1 Malcolm, Alexander, A Treatise of Musick, Speculative, Practical and Historical (Edinburgh: author, 1721)Google Scholar.

2 Alexander Malcolm, A New Treatise of Arithmetic and Book-Keeping (Edinburgh: Mosman and Brown for John Paton, 1718); A New System of Arithmetick, Theoretical and Practical (London: J. Osborn and T. Longman, 1730); A Treatise of Book-Keeping or Merchants Accounts (London: J. Osborn and T. Longman, 1731); and New Rudiments of the Latin Tongue (London: author, 1756). Thomas Jefferson owned a copy of Malcolm's New System of Arithmetic.

3 de Morgan, Augustus, Arithmetical Books from the Invention of Printing to the Present Time (London: Taylor and Walton, 1847), 66Google Scholar. Morgan calls Malcolm's New System of Arithmetick ‘one of the most extensive and erudite books of the last century’. More recently, Michael J. Mepham has written, ‘Although Malcolm had emigrated well before the peak of the Enlightenment, his books on mathematics, music and accounting were scholarly, analytical works which deserve recognition as part of the achievements of that movement’. Mepham, , ‘The Scottish Enlightenment and the Development of Accounting’, The Accounting Historians Journal 15/2 (1988), 155CrossRefGoogle Scholar. In a further testament to his mathematical abilities, in 1760, after having settled in Annapolis, Maryland, Malcolm was appointed by Lord Baltimore as one of the commissioners charged with determining the boundary between Maryland and Pennsylvania (the Mason–Dixon line). Malcolm ‘was said to have been one of the most learned mathematicians in the colonies’. Lloyd, Malcolm Jr, ‘Alexander Malcolm, Writer on Mathematics and Music’, Scottish Notes and Queries, third series, 6 (1928), 235–236Google Scholar.

4 Rameau, Jean-Philippe, Traité de l'harmonie (Paris: Ballard, 1722)Google Scholar.

5 See Heintze, J. R., ‘Alexander Malcolm: Musician, Clergyman, and Schoolmaster’, Maryland Historical Magazine 73 (1978), 227Google Scholar: ‘in the colonies, his treatise was read and praised in both New England and the middle colonies, particularly, Maryland and Virginia’.

6 Hawkins, John, General History of the Science and Practice of Music, five volumes, volume 5 (London: T. Payne, 1776), 222Google Scholar.

7 Malcolm broaches the subject of equal temperament in chapter 10, but determines it would be impossible to implement, because the numbers involved would be irrational. Nevertheless, he says all practical musicians tune by ear, and that some claim to diminish all fifths by a quarter of a comma, but he doubts anyone is able to do this exactly (Treatise of Musick, 306, 312).

8 Malcolm, Treatise of Musick, 210–214 (chapter 7). Malcolm explains that while a fourth may be a concord in some circumstances, when sounded against the fundamental (by which he sometimes means the tonic, as we understand it, or the bass note), it is a discord, and therefore is not to be admitted as a harmony.

9 For a fuller discussion of Malcolm's treatise see Louis Chenette, ‘Music Theory in the British Isles during the Enlightenment’ (PhD dissertation, The Ohio State University, 1967), and Herissone, Rebecca, Music Theory in Seventeenth-Century England (New York: Oxford University Press, 2000)Google Scholar.

10 Lester, Joel, Compositional Theory in the Eighteenth Century (Cambridge, MA: Harvard University Press, 1992), 76–77Google Scholar.

11 Christensen, Thomas, ‘The Règle de l'Octave in Thorough-Bass Theory and Practice’, Acta musicologica 64/2 (1991), 106–107Google Scholar.

12 Malcolm, Treatise of Musick, xxii.

13 According to Henry George Farmer (1882–1965), a musicologist and Arabist who had studied at the University of Glasgow, this was ‘the first independent work of its kind published in Scotland’: ‘Music in 18th Century Scotland’, Scottish Art and Letters 2 (1946), 11.

14 Herissone also discusses these similarities in Music Theory in Seventeenth-Century England, 21–22, 98 and passim.

15 Colvill's name is found with various spellings, including Colvil and Colville.

16 Thomas William Taphouse (1838–1905) was an English music and instrument dealer and collector. His collection became one of the finest in England. Albi Rosenthal, ‘Taphouse, Thomas William’, in Grove Music Online www.oxfordmusiconline.com (24 October 2017).

17 James Maidment (1793–1879) was born in London, studied arts and law at Edinburgh University and was called to the Scottish bar in 1817. He published many volumes and built up a library of over five thousand titles. J. C. Hadden, ‘Maidment, James’, in the Oxford Dictionary of National Biography www.oxforddnb.com (23 September 2004).

