GLOSSARY in progress

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-ad
Suffix used by Wilson to designate primary modules or factors. see page 5 of https://anaphoria.com/Fokker1typeset.pdf with following explanation. [KG]

-any
Suffix used by Wilson to designate name of Combinational sets. see page of  https://anaphoria.com/Fokker1typeset.pdf comment under A. points out that each combinational set contains the sets above it on Pascal's triangle. the first few -ad and -any overlap but then diverge except those at the beginning and end of the row. These have the forms 0/X or X/X. The 1/X set appears to coincide but are separate members of the set. [KG]

Combination-Product Set (CPS)
A musical structure “generated by taking the products of n harmonic factors [or elements] m at a time and reducing the derived tones to a common octave” (Chalmers 1993, p. 205). Wilson labels these structures as m)n (“m-out-of-n”) sets. For instance, starting with a set of four harmonic factors (i.e. n = 4) such as harmonics 1, 3, 5 and 7, and multiplying two of these factors at a time (i.e. m = 2), produces the following set: 1 3, 1 5, 1 7, 3 5, 3 7, 5 7. This set of six tones is called a 2)4 set which is also known as a Hexany. Other examples of CPS include the 2)5 or 3)5 Dekany (which has ten tones), 3)6 Eikosany (twenty tones) and 4)8 Hebdomekontany (seventy tones). CPS do not imply a single tonal centre; rather, “any tone [in a CPS] is equally capable of becoming a tonic” (Grady 1986, p. 1). Wilson considers the non-centred CPS as a complement to the centred Diamond. He represents the multidimensional geometric structures of CPS as multidirectional lattice diagrams (Wilson 1989). Whilst CPS cover similar harmonic territory to Euler-Fokker genera, what is significant about Wilson’s approach is that he treats the factor 1 as a meaningful member of the generating set. This difference allows CPS to be articulated as coherent centreless structures. [TN]

Constant Structure
A scale in which “each interval occurs always subtended by the same number of steps” (Wilson cited in Grady 1999). By definition, the category of Constant Structures includes MOS scales because every interval in an MOS spans a constant number of scale degrees, but the term “Constant Structure” is usually reserved for scales in just intonation that are built not from a single generator but one that fluctuates in size. Wilson viewed Constant Structures as scales that emulate MOS because even if the intervals in a Constant Structure do not conform to a rigid cyclic pattern in the same way as an MOS, they will still be drawn towards this tendency. On the other hand, Constant Structures broaden the harmonic possibilities of MOS by including pitches from more than one limit. Wilson maps these scales onto a generalized keyboard by using his layout system for MOS scales as a guide. [TN]

Co-Prime Grid
A matrix showing pairs of numbers that are “co-prime”, or share no common factors other than 1. The Co-Prime Grid forms the basis of Wilson’s Gral Keyboard Guide (1994; 2000). [TN]

Cross-Set
A multiplication table in which the products of any two members of a set are arranged on a two-dimensional grid. See also Diamond and Lambdoma.[TN]

Diamond
A term coined by Harry Partch to describe a type of Lambdoma in which a set of harmonic ratios (usually treated as a chord) is multiplied by their reciprocal. These elements are arranged in the shape of a rhombus, hence the name “Diamond”. Diagonals sloping in one direction of the Diamond represent harmonic chords (which Partch called “Otonalities”) and diagonals sloping in the other direction represent subharmonic chords (“Utonalities”). Each parallel diagonal is a transposition of the same chord starting on a different note of its reciprocal chord, thus forming a “chordal complex consisting of interlocking harmonic and subharmonic chords” (Chalmers 1993, p. 211). Wilson rearranges the chords (i.e. each diagonal) of a Partch Diamond around a single tonic to show that all transpositions and their inversions share a common tone, and that this tone is found in different positions within each chord. Wilson uses various geometric shapes to represent each interval of the generating chord as a kind of vector with unique size and direction: a triangle for a three-note chord (e.g. harmonics 1-3-5), a triangle with a point inside for a four-note chord (e.g. 1-3-5-7), a pentagon for a five-note chord (e.g. 1-3-5-7-9), etc. Each edge or line of the basic geometric shape represents an interval, and each vertex or point represents a tone of the chord. Furthermore, every parallel line in a Wilson Diamond represents the same interval size. This form of representation shows the reciprocal harmonic and subharmonic chords as inverted shapes. Organizing the transpositions of different-sized generating chords around a central point results in various types of structures, such as the Triadic, Tetradic, Pentadic, etc., Diamonds (see Wilson 1969-1970). Augusto Novaro independently produced a schema for the 15-limit Diamond (Novaro 1927, p. 15). [TN]

