# Generation of Melodies for the Lost Chant of the Mozarabic Rite

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Patterns and Templates

#### 2.2. Statistical Model

#### 2.3. Sampling Compatible Instances of Templates

## 3. Results

#### 3.1. Corpus

#### 3.2. Template Creation

#### 3.3. Statistical Model

#### 3.4. Concert of Generated Chants

#### 3.5. Singer and Audience Evaluation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

GRE | Gregorian corpus |

PPM | Prediction by Partial Match |

LSTM | Long Short-Term Memory |

IC | Information Content |

## Appendix A. Supplementary Information

#### Appendix A.1. GRE Corpus

#### Appendix A.2. 22 Templates

#### Appendix A.3. Scores for Concert Pieces

#### Appendix A.4. Links to Recordings

#### Appendix A.5. PPM Backoff Model

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**Figure 1.**Two lines of the Canticum Zachariae for the feast of St. John the Baptist from the León antiphoner (E–L 8, 215r4–5). Encircled is an intra-opus repeating pattern. On the second line of the León image the beginning of the last verse; Inluminare eis. Below the León image is a representation in contour letters of this second line, and below that the corresponding passage of our generated performance score with text.

**Figure 2.**(

**a**) The first line of the responsory Dominus ab utero for the feast of St. John the Baptist in the León antiphoner (E-L 8, 214r2), with two intra-opus patterns; (

**b**) a representation of the fragment in contour letters (with intra-opus patterns bracketed); (

**c**) the partial encoding of the contour sequence and intra-opus patterns as a template. $\mathcal{A}$, $\mathcal{B}$, and $\mathcal{C}$ are variables used to specify equal pitches; (

**d**) a random instantiation of the template: the two different colors indicate the beginning event for the two intra-opus patterns; (

**e**) a sample taken from a statistical model, ignoring any template constraints; (

**f**) the corresponding passage of our generated performance score.

**Figure 3.**(

**Left**): leave-one-out per event information content of the GRE corpus, under different orders of PPM(k) model. (

**Right**): the distribution of sequences generated by 10,000 iterations of random walk, for a template of 840 events and a PPM(2) model of the GRE corpus. The vertical black line marks the mean IC to the training corpus.

Viewpoint | Description | Codomain |
---|---|---|

$\mathsf{pitch}$ | set of 15 possible pitches | $\{57,59,60,\dots ,81\}$ |

$\mathsf{position}$ | position of event in sequence | $\{1,2,3,\dots \}$ |

$\mathsf{h},\mathsf{l},\mathsf{e},\mathsf{b},\mathsf{p}$ | contour viewpoints (see text) | Boolean |

${\mathsf{range}}_{x,y}$ | pitch in range $[x,y]$ | Boolean |

number of chants in GRE | 137 |

mean chant length | 473 notes |

mean number of words/syllables/neumes | 56/123/318 |

number of templates | 22 |

mean template length | 789 notes |

mean number of defined pitches | 14 |

mean number of words/syllables/neumes | 107/226/464 |

mean coverage by intra-opus patterns | 52% |

mean fraction of events with no specified contours | 34% |

**Table 3.**Chants performed at the concert, including genre (SNO: sono; RS: responsory; VAR: various; SCR: sacrificium), performance time, name of template, place in E-L 8, and for the generated performance score (see Results), IC (bits/event), audience and singer ratings.

Audience ($\mathit{n}=34$) | Singers ($\mathit{n}=5$) | |||||||
---|---|---|---|---|---|---|---|---|

Genre | Time | Incipit | E-L 8 | IC | Mean | Stdev | Mean | Stdev |

SNO | 07:03 | Haec dicit Dominus priusquam | 211v10 | 2.03 | 7.5 | 1.8 | 6.2 | 0.8 |

RS | 04:38 | Zaccarias sacerdos | 212v11 | 2.03 | 7.6 | 1.7 | 6.6 | 0.5 |

RS | 02:05 | Unde mici adfuit ut veniret | 213v10 | 2.08 | 8.0 | 1.6 | 5.8 | 1.8 |

RS | 02:31 | Fuit homo missus a Deo | 213v01 | 1.88 | 8.2 | 1.3 | 7.2 | 0.8 |

RS | 03:47 | Dominus ab utero formabit me | 214r02 | 1.95 | 7.7 | 1.6 | 7.8 | 1.1 |

RS | 02:14 | Spiritus Domini super me | 213r08 | 1.99 | 8.0 | 1.6 | 8.0 | 0.8 |

RS | 02:53 | Misit me Dominus sanare | 212v02 | 1.99 | 8.2 | 1.4 | 7.5 | 1.4 |

RS | 02:16 | Me oportet minui | 214r12 | 1.96 | 8.9 | 1.4 | 6.4 | 0.9 |

VAR | 07:06 | Benedictus Dominus Deus Israel | 214v12 | 2.08 | 9.4 | 1.0 | 5.9 | 2.5 |

SCR | 07:22 | Dum complerentur dies | 210r14 | 2.12 | 8.7 | 1.4 | 6.2 | 0.8 |

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**MDPI and ACS Style**

Conklin, D.; Maessen, G.
Generation of Melodies for the Lost Chant of the Mozarabic Rite. *Appl. Sci.* **2019**, *9*, 4285.
https://doi.org/10.3390/app9204285

**AMA Style**

Conklin D, Maessen G.
Generation of Melodies for the Lost Chant of the Mozarabic Rite. *Applied Sciences*. 2019; 9(20):4285.
https://doi.org/10.3390/app9204285

**Chicago/Turabian Style**

Conklin, Darrell, and Geert Maessen.
2019. "Generation of Melodies for the Lost Chant of the Mozarabic Rite" *Applied Sciences* 9, no. 20: 4285.
https://doi.org/10.3390/app9204285