This remarkable book, comprising 768 pages describing 30 to 40 historic temperaments, encompasses tunings and commentary from circa 1636 through circa 1920.  This has to be the ultimate reference for any questions regarding historic tunings.  (Jorgensen's work is incorporated in the Sanderson AccuTuner.)  What I enjoyed most was the staff notation for setting the bearings of each tuning.  These are quite easy to read, and comprise three or four pages for each tuning.

My impressions were that Jorgensen has captured the technical details of tuning historic temperaments in an excellent reference book.  His most important points were:

1.  Composers wrote for the instruments of the day.  So if the tuning was just, or equal, or something in between, the composers wrote, voiced, and annotated for *that* instrument/tuning.

2.  If you want accurate reproduction of a composer's intent, you should play the piece on his instrument, with the proper historic tuning.

3.  Most fascinating to me was:  the musical community generally realized (though hotly debated) the need for equal temperament circa 1800, but almost a century elapsed before for aural tuning techniques evolved which could provide reasonable accuracy.

(Note that the evolution of the method for tuning the equal temperament was coincident with the evolution of the piano itself, especially the scaling of the strings.  Until evenly drawn high strength wire, both unwrapped and wrapped, was available in high quality, the inharmonicity of the notes could not progress smoothly up and down the scale.  This, in turn, would prevent precise tuning of the beat rates of partials.  The ultimate test of a good temperament on any piano is a smooth change of the beat rates as progressive thirds are played -- both in the bearings octave, and outside it.)

Each of the tuning methods in the evolution had faults which tended to produce deviations from equal temperament.  These deviations were most pronounced in one or two intervals of the "bearings" octave.  Different tuning methods would favor/penalize different intervals -- though as the procedures evolved, the errors were made progressively smaller.

John Rhodes

jorgensen01.gif (41 kb) is the second page from the book, giving publisher, ISBN, etc.

jorgensen02.gif (87 kb) is a sample of the staff notation for a specific tuning. This selection is the second of 6 pages describing tuning by ear in 1917, probably William Braid White's procedure.

CONTENTS

LIST OF TABLES FOR ELECTRONIC TUNING xv
Temperaments Used as Substitutes for Equal Temperament
Regular Meantone Temperaments
Modified Meantone Temperaments
Well Temperaments
Quasi-equal Temperaments

LIST OF TABLES SHOWING THE SIZES OF MAJOR THIRDS IN CENTS IN PERSPECTIVES xvii
Temperaments Used as Substitutes for Equal Temperament
Regular Meantone Temperaments
Modified Meantone Temperaments
Well Temperaments
Quasi-equal Temperaments

