lsquo1E0Arsquo A COMPUTATIONAL APPROACH TO RHYTHM TRAINING

Noel AlbenElectronics and Communication

PESIT - BSC Bangalore

Ranjani HGGAIA

Ericsson Research Bangalore

ABSTRACT

We present a computational assessment system that pro-motes the learning of basic rhythmic patterns The systemis capable of generating multiple rhythmic patterns withincreasing complexity within various cycle lengths For agenerated rhythm pattern the performance assessment ofthe learner is carried out through the statistical deviationscalculated from the onset detection and temporal assess-ment of a learnerrsquos performance This is compared with thegenerated pattern and their performance accuracy formsthe feedback to the learner The system proceeds to gen-erate a new pattern of increased complexity when perfor-mance assessment results are within certain error boundsThe system thus mimics a learner-teacher relationship asthe learner progresses in their feedback-based learningThe choice of progression within a cycle for each pattern isdetermined by a predefined complexity metric This metricis based on a coded element model for the perceptual pro-cessing of sequential stimuli The model earlier proposedfor a sequence of tones and non-tones is now used for on-sets and silences This system is developed into a web-based application and provides accessibility for learningpurposes Analysis of the performance assessments showsthat the complexity metric is indicative of the perceptualprocessing of rhythm patterns and can be used for rhythmlearning

Keywords Music education rhythm onsets perfor-mance assessment complexity metrics coded element pro-cessing web application

1 IntroductionLearning to play a musical instrument is a complex pro-

cess that requires the acquisition of many interlinked skillssuch as tone intonation note accuracy timing rhythm pre-cision clear articulation and dynamic variation [1] An ac-knowledged important skill is the understanding of rhythmtiming and rhythm precision Rhythm is defined to be thedescription and understanding of the duration and dura-tional patterns of musical notes [2] The word rhythm isused to refer to all of the temporal aspects of a musicalwork [3]Two main contexts within which formal musical learning

copy Noel Alben Ranjani HG Licensed under a CreativeCommons Attribution 40 International License (CC BY 40) Attribu-tion Noel Alben Ranjani HG ldquolsquo1e0arsquo A COMPUTATIONAL AP-PROACH TO RHYTHM TRAININGrdquo in Proc of the 22nd Int Societyfor Music Information Retrieval Conf Online 2021

takes place are the classroom through playing and inter-acting with a teacher and at home practicing alone [1]From the perspective of a drum kit or percussive instru-ment a typical classroom setting involves the teacher and alearner The teacher decides what the learner must practiceand the teacherrsquos feedback helps them achieve accuracy intiming and quality in performance The learnerrsquos practic-ing habits at home aid in reaching performance goals Asoftware application cannot substitute a music teacher butit can be a compliment in the learning process especiallyin the performance assessment of daily practice at home[1]

11 Related LiteratureMost assessment methods are either the assessment of

learning used to measure competence or the assessmentfor learning used to enhance learning [4-6] The rapid de-velopment of music technology over the last few decadeshas dramatically changed the way that people interact withmusic today In [7] the authors explore the use of Mu-sic Information Retrieval (MIR) techniques in music ed-ucation and their integration in learning software Theyoutline Song2See as a representative example of a mu-sic learning system developed within the MIR commu-nity Songs2See is a music game developed based on pitchdetection sound separation music transcription interfacedevelopment and audio analysis technologies [8] Despiteadvancements in these sound analysis technologies Ere-menko V Morsi A et al in [1] revealed that the per-formance assessment tools present in these applicationsare still not reliable and effective enough to support thestrict requirements of a professional music education con-text In [1] they review some of the work done in thepractice of music assessment and present a proof of con-cept for a complete assessment system for supporting gui-tar exercises Furthermore they identify the challengesthat should be addressed to further advance these assess-ment technologies and their useful integration into profes-sional learning contexts Particularly those that will helplearners to plan monitor and evaluate their learning pro-gression They also highlight the importance and require-ment of presenting the assessment results to a learner ina way that promotes learning [1] Similarly Lerch A etal in [9] surveyed the field of Music Performance Analy-sis (MPA) from the perspective of performance assessmentand its ability to provide insights and interactive feedbackby analyzing and assessing the audio of practice sessionsFurthermore they highlight the necessity for individual as-sessment and curriculum in the context of a music edu-

arX

iv2

109

0444

0v1

[cs

MM

] 9

Sep

202

1

cation tool The work of Chih-Wei Wu and AlexanderLerch in [10] presents an unsupervised feature learningapproach to derive features for assessing percussive instru-ment performances amongst a large data of audition per-formances mimicking a judge in this scenario Specifi-cally they proposed using a histogram-based input repre-sentation to sparse coding to allow the sparse coding totake advantage of temporal rhythmic information Var-ious (commercially available) solutions exist specificallyfor rhythm education and performance assessment Exam-ples for rhythm tutoring applications are Perfect Ear [11]Rhythm Trainer [12] and Complete Rhythm Trainer [13]These form a class of mobile applications that help learn-ers practice and assess their rhythm skills by following aset curriculum presented in each of these applications andtouchscreen-based feedback for performance assessmentOther apps such as SmartMusic [14] Yousician [15] Mu-sic Prodigy [16] and SingStar [17] are available for musiceducation purposes however they do not have a dedicatedrhythm training section Furthermore none of the previousworks address musical rhythm complexity measures as afeature to aid in a learnerrsquos progression Evaluating variousrhythm complexity measures based on how accurately theyreflect human-based measures were studied by Eric Thul inhis thesis [3] Although his results suggest that none of themeasures accurately reflect the difficulty humans have per-forming or listening to rhythm the measures do accuratelyreflect how humans recognize a rhythmrsquos structure

12 Our ContributionIn this work we consider the individual assessment of

learning a particular rhythmic pattern at a fixed tempo Wepresent the proof of concept for a system that will assessa learnerrsquos audio recording and provide feedback to thelearner on their performance We will only focus on as-sessing the learnerrsquos temporal proficiency keeping the per-formance parameter categories of tempo dynamics pitchand timbre fixed Furthermore we focus on the progres-sion of a learner within a certain cycle length We do sowith the introduction of new patterns of increased com-plexity based on a pre-defined complexity metric that issimilar to a teacher who decides what the learner mustpracticeThis manuscript is organized as follows we first definethe terms notations and conventions to be held through-out that will help assess the performance of an individualThat is followed by the proposed system for the assess-ment where we go over the subsequent blocks that makeup the assessment system and understand the coded ele-ment model used to define the complexity metric Finallywe discuss the learner results and accuracy of this systemthrough our web application platform and conclude withfuture enhancements and improvements to the system

2 Background21 Definitions

We first provide a brief background of some of the termsused to define a rhythmic patternIn this work we consider the fundamental and individual

