282) argues that
Music differs from natural science in that the objects or events studied by the scientist are not created by him.... For while the scientist discovers or chooses a particular paradigm within which to work, he does not create the objective world which the paradigm was designed to illuminate. And it is the existence of such an objective world which makes it possible for the scientist to test and validate his theories. The composer of experimental music, however, often creates both the paradigm and the sound relationships which the paradigm makes possible. The composer's "reality" must ... be the aural perceptual-cognitive capabilities of sensitive knowledgeable listeners.
In short, unlike natural scientists, musicians select their new ornaments governed by the rule system in accordance with the cognitive capabilities of those "sensitive knowledgeable listeners" or what Lerdahl and Jackendoff (1983) call "the experienced listener."

To achieve this, we have written a computer program in Java that implements the rule system. The rules implemented in the program are {P1, P2,..., P18} and {D1, D2, D3}. Some extra parameters, which are latent in the previous discussion concerning the processes of derivation of ornaments in Section 3, need to be supplied to the program. They include the highest and the lowest notes of each ornament, the number of notes each ornament consists of, and so on.

And we need to test the program against "the experienced listener," the notion of which Lerdahl and Jackendoff (1983, 3) define as follows:
We will now elaborate the notion of "the musical intuitions of the experienced listener." By this we mean not just his conscious grasp of musical structure; an acculturated listener need never have studied music. Rather we are referring to the largely unconscious knowledge (the "musical intuition" that the listener brings to his hearing—a knowledge that enables him to organize and make coherent the surface patterns of pitch, attack, duration, intensity, timbre, and so forth. Such a listener is able to identify a previously unknown piece as an example of the idiom, to recognize elements of a piece as typical or anomalous, to identify a performer's error as possibly producing an ungrammatical configuration, to recognize various kinds of structural repetitions and variations, and, generally, to comprehend a piece within the idiom.
For now, we need to assume that we, Horiuchi and Takaoka, are such "experienced listeners" while developing the Java program.

What follows is a brief description of the Java code we have written. It automatically generates ornaments in the style of those musicians listed in the table of Example 3.1 and realizes Basso Continuo parts. The following is the opening five measures from the 1st edition of Corelli's Violin Sonata, op.5, V (Corelli 1700):


Example 4.2: Mm. 1-5 from Corelli's Violin Sonata, op.5, V (Corelli 1700)


The figured bass is fed into the program in the form of a series of arrays shown in Example 4.3 below:
Example 4.3: The figured bass of mm. 1-2 from Corelli's Violin Sonata, op.5, V (Corelli 1700) in the form of a series of arrays


The names of ornament patterns and some other parameters such as the highest and lowest notes and the numbers of notes in ornaments are also specified as a series of arrays as follows:
Example 4.4: The patterns of ornaments in mm. 1-2 from Corelli's Violin Sonata, op.5, V (Corelli 1700) in the form of a series of arrays


Since we have not yet finished the rule system of the pragmatics of ornamentation, the positioning of each ornament is not automated at this point but needs to be carried out manually.

The program consists of the following Java classes:
  1. Corelli_Op5_5_1.java // Threads of all the instruments
  2. Ornamentation.java // Methods for the patterns of ornamentation
  3. PlayViolin.java // Violin
  4. PlayViol.java // Viol
  5. PlayHarpsichord_R.java // The right hand of the harpsichord
  6. PlayHarpsichord_L.java // The left hand of the harpsichord
  7. SoloAndFBass.java // Data of figured bass
  8. Conversion.java // Data conversion (eg. SPN to MIDI note numbers)
Example 4.5: The classes of the program

A method in the program that generates ornaments of P1, "Stepwise motion between consecutive two notes," looks like the following:
Example 4.6: The method that generates ornaments by way of P1: Stepwise motion between consecutive two notes


The synchronization among the three instruments, violin, viol, and harpsichord, is a little tricky because, as you see those ornaments in Examples 4 and 18, many of them are non-metric. In other words, the duration of each beat constantly changes. In this Java program, all the instruments synchronize at the onsets of harmony change. If you feel that all the instruments synchronize well, perhaps human players also try to synchronize that way.

Four separate threads, those of violin, viol, and harpsichord L and R, concurrently run in the program. I have tried a few different ways to synchronize them and so far found that the join() method works best as shown in Example 4.7.
Example 4.7: The thread of the violin part


Our program works well in Java. We have tried Python as well. In Python, however, threads do not run concurrently even when the Global Interpreter Lock (GIL) is disabled. We have also tried multiprocessing in Python, but it doesn't work well either.

The following video clip demonstrates that the program automatically generates ornaments and realizes basso continuo using the data sets shown in Examples 4.3 and 4.4:





Example 4.8: Mm. 1-5 from Corelli's Violin Sonata, op.5, V (Corelli 1700)
The ornaments are generated and the B.C. part is realized by the rule system in the Java program.


After trying out this computer program, we are now quite confident that the rule system {P1, P2, P3, P5, P6, D1, D2, D3} with {P14, P15,..., P18} produces those ornaments that remain in the framework of the 18th-century style of ornamentation.