LIST OF MISCELLANEOUS TABLES xix

LIST OF FIGURES SHOWING THE FORMS OF TONALITY OR HARMONIC BALANCES xx

PREFACE xxi

HINTS ON HOW TO USE THIS BOOK xxii

SECTIONS
1. Equal temperament was not practiced on pianos in 1885 1
2. Why equal temperament was not commonly practiced on pianos before the twentieth century 4
3. Nomenclature 8
4. "These Half-tones whether they be Equal or Unequal, it is a question" ~in 1636 11
5. "He that desires to know the true Proportions . . . let him read . . . Mersenne" 13
6. The ratios of equal temperament by Mann Mersenne in 1636 15
7. Monsieur Boulliau's fourteenth-century Pythagorean temperament 18
8. Tuning the Boulliau unrestrictive irregular circulating Pythagorean temperament of 1373 in the theoretically correct manner 21
9. Tuning the Boulliau unrestrictive irregular circulating Pythagorean temperament of 1373 in the equal-beating manner 24
10. Tuning the Boulliau unrestrictive irregular circulating Pythagorean temperament in the style of Henricus Grammateus of 1518 26
11. Mann Mersenne and meantone temperament in 1636 28
12. Tuning Pietro Aaron's restrictive regular noncirculating one-fourth syntonic comma meantone keyboard temperament of 1523 in the theoretically correct manner 31
13. William Holder and meantone temperament in 1694 37
14. An authentic way to tune seventeenth-century meantone temperament 39
15. Equal-beating meantone temperament and an explanation of the 'Characters of the Keys'
16. Tuning the seventeenth-century irregular equal-beating meantone temperament 49
17. The tuning rules by Gottfried Keller in 1707 55
18. Tuning the equal-beating restrictive regular noncirculating almost one-fifth diatonic comma meantone temperament by using Gottfried Keller's tuning rules of 1707 58
19. Temperament conditions reported by Alexander Malcolm in 172162
20. Well temperament 64
21. An authentic way to tune late seventeenth- and early eighteenth-century well temperament 67
22. Tuning Francesco Antonio Vallotti's early eighteenth-century well temperament in the equal-beating manner 68
23. Roger North's attempt to write helpful and thorough tuning instructions in 1726 73
24. The amount that "ye Ear will permit" on wide major thirds in 1731 75
25. Tuning the unrestrictive circulating well temperament by using Peter Preulleur's rules of 1731 79
26. William Tansyur's tuning rules of 1746 83
27. Tuning the unrestrictive circulating well temperament by using William Tansy Tansyur's' s rules of 1746 85
28. The older forms of meantone temperament revived by Robert Smith in 1749 90
29. Tuning Christiaan Huygens's meantone temperament of 1661 based on 31 tones to the octave
30. Tuning Robert Smith's. equal-beating meantone temperament meant for "equal harmony" in 1749 103
31. Robert Smith's beat frequency formulas of 1749 109
32. Nicolo Pasquali's tuning rules from around 1743-1757 112
33. Tuning Nicolo Pasquali's meantone temperament from around 1743-1757 114
34. The most common tuning system after around 1759 116
35. The one-fifth syntonic comma meantone temperament by John Holden in 1770 118
36. Tuning John Holden's equal-beating meantone temperament of 1770 120
37. Robert Falkener's tuning rules of 1774 129
38. Tuning well temperament by using Robert Falkener's rules of 1774 or before 131
39. Jean-Jacques Rousseau's Dictionnaire De Musique translated into English in 1771 and 1779 134
40. Tuning Jean-Jacques Rousseau's well temperament of 1768 in the theoretically correct manner 139
41. Tuning Jean-Jacques Rousseau's well temperament of 1768 in the equal-beating manner 146
42. The philosophy of well temperament and key-coloring as described by Jean-Jacques Rousseau in 1768 151
43. Chart of key characteristics 155
44. Demonstrating the characters of the keys 157
45. George Frederick Handel's tuning rules 158
46. The authentic way to tune George Frederick Handel's well temperament in around 1780 162
47. Tuning George Frederick Handel's well temperament in the theoretically correct manner 168
48. The writings of William Jones on temperament in 1781 173
49. The authentic way to tune the Francesco Antonio Vallotti well temperament in 1781 176
50. Tuning Francesco Antonio Vallotti's well temperament of 1781 in the equal- beating manner 178
51. Francesco Antonio Vallotti's temperament tuned according to late eighteenth-century theory 179
52. Tuning Francesco Antonio Vallotti's well temperament of 1781 in the theoretically correct manner 182
53. William Jones's proposal that musicians ought to try equal temperament in 1781 187
54. Jean-Philippe Rameau's equal temperament proposal of 1737 reintroduced in 1781 189
55. The ordinary temperament commonly practiced in early eighteenth-century France introduced to the British in 1781 193
56. Tuning Jean-Le Rond D'Alembert's modified meantone temperament of 1752 in the theoretically correct manner 196
57. The ordinary temperament commonly practiced in late eighteenth-century English- speaking countries 203
