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CombinoChord: Project Defense

CombinoChordGraduate Research Project Defense

Nicholas Smith

CPSC 597 | California State University Fullerton 1/34


Outline

IntroductionThe ProblemObjectivesSignificanceRelated ResearchAssumptions

MethodologyHeuristicFretboard ModelHand ModelSound QualityPre-Processing

FilteringMulti-ThreadingAndroidResultsAnalysis

Summary



Introduction

• Project Overview

• Key Terms:

– Guitar: A Stringed Instrument

– Guitar Strings & Fretboard

– Fret position



Figure 1: An Electric Guitar



The Problem

Generate guitar chords based on the following parameters:

• The number of strings

• The number of frets

• The tuning of the strings

• The guitar setup

• The player’s hand

• The chord to play



Objectives

Goals for the system:

• Search for chords within 5 seconds for normal guitar configurations

• Use guitar tablature notation

• Conventional fingerings should be assigned a high score



Significance

Non-triviality:

• Guitar layout

• Definition of “goodness”

Brute force is unsatisfactory for two primary reasons:

1. There are a large number of possibilities

2. Most possibilities are undesirable



Significance

Brute force approach:

4∑i=0

[2i ×i−1∏j=0

(n− j)] = 16n4 − 88n3 + 156n2 − 82n + 1

Where n = s × f is the number of fret positions on the guitar, s is thenumber of strings on the guitar, and f is the number of frets.



Significance

Example for acoustic guitar:

4∑i=0

[2i ×i−1∏j=0

(120− j)] ≈ 3.17× 109.



Related Research

• Two similar papers:

– Graph theory based approach: Norman and Grozman fromKTH Royal Institute of Technology [2]

– Evolutionary based approach: Tuohy and Potter from UGA [3]

• Similar Android apps



Existing Solutions• Existing apps use static databases

• Drawbacks:

1. Cannot adapt to guitar tuning

2. Cannot adapt to guitar configuration

3. Cannot adapt to the user’s hand

4. Chord ordering is fixed

5. Substantial upfront work



Existing Solutions

• CombinoChord :

1. Can adapt to guitar tuning

2. Can adapt to guitar configuration

3. Can adapt to the user’s hand

4. Chord ordering is not fixed

5. No upfront work (besides mine)



Assumptions

• Thumb is not considered

• Only runs on Android

• Core can run on JVM



MethodologyOverview:

• Notation

• Heuristic Function

• Fretboard Model

• Hand Model

• Sound Quality

• Preprocessing

• Filtering

• Multi-threading

• Android Programming

• Results

• Analysis



Heuristic

Define a heuristic function that considers:

1. Anatomical distance-based score

2. Sound quality score



Fretboard Model

• Define fretboard in R2

• Given first fret size, compute size of other frets

• Distance between strings

• Use euclidean distance ‖p‖



Hand Model

Input table of max and min comfortable range values:

Finger 1 Finger 2 Min Range (mm) Max Range (mm)1 2 5.0 80.01 3 15.0 95.01 4 25.0 110.02 3 6.0 52.02 4 12.0 69.03 4 8.5 47.0



Hand Model

Use a score function:

SF (x, a, b) =

1 + (x− 0.99a)3 x < a

1− ((x− 0.99a)/(1.01b− 0.99a))2 x ≥ a.

Where a and b are the min and max range values for the pair of fingersrespectively, and x is the distance between the pair of fingers.



20 40 60 80

0.5

1

x

y

Figure 2: Plot of SF



Hand Model

• Average SF over all pairs used

• Use best choice of fingers

• Only need to consider case where fingers don’t cross

• For 3: {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}



Sound Quality

• Unison notes

• Number of mutes

• Number of strings played



Pre-Processing

• Only consider fret-positions that produce notes in chord

• Drastically reduces size of state space

• CM7 on an acoustic:

4∑i=0

[2i ×i−1∏j=0

(46− j)] ≈ 6.34× 107.



Filtering

Idea: At each step we can filter possible fret positions

• Fret positions on same string

• Fret positions out of reach

• ‖pi − pj‖ > MAX

• Fret positions beneath tonic note



Multi-Threading

Multi-thread the search:

• Sub-tasks based on tonics

• Split ordered list into t parts

• Card dealing method

• Thread pool approach



150 200 2500

20

40

60

80

n

Avg.

Search

Time(m

s)

2 Threads

Thread PoolShuffledOrdered

150 200 2500

20

40

60

n

Avg.

Search

Time(m

s)

4 Threads

Thread PoolShuffledOrdered



Android• Two packages:

– UI

– domain (to be made open source)

• UI:

– 7 Fragments

– Controlled by main activity

– Searching runs in background



(a) Home Fragment (b) Guitar Fragment



(a) Tuning Fragment (b) Hand Fragment



(a) Chord Fragment (b) Advanced Fragment



(a) About Fragment (b) Navigation Drawer



Results

#Strings # Frets Avg. Search Time Std. Search Time6 12 28.46 ms 19.52 ms6 20 74.80 ms 41.86 ms7 12 61.08 ms 51.22 ms7 20 127.63 ms 53.55 ms8 12 83.08 ms 51.32 ms8 20 261.46 ms 161.73 ms



Analysis

• Times well within goal

• Less than Doherty threshold (400ms) for normal guitars [1]



Summary

CombinoChord :

• Finds chords well within timing constraints

• Presents guitar tablature notation

• Allows modification of specified parameters



References

[1] Doherty, Walter J. and Arvind J. Thadhani. "The economic value ofrapid response time." IBM Report (1982)

[2] Vladimir Grozman, and Christopher Norman An Algorithm for OptimalGuitar Fingering. KTH Royal Institue of Technology, 2013

[3] D.R. Tuohy and W.D. Potter A Genetic Algorithm for the AutomaticGeneration of Playable Guitar Tablature. Proceedings of the Inter-national Computer Music Conference. Artificial Intelligence Center,University of Georgia Athens, 2005


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