Puncta consists of some fifty pages of explanations, rules, examples, raw musical materials, sample workings and graded tasks. Many of the sample workings have been written by the author’s students; when Puncta is updated, more student workings will be included. The tasks are strictly incremental: they range from the simplest of two-voice exercises to planning and composing a three-voice stretto fugue. They are to be worked out with pencil and manuscript paper. On completing each task, you must show your working to your teacher before venturing further. (A suggested scheme for college implementation of Puncta is given in Appendix A.) Puncta means ‘dots’ or ‘notes’, and is derived from the medieval Latin phrase punctus contra punctum, which means ‘dot against dot’ or ‘note against note’. Counterpoint and Fugue For centuries, counterpoint has proved the most effective way to teach and learn the syntax of western classical music. Its principal objective is the management of consonance and dissonance in relation to a regular musical pulse. The rules of counterpoint are too complex to assimilate all at once. Since they are governed chiefly by rhythm, however, they become far easier to grasp when they are presented in regulated rhythmic contexts. Five contexts, known as ‘species’, have been in general use since the eighteenth century: the first, second and third respectively concern the rules for semibreves, minims and crotchets; the fourth concerns the rules for syncopation; the fifth combines syncopation with minims, crotchets and quavers. No two counterpoint textbooks have ever laid down all the rules in exactly the same way, especially when it comes to the varieties of dissonance admitted in the third species. Most of the rules given in Puncta are derived from Johann Joseph Fux’s Gradus ad Parnassum of 1725, the celebrated textbook that—directly or indirectly—served Haydn, Mozart, Beethoven, Brahms and other great composers. In particular, Puncta sticks closely to Fux’s third-species rules because they admit only two varieties of dissonance. Once you are fluent in Fuxian third species, you can start to explore the further varieties of dissonance that are admitted by other authorities (rules for advanced third species are given in Appendix B, and suggestions for further reading in Appendix C). Fugue, the longest-lived method of thematic composition, is to music what the essay is to literature. Both the fugue and the essay are classic forms of student exercise that have also been cultivated as high art. Each is concerned with the structured treatment of a prescribed subject. Puncta introduces fugue as an almost seamless continuation of counterpoint, preserving the same note values and methods of dissonance management within similar template formats. These templates gradually increase in complexity, taking you to a point where you no longer need them, and can work out an entire fugue from scratch. Using Puncta To allow text and music examples to be readable without zooming, Puncta is functional in landscape orientation only. Pinch-zooming is nonetheless enabled on all text/music pages, with a double-tap returning the page to screen-width size. Most text/music pages require scrolling, and will remain in their last-viewed position for as long as Puncta is running. This means, for example, that if you need to navigate to a set of fugue subjects when half way down a fugue page, when you return to the fugue page it will still be exactly where it was when you left it. To return to the top of a page you are viewing, simply tap the status bar at the top of the screen. Quitting Puncta returns every page to its top. Comments and corrections may be sent to: puncta@me.com Click here to purchase Puncta from the App Store. Click here to download a printable worksheet for the Set One cantus firmi.

Puncta consists of some fifty pages of explanations, rules, examples, raw musical materials, sample workings and graded tasks. Many of the sample workings have been written by the author’s students; when Puncta is updated, more student workings will be included.

The tasks are strictly incremental: they range from the simplest of two-voice exercises to planning and composing a three-voice stretto fugue. They are to be worked out with pencil and manuscript paper. On completing each task, you must show your working to your teacher before venturing further.

(A suggested scheme for college implementation of Puncta is given in Appendix A.)

Puncta means ‘dots’ or ‘notes’, and is derived from the medieval Latin phrase punctus contra punctum, which means ‘dot against dot’ or ‘note against note’.

Counterpoint and Fugue

For centuries, counterpoint has proved the most effective way to teach and learn the syntax of western classical music. Its principal objective is the management of consonance and dissonance in relation to a regular musical pulse.

The rules of counterpoint are too complex to assimilate all at once. Since they are governed chiefly by rhythm, however, they become far easier to grasp when they are presented in regulated rhythmic contexts. Five contexts, known as ‘species’, have been in general use since the eighteenth century: the first, second and third respectively concern the rules for semibreves, minims and crotchets; the fourth concerns the rules for syncopation; the fifth combines syncopation with minims, crotchets and quavers.

No two counterpoint textbooks have ever laid down all the rules in exactly the same way, especially when it comes to the varieties of dissonance admitted in the third species. Most of the rules given in Puncta are derived from Johann Joseph Fux’s Gradus ad Parnassum of 1725, the celebrated textbook that—directly or indirectly—served Haydn, Mozart, Beethoven, Brahms and other great composers.

In particular, Puncta sticks closely to Fux’s third-species rules because they admit only two varieties of dissonance. Once you are fluent in Fuxian third species, you can start to explore the further varieties of dissonance that are admitted by other authorities (rules for advanced third species are given in Appendix B, and suggestions for further reading in Appendix C).

Fugue, the longest-lived method of thematic composition, is to music what the essay is to literature. Both the fugue and the essay are classic forms of student exercise that have also been cultivated as high art. Each is concerned with the structured treatment of a prescribed subject.

Puncta introduces fugue as an almost seamless continuation of counterpoint, preserving the same note values and methods of dissonance management within similar template formats. These templates gradually increase in complexity, taking you to a point where you no longer need them, and can work out an entire fugue from scratch.

Using Puncta

To allow text and music examples to be readable without zooming, Puncta is functional in landscape orientation only. Pinch-zooming is nonetheless enabled on all text/music pages, with a double-tap returning the page to screen-width size.

Most text/music pages require scrolling, and will remain in their last-viewed position for as long as Puncta is running. This means, for example, that if you need to navigate to a set of fugue subjects when half way down a fugue page, when you return to the fugue page it will still be exactly where it was when you left it. To return to the top of a page you are viewing, simply tap the status bar at the top of the screen. Quitting Puncta returns every page to its top.

Comments and corrections may be sent to: puncta@me.com

Click here to purchase Puncta from the App Store.

Click here to download a printable worksheet for the Set One cantus firmi.

Puncta is the first textbook app for students of the time-honoured musical techniques of counterpoint and fugue. To get started with Puncta, you need little more than a basic working knowledge of notation, intervals and transposition. You will not need to know anything about harmony.

Counterpoint and Fugue Textbook App by Andrew Johnstone

available for iPhone and iPod Touch from the iTunes App Store

(version 0.4 – requires iOS 4.2 or later)