Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

Complexity Analysis of Instrumental Performancebased on Ontology Structure for Music Selection
Nami Iino1,2,3 and Hideaki Takeda1
21
National Institute of Informatics
National Institute of Advanced Industrial Science and Technology
3
RIKEN Center for Advanced Intelligence Projectnami-iino@nii.ac.jp

Abstract. This paper analyzes the complexity of guitar renditions for learners.
We have been developing a domain ontology called the Guitar Rendition Ontology (GRO). GRO structurally describes the actual actions of a classical guitar
techniques for sharing information and learning the guitar. These descriptions canbe used to provide valid information on music for selecting music. Therefore, we
ﬁrst improved GRO because the several renditions lacked of detailed descriptions. Then, we investigated what types of renditions appear in ﬁve existing etude
books. After that, we analyzed indicators of the complexity of renditions using
the GRO’s classes and properties. Furthermore, we attempted to calculate the difﬁculty of each etude by implementing a novel analysis using TF-IDF and ourcomplexity indicators. Experimental results suggested that the difﬁculty value ofan etude corresponds to the creator’s subjectivity and intention.
Keywords: Complexity of Action, Music Selection, Guitar Rendition Ontology

1 Introduction and BackgroundIn playing an instrument, the music selected is an important factor. If players can ﬁgureout which techniques they are good or bad at and choose pieces appropriately, they can
improve their performance. However, it is not easy to take into account a lot of information, such as the actual sounds and body movements, from information on the musicalone. Musical pieces and the order that they are in existing instruction books or etudes
are empirically selected by composers or players. There are no quantitative indicators
at present. We need to start by deﬁning the difﬁculty as the difﬁculty appropriate foreach player: what is difﬁcult in the ﬁrst place and what are the factors. It is possible tomore accurately analyze difﬁculty by deﬁning the complexity of the actual actions ofspeciﬁc guitar techniques.
In our previous study, we developed the Guitar Rendition Ontology (GRO). It canserve as a guideline for playing classical guitar on learning and teaching sites [6]. The
ontology consists of 96 concepts that describe the relationships between renditions and18 properties that explain the features of the concepts. We deﬁned three properties fordescribing the processes of actions for each rendition as the core structure of the guitar
rendition concept, that is, action, primary-action, and conditional-action. The descriptions give information on the appropriate way to perform these actions.

289

Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

In addition, we focused on guitar renditions used in real performances and investigated the trends and patterns of renditions using GRO [5]. However, the number ofrenditions alone was not sufﬁcient for accurately determining the difﬁculty of a performance. To overcome this problem, we attempted to evaluate musical compositions
quantitatively by deﬁning the complexity of a rendition on the basis of the ontology
structure of GRO. This approach enables a new framework that can support music selection for various instruments. Our goal is to provide indicators for selecting music forclassical guitar through an analysis of traditional etude books and a discussion.
The organization of the paper is as follows. In Section 2, we mention related works,
and in Section 3, we brieﬂy describe the Guitar Rendition Ontology, discuss the problems with it and how to overcome them, and present a new version of it. In Section
4, we ﬁrst investigate the characteristics of guitar renditions in existing etude books.
Then, in Section 5, we present a detailed method for deﬁning the complexities of guitar
renditions and analyze the difﬁculty of etude pieces. In Section 6, we conclude with asummary and overview of future work.

2 Related Works
There are several approaches related to music selection. One of them is music recommendation, and many systems have been designed by using neural network [4], deeplearning [3], emotion recognition [9], and so on. Regarding the classical guitar, [7]analyzed guitar pieces from the perspective of information entropy and provided an indicator to support music selection. The situation we are trying to support in this study
is that of an instrumental player selecting a piece of music. We thus need to take into
account information related to movement that could represent the difﬁculty of the actual
performance.
The ﬁeld of knowledge processing, several ontologies related to music have beendeveloped: The Music Ontology (MO) for describing metadata about music in detail[12]; Music Theory Ontology for conceptualizing musical and performance symbols inmusic notation [13]; Two Ontologies focusing on Feedback in music education [16];Musical Forms and Structures Ontology (MFSO) and Musical Performance Ontology(MPO), which are developed by extending MO, deals with the musical form and its
components, as well as the subjective interpretation and advice (emotion, expression,
ﬁngering) of the individual [14]. In addition, MPO deﬁnes an ”InstrumentTechnique”
class that can handle the movements and ﬁngering necessary to realize musical expression. However, it does not specify the style of rendition and the actions involved, which
are the important elements of this paper, nor does it discuss the application of them tomusic selection. Therefore, we believe that our approach is novel and will contribute to
the study of instrumental performance.

