A Computer-based Approach to Teach Tonal Harmony to Young

Students

Marcella Mandanici

, Adriano Barat

, Luca A. Ludovico

and Federico Avanzini

Music Conservatory “Luca Marenzio”, Piazza A.B. Michelangeli 1, Brescia, Italy

LIM – Laboratorio di Informatica Musicale, Dipartimento di Informatica “Giovanni Degli Antoni”,

Universit

a degli Studi di Milano, Via G. Celoria 18, Milano, Italy

Keywords:

Tonal Harmony, Music Education, Web, Computer.

Abstract:

In this paper authors present Harmonic Touch, a web platform for the study and practice of tonal harmony. The

application is a step-by-step wizard that leads users through 3 experiences towards the discovery of important

features of tonal harmony. Leveraging on chord perception, gestural interaction and gamiﬁcation techniques

authors propose an easy and funny approach to a topic otherwise considered too abstract and difﬁcult for

young students or amateurs. Harmonic Touch has been presented in a workshop to primary and middle school

teachers, obtaining a good interest and appreciation as a didactic tool. Feedback received from participants

suggests further developments such us expanding the music database and providing teachers with tools to

customize Harmonic Touch for their teaching needs.

1 INTRODUCTION

Since early childhood, we are continuously and pas-

sively exposed to structured music stimuli, and build

an inner knowledge about them. The way we learn the

music language is a paradigmatic example of implicit

learning, i.e. the process of acquiring complex infor-

mation independently of our awareness of the pro-

cess of acquisition and of the knowledge acquired. In

particular, recent studies have shown that children in

preschool age have implicit knowledge of tonality and

harmonic structures (Schellenberg et al., 2005; Corri-

gall and Trainor, 2009).

Also, the child’s cognitive development is based

on enactive knowledge (Varela et al., 1991): any event

is represented through appropriate motor responses,

by which children learn to discover the world, the

relationships among objects, and cause-effect associ-

ations. Active exploration and playful behavior are

paramount activities to explore the world and to ac-

quire and master new skills.

Implicit learning and enactive knowledge provide

the theoretical and conceptual framework for this

work, which presents Harmonic Touch, a tool de-

signed for music learning in primary and secondary

school. Speciﬁcally, the tool is aimed at supporting

learning and practicing of tonal harmony.

Building on previous research involving the use

of a large scale responsive environment (Mandanici

et al., 2016), Harmonic Touch introduces three web-

based experiences with the use of a touch-screen or

computer connected to the internet. The activities are

designed for intuitive and immediate interaction, do

not rely on previously acquired explicit knowledge of

tonal harmony, and exploit the principles of gamiﬁca-

tion to introduce children to the topic. Moreover, full-

body activities mimicking the mouse or touch move-

ments can be arranged for the involvement of a class

group and/or for the embodied learning of harmonic

concepts (Mandanici et al., 2017).

Harmonic Touch has been preliminary tested in a

workshop with primary- and secondary-school teach-

ers. Responses from experimental interviews pro-

vided suggestions for improvements and conﬁrmed

that this tool be proﬁtably used for introducing tonal

harmony features to young students as well as to am-

ateurs and non-musicians.

The remainder of the paper is structured as fol-

lows. Section 2 describes the state of the art about the

visualization and the understanding of harmonic re-

lationships and progressions. Section 3 provides the

theoretical background of the proposed approach for

the study of tonal harmony, introducing its perceptual

qualities and a spatial representation of the harmonic

space. Section 4 describes the architecture of the web-

based prototype implementing the mentioned expe-

Mandanici, M., Baratè, A., Ludovico, L. and Avanzini, F.

A Computer-based Approach to Teach Tonal Harmony to Young Students.

DOI: 10.5220/0007700402710279

In Proceedings of the 11th International Conference on Computer Supported Education (CSEDU 2019), pages 271-279

ISBN: 978-989-758-367-4

271

riences. Results of the preliminary assessment with

teachers are reported in Section 5. Discussion and

conclusion follow in Sections 6 and 7, respectively.

2 RELATED WORK

Starting from Euler’s tonnetz (Euler, 1739), many

different theories have been developed for the vi-

sualization and the understanding of harmonic rela-

tionships and progressions (Cohn, 1998), (Longuet-

Higgins et al., 1962), (Schoenberg and Stein, 1969).