18 Maidment would have acquired these treatises some time before 1853; for more on this see footnote 39. A copy of Maidment's 1880 sale catalogue may be found in the British Library, General Reference Collection, shelfmark S. C. 1074, or online at https://catalog.hathitrust.org/Record/009982638. Curiously, the listing (4025) states that the manuscript (Institutions) is supposed to be by Colvill.

19 Jules Écorcheville (1872–1915) was a French musicologist and collector who studied with César Franck. John Trevitt and Jean Gribenski, ‘Ecorcheville, Jules’, in Grove Music Online www.oxfordmusiconline.com (24 October 2017).

20 Information regarding this auction purchase was communicated to me by a librarian at the Library of Congress.

21 David Laing (1793–1878) was the son of a publisher and bookseller who specialized in second-hand, antiquarian and foreign literature. In 1824 Laing was elected to a fellowship of the Society of Antiquaries of Scotland. At the time of his death, his library consisted of approximately twenty thousand printed books and a massive manuscript collection. Most of what he collected was important literary and historical material, mainly of Scottish interest. Murray C. T. Simpson, ‘Laing, David (1793–1878), antiquary and librarian’, in Oxford Dictionary of National Biography www.oxforddnb.com (15 April 2018).

22 Murray, David, ‘David Laing, Antiquary and Bibliographer’, The Scottish Historical Review 11/44 (1914), 345Google Scholar.

23 Sir Archibald Grant was President of the Aberdeen Musical Society in 1771–1772. This copy was subsequently owned by Henry George Farmer. See Farmer, A History of Music in Scotland (New York: Da Capo, 1970; reprint of 1947 first edition published in London), 321. On the basis of personal correspondence with a librarian from the University of Glasgow, it appears the treatise was donated by Farmer.

24 Cowan, William, ‘The Buildings at the East End of Princes Street and the Corner of the North Bridge: A Chapter in the Early History of the New Town of Edinburgh’, The Book of the Old Edinburgh Club, volume 1 (Edinburgh: T. and A. Constable, 1908), 137–154Google Scholar.

25 This acquisition information comes from personal correspondence with a librarian at the Berlin State library. J. Grant was probably Sir James Grant, Fifth Baronet of Monymoske (1791–1859), great-grandson of Sir Archibald Grant, Second Baronet of Monymoske.

26 Anonymous, Treatise of the Thoro'bass, Yale University Beinecke Rare Book and Manuscript Library, James Marshall and Marie-Louise Osborn Collection, call number Osborn Music MS 3 (acquired 1925).

27 Cummings was an assiduous collector of old music and is today remembered primarily for his extensive collection, so it is puzzling that the treatise is not listed in the sale catalogue of his library (Library of Congress call number ML 138.C9). Also puzzling, Dr Cummings's name and the date of 1917 are pencilled in above Cummings's bookplate, while, in the same hand, the name of Dr Pepusch is lightly pencilled in at the bottom of the page. No further information on these markings is available at this point, but see below for more on Pepusch. For more on Cummings see Hugh J. McLean, ‘Cummings, W(illiam) H(ayman)’, in Grove Music Online www.oxfordmusiconline.com (24 October 2017).

28 The Advocates Library is the Law Library. This copy of Institutions is catalogued under the title Treatise on Music (shelfmark Adv.MS.80.6.9), though that title does not appear anywhere in the treatise.

29 This untitled treatise is primarily about string division, string vibration, intervals, consonance and dissonance, and so on. The handwriting is consistent with the handwriting of the copy of Institutions bound with it. It is not inconceivable that the author of this treatise and Institutions are the same person, and this treatise may indeed be a preface to Institutions. Much study remains to be done.

30 Pretoria State Library, shelfmark FB6652.

31 David Laing, Introduction to William Stenhouse, The Scots Musical Museum, Consisting of Upwards of Six Hundred Songs, with Proper Basses for the Pianoforte, originally published by James Johnson, and now Accompanied with Copious Notes and Illustrations of the Lyric Poetry of Scotland, by the Late William Stenhouse, with Additional Notes and Illustrations, four volumes (Edinburgh: William Blackwood, 1853), volume 1, xlvii. The original publication by James Johnson consisted of six volumes printed between 1787 and 1803; see https://digital.nls.uk/87793664. See David Johnson, ‘Stenhouse, William’, in Grove Music Online www.oxfordmusiconline.com (16 April 2018) and ‘The Scots Musical Museum, a collection of songs’, British Library Website, https://www.bl.uk/collection-items/the-scots-musical-museum-a-collection-of-songs (1797) (16 April 2018).