3 Improving Guitar Rendition Ontology
In this section, we describe the problems with the present Guitar Rendition Ontology(version 2.4) and how to improve it.

290Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

Classes and properties: There are important techniques that are not deﬁned or named
as common guitar renditions but are used by many advanced players. One of themis Curve ceja, a subclass of Press string rendition. In this technique, the index ﬁnger
arches and presses down on the high and low strings, except for the middle string, inorder to play only the necessary strings with minimal force. We thus added the Curveceja. Regarding the Ornament rendition, we added the following four ornaments thatwere missing: Acciaccatura, Appogiatura, Double appoggiatura, and Schleifer. In theproperties, we added “action4” to describe an action in more detail, and we deﬁned“action” as the upper layer of actions 1 to 4.
Until GRO version 2, we classiﬁed several renditions by using numbers such as
Cutting1 and 2, Tremolo1 and 2, and Tune down1 and 2. However, these numbers cannot
characterize each rendition. Therefore, we gave detailed names to these renditions suchas Cutting with right hand and by both hand, Tremolo by four ﬁngers and by one ﬁnger,
and Tune down with right hand and with left hand.
Description of actions: We modiﬁed the action descriptions for about 30 renditions.
The problem with the previous version of GRO was that the details of the speciﬁcations for some of the actions were not enough. For example, for Tremolo, the orderof plucking with the right ﬁnger is usually p, a, m, and i (initials in Spanish, meaning
thumb, ring, middle ﬁnger, and index ﬁnger), so a description up to “action4” is necessary for each ﬁnger. However, the previous version described these four ﬁngers bygrouping them together in “action1.” To overcome this problem, we tried to break down
the actions into smaller pieces and describe them (Figure 1). As Ornament renditions
and Figueta are also techniques that consist of two or more notes, we improved them todescribe the action for each note. However, the explanation of which string is actually
plucked is not uniquely determined, and this is a subject for future work.

Entity / Axiom type
Axiom
Logical axiom
Declaration axiom
Class-Guitar rendition class
Object property

Count
1487
543
314
290
106
23

Table 1. Ontology metrics of GRO version 3.
Fig. 1. Description of actions in Tremolo by four
ﬁngersTable 1 is a overviews of the improved version4 . This ontology consists of a total of
313 entities, counting classes, and object properties. The number of classes regarding
Guitar rendition and the number of properties were increased from version 2.4, from 97
to 106 and from 21 to 23, respectively. Furthermore, axioms that were a combination of
4

https://github.com/guitar-san/Guitar-Rendition-Ontology

291

Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

logical, non-logical, and declaration axioms were increased in number by 119 to 1487
by improving the action descriptions in its subclass.