Similarly, also many computer interfaces and systems

aimed at real time generation of harmonic progres-

sions (Eigenfeldt and Pasquier, 2010) or at visualiza-

tion of harmonies (Chew and Francois, 2005; Hedges

and McPherson, 2013) have been realized and tested.

Holland’s Harmony Space (Holland, 1994) pro-

vides a grid of pitches where musical chords can

be visualized and selected. It allows the production

of scales, chords, inversions and chord progressions.

The same interface has been transposed in a large-

scale interactive environment where chords can be

played through full-body interaction (Holland et al.,

2009).

Involving genetic algorithms and Markov models,

Harmonic Navigator (Johnson et al., 2014) provides

both a harmonic palette for the production of follow-

up harmonic progressions and a tool for the visualiza-

tion of the progressions thus generated. Chords are

represented through the numbers of harmonic inter-

vals, while colors are used to express the harmonic

density. The system employs also motion tracking de-

vices for gestural interaction.

An innovative tool for visualizing the various

shifts through harmonic regions in real time is Map-

ping Tonal Harmony

. It is based on the visualization

of chords placed along ﬁfth circles, with progressions

highlighted through popping chord names and brack-

ets. These systems account for the complexity of har-

monic relationships in tonal music compositions and,

seemingly, are aimed at music students or at people

already experienced in tonal harmony features such

as chord notation or intervals.

Conversely, Harmonic Touch skips harmonic

complexity for the beneﬁt of a very simple interface

which allows the perception and intuitive position-

ing of the primary harmonic relationships from which

all other more complex chords derive (see Section

3.3). Moreover Harmonic Touch is a task-oriented

tool, which promotes the knowledge of tonal harmony

features through playful experiences focused on con-

https://mdecks.com/mapharmony.phtml

cepts such as implicit harmony, harmonic rhythm and

melody harmonization.

3 A NEW APPROACH TO THE

STUDY OF TONAL HARMONY

Tonal harmony is an idiom, or system of rules, which

“. . . governs how melodies and chords are organized

throughout the duration of a tonal musical composi-

tion” (Butler and Brown, 1994, p.194). Systemati-

cally deﬁned in (Rameau, 1722), tonal harmony has

been declined through various musical styles, span-

ning from the Baroque period to contemporary popu-

lar songs (Butler and Brown, 1994; Laitz, 2012).

Thus, the tonal system can be considered as a

structure of higher level, embracing various stylistic

experiences (Brody, 1985). Keys, chords and scales

are the abstractions through which tonal harmony

is usually described in dozen of treatises and hand-

books, e.g. (Rimsky-Korsakov, 1930), (Koechlin,

1930), (Schoenberg, 1983), (Piston, 1948), (Kostka

et al., 1984), to name but a few.

But, if on one side these features represent use-

ful tools for analysis and theoretical pedagogy, on

the other they miss to explain the perceptual qualities

of chord relationships that are peculiar to the tonal

system (Butler and Brown, 1994). This formal ped-

agogical approach has been severely challenged by

many didactic scholars (Jaques Dalcroze, 1935) and

has been held responsible for failure and disaffec-

tion towards harmony studies. Eberlein in particular,

in addition to criticizing the abstraction of tonal har-

mony pedagogy, complains about the use of rules that

are in contrast with practice and perception and about

the absence of explicit stylistic references in tonal har-

mony treatises (Eberlein, 1997).

With such premises, it is not surprising that ped-

agogical approaches to tonal harmony have been

scarcely developed outside the strictly professional

music curricula, and that little attention has been paid

to harmony education programs for children, high

school students, and amateurs.

Yet it has been demonstrated that both children

and adults who are not musicians have a strong feel-

ing for harmony and are able to recognize the tonic

chord (Schellenberg et al., 2005), implicit harmonies

(Trainor and Trehub, 1994), and chord progressions

(Corrigall and Trainor, 2009).

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272

3.1 Perceptual Qualities of Tonal

Harmony

One of the most outstanding elements of the tonal har-

mony system is the tonic: “. . . the central tone of the

key, (it) forms the point of departure from which the

other tones move and the goal to which they are di-

rected” (Aldwell and Schachter, 2003).