Figure 1 Diagrammatic illustration of the terms used inthis article

time unit for a rhythmic pattern to be a pulse Pulse isdefined to be ldquoone of a series of regularly recurring pre-cisely equivalent stimulirdquo [18] The duration of a rhythmicpattern is composed of a number of pulses Tempo refersto the rate at which the musical pulses are generated and italso controls the number of pulses for a given duration Forour proposed system the total duration of a rhythmic pat-tern is determined by the total number of samples presentin the audio signal The uniform number of samples orduration between two subsequent pulses is defined to bethe inter-pulse interval (IPI) The IPI depends on the sam-pling frequency and the tempo used for the rhythmic pat-tern Figure 1 shows a duration of 300000 samples withpulses generated at a fixed Inter Pulse Interval (IPI) deter-mined by a tempo of 160 Pulses Per Minute (PPM)To generate a rhythmic pattern we consider instantaneousattacks on the marked time units (pulses) ie striking adrum clapping or tapping The instantaneous attacks aredefined as onsets The duration that is marked between twoonsets is defined as the inter-onset interval (IOI) The IPIonsets and the IOI together create a rhythmic pattern asshown in figure 1A cycle determines the number of pulses beyond which therhythmic pattern begins to repeat itself The cycle repre-sents a structure for the pulses and this structure is realisedby the rhythmic pattern For example we use 7 to indicatea repeating rhythmic pattern of 7 pulses Rhythm patternscan be composed in any predetermined cycle number forthis article we will only be following cycles of 4357 and1622 Representation

We will now introduce the rhythm pattern representa-tion used in the proposed system with the help of a famousAfro-Cuban rhythm the clave son shown in figure 2 (a)

(a) (b)

Figure 2 (a) The clave son rhythm in music (stave) nota-tion (b) The clave son rhythm in binary notation

Figure 2 (b) shows the clave son rhythm as a binarystring a notation that describes the position of the onsetsand silences This notation is used in the domain of com-puter science [19] The onsets are marked by a ldquo1rdquo and thesilent pulses are marked by a ldquo0rdquo This representation en-ables faster computation and integration of rhythm patternsinto our system This representation of a rhythm patternhenceforth will be referred to as the binary representation23 Naming 1e0a

The name lsquo1e0arsquo for the proposed system is derivedfrom a mixture of the binary representation with its 1rsquosand 0rsquos and a western rhythm counting technique used by alarge majority of music educators called the Harr systemThe system that Harr used assigned a set of numbers andsyllables For a cycle of length 4 numbers are assigned toonsets that occur at the beginning of the rhythmic patternrsquosduration and its repeats Syllables are assigned to those on-sets that fall everywhere else The syllables remain consis-tent for all the pulses with only the number for each repeatchanging For example the rhythm [11111111] would beread ldquo1 e amp a 2 e amp ardquo [20] Thereby giving us the namelsquo1e0arsquo

3 Proposed System

Figure 3 Block diagram of the proposed system forlsquo1e0arsquo

Figure 3 shows the block diagram of our proposed sys-tem for rhythm training and progression in learning Thissystem consists of two distinct blocks (1) The rhythm pat-tern generator with the complexity metric and (2) the per-formance assessment of the learner input with feedback31 Pattern Generator311 Pattern Generation

The pattern generator as shown in figure 5 begins witha pulse generator function This function takes inputparameters that determine the cycle length pattern arraytempo (PPM) and the total number of repeats required togenerate a collection of pulses whose inter-pulse interval(IPI) is determined by the equation 1

IPI = (60PPM)(1fs) (1)

PPM represents the pulses per minute of the generatedcollection of pulses fs represents the sampling frequency

and IPI represents the fixed inter-pulse intervalThe pattern array in binary representation determines thelocation of onsets and the number of silences to be incor-porated into the duration of pulses Furthermore we pro-pose the selection of pattern arrays for generating subse-quent sequences using complexity metrics detailed in sec-tion 312For the clave son [1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0] at 160PPM with 4 repeats at an fs of 44100 The functiongenerates an array of pulses as shown in figure 4(a) Thefixed inter-pulse interval for 160 PPM as calculated byequation 1 is 16539 samples

(a) (b)

(c)

Figure 4 Pattern Generator plots (a) Pulse GeneratorOutput (b) Hi-Hat Drum sample impulse signal (c) Con-volution result of (a) and (b)

The next stage of the pattern generator block adds tonalquality to the output of the pulse generator We achieve thisby convolving the pulse generator output with an appropri-ate drum sample impulse signal The drum sample impulsesignal is a short recording of an onset played using a par-ticular drum sound The drum sound selected must have aninstantaneous attack and a short decay as shown in figure4(b)The convolution process requires the loaded sample im-pulse to have the same fs as the pulse generator outputFor a pulse generator output and drum impulse figure 4(c)shows the output of the convolution function We makeuse of the Discrete Fourier Transform convolution prop-erty [21] This allows our result to have the same numberof samples as the pulse generator output We use the FastFourier Transform (FFT) [21] algorithm to achieve this re-sultThe resultant clave son rhythm from the pattern generatorblock at 160 PPM and 4 cycles is an audio signal whoseplot is shown in figure 4(c)

312 Complexity MetricVarious measures of musical rhythm complexity have

been studied in [3] Rhythm complexity measures were di-vided intoRhythm syncopation measures that use metrical weights

determined from the metrical hierarchy to find syncopatedonsets in a rhythm [1922]Pattern matching measures which chop up a rhythm asdetermined by the levels of the metrical hierarchy andsearch each sub-rhythm for patterns that indicate the com-plexity [2324]Distance measures which measure how far away arhythm is from a more simple rhythm composed of beats[192526]Finally mathematical measures which are based uponShannonrsquos information entropy [2728] Shannonrsquos in-formation entropy uncertainty equations are given inequations 456We propose to use the rhythmic complexity measure thatcalculates information entropy in the sense of Shannonrsquosentropy for a particular rhythm pattern Vitz and Todd in[28] present a method that can be used to calculate thecomplexity of cyclic binary patterns Their work definedthat the complexity measure of a certain periodic or repeat-ing pattern is the sum of the total amount of uncertaintyevaluated in processing the stimulus sequence In [28]they achieved this by proposing a set of rules (axioms) de-scribing a perceptual coding process As the method im-plies an emphasis on coded elements it is referred to as acoded element processing system (CEPS) [3]We consider this model for our application due to its al-gorithmic approach to measure rhythm complexity thusmaking it viable for coding as against rhythm syncopa-tion models in [1921] CEPS also has an improved abil-ity to distinguish rhythm patterns within a cycle based oncomplexity as compared to pattern matching [2324] anddistance measures [192526]The axioms in [28] proposed originally for tones and non-tones break down sequences into code levels In our workwe extend it to rhythmic patterns composed of onsets andsilences Each code level successfully codes the patternfrom single elements to larger elements which continuesuntil the entire pattern is constructed To calculate thecomplexity of the rhythmic pattern we measure two uncer-tainty values at each Code Level in the algorithm as pro-posed in [28] Uncertainty in this case means informationentropy The uncertainty values are the maximum uncer-tainty Hmax and the joint uncertainty Hjoint representedin equations 2 and 3 respectively

