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CombinoChord: Project Defense
CombinoChord
Graduate Research Project Defense
Nicholas Smith
CPSC 597 | California State University Fullerton 1/34

Outline
Introduction
The Problem
Objectives
Signiﬁcance
Related Research
Assumptions
Methodology
Heuristic
Fretboard Model
Hand Model
Sound Quality
Pre-Processing
Filtering
Multi-Threading
Android
Results
Analysis
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 the
number 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 from
KTH 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

Methodology
Overview:
• 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 80.0
1 3 15.0 95.0
1 4 25.0 110.0
2 3 6.0 52.0
2 4 12.0 69.0
3 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 ﬁngers
respectively, 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

150 200 250
0
20
40
60
80
n
Avg.SearchTime(ms)
2 Threads
Thread Pool
Shuﬄed
Ordered
150 200 250
0
20
40
60
n
Avg.SearchTime(ms)
4 Threads
Thread Pool
Shuﬄed
Ordered

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 Time
6 12 28.46 ms 19.52 ms
6 20 74.80 ms 41.86 ms
7 12 61.08 ms 51.22 ms
7 20 127.63 ms 53.55 ms
8 12 83.08 ms 51.32 ms
8 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 of
rapid response time." IBM Report (1982)
[2] Vladimir Grozman, and Christopher Norman An Algorithm for Optimal
Guitar Fingering. KTH Royal Institue of Technology, 2013
[3] D.R. Tuohy and W.D. Potter A Genetic Algorithm for the Automatic
Generation of Playable Guitar Tablature. Proceedings of the Inter-
national Computer Music Conference. Artiﬁcial Intelligence Center,
University of Georgia Athens, 2005

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