32 Anonymous, Airs for the Flute, with a Thorough Bass for the Harpsichord (Edinburgh: Alexander Baillie, 1735), National Library of Scotland, shelfmark Glen.135.

33 Barsanti, Francis, Collection of old Scots Tunes with the bass for the Violoncello or Harpsichord (Edinburgh: Alexander Baillie, 1742)Google Scholar. Though the score itself bears no date, David Laing, in the Introduction to The Scots Musical Museum (liii), states the collection was published on 14 January 1742, and cites the Caledonian Mercury and Scots Magazine (1742).

34 See, for example, Ottley, William Young, Notices of Engravers and Their Works (London: Longman, Rees, Orme, Brown, and Green, 1831)Google Scholar; Brown, Stephen W., and McDougall, Warren, The Edinburgh History of the Book in Scotland, volume 2: Enlightenment and Expansion 1707–1800 (Edinburgh: Edinburgh University Press, 2011), 94, 101–102Google Scholar; and Brown and McDougall, ‘Baillie, Alexander’, in Benezit Dictionary of Artists www.oxfordartonline.com/benezit (31 October 2011).

35 Farmer, History of Music in Scotland, 330. RISM (Répertoire international des sources musicales), A/I/I, 198. Farmer also speculates that these may have been composed by Lord Colvill, the dedicatee of the Thoro'Bass treatise.

36 Frank Kidson suggests the dedication to Lady Gairlies is Baillie's handwriting, stating that it was signed by Baillie. Kidson, , British Music Publishers, Printers and Engravers (London: W. E. Hill, 1900), 178Google Scholar. See also Humphries, Charles and Smith, William C., Music Publishing in the British Isles (London: Cassell, 1954), 59Google Scholar.

37 For more on the Edinburgh Musical Society see Helen Goodwill, ‘The Musical Involvement of the Landed Classes in Eastern Scotland, 1685–1760’ (PhD dissertation, University of Edinburgh, 2000), and Jennifer Macleod, ‘The Edinburgh Musical Society: Its Membership and Repertoire 1728–1797’ (PhD dissertation, University of Edinburgh, 2001).

38 In other words, Maidment owns the dedication copy by 1853 but Laing has not yet acquired his own copy, since his listing suggests Maidment's copy is unique.

39 Laing, Appendix, The Scots Musical Museum, xcii. Whether there had been any earlier attribution to Baillie is unknown – Laing is writing 136 years after the publication of the treatise. Why does he mention Baillie at all? He may simply be referring to his own earlier entry on Baillie's engraving of the Airs for Flute, in his Introduction, xlvii.

40 Maidment appears to be quoting from William Tytler's article ‘On the Fashionable Amusements and Entertainments in Edinburgh in the last Century, with a Plan of a grand Concert of Music on St. Cecilia's Day, 1695’, Archaeologia Scotica: Transactions of the Society of Antiquaries of Scotland volume 1 (1792), 508 https://doi.org/10.5284/1000184. Tytler writes, ‘Lord Colvill, it is said, was a thorough master of music, and understood counterpoint well. He played on the harpsichord and organ.’

41 Peter Holman offers convincing evidence that the concert actually took place in 1703 or 1704. Holman, , Life After Death: The Viola da Gamba in Britain from Purcell to Dolmetsch (Woodbridge: Boydell, 2010), 89–90Google Scholar, and ‘An Early Edinburgh Concert’, Early Music Performer 13 (2004), 9–17Google Scholar. See also Goy, François-Pierre, ‘The “British” Sainte-Colombes’, The Viola da Gamba Society Journal 11 (2017), 1–45Google Scholar.

42 Maidment is referring to Laing's comments in The Scots Musical Museum.

43 Halkett, Samuel and Laing, John, A Dictionary of the Anonymous and Pseudonymous Literature of Great Britain, four volumes, volume 2 (Edinburgh: William Paterson, 1883), 1245Google Scholar.

44 Farmer, History of Music in Scotland, 321–322, and Kidson, , ‘Baillie, Alexander’, in Grove's Dictionary of Music and Musicians, fifth edition, ed. Blom, Eric, nine volumes (London: Macmillan, 1954)Google Scholar, volume 1, 355.

45 The following biographical information is drawn from John W. Cairns, ‘Bayne, Alexander, of Rires (c. 1684–1737), advocate and jurist’, in Oxford Dictionary of National Biography www.oxforddnb.com (4 January 2007); Goodwill, ‘Musical Involvement’, 216–218; and Charles Knight, The English Cyclopædia: A New Dictionary of Universal Knowledge, seven volumes, volume 1 (London: Bradbury and Evans, 1856), 587–588.