58. Tuning the English equal-beating well temperament by using Jean-Le Rond D'Alembert's rules of 1752 207
59. The Preceptor For the Piano-Forte, Organ, or Harpsichord 214
60. Tuning Mr. Preston's well temperament of 1785 in the equal-beating manner 216
61. Tuning Mr. Preston's well temperament of 1785 in the theoretically correct manner 218
62. "This temperature of Mr. Huygens deserves to be introduced into the practice of music" in 1786 224
63. Tiberius Cavallo's equal temperament proposal in 1788 226
64. The British rejection of equal temperament proposals in 1790229
65. The modified equal-beating one-fifth syntonic comma meantone temperament of 1797 230
66. Tuning the modified equal-beating one-fifth syntonic comma meantone temperament of 1797 233
67. The modified one-fifth syntonic comma meantone temperament by William Hawkes in 1798 241
68. Tuning the William Hawkes modified meantone temperament of 1798 in the theoretically correct manner 243
69. Thomas Young's representative eighteenth-century well temperament of 1799 251
70. Tuning the transposed Vallotti well temperament of 1781 according to Thomas Young's rules of 1799 in the theoretically correct manner 256
71. Tuning Thomas Young's representative well temperament of 1799 in the theoretically correct manner 260
72. The representative eighteenth-century temperament tuned by personal taste 266
73. Instructions for tuning the representative eighteenth-century temperament according to one's own personal taste 269
74. John Robison's proposal that harpsichords and pianofortes should be tuned by beats in 1801 272
75. The Johann Philipp Kirnberger well temperament introduced to the British and Americans in 1801 277
76. Tuning the easiest temperament to tune that was ever published, the one-half syntonic comma temperament by Johann Philipp Kirnberger in 1771 281
77. The improved Kirnberger well temperament by Charles Earl Stanhope in 1806 284
78. Tuning the Kirnberger temperament as improved by Charles Earl Stanhope in the theoretically correct manner 287
79. Tuning the improved Kirnberger temperament according to Charles Earl Stanhope's equal-beating bearing plan of 1806 290
80. "That ill contrived mode of tuning called the equal temperament" 293
81. The temperament controversies of 1806 to 1812 295
82. The modified meantone temperament improved in 1807 by William Hawkes 298
83. Tuning the William Hawkes improved modified meantone temperament of 1807 in the theoretically correct manner 301
84. The distinction between equal-beating temperament and theoretically correct temperament clarified in 1807 310
85. Tuning equal temperament by using just intonation techniques in 1807 312
86. Instructions from 1807 for tuning equal temperament through just intonation 314
87. The Prinz, Kirnberger III, and Aron-Neidhardt well temperaments 319
88. Tuning the Prinz well temperament of 1808 in the theoretically correct manner 321
89. Tuning the equal-beating Prinz well temperament of 1808 325
90. The Pythagorean temperaments by Anton Bemetzrieder used as substitutes for equal temperament in 1808 328
91. Tuning the Henricus Grammateus Pythagorean temperament of 1518 (Anton Bemetzrieder Number One) in the theoretically correct manner 332
92. Tuning the Vallotti-Young temperament transposed down one semitone according to the rules of Anton Bemetzrieder's Temperament Number Two of 1808 in the theoretically correct manner 336
93. The four twenty-fifths syntonic comma meantone temperament by John Marsh in 1809 341
94. The authentic way to tune John Marsh's meantone temperament of 1809 344
95. Tuning the John Marsh regular meantone temperament of 1809 in the theoretically correct manner 346
96. The beat frequencies for equal temperament published by C. J. Smyth in 1810 352
97. Well temperament and meantone temperament called equal temperament in the nineteenth century 353
98. The first workable instructions for tuning equal temperament on organs in 1810 356
99. Tuning quasi-equal temperament by using the melodic method without beats in 1811 361
100. Tuning the Merrick quasi-equal temperament of 1811 364
101. The results of "nearly the equal" temperament tuned on a pianoforte analyzed in 1811 369
102. Building keyboard instruments with 25 or more pitches per octave as a solution for avoiding equal temperament 371
103. Tuning the William Hawkes regular one-sixth Mercator comma meantone temperament of 1808 (published in 1811) in the theoretically correct manner 374
104. The successes of Hawkes, Loeschman, and Liston implying that equal temperament "must be abolished" 380
105. The "Essay on Musical Temperament" by Alexander Metcalf Fisher in 1818 381
106. Tuning the Gioseffo Zarlino equal-beating meantone temperament of 1558 proposed for adoption in 1818 384
107. Tuning the Alexander Metcalf Fisher modified meantone temperament of 1818 in the theoretically correct manner 394
