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Exploring the Effects of Pitch Layout on Learning a New Musical Instrument^{ †}

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## Abstract

**:**

## Featured Application

**The results obtained in this paper are applicable to the design of new musical instruments intended to facilitate the learning and playing of music.**

## Abstract

## 1. Introduction

#### 1.1. Isomorphic Layout Properties

- The octave axis is here defined as any axis that passes through the closest button centres that are an octave apart.
- The major second axis (M2 axis, for short) is here defined as any axis that passes through the closest button centres that are a major second apart.

#### 1.1.1. Adjacent (A) or NonAdjacent (${A}^{\prime}$) Seconds

#### 1.1.2. Sheared (S) or Unsheared (${S}^{\prime}$)

#### 1.2. Motor Skill Learning in Music Performance

- A cognitive stage, encompassing the processing of information and detecting patterns. Here, various motor solutions are tried out, and the performer finds which solutions are most effective.
- A fixation stage, when the general motor solution has been selected, and a period commences where the patterns of movement are perfected. This stage can last months, or even years.
- An autonomous stage, where the movement patterns do not require as much conscious attention on the part of the performer.

#### 1.3. Study Design

- Adjacency $\in \{0,1\}$, where 0 is the code for a layout with non-adjacent major seconds (${A}^{\prime}{S}^{\prime}$ or ${A}^{\prime}S$), and 1 is the code for a layout with adjacent major seconds ($A{S}^{\prime}$ or $AS$).
- Shear $\in \{0,1\}$, where 0 is the code for an unsheared layout (${A}^{\prime}{S}^{\prime}$ or $A{S}^{\prime}$), and 1 is the code for a sheared layout (${A}^{\prime}S$ or $AS$).
- LayoutNo $\in \{0,1,2\}$, where 0 is the code for the first layout played by a participant, 1 is the code for the second layout they played, and 2 is the code for the third and final layout they played.
- PerfNo $\in \{0,1,2,3\}$, where 0 is the code for their first performance of a given layout, 1 is the code for their second performance of a given layout, 2 is the code for their third performance of a given layout, 3 is the code for their fourth performance of a given layout. Note that participants gave three performances for the training, two performances for the immediate retention tasks, and four performances for the transfer task.

- $A{S}^{\prime}$ then ${A}^{\prime}{S}^{\prime}$ then $AS$
- $A{S}^{\prime}$ then ${A}^{\prime}S$ then $AS$
- $AS$ then ${A}^{\prime}{S}^{\prime}$ then $A{S}^{\prime}$
- $AS$ then ${A}^{\prime}S$ then $A{S}^{\prime}$.

## 2. Results

#### 2.1. Modelling Approach

`lme-4`package in

`R`, and p-values estimated by the

`drop1`function using the

`Chisq`option, or the

`anova`function. The ${r}^{2}$ value shown in each table is the squared correlation between the model’s predictions and the observed data, hence loosely analogous to ${R}^{2}$ in linear regression.

#### 2.2. Training Performances

#### 2.3. Immediate Retention

#### 2.4. Transfer

## 3. Discussion

#### 3.1. PerfNo and LayoutNo

#### 3.2. Adjacency

#### 3.3. Shear

#### 3.4. Limitations

#### 3.5. Summary

## 4. Methods

#### 4.1. Participants

#### 4.2. Materials

#### 4.2.1. Hardware and Software

#### 4.2.2. Musical Tasks

#### 4.3. Procedure

#### 4.3.1. Training Paradigm and Testing of Immediate Retention

- watching the sequence once as demonstrated by audiovisual highlighting
- playing along with the audiovisual highlighted sequence three times (training)
- reproducing the sequence in the absence of audiovisual highlighting, for two consecutive performances (immediate retention task)

#### 4.3.2. Transfer Task

#### 4.4. Measuring Performance Inaccuracy

#### 4.4.1. Training Tasks

- N is the total number of notes in the target sequence
- ${t}_{n}$ is the time in milliseconds of nth target note
- ${t}_{p}$ is the time in milliseconds of first performed note within the ${t}_{n}\pm 333$ time window that matches the pitch of the target note.

#### 4.4.2. Retention and Transfer Tasks

- N is the total number of notes in the target sequence.
- C is the total number of notes in the corrected performance.
- ${t}_{c}$ is the time in milliseconds of the cth note in the corrected performance.
- ${t}_{m}$ is the time of the metronome beat closest to the performed note ${t}_{c}$.
- E is the number of errors calculated as explained above.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The four isomorphic layouts tested in the experiment. They have differently angled pitch axes and major seconds axes. An easy way to understand the meaning of the pitch axis is to place a ruler on any of the above subfigures so that it is at right angles to the pitch axis. If the ruler is then slid in the direction of the pitch axis, with its angle kept constant, the button-centres passing under the ruler’s edge will always be encountered in ascending pitch order. This occurs only when the ruler is oriented and moved, in this way, with the pitch axis. This means that, when the pitch axis is vertical, as in (

**c**,

**d**), the pitch of each button is proportional to its vertical position. In all four layouts, the octave axis is vertical; that is, buttons that are an octave apart are vertically aligned. (

**a**) ${A}^{\prime}{S}^{\prime}$: nonadjacent M2s, unsheared; (

**b**) $A{S}^{\prime}$ (the Wicki layout [4]): adjacent M2s, unsheared; (

**c**) ${A}^{\prime}S$: nonadjacent M2s, sheared; (

**d**) $AS$: adjacent M2s, sheared.

**Figure 2.**Inaccuracies, averaged across participants, for the scale training task. The higher the line, the more accurate the average performance. The bootstrapped confidence intervals cover a 95% range. Adjacent layouts have solid lines, nonadjacent have dashed lines. Sheared layouts have orange lines, unsheared have blue lines. The first performance is coded 0, the second is coded 1, ...; the first layout is coded 0, the second is coded 1.

