Rule of the octave

The rule of the octave is a way of harmonizing each note of the diatonic scale, reflecting common practice, and has its origin in the practice of thorough bass, or basso continuo. The rule of the octave also formed the cornerstone of the "regole" (rules) of partimento collections. The rule of the octave was first mentioned in the 17th century in treatises for thorough bass written for lute-like instruments. There is normally a different harmonization for ascending and descending bass lines, and, although called a rule, there are several variants with different chords. Different versions for the major and minor scales are recorded. One example for the major scale by John Hiles:
<score %vorbis="1"%%T257066% lang="lilypond">
\new PianoStaff «
 \new Staff {
 \new Voice = "right" {
 \relative c' { \clef treble \time 4/4 <e g c>4 <f g b> <e g c> <d a' c> | <d g b> <c f c'> <f g d'> <e g c> \bar "||" | <g c e> <d g d'> <d fis c'> <d g b> | <d g b> <c g' c> <f g b> <e g c> \bar "|." |
 \new Staff {
 \new Voice = "left" {
 \relative c { \clef "bass" c4 d e f | g a b c | c b a g | f e d c |
 \new FiguredBass {
 \figuremode { <_>4 <4 3> <6> <6 5> | <_> <6> <6 5> <_> | <_> <6> <6+ 4 3> <_> | <2> <6> <4 3> <_> |
 \new Lyrics {
 \lyricsto "left" { I V I II | V IV V I | I V V/V V | V I V I |
</score>