Meaning of apotome | Babel Free

Definitions

1. The difference between two quantities or lengths commensurable only in power, as between 1 and the square root of 2, or between the diagonal and side of a square.
2. The remaining part of a whole tone after a minor second has been deducted from it; an augmented unison. Most commonly used to refer to the Pythagorean chromatic semitone, which has a ratio of 2187/2048.
3. A distinct division of an insect which is divided from the other divisions by a pinch point.

Equivalents

Examples

“Yet it is not until Book X that the properties of such a line (with greater length is an apotome and lesser length a first apotome) are explained and not until Book XIII that this type⟳ of line is applied, which will be discussed in more detail later.[…]The likewise is true of apotomes (X. 97).”

“2014, Jacques Sesiano (translator), Liber Mahameleth, Part Two: Translation, Glossary, [12th c, Anonymous (possibly John of Seville), Liber Mahameleth], Springer, page 767, If some number⟳ and the root of the root of a number⟳ are multiplied by the corresponding apotome, the result⟳ will be an apotome.”

“1813, Music, article in John Mason Good, Olinthus Gregory, Newton Bosworth, Pantologia: A New Cyclopaedia, Volume 8: MID—OZO, unnumbered page, This semitone was termed by the Pythagoreans apotome, and the diatonic semitone was termed limma. They contended, that the apotome, or distance from B flat to B natural, was larger than the limma, or distance from A to B flat.”

“For the ratio of the excess of the apotome, above that which is truly a semitone, and which cannot be obtained in numbers, is thus called. This then is demonstrated. To what has been said however, it must be added, that we have⟳ called the ratio of d b a semitone, not that a sesquioctave is divided into two equal ratios; for no superparticular ratio is capable of being so divided; but because the followers of Aristoxenus assume⟳ a semitone after two sesquioctaves, the ratio of a semitone is assumed, as we have⟳ said, according to their position, in order⟳ to discover⟳ what the ratio is of the comma and apotome to the ratio of the leimma.”

“The traditional term, from ancient Greek theory, for the diatonic pythagorean semitone is 'limma'; and for the larger, chromatic semitone, ‘apotome’. The oldest extant fretting formula, that of the ninth-century theorist Al-Kindi for the ud (the Arabic lute), is pythagorean. It calls for five frets, to make⟳ the following succession of semitones down from nut: limma, apotome, limma, apotome', limma.”

“The bands pass⟳ inside the margins of the apotome as they approach⟳ its constriction and form⟳ two pigmented areas broadly based on the frontal sutures and becoming dispersed towards the mid-line.”

“In generalized Diplura, Archaeognatha and some Thysanura, five parts or apotomes are distinguished, which from the anterior to the posterior part are: the presternum, the basisternum, the furcasternum, the spinasternum and the poststernum.”

CEFR level