**Figure 3.**Inaccuracies, averaged across participants, for the arpeggio training task. The higher the line, the more accurate the average performance. The bootstrapped confidence intervals cover a 95% range. Adjacent layouts have solid lines, nonadjacent have dashed lines. Sheared layouts have orange lines, unsheared have blue lines. The first performance is coded 0, the second is coded 1, ...; the first layout is coded 0, the second is coded 1.

**Figure 4.**Inaccuracies, averaged across participants, for the scale retention task. The higher the line, the more accurate the average performance. The bootstrapped confidence intervals cover a 95% range. Adjacent layouts have solid lines, nonadjacent have dashed lines. Sheared layouts have orange lines, unsheared have blue lines. The first performance is coded 0, the second is coded 1; the first layout is coded 0, the second is coded 1.

**Figure 5.**Inaccuracies, averaged across participants, for the transfer task (Frère Jacques). The higher the line, the more accurate the average performance. The bootstrapped confidence intervals cover a 95% range. Adjacent layouts have solid lines, nonadjacent have dashed lines. Sheared layouts have orange lines, unsheared have blue lines. The first performance is coded 0, the second is coded 1, ...; the first layout is coded 0, the second is coded 1.

Fixed Effect | Estimate | Factor | p-Value |
---|---|---|---|

(Intercept) | 3.48 | 32.61 | <0.001 *** |

Adjacency | −0.06 | 0.94 | 0.263 |

Shear | 0.13 | 1.14 | 0.026 * |

LayoutNo | −0.37 | 0.69 | 0.001 *** |

PerfNo | −0.27 | 0.77 | <0.001 *** |

LayoutNo:PerfNo | 0.12 | 1.13 | 0.003 ** |

Log Likelihood | −727.67 | ||

Num. obs. | 208 | ||

Num. groups: ID | 24 | ||

Var: ID (Intercept) | 0.04 | ||

Var: Residual | 0.17 | ||

${r}^{2}$ | 0.44 |

Fixed Effect | Estimate | Factor | p-Value |
---|---|---|---|

(Intercept) | 3.92 | 50.36 | <0.001 *** |

Adjacency | −0.43 | 0.65 | <0.001 *** |

Shear | 0.08 | 1.08 | 0.037 * |

LayoutNo | −0.22 | 0.80 | <0.001 *** |

PerfNo | −0.09 | 0.91 | <0.001 *** |

Log Likelihood | −738.65 | ||

Num. obs. | 209 | ||

Num. groups: ID | 24 | ||

Var: ID (Intercept) | 0.05 | ||

Var: Residual | 0.08 | ||

${r}^{2}$ | 0.78 |

Fixed Effect | Estimate | Factor | p-Value |
---|---|---|---|

(Intercept) | 2.85 | 17.32 | <0.001 *** |

Adjacency | −0.54 | 0.58 | <0.001 *** |

Shear | −0.08 | 0.92 | 0.305 |

LayoutNo | −0.04 | 0.96 | 0.412 |

PerfNo | 0.04 | 1.04 | 0.581 |

Log Likelihood | −437.37 | ||

Num. obs. | 142 | ||

Num. groups: ID | 24 | ||

Var: ID (Intercept) | 0.06 | ||

Var: Residual | 0.26 | ||

${r}^{2}$ | 0.38 |

Fixed Effect | Estimate | Factor | p-Value |
---|---|---|---|

(Intercept) | 3.43 | 30.85 | <0.001 *** |

Adjacency | −0.05 | 0.96 | 0.408 |

Shear | −0.50 | 0.61 | <0.001 *** |

LayoutNo | −0.38 | 0.68 | <0.001 *** |

PerfNo | −0.13 | 0.88 | <0.001 *** |

LayoutNo:Shear | 0.33 | 1.39 | 0.002 ** |

LayoutNo:PerfNo | 0.07 | 1.07 | 0.021 * |

Log Likelihood | −996.89 | ||

Num. obs. | 288 | ||

Num. groups: ID | 24 | ||

Var: ID (Intercept) | 0.11 | ||

Var: Residual | 0.26 | ||

${r}^{2}$ | 0.66 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

MacRitchie, J.; Milne, A.J. Exploring the Effects of Pitch Layout on Learning a New Musical Instrument. *Appl. Sci.* **2017**, *7*, 1218.
https://doi.org/10.3390/app7121218

**AMA Style**

MacRitchie J, Milne AJ. Exploring the Effects of Pitch Layout on Learning a New Musical Instrument. *Applied Sciences*. 2017; 7(12):1218.
https://doi.org/10.3390/app7121218

**Chicago/Turabian Style**

MacRitchie, Jennifer, and Andrew J. Milne. 2017. "Exploring the Effects of Pitch Layout on Learning a New Musical Instrument" *Applied Sciences* 7, no. 12: 1218.
https://doi.org/10.3390/app7121218