Even though the presence of a tonal center is

a characteristics common to many musical idioms

(modal music, various Eastern musical traditions, a

relevant portion of 20

century and contemporary

music, etc.), in tonal harmony the tonic chord plays

a particularly strong role of closure when preceded

by the dominant chord.

To explain the sense of motion delivered to the

listeners by tonal music, the scale degrees can be

grouped into stable ones (I, III, and V) and active

ones (the remaining degrees of the diatonic scale).

Active tones tend to move towards stable ones, thus

generating expectation, tension and closure (Aldwell

and Schachter, 2003, p.9). Therefore, even if it has

been demonstrated that the essence of the strong di-

rected motion typical of the dominant-tonic cadence

is linked to the occurrence of “rare” intervals such

as the tritone and the semitones (Butler and Brown,

1994, pp.200-201), in a tonal piece there are many

other secondary or weaker motions which are learned

through experience and that can be recognized when

listening (Krumhansl, 2001).

3.2 Theoretical Background

Following H. Riemann’s harmonic theory (Riemann,

1896), authors divide the tonal space in primary

chords, namely tonic (T), subdominant (SD) and dom-

inant (D), and parallels, i.e. parallel tonic (Tp), paral-

lel subdominant (SDp) and parallel dominant (Dp).

Figure 1 depicts the three tonal functions T, SD,

and D (primary chords, namely I, IV, and V de-

gree). The Pythagorean relationships reported below

the pitches show the origin of the major harmonic

functions and chords starting from c (tonic).

Riemann considered the minor chords as the prod-

uct of the inversion of the harmonic series. Thus,

he derived the remaining chords (II, III, and VI de-

gree) from the reversed harmonic series starting from

e (marked with an asterisk in Figure 2). This is an

abstract scheme from which much more complex har-

monies can be derived. However, it can ﬁt a number

of popular songs as well as classic music harmoniza-

tion patterns which can be a good starting point for

understanding harmonic functions.

Figure 1: Chart of the relationships of the three tonal func-

tions, also known as primary chords; picture adapted from

(Riemann, 1896, p. 7).

Figure 2: Chart of the relationships of the three parallel

chords; picture adapted from (Riemann, 1896, p. 7).

3.3 Representation of the Harmonic

Space and Computer Interface

Building on the above presentation, we propose a new

approach to the learning of tonal harmony based on

musical perception and embodiment of harmonic pro-

gressions. If the tonal harmony system is able to de-

liver different feelings about the various chord pro-

gressions, listeners can be trained in recognizing and

naming them. This can be done through a spatial ar-

rangement of the musical chords that allows listeners

to link the sound of the harmonic progression to a mo-

tion scheme. We propose to train this harmonic inter-

action both through full-body movements and through

the touch screen or mouse input.

To this end, the six chords of the harmonic space

must be spatially disposed in such a way that each of

them can be reached without touching the neighbors.

To ease the navigation of the harmonic space and to

enhance the perceptual differences between the pri-

mary chord zone (all major chords) and the parallel

chord zone (all minor chords), we propose to place

the chords along a circle with the tonic, dominant and

subdominant in the lower part of the circle and the

parallels in front of their relatives, as depicted in Fig-

ure 3 (white arrows). This is a very simple spatial

arrangement with some important peculiarities:

• The user can get acquainted with the sound of the

various chords by simply clicking or touching a

set of buttons that follow this arrangement: an im-

A Computer-based Approach to Teach Tonal Harmony to Young Students

273

portant facility for people who cannot play a poly-

phonic instrument or for children (Manzo, 2014);

• The user can intuitively couple the chord qualities

with their location (i.e. the Tonic chord is always

in the middle, the other primary chords are one

in the left and the other in right, etc.). This can

help the memorization of the sound of the various

chords as well as the routes of the most important

harmonic progressions, as shown by the colored

arrows in Figure 3.

4 A WEB-BASED PROTOTYPE

A web prototype has been released in order to show

our approach to an audience of music teachers and

conduct an early experimentation, as discussed in

Section 5. The application was written in HTML5,

CSS and JavaScript; server-side interaction, imple-

mented in PHP, was required only to save user per-

formances into a database.

