Leaving Some Notes Out
Many chord types can be voiced by leaving out some notes, which can reduce muddiness or heaviness, especially since (for example) fifths and thirds tend to be harmonics of the root anyway, so these sonorities may be present to some degree in the final audible chord.
Chord types such as major and dominant seventh chords, or chords with added tensions (ninths, elevenths, and thirteenths) tend to be voiced by leaving out certain notes, especially the major third and perfect fifth. These chords are listed under See Also headings on chord pages or interactive search results and are denoted with names such as “X no 3” or “Y no 5,” etc.
But leaving out a note does something more amazing than just making a chord simpler to hear or to play: it explains how to voice a chord of, say, cardinality five, using a set class of just four notes, or to voice a chord with four (theoretical) notes with only three notes. This can often completely change (and hopefully lower) the evenness of the chord, though it will certainly simplify it acoustically.
Rootless & Slash Chords
Surprisingly, one of the easiest notes to leave out is the root. Chords can then be voiced with their upper notes, often making the voicing easier to play, especially with one hand on piano, or with fewer fingers on guitar, allowing another instrument to play the bass (piano left hand, bass player, horn section, etc.)
Slash chords describe how to re-formulate a given complicated chord (usually more than three notes) in terms of a simpler chord with fewer notes, breaking the chord into “Chord (Over) Root” notation.
For example C/A, “C Slash A” or “C major triad Over A” would be A min 7, a C major triad chord played over an A root. This approach can help reduce some memorization and help voice chords with a single hand, letting the bass player take over the root (see rootless chords), etc. Slash chords are denoted throughout Harmonious when it is possible to generate a name of that form for a given chord inversion.
A min 7 (C/A) and C Maj. Alternately, Rootless A min 7 on the right.
The following tables collect up (1) all slash chords over a C root, and (2) all slash chords with a C-root chord in the upper part. Similar tables are available for every pitch class and can be found on pages such as All C Chords and All D Chords.
Slash Chords, Over C
Slash Chords, Upper C Chords
The last section will show the approach Harmonious takes to connect musical set theory and jazz theory, explaining where we get the meat and potatoes of the app: an exhaustive but carefully curated source of every possible chord.