Musical intervals and temperament

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

The Diapason Press

Tuning and Temperament Library

R. H. M. Bosanquet

AN ELEMENTARY TREATISE
ON
MUSICAL INTERVALS AND
TEMPERAMENT
(London 1876)

edited by Rudolf Rasch

TTL 4

Contents