Hmax(XY ZW ) = H(X) +H(Y ) +H(Z) +H(W )(2)

Hjoint(XY ZW ) =H(X) +H(Y |X) +H(Z|XY )

+H(W |WYZ) (3)

where

H(X) = minussumxisinX

p(x)log2p(x) (4)

H(XY ) = minussumxisinX

sumyisinY

p(x)p(x y)log2p(x y) (5)

H(X|Y ) = minussumxisinX

sumyisinY

p(y x)log2p(yx) (6)

Let the value Hk be the sum of Hkmax and Hk

joint atCode Level k The total sum of H at each Code Level rep-resents the complexity of the pattern This value is termedHcode

Hcode =

nsumk=1

Hk =

nsumk=1

Hkmax +Hk

joint (7)

The complexity measure for [1001001000101000] is cal-culated to be 205538 Similarly we were able to calculatecomplexity measures for all the combinations of patternswithin the cycle lengths of 435 and 7 Upon calculatingthe complexity measures we arrange patterns according totheir increasing order of complexity as shown in sheets 1 We observed that for patterns that are a shifted version ofanother where 1rsquos (onsets) replace the 0rsquos (silences) andvice versa the complexity measures are identical For ex-ample [1100] and [0011] have a complexity measure of50 To tackle this we considered those patterns that be-gin with a 0 as off-beat patterns and assumed that theypresent a higher challenge to learners Hence we incre-mented a constant value to the complexity measures for allthose patterns that begin with a 0 (silence) The constantvalue within a cycle was determined by the highest com-plexity measure for the patterns that begin with 1 (onsets)for that cycle length This can be observed in sheets1Furthermore this complexity metric does not account forthe complexity that arises with changes in tempo There-fore in this work we only assess the performances at aconstant PPM 32 Performance Assessment

Once the learner listens to the generated pattern theirperformance is recorded and loaded onto the system Werectify the recorded audio signal (z) with a thresholdzthreshold = zmax4 to improve the results of the onsetdetection function and it also accounts for low magnitudenoise in the live recording environment

(a) Recorded input (b) Onsets from rectified inputs

Figure 5 Plots of onset detection in one cycle

Any onset detection function can be used to extract theonsets from the rectified recorded input We used the onsetdetection function defined by the Librosa python library

1 httpsdocsgooglecomspreadsheetsde2PACX-1vTSDSqil264H6-M2kLdQUuD6VYnRqYPQePhKl8C_STD1j-54rFdhbLag-ep_15ggiHpo8-DOpJWyQ-Opubhtml

cation tool The work of Chih-Wei Wu and AlexanderLerch in [10] presents an unsupervised feature learningapproach to derive features for assessing percussive instru-ment performances amongst a large data of audition per-formances mimicking a judge in this scenario Specifi-cally they proposed using a histogram-based input repre-sentation to sparse coding to allow the sparse coding totake advantage of temporal rhythmic information Var-ious (commercially available) solutions exist specificallyfor rhythm education and performance assessment Exam-ples for rhythm tutoring applications are Perfect Ear [11]Rhythm Trainer [12] and Complete Rhythm Trainer [13]These form a class of mobile applications that help learn-ers practice and assess their rhythm skills by following aset curriculum presented in each of these applications andtouchscreen-based feedback for performance assessmentOther apps such as SmartMusic [14] Yousician [15] Mu-sic Prodigy [16] and SingStar [17] are available for musiceducation purposes however they do not have a dedicatedrhythm training section Furthermore none of the previousworks address musical rhythm complexity measures as afeature to aid in a learnerrsquos progression Evaluating variousrhythm complexity measures based on how accurately theyreflect human-based measures were studied by Eric Thul inhis thesis [3] Although his results suggest that none of themeasures accurately reflect the difficulty humans have per-forming or listening to rhythm the measures do accuratelyreflect how humans recognize a rhythmrsquos structure

12 Our ContributionIn this work we consider the individual assessment of

learning a particular rhythmic pattern at a fixed tempo Wepresent the proof of concept for a system that will assessa learnerrsquos audio recording and provide feedback to thelearner on their performance We will only focus on as-sessing the learnerrsquos temporal proficiency keeping the per-formance parameter categories of tempo dynamics pitchand timbre fixed Furthermore we focus on the progres-sion of a learner within a certain cycle length We do sowith the introduction of new patterns of increased com-plexity based on a pre-defined complexity metric that issimilar to a teacher who decides what the learner mustpracticeThis manuscript is organized as follows we first definethe terms notations and conventions to be held through-out that will help assess the performance of an individualThat is followed by the proposed system for the assess-ment where we go over the subsequent blocks that makeup the assessment system and understand the coded ele-ment model used to define the complexity metric Finallywe discuss the learner results and accuracy of this systemthrough our web application platform and conclude withfuture enhancements and improvements to the system

2 Background21 Definitions

We first provide a brief background of some of the termsused to define a rhythmic patternIn this work we consider the fundamental and individual

Figure 1 Diagrammatic illustration of the terms used inthis article

time unit for a rhythmic pattern to be a pulse Pulse isdefined to be ldquoone of a series of regularly recurring pre-cisely equivalent stimulirdquo [18] The duration of a rhythmicpattern is composed of a number of pulses Tempo refersto the rate at which the musical pulses are generated and italso controls the number of pulses for a given duration Forour proposed system the total duration of a rhythmic pat-tern is determined by the total number of samples presentin the audio signal The uniform number of samples orduration between two subsequent pulses is defined to bethe inter-pulse interval (IPI) The IPI depends on the sam-pling frequency and the tempo used for the rhythmic pat-tern Figure 1 shows a duration of 300000 samples withpulses generated at a fixed Inter Pulse Interval (IPI) deter-mined by a tempo of 160 Pulses Per Minute (PPM)To generate a rhythmic pattern we consider instantaneousattacks on the marked time units (pulses) ie striking adrum clapping or tapping The instantaneous attacks aredefined as onsets The duration that is marked between twoonsets is defined as the inter-onset interval (IOI) The IPIonsets and the IOI together create a rhythmic pattern asshown in figure 1A cycle determines the number of pulses beyond which therhythmic pattern begins to repeat itself The cycle repre-sents a structure for the pulses and this structure is realisedby the rhythmic pattern For example we use 7 to indicatea repeating rhythmic pattern of 7 pulses Rhythm patternscan be composed in any predetermined cycle number forthis article we will only be following cycles of 4357 and1622 Representation