Disjunction
The closing interval that is needed to complete the cycle when building a linear scale from a chain of generators. The disjunction is the ‘leftover’ interval that closes the gap between the beginning and end of the chain. It is not the same size as the generator but spans the same number of scale steps. Wilson treats the disjunction as melodically equivalent to the generator. Although it is the odd or atypical interval, it is an important signpost for determining one’s place in a scale. The term “disjunction” is also used separately in relation to ancient Greek tetrachordal scales to describe the interval that separates two tetrachords (Chalmers 1993, p. 206). [TN]

Farey series
A sequence of all fractions in lowest terms whose denominators do not exceed n, where n is the order of the Farey series, arranged in order of magnitude (Bogomolny 2012). [TN]

Generalized keyboard
A keyboard in which all identical intervals have the same geometric shape with relation to the topology of the keyboard. This enables chords or sequences of notes to be transposed to any key whilst maintaining the same hand shape or fingering pattern. For example, a major triad will always form the same hand shape on a generalized keyboard, in contrast to a traditional Halberstadt keyboard which requires the shape of the hand to change for different transpositions. Generalized keyboards were first invented by R. H. M. Bosanquet in the 1870s. [TN]

Horogram
A graphic representation of MOS scales on a series of concentric rings which are divided into small (s) and large (L) segments by radial lines that represent successive superimpositions of the generator. The size of the period of an MOS scale is represented as a full 360 degree turn and the size of the generator is represented by an angle that is proportional to the period. Starting from the innermost ring, Horograms show the process of interval division from one ring to the next, with each new ring representing a new MOS scale produced from superimpositions of the generator. [TN]

Lambdoma
A cross-set showing the results of multiplying ratios from the harmonic series (i.e. 1/1, 2/1, 3/1, …) on one axis of the table with ratios from the subharmonic series (i.e. 1/1, 1/2, 1/3, …) on the other axis. It is believed that the Lambdoma, which was used as a multiplication and division table by the ancient Greeks, was also applied to musical intervals from early times (Hero 1999, p. 61). Harry Partch’s Tonality Diamond can be seen as a variation on the Lambdoma. Wilson showed that ratios found on the Lambdoma correspond to those of the Farey series (Wilson 1996), and the intervals between each of these ratios are superparticular. Furthermore, the Lambdoma (Farey series) is embedded in the Scale Tree, and removing all repeated ratios from the Lambdoma results in the Co-Prime Grid which also forms the basis of Wilson’s Gral Keyboard Guide. [TN]

Lattice
A diagram or model for representing tuning relationships in multidimensional space. Pitches are represented as points in an array that are connected to each other along different axes. By convention, the horizontal axis represents a sequence of fifths (3/2s) ascending from left to right, the vertical axis represents thirds (5/4s) ascending from bottom to top, and the oblique axis represents sevenths (7/4s) ascending from lower left to upper right. Wilson uses other axes to represent higher tuning dimensions. Lattices are useful for seeing intervallic relationships between pitches and an important characteristic of most lattices is that parallel lines represent the same interval.[TN]

Linear scale
A generic term to describe scales built by superimposing a generating interval (such as a perfect fifth) and reducing the notes to within an interval of equivalence or period (typically an octave). [TN]

Master set
A group of harmonic factors used to generate a Combination-Product Set (CPS). For example, a Hexany generated from a master set of harmonics 1, 3, 5 and 7 would be named a 1-3-5-7 Hexany. The master set is treated like a chord and is labelled with the suffix –ad, such as a tetrad, pentad, or hexad to represent four-, five-, or six-tone chords respectively. The harmonics of the master set are arranged on the points of a geometric figure, such as a tetrahedron, and its reciprocal chord is arranged on an inverted version of the same shape, such as an upside-down tetrahedron. These geometric figures form the template for the lattice of the CPS. [TN]

Meta-
Wilson used this prefix to mean' like' or 'similar to' [KG]