108. A "Plain Direction To Tune The Piano Forte" by Johann Christian Gottlieb Graupner 400
109. The authentic way to tune the Johann Christian Gottlieb Graupner temperament of 1819 403
110. The "Easy and Convenient" temperament by Johann Nepomuk Hummel in 1829 406
111. Tuning Hummel' s temperament according to the rules of Viennese tuners in 1829 409
112. Hummel's easier bearing plan for the "unpracticed ear" in 1829 411
113. Avoidance of the direct tuning of just intervals by organ tuners in 1830 413
114. The tuning of Pietro Aaron's meantone temperament on organs in 1830 and later 414
115. Strict mathematically correct equal temperament "cannot be obtained" in 1832 417
116. Tuning Jean Jousse's well temperament of 1832 in the authentic manner by using his bearing plan number one 420
117. The authentic way to attempt tuning equal temperament in 1832 by using Jean Jousse's bearing plan number two 423
118. The method of W. S. B. Woolhouse for tuning equal temperament by specific numbers of beats in 1835 425
119. Tuning equal temperament in 1835 according to the rules by W. S. B. Woolhouse 427
120. "A good tuner can accommodate the temperament to the taste of those who play in particular keys, which they wish to be more perfect than the rest" in 1840 430
121. Piano care in 1840 434
122. Tuning The Tuner's Guide well temperament number one of 1840 in the theoretically correct manner 435
123. Tuning The Tuner's Guide well temperament number two of 1840 in the theoretically correct manner 439
124. Tuning The Tuner's Guide well temperament number three of 1840 in the theoretically correct manner 442
125. Tuning quasi-equal temperament in 1840 by using John Marsh's bearing plan 445
126. Tuning quasi-equal temperament in 1840 by using the bearing plan of Becket and Company 447
127. Tuning quasi-equal temperament in 1840 according to the rules of the best factory tuners 452
128. Encyclopedists who advocated the practice of well temperament in 1842 through 1848 455
129. Tuning the Augustus De Morgan unequal temperament of 1843 in the theoretically correct manner 459
130. How one endeavoured to tune quasi-equal temperament in 1843 464
131. Rules for tuning quasi-equal temperament in 1843 465
132. "There never was a man capable of tuning by ear a pianoforte or an organ" in equal temperament before 1834 in Germany 467
133. Tuning equal temperament by using Johann Heinrich Scheibler's metronome method of 1836 introduced to the British before 1853 469
134. "Equal temperament was equal nonsense" in 1858 472
135. Tuning the Johann George Neidhardt Fifth Temperament Number Three of 1732 proposed for common practice in 1858 475
136. Tuning the Neidhardt-Marpurg-De Morgan unequal temperament of 1858 in the theoretically correct manner 479
137. Equal temperament had "never been attained" on pianos through the year 1864 484
138. Tuning quasi-equal temperament in 1869 according to the rules by William Geib 487
139. A special warning in 1869 492
140. "Strictly equal temperament is a thing unknown in practice" in 1875 493
141. Tuning quasi-equal temperament in 1875 according to the rules by Alexander John Ellis 495
142. How the methods of the factory tuners changed in the thirty-six years since 1840 499
143. Tuning quasi-equal temperament in 1876 according to the rules by A. Hemstock 500
144. "There are few tuners who can produce a tolerable equal temperament" in 1876 502
145. Tuning equal temperament in 1876 by the metronome method of Robert Halford Macdowall Bosanquet 504
146. Tuning unequal temperament in 1877 according to the rules by Edward John Hopkins 508
147. Tuning quasi-equal temperament in 1877 by using Edward John Hopkins's bearing plan 510
148. The methods of the best factory tuners of America in 1877 512
149. Tuning quasi-equal temperament in 1877 according to the rules by Louis 0. Peltier 513
150. Tuning quasi-equal temperament in 1879 according to the rules by Edgar Brinsmead 515
151. "The key is in music what colour is in painting." Do the characters of the keys still exist? 517
152. Tuning quasi-equal temperament in 1880 according to the rules by C. A. Edwards 519
153. Tuning quasi-equal temperament in 1880 according to the rules by H. T. Martin 520
154. The H. T. Martin bearing plan number one 521
155. The H. T. Martin bearing plan number two 523
156. The H. T. Martin bearing plan number three 525
157. The H. T. Martin bearing plan number four 527
158. Tuning quasi-equal temperament in 1880 according to the rules by Charles Babbington 529
159. "Fine Tuning" by Charles Babbington in 1880 530
160. The bearing plans of the English factory tuners in 1885 533
161. The analyses by Alexander John Ellis showing that equal temperament was still not possible on pianos in 1885 534
162. Interpreting the Alexander John Ellis analyses of 1885 536
163. Tuning the representative Victorian (Moore and Moore Company) temperament of 1885 540
164. Tuning Victorian temperament in the manner of a "usual" Broadwood tuner in 1885 547