We will now introduce the rhythm pattern representa-tion used in the proposed system with the help of a famousAfro-Cuban rhythm the clave son shown in figure 2 (a)

(a) (b)

Figure 2 (a) The clave son rhythm in music (stave) nota-tion (b) The clave son rhythm in binary notation

Figure 2 (b) shows the clave son rhythm as a binarystring a notation that describes the position of the onsetsand silences This notation is used in the domain of com-puter science [19] The onsets are marked by a ldquo1rdquo and thesilent pulses are marked by a ldquo0rdquo This representation en-ables faster computation and integration of rhythm patternsinto our system This representation of a rhythm patternhenceforth will be referred to as the binary representation23 Naming 1e0a

The name lsquo1e0arsquo for the proposed system is derivedfrom a mixture of the binary representation with its 1rsquosand 0rsquos and a western rhythm counting technique used by alarge majority of music educators called the Harr systemThe system that Harr used assigned a set of numbers andsyllables For a cycle of length 4 numbers are assigned toonsets that occur at the beginning of the rhythmic patternrsquosduration and its repeats Syllables are assigned to those on-sets that fall everywhere else The syllables remain consis-tent for all the pulses with only the number for each repeatchanging For example the rhythm [11111111] would beread ldquo1 e amp a 2 e amp ardquo [20] Thereby giving us the namelsquo1e0arsquo

3 Proposed System

Figure 3 Block diagram of the proposed system forlsquo1e0arsquo

Figure 3 shows the block diagram of our proposed sys-tem for rhythm training and progression in learning Thissystem consists of two distinct blocks (1) The rhythm pat-tern generator with the complexity metric and (2) the per-formance assessment of the learner input with feedback31 Pattern Generator311 Pattern Generation

The pattern generator as shown in figure 5 begins witha pulse generator function This function takes inputparameters that determine the cycle length pattern arraytempo (PPM) and the total number of repeats required togenerate a collection of pulses whose inter-pulse interval(IPI) is determined by the equation 1

IPI = (60PPM)(1fs) (1)

PPM represents the pulses per minute of the generatedcollection of pulses fs represents the sampling frequency

and IPI represents the fixed inter-pulse intervalThe pattern array in binary representation determines thelocation of onsets and the number of silences to be incor-porated into the duration of pulses Furthermore we pro-pose the selection of pattern arrays for generating subse-quent sequences using complexity metrics detailed in sec-tion 312For the clave son [1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0] at 160PPM with 4 repeats at an fs of 44100 The functiongenerates an array of pulses as shown in figure 4(a) Thefixed inter-pulse interval for 160 PPM as calculated byequation 1 is 16539 samples

(a) (b)

(c)

Figure 4 Pattern Generator plots (a) Pulse GeneratorOutput (b) Hi-Hat Drum sample impulse signal (c) Con-volution result of (a) and (b)

The next stage of the pattern generator block adds tonalquality to the output of the pulse generator We achieve thisby convolving the pulse generator output with an appropri-ate drum sample impulse signal The drum sample impulsesignal is a short recording of an onset played using a par-ticular drum sound The drum sound selected must have aninstantaneous attack and a short decay as shown in figure4(b)The convolution process requires the loaded sample im-pulse to have the same fs as the pulse generator outputFor a pulse generator output and drum impulse figure 4(c)shows the output of the convolution function We makeuse of the Discrete Fourier Transform convolution prop-erty [21] This allows our result to have the same numberof samples as the pulse generator output We use the FastFourier Transform (FFT) [21] algorithm to achieve this re-sultThe resultant clave son rhythm from the pattern generatorblock at 160 PPM and 4 cycles is an audio signal whoseplot is shown in figure 4(c)

312 Complexity MetricVarious measures of musical rhythm complexity have

been studied in [3] Rhythm complexity measures were di-vided intoRhythm syncopation measures that use metrical weights

determined from the metrical hierarchy to find syncopatedonsets in a rhythm [1922]Pattern matching measures which chop up a rhythm asdetermined by the levels of the metrical hierarchy andsearch each sub-rhythm for patterns that indicate the com-plexity [2324]Distance measures which measure how far away arhythm is from a more simple rhythm composed of beats[192526]Finally mathematical measures which are based uponShannonrsquos information entropy [2728] Shannonrsquos in-formation entropy uncertainty equations are given inequations 456We propose to use the rhythmic complexity measure thatcalculates information entropy in the sense of Shannonrsquosentropy for a particular rhythm pattern Vitz and Todd in[28] present a method that can be used to calculate thecomplexity of cyclic binary patterns Their work definedthat the complexity measure of a certain periodic or repeat-ing pattern is the sum of the total amount of uncertaintyevaluated in processing the stimulus sequence In [28]they achieved this by proposing a set of rules (axioms) de-scribing a perceptual coding process As the method im-plies an emphasis on coded elements it is referred to as acoded element processing system (CEPS) [3]We consider this model for our application due to its al-gorithmic approach to measure rhythm complexity thusmaking it viable for coding as against rhythm syncopa-tion models in [1921] CEPS also has an improved abil-ity to distinguish rhythm patterns within a cycle based oncomplexity as compared to pattern matching [2324] anddistance measures [192526]The axioms in [28] proposed originally for tones and non-tones break down sequences into code levels In our workwe extend it to rhythmic patterns composed of onsets andsilences Each code level successfully codes the patternfrom single elements to larger elements which continuesuntil the entire pattern is constructed To calculate thecomplexity of the rhythmic pattern we measure two uncer-tainty values at each Code Level in the algorithm as pro-posed in [28] Uncertainty in this case means informationentropy The uncertainty values are the maximum uncer-tainty Hmax and the joint uncertainty Hjoint representedin equations 2 and 3 respectively

Hmax(XY ZW ) = H(X) +H(Y ) +H(Z) +H(W )(2)

Hjoint(XY ZW ) =H(X) +H(Y |X) +H(Z|XY )

+H(W |WYZ) (3)

where

H(X) = minussumxisinX

p(x)log2p(x) (4)

H(XY ) = minussumxisinX

sumyisinY

p(x)p(x y)log2p(x y) (5)

H(X|Y ) = minussumxisinX

sumyisinY

p(y x)log2p(yx) (6)

Let the value Hk be the sum of Hkmax and Hk

joint atCode Level k The total sum of H at each Code Level rep-resents the complexity of the pattern This value is termedHcode

Hcode =

nsumk=1

Hk =

nsumk=1

Hkmax +Hk

joint (7)