This version was developed as a step-by-step wiz-

ard containing self-explanatory descriptions. The pro-

totype focused on three groups of experiences, con-

ceived as a step-by-step process towards harmony

awareness:

1. Recognition of the Implicit Harmony – The user

is asked to match a short music tune with a single

chord that, in his/her opinion, best ﬁts the whole

melody (Bigand, 1993). The chord is chosen from

a set of the 6 primary and parallel chords dis-

cussed above. In the interface, chords are repre-

sented on the circle of Figure 4, randomly rotated

and with no indication of degrees. Understanding

the relative layout of chords is left to the user, who

can explore them freely during a training phase;

Figure 3: The spatial arrangement of primary and parallel

chords with the route of three common chord progressions.

2. Timed Recognition of Harmonic Changes – After

carefully listening to a complete piece (melody

and chords), the user is asked to reconstruct it

by moving one step ahead over the map when a

new chord is expected. An example of interface is

shown in Figure 5. If the click does not occur at

the right timing, music stops; if it is performed in

advance, a part of the tune is skipped;

3. Melody Harmonization – This activity requires to

select the right chords at the right timing in order

to accompany a known music tune. This last ac-

tivity is conceived as the natural evolution of the

previous ones, focusing on the recognition of the

best-ﬁtting chord and the occurrence of harmonic

changes. The graphical interface, shown in Figure

6, recalls the chord circle previously mentioned,

where the spatial relationship among chords is

maintained, but chord functions are made explicit.

In the current implementation, each group of ex-

periences starts with a training phase to make the user

get accustomed to the interface and implicitly under-

stand the principles of that activity. After the training

phase, three exercises per group are proposed.

The structure of the prototype (e.g., its wizard-

like form, the number of exercises, etc.) has been

conceived to condense the whole experience within

2 hours, including a brief oral presentation of the

project and initial and ﬁnal surveys. However the edu-

cational activities brieﬂy presented here should be ex-

panded into an adequate number of lessons, and mu-

sic examples should be rethought on the base of the

target audience.

Timings and sequences of mouse clicks can be

tracked and recorded in a database in order to assess

user performances and analyze typical behaviors.

The prototype is publicly available at

http://didacta18.lim.di.unimi.it/. At the moment

of writing, the interface is available in Italian only,

but an English version is expected to be released soon

in order to present the approach to the international

scientiﬁc community.

5 EXPERIMENTATION AT

DIDACTA 2018

The mentioned approach was publicly presented and

discussed during a workshop titled “Didattica della

musica e linguaggi digitali” (music education and dig-

ital languages) in occasion of the 2

edition of Fiera

Didacta Italy, Florence, October 18-20, 2018.

Established more than 50 years ago in Germany

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274

Figure 4: The interface of the ﬁrst activity group, focusing

on the recognition of the implicit harmony of a music tune.

No indication is provided to the user about harmonic func-

tions and their spatial disposition, that can be reconstructed

only through exploration.

Figure 5: The interface of the second activity group, focus-

ing on the timed recognition of harmonic changes. When a

new chord is expected, the user is required to move one step

ahead over the map.

Figure 6: The interface of the third activity group, focusing

on the melody harmonization. The same chord circle of

Figure 4 is used, but the orientation is kept and harmonic

functions are explicit.

and recently exported to Italy, Fiera Didacta

is the

most important Italian fair focused on education, vo-

cational training and relation among school and work.

The goal is to foster innovation and discussion among

institutions, teachers, school directors, educators and

trainers, as well as professionals and entrepreneurs

operating in the school and technology sector.

In this context, the workshop about music educa-

tion and digital languages aimed to present the proto-

type described above and to test it with primary- and

secondary-school teachers. More in detail, the goals

of the workshop were the following:

• To test an early implementation on real users be-

fore starting an experimentation phase on young

students;

• To proﬁle people interested in this kind of pro-

posal, in terms of age, job, conﬁdence with music

practice, etc., thanks to an anonymous question-

naire administered before the experimentation;

• To track their results on a set of increasingly difﬁ-

cult harmony exercises. Please note that the music

examples had been conceived for young students,

so the performance of domain experts could eas-

ily bring to biased results. For this reason, such

data will not be commented in this work;

• To gather user observations and suggestions about

content and technology-related issues, thanks to a

ﬁnal anonymous survey about the whole experi-

ence.