165. Tuning Victorian temperament in the manner of a "best" Broadwood tuner in 1885 554
166. Quasi-equal temperament as tuned by a "best" Broadwood tuner in 1885 559
167. The new equal-beating method by Alexander John Ellis in 1885 561
168. Tuning pianofortes in 1885 by using Alexander J. Ellis's new equal-beating rules 565
169. "Tuning . . . is an art" in 1887 568
170. Tuning equal temperament in 1887 according to the rules by Edward Quincy Norton 570
171. The equal-beating rules by Mark Wicks in 1887 573
172. Tuning Organs in 1887 by using Mark Wicks's equal-beating rules 574
173. Tuning quasi-equal temperament in 1888 according to the new rules by W. S. B. Woolhouse 577
174. "There are . . . several shades or degrees of equal temperament" in 1889; or, the philosophy of Victorian temperament in practice 579
175. How key-coloring and the characters of the keys were used in the technique of temperament setting 580
176. Examples of how the characters of the keys are preserved in the music itself when played in equal temperament 582
177. "Beats . . . are due to the presence of upper partials" in 1892 583
178. Tuning equal temperament in 1892 according to the rules by Henry Fisher 585
179. "The most expert and rapid tuners are men . . . verging on the border of insanity" 588
180. Using the C tuning fork in tuning quasi-equal temperament according to Daniel Spillane's rules of 1893 590
181. Using the A tuning fork in tuning quasi-equal temperament according to Daniel Spillane's rules of 1893 592
182. "Some piano tuners now have a hankering after the old system," in 1893 594
183. Outlawing the equal-beating tempering techniques in 1893 595
184. Tuning equal temperament in 1893 by using the bearing plan of Becket and Company
185. Tuning equal temperament in 1893 by using the bearing plan of Louis 0. Peltier 602
186. Tuning equal temperament in 1893 by using Hermann Smith's circle of fourths and octaves 605
187. Thomas Elliston may or may not have tuned the exact theoretical equal temperament in 1894 610
188. Tuning quasi-equal temperament in 1894 according to the rules by Thomas Elliston 612
189. "Not one percent of the professors of piano can tune their own instruments" in 1895 615
190. Tuning pianos in 1895 by using Charles E. Moscow's equal-beating rules 616
191. The bearing plans by Frederick Ewart Robertson in 1897 617
192. "Try to find out what style of pieces the organist plays"
193. The 'Temperella' of 1903 622
194. Tuning quasi-equal temperament in 1905 according to the rules by Paul Nooncree Hasluck 623
195. Tuning equal temperament in 1905 according to the rules by George Ashdown Audsley 625
196. Tuning equal temperament in 1905 by using George Ashdown Audsley's circle of fourths and octaves
197. The correspondence courses by Niles Bryant in 1906 631
198. The modem bearing plan published by Howard Willet Pyle in 1906
199. The evolution of the modern bearing plan 634
200. The modem bearing plan as amended by William Braid White in 1906 636
201. The bearing plan published by The British College of Pianoforte Tuning in 1907
202. The bearing plans by Henry Spain in 1907 641
203. "Many good tuners" of 1907 tuned as well as the tuners of today 645
204. The first somewhat complete instructions for tuning equal temperament in 1907 by Jerry Cree Fischer 649
205. Jerry Cree Fischer's revival of the most ancient bearing plans in 1907 655
206. The Jerry Cree Fischer system of tuning written for amateur tuners
207. The bearing plan by James F. Cooke in 1908 661
208. William Braid White's explanation that beats exist at the nearly-coinciding harmonics
209. William Braid White's bearing plan of 1909 665
210. W. A. Butterfield's major third-major seventeenth 4:1 ratio double octave or fifteenth test published in 1910 668
211. A bearing plan for equal-beating temperament by W. A. Butterfield in 1910 669
212. The bearing plan by Walter and Thomas Lewis in 1911
213. The bearing plan by Leon 0. Underhill in 1911 675
214. The technique of using twelve contiguous major thirds for temperament setting and also the tests for proving that fifths are narrow and that fourths are wide published by Oliver Cromwell Faust in 1913 678
215. The bearing plan by Oliver Cromwell Faust in 1913 680
216. Two bearing plans by Charles E. Ewing in 1913 682
217. The technique of using three contiguous major thirds for temperament setting and also the tests for proving that fifths are narrow and that fourths are wide published in Charles E. Ewing's second bearing plan of 1913 685
218. William Braid White's bearing plan of 1915 689
219. The quality of piano tuning done during the years 1911 through 1917 692
220. How the 'Classic Bearing Plan' might have been utilized by the best tuners of 1917 697
221. Tuning equal temperament by ear in 1917 698
222. Why the 'Classic Bearing Plan' was preferred 712
223. Listing of historical developments 714