The complexity measure for [1001001000101000] is cal-culated to be 205538 Similarly we were able to calculatecomplexity measures for all the combinations of patternswithin the cycle lengths of 435 and 7 Upon calculatingthe complexity measures we arrange patterns according totheir increasing order of complexity as shown in sheets 1 We observed that for patterns that are a shifted version ofanother where 1rsquos (onsets) replace the 0rsquos (silences) andvice versa the complexity measures are identical For ex-ample [1100] and [0011] have a complexity measure of50 To tackle this we considered those patterns that be-gin with a 0 as off-beat patterns and assumed that theypresent a higher challenge to learners Hence we incre-mented a constant value to the complexity measures for allthose patterns that begin with a 0 (silence) The constantvalue within a cycle was determined by the highest com-plexity measure for the patterns that begin with 1 (onsets)for that cycle length This can be observed in sheets1Furthermore this complexity metric does not account forthe complexity that arises with changes in tempo There-fore in this work we only assess the performances at aconstant PPM 32 Performance Assessment

Once the learner listens to the generated pattern theirperformance is recorded and loaded onto the system Werectify the recorded audio signal (z) with a thresholdzthreshold = zmax4 to improve the results of the onsetdetection function and it also accounts for low magnitudenoise in the live recording environment

(a) Recorded input (b) Onsets from rectified inputs

Figure 5 Plots of onset detection in one cycle

Any onset detection function can be used to extract theonsets from the rectified recorded input We used the onsetdetection function defined by the Librosa python library

1 httpsdocsgooglecomspreadsheetsde2PACX-1vTSDSqil264H6-M2kLdQUuD6VYnRqYPQePhKl8C_STD1j-54rFdhbLag-ep_15ggiHpo8-DOpJWyQ-Opubhtml

Figure 2 (b) shows the clave son rhythm as a binarystring a notation that describes the position of the onsetsand silences This notation is used in the domain of com-puter science [19] The onsets are marked by a ldquo1rdquo and thesilent pulses are marked by a ldquo0rdquo This representation en-ables faster computation and integration of rhythm patternsinto our system This representation of a rhythm patternhenceforth will be referred to as the binary representation23 Naming 1e0a

The name lsquo1e0arsquo for the proposed system is derivedfrom a mixture of the binary representation with its 1rsquosand 0rsquos and a western rhythm counting technique used by alarge majority of music educators called the Harr systemThe system that Harr used assigned a set of numbers andsyllables For a cycle of length 4 numbers are assigned toonsets that occur at the beginning of the rhythmic patternrsquosduration and its repeats Syllables are assigned to those on-sets that fall everywhere else The syllables remain consis-tent for all the pulses with only the number for each repeatchanging For example the rhythm [11111111] would beread ldquo1 e amp a 2 e amp ardquo [20] Thereby giving us the namelsquo1e0arsquo

3 Proposed System

Figure 3 Block diagram of the proposed system forlsquo1e0arsquo

Figure 3 shows the block diagram of our proposed sys-tem for rhythm training and progression in learning Thissystem consists of two distinct blocks (1) The rhythm pat-tern generator with the complexity metric and (2) the per-formance assessment of the learner input with feedback31 Pattern Generator311 Pattern Generation

The pattern generator as shown in figure 5 begins witha pulse generator function This function takes inputparameters that determine the cycle length pattern arraytempo (PPM) and the total number of repeats required togenerate a collection of pulses whose inter-pulse interval(IPI) is determined by the equation 1

IPI = (60PPM)(1fs) (1)

PPM represents the pulses per minute of the generatedcollection of pulses fs represents the sampling frequency

and IPI represents the fixed inter-pulse intervalThe pattern array in binary representation determines thelocation of onsets and the number of silences to be incor-porated into the duration of pulses Furthermore we pro-pose the selection of pattern arrays for generating subse-quent sequences using complexity metrics detailed in sec-tion 312For the clave son [1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0] at 160PPM with 4 repeats at an fs of 44100 The functiongenerates an array of pulses as shown in figure 4(a) Thefixed inter-pulse interval for 160 PPM as calculated byequation 1 is 16539 samples

(a) (b)

(c)

Figure 4 Pattern Generator plots (a) Pulse GeneratorOutput (b) Hi-Hat Drum sample impulse signal (c) Con-volution result of (a) and (b)

The next stage of the pattern generator block adds tonalquality to the output of the pulse generator We achieve thisby convolving the pulse generator output with an appropri-ate drum sample impulse signal The drum sample impulsesignal is a short recording of an onset played using a par-ticular drum sound The drum sound selected must have aninstantaneous attack and a short decay as shown in figure4(b)The convolution process requires the loaded sample im-pulse to have the same fs as the pulse generator outputFor a pulse generator output and drum impulse figure 4(c)shows the output of the convolution function We makeuse of the Discrete Fourier Transform convolution prop-erty [21] This allows our result to have the same numberof samples as the pulse generator output We use the FastFourier Transform (FFT) [21] algorithm to achieve this re-sultThe resultant clave son rhythm from the pattern generatorblock at 160 PPM and 4 cycles is an audio signal whoseplot is shown in figure 4(c)

312 Complexity MetricVarious measures of musical rhythm complexity have

been studied in [3] Rhythm complexity measures were di-vided intoRhythm syncopation measures that use metrical weights

determined from the metrical hierarchy to find syncopatedonsets in a rhythm [1922]Pattern matching measures which chop up a rhythm asdetermined by the levels of the metrical hierarchy andsearch each sub-rhythm for patterns that indicate the com-plexity [2324]Distance measures which measure how far away arhythm is from a more simple rhythm composed of beats[192526]Finally mathematical measures which are based uponShannonrsquos information entropy [2728] Shannonrsquos in-formation entropy uncertainty equations are given inequations 456We propose to use the rhythmic complexity measure thatcalculates information entropy in the sense of Shannonrsquosentropy for a particular rhythm pattern Vitz and Todd in[28] present a method that can be used to calculate thecomplexity of cyclic binary patterns Their work definedthat the complexity measure of a certain periodic or repeat-ing pattern is the sum of the total amount of uncertaintyevaluated in processing the stimulus sequence In [28]they achieved this by proposing a set of rules (axioms) de-scribing a perceptual coding process As the method im-plies an emphasis on coded elements it is referred to as acoded element processing system (CEPS) [3]We consider this model for our application due to its al-gorithmic approach to measure rhythm complexity thusmaking it viable for coding as against rhythm syncopa-tion models in [1921] CEPS also has an improved abil-ity to distinguish rhythm patterns within a cycle based oncomplexity as compared to pattern matching [2324] anddistance measures [192526]The axioms in [28] proposed originally for tones and non-tones break down sequences into code levels In our workwe extend it to rhythmic patterns composed of onsets andsilences Each code level successfully codes the patternfrom single elements to larger elements which continuesuntil the entire pattern is constructed To calculate thecomplexity of the rhythmic pattern we measure two uncer-tainty values at each Code Level in the algorithm as pro-posed in [28] Uncertainty in this case means informationentropy The uncertainty values are the maximum uncer-tainty Hmax and the joint uncertainty Hjoint representedin equations 2 and 3 respectively

