Where does evenness collide?

Evenness measures how equally the individuals in a community are divided among the species that are present, one of the two parts of biological diversity alongside richness, which just counts how many species there are. Pielou's 1966 The measurement of diversity in different types of biological collections set out the standard index, written J, which divides a community's observed Shannon diversity by the largest value it could reach if every species were equally common, so J runs from near zero, when one species dominates, up to one, when all are equally abundant. Here the referent is a property of a whole community's abundance distribution, read off a count of how many individuals belong to each species. It is not the uniformity of a spun thread or the spacing of notes around a scale.[1]

Unit

One community's departure from equal abundance among its species, scaled from 0 to 1

Recovery means

Not applicable

Measured by

Computed as Pielou's J, the observed Shannon diversity divided by its maximum for that number of species

In yarn manufacture, evenness, whose defect is called unevenness or irregularity, is how constant the mass per unit length of a spun thread stays as you travel along it, because thick and thin places weaken the yarn and mar the finished cloth. Martindale's 1945 A new method of measuring the irregularity of yarns gave the measure still in use, the coefficient of variation of mass over short lengths, and worked out the smallest irregularity a yarn of a given fibre count could have, its limiting irregularity. Here the referent is a physical quality of one manufactured thread, gauged along its length by a capacitance or optical tester and reported as a percentage. It is not a community's abundance spread or the structure of a musical scale.[2]

Unit

One yarn's variation in mass per unit length, as a coefficient of variation percentage

Recovery means

Not applicable

Measured by

Read on an evenness tester as the coefficient of variation CV%, or the older irregularity U%, of mass per unit length

In the mathematical study of scales, evenness is how uniformly a chosen set of notes is spaced around the twelve-step chromatic circle, and a set is called maximally even when its notes are as spread out as they can be for that many notes. Clough and Douthett's 1991 Maximally even sets defined the property precisely, placing each note at a rounded fraction of the circle, and showed that the familiar diatonic major scale and the pentatonic scale come out maximally even. Here the referent is a structural property of a set of pitch classes arranged on a circle, a matter of combinatorics rather than physics or biology. It is not a community's evenness or a thread's uniformity, though all three lean on the loose idea of things spread out equally.[3]

Unit

A pitch-class set's spacing on the chromatic circle, as a graded or yes-or-no property

Recovery means

Not applicable

Measured by

Judged combinatorially by whether the set matches the rounded even spacing given by the maximally-even generating rule