## The Diapason Press## Tuning and Temperament Library |

ON

MUSICAL INTERVALS AND

TEMPERAMENT

(London 1876)

One of the most intriguing theoretical texts from the 19th century, with a formal treatment of tuning and temperament systems. Bosanquet’s keyboard design has turned out to be of paramount importance for the development of 20th-century microtonal keyboards.

Includes a comprehensive new introduction by Rudolf Rasch, as well as a bibliography and index. Reprinted from the original (1876) edition as published by Macmillan and Co. in London

- 1987
- ISBN 90-70907-12-7 (paper)
- 80 + xx + 94 pp. - 15 illus.
- 15 x 21 cm
- €30 or US$30

Preface | 7 | |

Introduction | ||

1. | Biography | 11 |

2. | Bosanquet’s scientific writings | 17 |

3. | The English tuning and temperament background | 24 |

4. | The Elementary treatise on musical intervals and temperament | 27 |

5. | Prior versions | 33 |

6. | The general theory of the division of the octave | 50 |

7. | The generalized keyboard | 52 |

8. | Later writings on tunings and temperament | 58 |

9. | Bosanquet’s significance | 64 |

Bibliography | 68 | |

Index | 73 | |

Note about Bosanquet on Tenerife | 79 | |

R. H. M. BOSANQUET | ||

AN ELEMENTARY TREATISE ON MUSICAL INTERVALS AND TEMPERAMENT | ||

1876 | ||

Preface | vii | |

Chapter I. | Harmonious chords | 1 |

Chapter II. | Equal temperament | 4 |

Chapter III. | Perfect fifths. Pythagorean system | 7 |

Note on the calculation of beats | 14 | |

Chapter IV. | The generalised keyboard | 19 |

Chapter V. | Mean-tone system. Old unequal temperament | 24 |

Chapter VI. | Applications of the mean-tone system | 33 |

Chapter VII. | Harmonic seventh | 41 |

Chapter VIII. | Applications of the system of perfect fifths and allied systems | 43 |

Chapter IX. | Enharmonic harmonium. Enharmonic organ, positive stop | 51 |

Chapter X. | General theory of the division of the octave | 60 |

Chapter XI. | Musical employment of positive systems having perfect or approximately perfect fifths | 69 |

Appendix. | On the theory of the calculation of intervals | 81 |

ILLUSTRATIONS | ||

Introduction | ||

Figure 1. | Letter by Bosanquet of 23 November 1874 | 34 |

Figure 2. | Diagram of systems of various orders | 47 |

Figure 3. | Diagram of departures in various systems | 49 |

Figure 4. | Bosanquet’s enharmonic harmonium | 57 |

Figure 5. | Letter by Bosanquet of 28 April 1877 | 59 |

Figure 6. | Diagram of second-order keyboard | 61 |

Figure 7. | Portrait of R. H. M. Bosanquet | 77 |

Figure 8. | Arms of the Bosanquet family | 78 |

An elementary treatise | ||

Diagram 1. | Symmetrical arrangement of the notes of Thompson’s enharmonic organ | 22 |

Diagram 2. | Section, elevation, and plan [of the generalized keyboard] | 23 |

Diagram 3. | [Arrangement of notes in meantone tuning] | 34 |

Diagram 4. | [Arrangement of notes in meantone tuning] | 34 |

Diagram 5. | Poole’s keyboard. Colin Brown’s keyboard. Arrangement of key-notes | 46 |

Diagram 6. | Poole’s keyboard. Arrangement of accessories | 47 |

Diagram 7. | Knight’s move arrangement of Colin Brown’s keyboard | 48 |

[Music] example for systems of approximate perfect fifths, with a compass of three octaves | 77 |