The workshop was attended by an audience of

45 educators, mainly teaching in lower secondary

school (57%) and in primary school (25%); only

8% of them came from higher secondary school, 6%

from preschool, and 4% from other grades. Con-

cerning gender, 80% in the audience were females,

16% males, and 4% of them did not declare their

gender. The mean of participants’ age was 49.8

and the median was 51. Concerning the working

age, the mean was 22.7 years and the median was

20 years. Educators were mainly music teachers

(39 vs. 6), often having experience as music play-

ers or singers (35 vs. 10). It is worth noting that,

before the experience started, everyone declared to

be in favor of using technology in teaching. These

data were collected through an initial anonymous sur-

vey. The complete dataset of answers is available at

http://www.lim.di.unimi.it/data/didacta survey/.

Figures 7 and 8 show two snapshots of the work-

shop, with teachers performing exercises of harmony

embodiment and practising with the prototype de-

scribed in Section 4.

http://ﬁeradidacta.indire.it/

A Computer-based Approach to Teach Tonal Harmony to Young Students

275

Figure 7: Teachers performing an exercise of harmony em-

bodiment during the workshop at Didacta 2018.

Figure 8: A teacher experiencing the prototype during the

workshop at Didacta 2018.

In order to assess the music competences and the

opinions about the application of technology in teach-

ing, we administered to participants the same set of

questions before and after the proposed activities.

Speciﬁcally, we asked to what extent technology in

education:

Q1. encourages a customized learning;

Q2. provides students with a broad range of informa-

tion;

Q3. does not encourage the loss of human relation-

ships;

Q4. does not promote distraction in students;

Q5. does not encourage inequality in the possibilities

of access to technology;

Q6. prepares students for the use of technology;

Q7. does not encourage an improper use of techno-

logical devices;

Q8. increases student involvement;

Q9. supports students with disabilities or special

needs;

Q10. does not encourage the violation of privacy.

Please note that in the original survey questions

with positive and negative ﬂavor had been mixed. For

the sake of clarity, in the list above the questions de-

noting criticism have been reformulated (e.g., from

”promotes distraction” into ”does not promote dis-

traction”), and the Likert scale has been turned ac-

cordingly.

The results are reported in Fig. 9. From the pre-

survey ratings, it can be noted that on average the

teachers had in general positive a priori expectations

about the use of technology for music teaching: posi-

tive answers (ratings 1 and 2 on the Likert scale) dom-

inated in all the pre-questions, with the only exception

of Q5: this suggests that teachers were particularly

concerned with equal opportunities in the access to

technology.

Note that the total number of answers to each

question varies between the pre- and the post-survey:

this is because some of the participants left the work-

shop without completing the post-survey. Despite the

discrepancy, it can be noted that the percentage of

positive answers (ratings 1 and 2 on the Likert scale)

increased from the pre- to the post-survey, with the

only exceptions of questions Q2 and Q6. This indi-

cates that the workshop conveyed in an effective way

the potential of the proposed approach. The questions

with the highest pre-post positive delta are Q3, Q5,

Q7, and Q10. From these results, it can be inferred

that the workshop was especially effective in reduc-

ing teachers’ concerns about possible drawbacks in

the use of technology for music teaching. Note that

Q5, the only one with a negative balance in the pre-

interview, received extremely positive answers in the

post-interview.

The prototype raised the interest of the audience,

who expressed positive comments through the anony-

mous ﬁnal survey. For us, it was particularly inter-

esting to track the opinion of participants on three

aspects. First, we asked how clear the overall pro-

posal was, including the aspects of embodiment and

the computer-based support activities. Results, ex-

pressed in a 5-point Likert scale where 5 is the high-

est score and 1 is the lowest, are shown in Figure 10.

Then, we investigated to what extent the interface was

considered user-friendly by users (see Figure 11). Fi-

nally, we measured the teaching effectiveness of the

solution in users’ opinion, obtaining all values greater

than or equal to 3, i.e. from neutral to positive re-

sponses, as shown in Figure 12.