4 Guitar Renditions in Existing Etude Books
This section focuses on learners and investigates what types of renditions appear inexisting etude books. There are two cases when making an etude book: (1) books created by the composers themselves and (2) books chosen and organized by performers.
Therefore, we tried to identify the differences in renditions when etude books werecreated from different perspectives.
Since the number of musical pieces varies from book to book, we chose etudes No.
1 to 10 as the subject of our music analysis. We added technique-related information to
the musical scores’ data and extracted information from MusicXML. Here, one of theauthors, who is a guitarist, arranged renditions based on the information already written
in the scores.
4.1 Etude books created by composers
The etude books we analyzed are as follows. These were created by two composers
from the classical period and a modern composer.
Estudios Sencillos by Leo Brouwer: Leo Brouwer, who was born in Havana in 1939,
is a composer, guitarist, conductor, researcher, teacher, and cultural promoter in themodern age. Estudios Sencillos [2] is a famous material that has been embraced bymany players and by many music schools in their curricula [11].
25 Etudes Op. 60 by Mauro Carcassi: Matteo Carcassi (1796-1853) was an Italian
guitarist, composer, and pedagogue and is best known for his pedagogical works.
His 25 Etudes Op.60 are considered essential works for guitar students. After guitarist Miguel Llobet (1878-1938) added information on ﬁngering, it has been highly
regarded as a good teaching tool for learning modern ﬁngering [10].
12 Etudes Op. 6 by Fernando Sor: The great Spanish composer and guitarist Fernando Sor (1778-1839) is known for his many guitar compositions. His opus numbers range up to about 63, and these consist of many solo pieces, guitar duets, andsongs and guitar pieces. We chose his opus 6, which is known as advanced grade,from several etudes to compare the above books.
Figures 2 to 4 indicate the number of renditions to each etude and the information
entropy calculated from them. The etudes of Brouwer and Carcassi have a similar tendency of using Full planting in early numbers and Descending slur and Ascending slurin late numbers. In comparison, the etudes of Sor are structured in such a way that these
are used alternately.
Carcassi’s etude is often used most on a lesson sites among the above three etudes.
The edition by Yasumasa and Seiko Obara, which is often used in Japan, notes that
“There are 25 pieces in this collection, and we would like you to follow them in order.
The reason is that this is one composition consisting of 25 pieces, all of which are
related to each other in key. When you can play all 25 pieces correctly from memory,292

Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

you are considered to have achieved a certain level of perfection, hence it is not desirable
to practice only one or two pieces” [10]. This suggests that the composer arranged
the pieces with the same intention, as the order of the pieces is an important factor inlearning the guitar. In fact, Figure 3 demonstrates an increase in both the number ofrenditions and the information entropy.
In Estudios Sencillos, Brouwer stated that “This is the beginning of a series of etudes
that were composed for the real guitar apprentice. Every technical problem is separated
by the degree of difﬁculty of the rest of information. If, for instance, there is an arpeggio
for the left hand, we are going to do it so that the other hand, in this case the right one,does not ﬁnd much problem.” This suggests that he was as meticulous in composing
and structuring his etudes as Carcassi, or even more so. At least, his etudes showed asimilar trend to Carcassi’s than to Sor’s.






















































 












































































Fig. 2. Change of renditions in Estudios Sencil- Fig. 3. Change of renditions in etude op. 60 bylos by Leo Brouwer.
Matteo Carcassi.















































              
























Fig. 4. Change of renditions in etude op. 6 by Fernando Sor.







































































































































Fig. 5. Change of renditions in Sor’s etudes by
Fig. 6. Change of renditions in Sor’s etudes byAndrés Segovia.
Yasuo Abe.

293

Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

4.2 Etude books created by players
We took up Fernando Sor, the composer described in the previous section, and analyzed two etude books collecting his works. These books were published by famous
guitarists, and they include pieces other than Op. 6, regardless of the opus number. The
data was extracted on the basis of the ﬁngering of each guitarist written in the score.
Twenty Studies by Andrés Segovia: Master musician Andrés Segovia (1893-1987)
has selected 20 of Sor’s etudes and edited them in a rational order with instructions
on ﬁngering, conception, and speed [15].
25 Etudes by Yasuo Abe: This book, which was published by Yasuo Abe (19251999), is a collection of Sor’s most important etudes for learning all the advanced
techniques of the guitar [1].
As shown in Figures 5 and 6, the result differs from Sor’s 12 Etudes Op. 6 in thatthe overall number of renditions is small but that of a few etudes is extremely large.
According to Segovia, Twenty Studies can be used not only for improving students’technique, but also for maintaining advanced players’ technique to a certain level [15].
It includes arpeggio, chords, legato, left hand ﬁngerings, ceja exercises, and many more
forms.
Concerning the order of the pieces, Abe noted that “This book is arranged in aneasy-to-follow order, which is not the same as Sor’s opus numbers,” and “Please practice in order from the beginning.” This means that the order of the pieces is an important factor in this book. However, it was difﬁcult to identify a speciﬁc pattern fromthese graphs that indicates the above intents. This suggests that, unlike the composer,
the players made their selections and ordered the pieces on the basis of their very subjective impressions when playing the pieces.