A further issue we need to tackle is the "pragmatics of ornamentation" as opposed to the lexicology we have so far worked on. For example, the long, nonmetric ornamentation in Example 3.4, involving descending seventh leaps and chromatic steps, would sound rather strange if played at the beginning of a section. Therefore, as Meyer (1967, 14–16) argues, if music is a Markov process, the probabilistic order of successive musical events, including ornamentation patterns, is semantically crucial. Therefore, to avoid the use of ornamentation patterns that sound strange, a set of preference rules governing the application of the rules is necessary as part of the pragmatics.

The Java program we have developed will be available as a Web app on this Web page so that any performers and researchers of Baroque music can easily try out their own ornamentation.

5. Conclusions: Further Issues and Some Music-Theoretical Remarks

5.1. Towards the Pragmatics of the Ornamentation of the 18th Century

The application of formal systems to music has a long history. Even after the 20th century, Kassler (1963, 1968) tries to formalize the production of 12-tone music; Boretz' monumental work (Boretz 1970, 1971, 1972, 1973) tries to reconstruct music-theoretical discourse in terms of formal logic; Xenakis (1971) applies naive set theory as a rule system to produce pieces of music; and so on. Because of its high abstraction, however, systems of formal logic, such as that of natural deduction shown in Example 4.1 are not easy to handle in the field of music. Perhaps the most frequent attempts to apply formal systems to music are those of the grammar of formal linguistics. Bernstein (1976) is a well-known example of attempts to construct "musical grammar" based on Phrase Structure Rules. We need to be aware, however, that phrase structure rules generate not only meaningful sentences but also those such as the following:

Example 5.1: A syntactically well-formed but nonsensical sentence (Chomsky 2002, 15)


This is a well-known example of sentences that are syntactically valid but at the same time nonsensical. Likewise, our rule system may well derive those ornaments that are in the style of 18th-century ornamentation, but, if allocated in the wrong way, sound not appropriate. We need to consider a rule system of pragmatics of ornamentation that is somehow equivalent to "the preference rules" formulated in Lerdahl and Jackendoff (1983) or Cope's "SPEAC System" (Cope 1991, 33-4; 2000, 191-204).

5.2. Style Change in Ornamentation

Now, we would like to discuss whether all those numerous derived ornaments, even those musicians in the 18th century never performed, can be considered "appropriate" for 18th-century free ornamentation, and how this "appropriateness" can be determined in the first place. Before doing so, we need to make clear the relationships between styles and their constraints.

Meyer (1996, 3) defines the notion of "style" as follows: "Style is a replication of patterning … that results from a series of choices made within some set of constraints." He argues that those constraints are classified into three categories, namely, "Laws," "Rules," and "Strategies":
And they constitute a layered hierarchy as shown in Example 5.2:

Example 5.2: Hierarchies of constraints that govern various styles of free ornamentation
based on Meyer's model of style change (Meyer 1996)


Meyer further argues that "... it should be mentioned here that most changes in the history of Western music have involved the devising of new strategies for the realization of existing rules, rather than the invention of new rules. (20)"

According to Meyer's definition of style cited above, therefore, if we recognize the set of various 18th-century free ornaments as a single category of style, it is because, as the table in Example 5.2 shows, that category has resulted from repeated applications of the rule system {P1, P2, P3, P5, P6, D1, D2, D3}. Consequently, since the rule system is necessary conditions for defining that style, the new ornamentation in Example 3.4 does not entirely deviate from the 18th-century style of free ornamentation as far as its lexicology is concerned. At least in this sense, therefore, the ornamentation in Example 3.4 is appropriate. Needless to say, however, the justification of this argument relies on the soundness of the inductive generalization, and thus, there is a chance that our argument might turn out to be false.

Hogwood (2013a, IX) observes, as already cited at the beginning of Section 1 on this page:
The art of ornamentation is always a balancing-act between the performer's intuition and the composer's specification; all that can be demonstrated from historical sources is a series of such reconciliations as proved acceptable to (some) 18th-century tastes. (emphasis added)"
In fact, concerning ornamentation by means of chromatic diminution, that is, a new strategy, Galeazzi (1817, 226) argues that:
... ella produce un maravigliosissimo effetto e può essere una sorgente inesausta di nuove, e sorprendenti diminuzioni,...
( [chromatic diminution] produces a most marvelous effect and can be an inexhaustible source of new and surprising diminutions.)
Likewise, it should also be possible for today's performers to introduce new strategies, new combinations of patterns P1 to P18, or even new rules to carry out the "balancing-act." If so, when today's performers play 18th-century music, they may want to follow the steps shown below in Example 5.2:

Example 5.2: Process of style change in ornamentation


In this way, we believe that today's musicians can also keep reviving 18th-century violin music.


Yuki Horiuchi and Akira Takaoka

Tokyo, Japan
September, 2025

E-mail: akira.takaoka (at) columbia (dot) edu

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Copyright (C) 2025 Yuki Horiuchi and Akira Takaoka