Dinner party rules

First compiled by "Quartertone Harmony", a YouTuber who had been exploring and experimenting with 24edo for some time, the Dinner Party Rules are a set of rules which aim to simplify expansion of 12edo harmony into 24edo. The three rules are as follows:

• Every chord must be comprised of a chain of friends in which each note is a friend to every other note
• No note can have an enemy
• No crowding (except for ension chords)

Once these are taken into consideration, finding usable chords and chord progressions in systems like 24edo is considerably easier.

Terms

Each rule contains terms that require explanation, especially for purposes of generalizing these rules to other EDOs.

A friend here is defined as a note separated from the starting note by either a close approximation of an LCJI interval, or else, a close approximation of a delta-rational interval, without being too close to one another in acoustic proximity. Friends are most frequently prefect consonances such as 3/2 or 4/3, imperfect consonances such as 5/4 or 8/5, or ambisonances such as 7/4 or 8/7. However, sometimes imperfect dissonances also meet the definition of a friend, for example, a neutral third like 11/9.

An enemy is defined here as a note separated from the starting note by an interval that causes intense discordance, or else, does not easily connect the two notes through LCJI or through delta-rational relationships. Perfect dissonances are always enemies in some capacity or other, while imperfect dissonances are less likely to meet this criterion. Just about the only way to get away with enemies in a chord is to space them really far apart.

Friends and enemies are basically the two ends of a spectrum of compatibility. In higher EDO systems, this spectrum comes noticeably into play, and a numerical compatibility rating along this spectrum is generally going to be helpful. Furthermore, some notes can be called frenemies since they meet the definition of either an enemy or a friend only part of the time, or else, meet the definitions of both at the same time. In addition, one frequently has to worry about "ratio ambiguity"- that is, notes which can have more than one relationship to each other.

The phenomenon of crowding is a major source of dissonance. Specifically, it results when an interval separating two notes is either too small or too close to an octave-reduplication of the starting note. Perhaps the most common examples of intervals that cause this are 9/8 and 15/8, though intervals such as 17/15 are also known to cause crowding. (However, in some harmonic systems crowding can be seen as characteristic of intervals smaller than ~10/9, with 9/8 notably *not* crowding.)

Application Examples

Application of these rules to smaller EDO systems is more likely to be straightforward, however, even larger systems can have these rules applied.

24edo

24edo was the first EDO system to which these rules were applied. Examples of friends in this system are a major third, a minor third, a neutral third, an inframinor third, an ultramajor second, and, of course, the perfect fourth and perfect fifth. Examples of enemies are an ultraprime, an inframinor second, an infraoctave, and an ultramajor seventh, and, in the majority of cases, an ultramajor third/paraminor fourth and an inframinor sixth/paramajor fifth also make this list. Crowding in this system is caused by intervals smaller than or equal to a major second relative to the unison or octave.

159edo

For a complete list of Interval Amity and-or Compositional Theory, see Aura's 159edo Guides