5 Analyzing Complexity of the Performance
Each guitar rendition requires a different set of actions. The load on the player is different when using a rendition that requires multiple actions or when using a rendition
with simple actions. In other words, the complexity of an action relates to the difﬁculty of the performance. Therefore, we clariﬁed the complexity of each rendition on
the basis of the description of actions in the GRO in this section. Here, we analyzed
renditions that are located at the bottom of the Guitar Rendition Class hierarchy andcontain descriptions of actions.
5.1 Complexity of guitar rendition
The calculation rules for weighting properties and classes are as follows.
1. Action Related Properties: Weight of 1 to each of the following properties that represent the relationship of the actions: “action1,” “action2,” “action3,” “action4,”“conditional-action1,” and “conditional-action2.” We excluded “primary-action”
and “playing-action” because actions 1–4 contain them.

294Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

2. Detailed Properties: Some actions have restrictions or requirements in describing
the actions in detail such as “direction,” “number,” “place of action,” “part of handor ﬁnger,” ”timing,” “used ﬁnger,” “used string,” “tool,” and “ornament tone.” We
believe that these are related to the complexity of an action. Therefore, the numberof properties described in each rendition was additionally weighted.
3. Player’s Action: It is not only the relationship between actions, but also the type of
movement that is important. In the GRO, 22 actions are deﬁned in the class called
Guitar player’s action. We weighted these actions on a scale of 0 to 3. For example,“pluck string” and “touch string” are 0, “press string” and “pick up string” are 1,
and “rub string” and “cross strings” are 2. Regarding “use slur,” we used the highest
value of 3 because Slur is deﬁned as a rendition. These values are arbitrary and canbe individually adapted to the player.
Figure 7 shows a treemap chart with the complexity value of each rendition represented by the area of the rectangle. The range of values is from a complexity of 1 to
16. Turn with left hand, a subclass of the Ornament rendition, showed the largest value
16, and other renditions in the same category also tended to map high values. In comparison, the Fingering rendition values tended to be low, ranging from the lowest valueof 1 for Al aire to 8 for Figueta, because this is a basic technique of classical guitar.
Percussive rendition was also similar, with values ranging from 3 to 8. Moreover, allrenditions of Note value rendition were low at 2.
The values of Articulation rendition, Chord rendition, Pitch change rendition, andTimbre rendition varied. The reason for the large difference in values between both Slur(also Slide) and Tapping for the Articulation rendition is that the former is a techniquelearned at the beginning stage, while the latter is an applied technique and uses theattribute “use slur” in GRO. For Chord rendition, which requires techniques using multiple strings, Tremolo and Rasgueado had a large area. Tremolo is an especially difﬁcult
technique that even some professional guitarists are not good at.
The 12 renditions, extracted in the previous section are represented by black boxes.
As mentioned above, Tremolo had the largest value because it is a difﬁcult technique.
Ceja related renditions were large because they required advanced techniques that are
performed by pressing multiple strings with a single ﬁnger. It is reasonable that the
Descending slur, which is played by hooking and plucking the string with the left ﬁnger,
was larger than the Ascending slur, which is played just by tapping the string with theleft ﬁnger. Descending slur and Acciaccatura are the same action, so the complexity
values are equivalent. Staccato and Sul ponticello were small because they require thesimple action of mufﬂing or changing the plucking position with the right ﬁnger.
From these results, we found that the complexity indicator corresponds generally
to the intuitive difﬁculty of a rendition. Applying these complexity values to musicalpieces can be provided an effective indicator for music selection. However, there is aproblem with a few of the rendition values. Full planting is a simple technique where theﬁngers are set before plucking, so the value should be lower than that of Arpeggio. We
will discuss this further towards a more complete complexity calculation that matches
the player’s intuition.