46 Goodwill, ‘Musical Involvement’, 216.

47 Bayne, Alexander, Institutions of the Criminal Law of Scotland (Edinburgh: Thomas and Walter Ruddiman, 1730)Google Scholar; Sir Mackenzie, George, Institutions of the Law of Scotland (Edinburgh: J. Reid for T. Broun, 1688)Google Scholar.

48 Two of Bayne's cantatas, ‘Quando voglio’ and ‘Qual Tortorella’, dated 1722, are in the George Baillie Collection of Music Manuscripts, Coll-1061/3 (Box: CLX-A-653), Edinburgh University Library Special Collections. They are dedicated to Mrs Murray, who is Griselda, Lady Murray of Stanhope, daughter of George Baillie. See Lindgren, Lowell, ‘Cantatas and Arias in the Collection of Griselda Baillie (1692–1759)’, The Handel Institute Newsletter 23/1 (2012)Google Scholarhttps://handelinstitute.org/newsletter. For Colvill's sale catalogue, including works by Bayne, see Goodwill, ‘Musical Involvement’, 153–154, 217.

49 Emerson, Roger L. and Macleod, Jenny, ‘The Musick Club and The Edinburgh Musical Society’, Book of the Old Edinburgh Club New Series, volume 10 (2014), 46Google Scholar. According to Emerson and MacLeod, this society existed by 1695.

50 ‘A catalogue of curious and valuable books, being chiefly the library of the late Mr. Alexander Bane Professor of Scots law in the University of Edinburgh’, National Library of Scotland Reading Room, shelfmark Ferg.71.

51 It is possible they were never sold. There is or was a privately held collection of Bayne's papers, but I have not had access to them, nor have I been able to determine who holds them.

52 Tytler, ‘On the Fashionable Amusements’, 508.

53 Goodwill, ‘Musical Involvement’, 153–154, 217.

54 Goodwill, ‘Musical Involvement’, 217. Chenette, ‘Music Theory in the British Isles’, 288, speculates that the author of Malcolm's chapter 13 may have been Pepusch himself, or at least someone familiar with the work of Pepusch, since there are similarities in terminology and concepts. I am not aware of any relationship between Malcolm and Pepusch.

55 From personal correspondence with Jane Blackie, a harpsichordist who edits eighteenth-century dance music for the Edinburgh Early Dancers, and author of ‘A New Music Room: A Short History of St. Cecilia's Hall’, 2002 (University of Edinburgh pamphlet).

56 Institutions of the Criminal Law (1730) and Notes for the use of the Students of the Municipal Law (Edinburgh: Thomas and Walter Ruddiman, 1731).

57 See Brown and McDougall, Enlightenment and Expansion 1707–1800, 9.

58 Malcolm, New Rudiments of the Latin Tongue, vi–vii.

59 Falconer Madan, A Summary Catalogue of Western Manuscripts in the Bodleian Library, seven volumes in eight, volume 5 (Oxford: Clarendon, 1905), 574, No. 29165. This treatise is bound with thirty-two mostly instrumental scores by Valentini, Purcell, Corelli, Loeillet, Handel, Bononcini and Campra, and a number of anonymous pieces. For more information see the RISM listing at https://opac.rism.info/search?id=800227803&View=rism.

60 David Murray, born the same year as Colvill, would have been approximately twenty years older than Bayne. His granddaughter, Margaret Lindsay, married the widowed painter Allan Ramsay, whose first wife was Bayne's daughter.

61 This is presumably George Dundas, Twenty-Third Laird of Dundas, born c1690, a contemporary of Bayne's.

62 Shelfmark Adv. MS 80.6.9. Since Institutions was attributed to Bayne, who in 1722 was appointed curator of the Advocates Library, it is perhaps not too surprising that this copy was eventually acquired by the law library.

63 As late as 1900, Kidson still suggests there is just one copy of the Thoro'Bass treatise, in Taphouse's possession, even though Laing's copy was acquired by the Bodleian in 1879. Kidson also writes that while Laing suggested the Thoro'Bass treatise was by Baillie, that was quite unlikely. Kidson, British Music Publishers, 178. However, when Kidson writes the ‘Baillie’ entry for the New Grove fifth edition (1954, 355), he claims that Bayne is the author of the treatise.

64 For more on Pepusch see Donald Frederick Cook, ‘The Life and Works of Johann Christoph Pepusch (1667–1752), with Special Reference to His Dramatic Works and Cantatas’ (PhD dissertation, King's College London, 1982).