In the ﬁnal survey we asked participants also to

provide yes/no answers to the following questions:

a. During the introduction, was the focus of the ex-

perience clearly explained?

b. Was the content coherent with respect to the ex-

pected subject of the experience?

c. Were your expectations satisﬁed?

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Figure 9: Comparison among the answers provided before and after workshop activities.

d. If you are an educator, are you planning to propose

these activities in your classroom?

Most answers were positive: 97.7% for a, 100%

for b, 97.7% for c, and 90.7% for d.

6 DISCUSSION

As already mentioned, the primary aim of the prelim-

inary experimentation was to collect feedback from

teachers about the effectiveness of the proposed ap-

proach. On the other hand, we were not interested in

assessing the performance of teachers in completing

the activities, mainly because such an analysis would

bring to biased results, as teachers are already pro-

ﬁcient in the concepts conveyed by the experiences.

For this reason, we will not discuss performance re-

sults in this work.

The pre- and post-interviews, as well as the in-

formal comments given by teachers at the end of the

workshop, provided useful insights for further im-

provements on the prototype.

Concerning available materials, the solution has to

be ﬂexible. The idea is to release a large database of

music tunes for each group of activities, trying to meet

multiple educational purposes, e.g., considering dif-

ferent students’ age, geographical area, culture, and

previous music knowledge. Content archive should

embrace nursery rhymes, regional tunes, pop songs,

well-known music themes, etc.

One desirable additional feature would be a web-

based tool that allows teachers to generate their own

music materials for the experiences. The tool should

include functions and a graphical interface to (i) up-

load a music tune, and (ii) manually insert a har-

monic segmentation the tune, which could then be

used in an exercise. As a further alternative to man-

ual segmentation, automatic methods may also be em-

ployed (Mauch and Dixon, 2010).

The structure itself of the prototype has to be

rethought. First, a wizard-like structure is no more

required when a facilitator is available to explain the

activities, or users are accustomed to the application

features. Needless to say, also the initial and ﬁnal sur-

veys to proﬁle users and record their suggestions are

no more needed.

Any activity should be selectable in an indepen-

dent way, and without constraints about the number

of exercises to administer within a didactic unit. Af-

ter all, that prototype had been conceived for demon-

stration purposes, so it had to condense the whole ex-

perience in a very limited time span (one of the crit-

icisms emerging from the ﬁnal survey), whereas har-

mony awareness is often the result of a long and grad-

ual process.

In order to use Harmonic Touch as a teaching tool

with children or young students, some reliable met-

rics have to be developed to automatically assess the

performance of the pupil in a given exercise. One pos-

sible approach, which is coherent with the gamiﬁca-

A Computer-based Approach to Teach Tonal Harmony to Young Students

277

Figure 10: Clarity of the proposal expressed in a 5-point

Likert scale.

Figure 11: User-friendliness of the proposal expressed in a

5-point Likert scale.

Figure 12: Teaching effectiveness of the proposal expressed

in a 5-point Likert scale.

tion approach followed so far, is to generate a score

at the end of the exercise. Research on objective as-

sessment of music performance provides examples of

how objective descriptors can be correlated to human

assessment, e.g., in terms or rhythmic accuracy (Wu

et al., 2016).

Also, when the approach is tested on children or

young students, the analysis of the outcome of single

activities can provide interesting results, that, in turn,

can drive further developments or require the imple-

mentation of new features.

7 CONCLUSION

In this paper we have presented a prototype of Har-

monic Touch, a web-based music learning application,

focused on tonal harmony. We have discussed the the-

oretical background which led to the current design

of the application, as well as its implementation. We

have presented the results of a preliminary evaluation

with primary- and secondary-school teachers.

The evaluation showed extremely positive reac-

tions from teachers, with regard to both the teaching

potential of the approach and the user friendliness of

the current implementation. Furthermore, it provided

several insights about possible improvements and fur-

ther developments.

Further research in the near future will focus on

two main directions. On the one hand, the function-

alities of Harmonic Touch will be expanded and the

structure will be redesigned, following the discussion

reported above. On the other hand, the application

will be tested with children and young students in or-

der to objectively assess its effectiveness in aiding the

learning of tonal harmony in the classroom.

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