You must specify an octave relative to the current notes. You can do this using a comma (,) (to go lower) and an apostrophe (') (to go higher). So, in the first example regarding a chord, before you need to drop D down an octave (and then bring Bb back). Similarly, in another chord, lower F and return D. See the following code to achieve the desired ...

\version "2.14.2" \book { \header { title = \markup \center-column {"Dyad, Triad Permutations"} arranger = \markup \center-column { "Sean O'Donnell" } } \score { \relative { <bes d>1 <d, bes'> } } \score { \relative { <bes d f>1 <bes f d> <d bes f> <df bes> <f bes d> <f, d' bes> } } }
To fully understand how positioning notes works in relative mode, see the Pitches section of the manual here:
http://lilypond.org/doc/v2.12/Documentation/user/lilypond-learning/Simple-notation#Simple-notation
which reads:
The easiest way to enter notes is to use \ relative mode. In this mode, the octave is automatically selected, assuming the next note should always be closest to the previous note, that is, to place the previous note in the octave, which is located in three office spaces.
[...]
By adding (or removing) quotation marks or commas from \ relative c '{commands, we can change the initial octave
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Relative mode may be confusing initially, but this is the easiest way to enter most tunes.
The manual page also shows examples of work code in relative mode.
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