APPENDICES
224. An Experimental Bearing Plan
225. Tuning Equal Temperament 720
226. Tuning the Notes Below and Above the Bearing Section in Equal Temperament
227. Various Tests
228. Inharmonicity 739
229. The General Locations Where Various Sizes of Octaves are Tuned
230. Tests for Octaves 747
231. A Catalogue of Test Intervals through Eight Harmonics. 752
232. The Frequencies and Beat Frequencies of Equal Temperament 766
233. Metronome Speeds at A =440 Hz for Fifths and Fourths Between F and F in Equal Temperament . 768

GLOSSARY 769

BIBLIOGRAPHY 780

INDEX 796

To my surprise the name of Simon Stevin does not seem to be mentioned in the book. It was Stevin, a Dutch mathematician, who published the first proposal for the modern equal tempering as early as 1584!

[29.] Christiaan Huygens was a Dutch mathematician and inventor of devices like the pendulum clock. An organ tuned to his 31-tone system survives in a museum in Haarlem, near Amsterdam, and it is still played regularly!

[35.] Please note that the syntonic, or Didymic, comma, of 22 cents, is different from the Pythagoraeic comma of 24 cents.

Many mechancial music instruments, some of them chromatic, are still tuned in a semi-equally tempered way. Organs, especially, with their high-sounding mixture ranks, sound a lot better when the most used thirds are improved!