Hmax(XY ZW ) = H(X) +H(Y ) +H(Z) +H(W )(2)

Hjoint(XY ZW ) =H(X) +H(Y |X) +H(Z|XY )

+H(W |WYZ) (3)

where

H(X) = minussumxisinX

p(x)log2p(x) (4)

H(XY ) = minussumxisinX

sumyisinY

p(x)p(x y)log2p(x y) (5)

H(X|Y ) = minussumxisinX

sumyisinY

p(y x)log2p(yx) (6)

Let the value Hk be the sum of Hkmax and Hk

joint atCode Level k The total sum of H at each Code Level rep-resents the complexity of the pattern This value is termedHcode

Hcode =

nsumk=1

Hk =

nsumk=1

Hkmax +Hk

joint (7)

The complexity measure for [1001001000101000] is cal-culated to be 205538 Similarly we were able to calculatecomplexity measures for all the combinations of patternswithin the cycle lengths of 435 and 7 Upon calculatingthe complexity measures we arrange patterns according totheir increasing order of complexity as shown in sheets 1 We observed that for patterns that are a shifted version ofanother where 1rsquos (onsets) replace the 0rsquos (silences) andvice versa the complexity measures are identical For ex-ample [1100] and [0011] have a complexity measure of50 To tackle this we considered those patterns that be-gin with a 0 as off-beat patterns and assumed that theypresent a higher challenge to learners Hence we incre-mented a constant value to the complexity measures for allthose patterns that begin with a 0 (silence) The constantvalue within a cycle was determined by the highest com-plexity measure for the patterns that begin with 1 (onsets)for that cycle length This can be observed in sheets1Furthermore this complexity metric does not account forthe complexity that arises with changes in tempo There-fore in this work we only assess the performances at aconstant PPM 32 Performance Assessment

Once the learner listens to the generated pattern theirperformance is recorded and loaded onto the system Werectify the recorded audio signal (z) with a thresholdzthreshold = zmax4 to improve the results of the onsetdetection function and it also accounts for low magnitudenoise in the live recording environment

(a) Recorded input (b) Onsets from rectified inputs

Figure 5 Plots of onset detection in one cycle

Any onset detection function can be used to extract theonsets from the rectified recorded input We used the onsetdetection function defined by the Librosa python library

1 httpsdocsgooglecomspreadsheetsde2PACX-1vTSDSqil264H6-M2kLdQUuD6VYnRqYPQePhKl8C_STD1j-54rFdhbLag-ep_15ggiHpo8-DOpJWyQ-Opubhtml

determined from the metrical hierarchy to find syncopatedonsets in a rhythm [1922]Pattern matching measures which chop up a rhythm asdetermined by the levels of the metrical hierarchy andsearch each sub-rhythm for patterns that indicate the com-plexity [2324]Distance measures which measure how far away arhythm is from a more simple rhythm composed of beats[192526]Finally mathematical measures which are based uponShannonrsquos information entropy [2728] Shannonrsquos in-formation entropy uncertainty equations are given inequations 456We propose to use the rhythmic complexity measure thatcalculates information entropy in the sense of Shannonrsquosentropy for a particular rhythm pattern Vitz and Todd in[28] present a method that can be used to calculate thecomplexity of cyclic binary patterns Their work definedthat the complexity measure of a certain periodic or repeat-ing pattern is the sum of the total amount of uncertaintyevaluated in processing the stimulus sequence In [28]they achieved this by proposing a set of rules (axioms) de-scribing a perceptual coding process As the method im-plies an emphasis on coded elements it is referred to as acoded element processing system (CEPS) [3]We consider this model for our application due to its al-gorithmic approach to measure rhythm complexity thusmaking it viable for coding as against rhythm syncopa-tion models in [1921] CEPS also has an improved abil-ity to distinguish rhythm patterns within a cycle based oncomplexity as compared to pattern matching [2324] anddistance measures [192526]The axioms in [28] proposed originally for tones and non-tones break down sequences into code levels In our workwe extend it to rhythmic patterns composed of onsets andsilences Each code level successfully codes the patternfrom single elements to larger elements which continuesuntil the entire pattern is constructed To calculate thecomplexity of the rhythmic pattern we measure two uncer-tainty values at each Code Level in the algorithm as pro-posed in [28] Uncertainty in this case means informationentropy The uncertainty values are the maximum uncer-tainty Hmax and the joint uncertainty Hjoint representedin equations 2 and 3 respectively

Hmax(XY ZW ) = H(X) +H(Y ) +H(Z) +H(W )(2)

Hjoint(XY ZW ) =H(X) +H(Y |X) +H(Z|XY )

+H(W |WYZ) (3)

where

H(X) = minussumxisinX

p(x)log2p(x) (4)

H(XY ) = minussumxisinX

sumyisinY

p(x)p(x y)log2p(x y) (5)

H(X|Y ) = minussumxisinX

sumyisinY

p(y x)log2p(yx) (6)

Let the value Hk be the sum of Hkmax and Hk

joint atCode Level k The total sum of H at each Code Level rep-resents the complexity of the pattern This value is termedHcode

Hcode =

nsumk=1

Hk =

nsumk=1

Hkmax +Hk

joint (7)

The complexity measure for [1001001000101000] is cal-culated to be 205538 Similarly we were able to calculatecomplexity measures for all the combinations of patternswithin the cycle lengths of 435 and 7 Upon calculatingthe complexity measures we arrange patterns according totheir increasing order of complexity as shown in sheets 1 We observed that for patterns that are a shifted version ofanother where 1rsquos (onsets) replace the 0rsquos (silences) andvice versa the complexity measures are identical For ex-ample [1100] and [0011] have a complexity measure of50 To tackle this we considered those patterns that be-gin with a 0 as off-beat patterns and assumed that theypresent a higher challenge to learners Hence we incre-mented a constant value to the complexity measures for allthose patterns that begin with a 0 (silence) The constantvalue within a cycle was determined by the highest com-plexity measure for the patterns that begin with 1 (onsets)for that cycle length This can be observed in sheets1Furthermore this complexity metric does not account forthe complexity that arises with changes in tempo There-fore in this work we only assess the performances at aconstant PPM 32 Performance Assessment

Once the learner listens to the generated pattern theirperformance is recorded and loaded onto the system Werectify the recorded audio signal (z) with a thresholdzthreshold = zmax4 to improve the results of the onsetdetection function and it also accounts for low magnitudenoise in the live recording environment

(a) Recorded input (b) Onsets from rectified inputs

Figure 5 Plots of onset detection in one cycle

Any onset detection function can be used to extract theonsets from the rectified recorded input We used the onsetdetection function defined by the Librosa python library