295

Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

Bottle neck with righthand, 8Turn by plucking, 8Tremolo by four
fingers, 8

Inverted turn byplucking, 8Figueta, 8

Artificial harmonics,
11
Turn with left hand, 16Mordento with left
hand, 11

Portamento, 7

Rasgueado, 7Mordento byplucking, 6Acciaccatura, 6Tapping, 14
Glissando, 6

Appoggiatura by
plucking, 6Tremolo by one
finger, 7

Semi apoyando, 7Curve ceja, 7

Bottle neck withleft hand, 6

pralltriller by
plucking, 6Blassing, 6Trill with left hand, 14

Arpeggio, 4Vibrato, 4

Cutting byboth hand, 4

Close, 4

Slapping, 5Scratch withright hand, 4

Naturalharmonics
by both hand,
4

Tambora, 4

Full planting,
4

Inverted turn with left
hand, 12Tune up withleft hand, 3

Slant ceja, 6
Prepared, 5

Pralltriller with left
hand, 9

Appoggiatura withleft hand, 9Percussi
on onfingerboard, 3

Apoyando, 3
Tabalet, 6

Slide, 6

Few ceja, 6

All ceja, 6

Cutting withright hand, 5

Naturalharmonics withright hand, 5

Choking, 9Descending slur,
6

Root ceja, 7

Trill by plucking,5

Bartók pizzicato,
5

Tune downwith righthand, 3
Percussion
on body, 3

Pizzicat
o, 3

Tune
down
with left
hand, 3
Plucking
on thehead, 2
Open, 2

Ascending slur,3

Out sideplucking,
2

Scratchwith left
hand, 3Tune upwith
right
hand, 3

Staccato,2

Staccatissimo, 2Mezo
staccato, 2Sul
poticello, 2Separate
planting,
2

Sul tasto,2
Al aire, 1         

Fig. 7. Treemap of complexity of each guitar rendition.

5.2 Analyzing difﬁculties of etudes
In regarding to guitar renditions, we think that there are three types of difﬁculty whenplaying a musical instrument:
1. Difﬁculty of the rendition itself
2. Difﬁculty with the number of renditions
3. Difﬁculty with the order of the renditions
In this study, we considered the complexity value of a rendition (deﬁned as complexityr,e )presented in Section 5.1 as an indicator of type 1. In addition, we attempted to extract
indices related to types 2 and 3 by calculating TF-IDF (Term Frequency Inverse Document Frequency) [17] by focusing on the number of occurrences of a rendition. The
TF-IDF value is expressed by the following formulas:
TF-IDF = tfr,e · idfr

nr,e
tfr,e = log ∑+1
k nk,e296

idfr = log

|D|
+ 1,
|{d : tr ∈ d}|Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

where nr,e is the value∑ obtained by weighting complexityr,e to the rendition frequency
for an etude fe , k nk,e is the total number of renditions (including the weight ofcomplexityr,e ) in the etude, |D| is the total number of etudes in a corpus, and {d :ti ∈ d} is the number of etudes that contain at least one rendition. Furthermore, thedifﬁculty level of each etude, which is expressed by dif f iculty(e), is calculated fromthe following formula:∑
TF-IDFk,e .
dif f iculty(e) =k∈eFigure 8 indicates the difﬁculty level of each etude number for the ﬁve etude books
analyzed in Section 4. Although Carcassi’s etude was relatively high and Brouwer’s
etude was low, both of them had a tendency for the difﬁculty level to increase: R2 =0.470
and R2 =0.276. Moreover, Abe’s etude showed the similar tendency of the line as Carcassi’s etude (R2 =0.261). These etudes are popular pedagogical materials around theworld. As described in Section 4, it is clear that they took into account the order inwhich learners can easily practice. For the etude books made by Sor and Segovia, we
could not determine whether the difﬁculty level corresponded to the etude number because the graphs remained almost unchanged. In fact, there are no explicit instructionsin those two books regarding the order of the pieces. Therefore, we found that our approach was somewhat consistent with the subjectivity and intentions of the creator (i.e.,
the author of the etude book). We need to increase the number of analyzed musicalpieces and conduct a subjective evaluation of the players using the results obtained inthis study.












































Fig. 8. Difﬁculties of etudes in ﬁve books.

6 Conclusion
In this study, we presented an approach to providing an indicator of the complexityof a guitar rendition and the difﬁculty of a piece on the basis of the Guitar Rendition
Ontology (GRO). We ﬁrst modiﬁed the GRO to describe detailed actions of renditions.
Second, we investigated the number of renditions in existing traditional etude books.