1 httpsdocsgooglecomspreadsheetsde2PACX-1vTSDSqil264H6-M2kLdQUuD6VYnRqYPQePhKl8C_STD1j-54rFdhbLag-ep_15ggiHpo8-DOpJWyQ-Opubhtml

Figure 6 4X5 Matrix of error deviation result

[29] A sample of the recorded input and the extractedonsets are shown in figure 5

Inter onset intervals are calculated from onsets esti-mated from both recorded (IOIinput) and generated sig-nals (IOIgenerated)The deviation IOIgenerated minus IOIinput for each interonset interval is calculated to be the error in temporal per-formance at each onset

The error is recorded in a matrix format where the num-ber of columns is equivalent to the number of onsets in acycle and the number of rows is determined by the totalnumber of cycles For the son clave rhythm there are 5lsquo1rsquosrsquo (onsets) and 11 lsquo0rsquosrsquo (silence) played for 4 cycles re-sulting in a 4X5 matrix as shown in 6

From the error matrix two sets of averages are calcu-lated One set of average values represent the deviation ofeach inter onset interval within a cycle (average of all thevalues in one column of the error matrix) This results ina 5X1 average onset error array This average onset errorarray is plotted on a graph with the horizontal axis rep-resenting each onset and the vertical axis representing thepercentage of deviation (-100 to 100) This is shown in fig-ure 7(left) This result indicates to the learner their timingerror at each onset The negative error implies slowly play-ing speed and the positive indicates fast playing speedThe next set of average values represent the error deviationof a learner across the cycles (average all the values in onerow of the error matrix) which results in a 4X1 averageresult array This result is plotted on a graph with the hor-izontal axis representing the number of cycles and the ver-tical axis representing the deviation (-100 to 100) shown infigure 7(right) This result gives the learner information ontheir consistency throughout the performance and indicatesif the timing error is consistent across cycles

Figure 7 Deviation graph results of the performance as-sessment block

The graphs in figure 7 give the learner comprehensiveperformance feedback concerning their timing and consis-

tency We achieve this through the graphical representationwherein a positive deviation (above 0 line) in figure 7 (left)infers that the learner is rushing or playing the beat fasterthan intended and a negative deviation (below 0 line) infersthat the learner is dragging or playing the beat slower thanintended Each onset in figure 7 (left) is marked by an x

4 1e0a - The Web ApplicationFor improved accessibility to this system to aid in learn-

ing we developed a web application hosted at https1e0anoelalbencom

Our goal was to implement the proposed system witha simple user interface and a server to collect learnersrsquodata We were able to achieve both by using Flask a microweb framework written in Python [30] The website washosted on AWS [31] with certbot SSL certification [32]

(a) Learning platform (b) Performance Assessment results

Figure 8 lsquo1e0arsquo Web Application

Every new learner must register with the website andprovide consent to use their registration information andperformance assessment results for research purposesPost-registration the learner is given a login id and pass-word Upon logging in to the system they enter the learn-ing platform as shown in figure 8 (a) They must listento the generated pattern and record their respective perfor-mance The lsquoAnalyzersquo button conducts performance as-sessment on the learnerrsquos recording and takes them to theresults as shown in figure 8 (b) If they choose to progressin their learning by clicking lsquoLearn Anotherrsquo the systemwill generate the next pattern based on the complexity met-rics defined in section 312 and take the learner back tothe learning platform When they log out the most recentgenerated pattern is stored into the database and they cancontinue where they left upon logging in again

5 Experiments and Results51 Experimental Setup

To assess and quantify the effectiveness of our rhythmlearning system each learner on the 1e0a web applicationwas required to perform and record 23 distinct patternsover 4 different cycle lengths of (435 and 7) at a con-stant PPM of 160 The learners were asked to use a desk-toplaptop to access the web application and to maintain aconstant interface to perform the rhythmic patterns (clap-ping or a single percussive instrument) They were not al-lowed to use accents in their performance nor take breakswhile performing a given pattern Throughout the exper-

4(a) 3(a) 5(a) 7(a)

4(b) 3(b) 5(b) 7(b)

4 (c) 3(c) 5(c) 7(c)

Figure 9 Graphical analysis of performance assessment for 6 learners categorised by professional(bull) amateur(times) andbeginner() on the 1e0a web application at each cycle (a)Top Panel Total number of attempts taken by learners (b)Center Panel Absolute average beat error in performance (c) Bottom Panel absolute average error over the cycle inperformance

iment the application recorded the number of attemptseach learner takes to achieve performance assessment re-sults within the error bounds presented in section 32 Fur-thermore we stored the performance assessment results ofthe learner for each rhythmic pattern where their resultswere within the error bounds The results of 6 learnersare shown in fig 9 Each learner is categorized based ontheir years of experience with music education Profes-sionals (gt10 years) Amateur (gt2 years) and Beginners(0-2 years)

52 ResultsFrom the resulting graphs in figure 9 it can be observed

that compared to an amateur or a beginner for any givenpattern the professional requires less number of attemptsto achieve performance accuracy within the error boundsThis is reflective of a learning system where beginnersmake more mistakes and progressively improve in theirperformance as they spend more time on the applicationWe also observe that the learners were able to correct theirmistakes and achieve performance accuracy within the er-ror bounds after a sufficient number of attempts This in-dicates that the performance assessment feedback of thesystem aids the learner in understanding and correctingtheir performance to achieve accuracy Furthermore it canbe observed that across different patterns within the cy-cle there exists complexity because the number of attempts

taken by the learner increases with the progression of pat-terns within a cycle However this does not directly re-flect the difficulty that learners have while performing orlistening to the rhythm but does accurately reflect howbeginners and amateurs struggle to recognize a rhythmrsquosstructure as the complexity increases

6 ConclusionIn this article we introduce lsquo1e0arsquo the proof of concept

for a rhythm learning and assessment system that helpslearners progress in their learning with a new pattern gen-erated based on a pre-defined rhythm complexity measureWe describe the rhythm complexity measure that was usedand present the methodology for rhythm performance as-sessment The results of the proposed system show thatwe can successfully test a learnerrsquos proficiency on rhythmpatterns over a single PPM and monitor their progressionwithin a cycle of patterns of increasing complexity valuesThis system does not test the learnerrsquos proficiency acrossdifferent tempos neither does it test for mixed cycle com-plexityThe future work is to implement a complexity measure thatextends to various tempos accents and mixed cycle lengthprogression Furthermore we aim to have an improvedonset detection and noise removal on the recorded audiosignal for a performance assessment that is robust to noise

and disturbances 7 References[1] Eremenko V Morsi A Narang J Serra X Performance

assessment technologies for the support of musical in-strument learning Paper presented at CSEDU 2020The 12th International Conference on Computer Sup-ported Education 629-640 Volume 1 2020 May