297

Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

Third, we analyzed the renditions’ complexities and visualized them with a treemap.
Finally, we calculated the difﬁculty for each etude by using TF-IDF and complexity
indicators. As a result, we found that the etude number in etude books corresponded
to the subjective perceived difﬁculty of the creator. The contribution of this paper is to
propose a novel approach that quantitatively measures the difﬁculty of music itself byusing a complexity indicator calculated on the basis of the ontology structure of GRO.
The advantage of our method is that it is individually adaptable. As a future work, wewill construct a framework that will enable music to be selected from more diverse
perspectives.

References
1. Abe, Y.: Fernando Sor 25 Etudes, ZEN-ON Music co., Ltd. (1966)
2. Brouwer, L.: Guitar Works for guitar solo, Max Eschig (2006)
3. Fessahaye, F. et al.: T-RECSYS: A Novel Music Recommendation System Using Deep Learning, 2019 IEEE International Conference on Consumer Electronics (ICCE), pp.1–6, (2019)
4. Hansen, C. et al.: Contextual and Sequential User Embeddings for Large-Scale Music Recommendation, In Fourteenth ACM Conference on Recommender Systems (RecSys’20). Association for Computing Machinery, pp.3–62 (2020).
5. Iino, N., Hamanaka, M., Nishimura, T,. K., Takeda H.: Music Analysis with focusing on Techniques by using the Guitar Rendition Ontology, Vol.2019-MUS-124 No.13, (2019)
6. Iino, N., Nishimura, S., Nishimura, T., Fukuda, K., Takeda H.: The Guitar Rendition Ontology
for Teaching and Learning Support, The 13th IEEE International Conference on Semantic
Computing (ICSC), Resource track, Vol. 1, pp.404–411 (2019)
7. Iino, N., Iizuka, Yasuki., Okino, Shigeki.: Study on Performance Program in Classical Guitar
Competitions for Supporting Piece Selection, IPSJ Journal, 59(3), pp.904–911, (2018)
8. Lim, K. A. and Raphael, C.: InTune: a musician’s intonation visualization system, ACM SIGGRAPH (2009)
9. Maningo, J.M.Z. et al.: A Smart Space with Music Selection Feature Based on Face andSpeech Emotion and Expression Recognition, 2020 IEEE REGION 10 CONFERENCE(TENCON), pp.696–701 (2020)
10. Obara, Y., Obara, S.: 25 Estudios Op.60 Matteo Carcassi, Edition Casa de la Guitarra, No.101(1965)
11. Penaranda, C., Isaac, C.: Leo Brouwer’s Estudios Sencillos for Guitar: Afro-Cuban Elements
and Pedagogical Devices, Dissertations, 1002 (2009)
12. Raimond, Y., Abdallah, S.A., and Sandler, M.B., Giasson, F.: The Music Ontology, Proceedings of the 8th International Conference on Music Information Retrieval (2007)
13. Rashid, S.M., Roure, D.D., McGuinness, D.L.: A Music Theory Ontology, Proceedingsof the 1st International Workshop on Semantic Applications for Audio and Music, pp.6–14(2018)
14. Sébastien, V., Sébastien D., Conruyt, N.: Annotating works for music education: propositions
for a musical forms and structures ontology and a musical performance ontology, Proceedingsof the International Conference on Music Information Retrieval (2013)15. Segovia, A.: Twenty Studies for the guitar by Fernando Sor, EMI Music Publishing Japan
Ltd. (2000)
16. Yee-King, M.J., and Wilmering, T., Rodriguez, M.T.L., and Krivenski, M., d Inverno, M.:
Technology Enhanced Learning: The Role of Ontologies for Feedback in Music Performance,
Frontiers in Digital Humanities, Vol.5, No.29 (2019)17. Zhang, W., Yoshida, T., Tang, X.: A comparative study of TF*IDF, LSI and multi-words fortext classiﬁcation, Expert Systems with Applications, Vol.38, No.3, pp.2758–2765 (2011).

298