[2] J London Rhythm In L Macy editor Grove MusicOnline Oxford University Press 2008 Accessed 20March 2008

[3] Eric Thul Measuring the Complexity of MusicalRhythmrsquo Masterrsquos thesis McGill University MontrealQuebec 2008

[4] Mantie R The Philosophy of Assessment in Music Ed-ucation In The Oxford handbook of assessment policyand practice in music education (32-55) Volume 1 Oxford University Press 2019

[5] Schneider M C McDonel J S DePascale C APerformance Assessment and Rubric Design In TheOxford handbook of assessment policy and practice inmusic education Volume 1 2019

[6] Wesolowski B C Understanding and DevelopingRubrics for Music Performance Assessment Music Ed-ucators Journal 98(3) 36-422012

[7] Dittmar Christian et al Music information retrievalmeets music education Dagstuhl Follow-Ups Vol3 Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik2012

[8] Cano Estefaniacutea Christian Dittmar and SaschaGrollmisch Songs2See learn to play by playing12th International Society for Music Information Re-trieval Conference (ISMIR 2011) Miami 2011

[9] Lerch A Arthur C Pati A amp Gururani S Mu-sic performance analysis A survey arXiv preprintarXiv190700178 2019

[10] Wu Chih-Wei and Alexander Lerch Learned fea-tures for the assessment of percussive music perfor-mances 2018 IEEE 12th International Conference onSemantic Computing (ICSC) IEEE 2018

[11] Crazy Ootka Software AB Perfect Ear ver-sion 3871 httpsplaygooglecomstoreappsdetailsid=comevilduckmusiciankit last accessed 14052021

[12] Demax Rhythm Trainer version02104261849httpsplaygooglecomstoreappsdetailsid=rudemaxrhythmerr lastaccessed 14052021

[13] Steacutephane Dupont Complete Rhythm Trainerversion1310httpsplaygooglecomstoreappsdetailsid=combinaryguiltcompleterhythmtrainerlast accessed 14052021

and disturbances 7 References[1] Eremenko V Morsi A Narang J Serra X Performance

assessment technologies for the support of musical in-strument learning Paper presented at CSEDU 2020The 12th International Conference on Computer Sup-ported Education 629-640 Volume 1 2020 May

[2] J London Rhythm In L Macy editor Grove MusicOnline Oxford University Press 2008 Accessed 20March 2008

[3] Eric Thul Measuring the Complexity of MusicalRhythmrsquo Masterrsquos thesis McGill University MontrealQuebec 2008

[4] Mantie R The Philosophy of Assessment in Music Ed-ucation In The Oxford handbook of assessment policyand practice in music education (32-55) Volume 1 Oxford University Press 2019

[5] Schneider M C McDonel J S DePascale C APerformance Assessment and Rubric Design In TheOxford handbook of assessment policy and practice inmusic education Volume 1 2019

[6] Wesolowski B C Understanding and DevelopingRubrics for Music Performance Assessment Music Ed-ucators Journal 98(3) 36-422012

[7] Dittmar Christian et al Music information retrievalmeets music education Dagstuhl Follow-Ups Vol3 Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik2012

[8] Cano Estefaniacutea Christian Dittmar and SaschaGrollmisch Songs2See learn to play by playing12th International Society for Music Information Re-trieval Conference (ISMIR 2011) Miami 2011

[9] Lerch A Arthur C Pati A amp Gururani S Mu-sic performance analysis A survey arXiv preprintarXiv190700178 2019

[10] Wu Chih-Wei and Alexander Lerch Learned fea-tures for the assessment of percussive music perfor-mances 2018 IEEE 12th International Conference onSemantic Computing (ICSC) IEEE 2018

[11] Crazy Ootka Software AB Perfect Ear ver-sion 3871 httpsplaygooglecomstoreappsdetailsid=comevilduckmusiciankit last accessed 14052021

[12] Demax Rhythm Trainer version02104261849httpsplaygooglecomstoreappsdetailsid=rudemaxrhythmerr lastaccessed 14052021

[13] Steacutephane Dupont Complete Rhythm Trainerversion1310httpsplaygooglecomstoreappsdetailsid=combinaryguiltcompleterhythmtrainerlast accessed 14052021

[14] MakeMusic Inc SmartMusicApril 2019 httpswwwsmartmusiccom last accessed 05142021

[15] Yousician Oy Yousician April 2019 httpswwwyousiciancom last accessed 05142021

[16] The Way of H Inc (dba Music Prodigy) MusicProdigy April 2019 httpwwwmusicprodigycomlast accessed 05142021

[17] Sony Interactive Entertainment Europe SingStarApril 2019 httpwwwsingstarcom lastaccessed 05142021

[18] G W Cooper and L B Meyer The Rhythmic Structureof Music The University of Chicago Press 1960

[19] G T Toussaint A mathematical analysis ofAfricanBrazilian and Cuban clave rhythms InBRIDGES Mathematical Connections in Art Musicand Science pages 157-168 Jul 2002

[20] Janssen Brett Allen A preliminary comparative studyof rhythm systems employed within the first-year col-lege aural skills class Diss Kansas State University2017

[21] Proakis John G and Dimitris G Manolakis Digitalsignal processing PHI Publication New Delhi India(2004)

[22] H Longuet-Higgins and C Lee The rhythmic in-terpretation of monophonic music Music Perception1(4)424-441 1984

[23] J Pressing Cognitive complexity and thestructure of musical patterns httpwwwpsychunimelbeduaustaffjpcog-musicpdf 1999

[24] M Keith From Polychords to Poacuteya Adventures inMusical Combinatorics Vinculum Press 1991

[25] G T Toussaint Classification of phylogenetic analy-sis of African ternery rhythm timelines In BRIDGESMathematical Connections in Art Music and Sciencepages 23-27 Jul 2003

[26] F Goacutemez A Melvin D Rappaport and G ToussaintMathematical measures of syncopation In BRIDGESMathematical Connections in Art Music and Sciencepages 73-84 Jul 2005

[27] P C Vitz Information run structure and binarypattern complexity Perception and Psychophysics3(4A)275-280 1968

[28] P C Vitz and T C Todd A coded element model of theperceptual processing of sequential stimuli Psycologi-cal Review 75(6)433-449 Sep 1969

[29] McFee Brian et al librosa Audio and music signalanalysis in python Proceedings of the 14th python inscience conference Vol 8 2015

[30] Grinberg Miguel Flask web development developingweb applications with python OrsquoReilly Media Inc2018

[31] Amazon E C Amazon web services Avail-able in httpawsamazoncomesec2(November 2012) 2015

[32] Tiefenau Christian et al A Usability Evaluation ofLetrsquos Encrypt and Certbot Usable Security DoneRight Proceedings of the 2019 ACM SIGSAC Con-ference on Computer and Communications Security2019