septendecimal

English

Etymology 1

From Latin septendecim (“seventeen”) +‎ -al,[1] after decimal. By surface analysis, septen- +‎ decimal.

Adjective

septendecimal (not comparable)

  1. Relating to or based on the number 17.

Etymology 2

From Latin septendecimus +‎ -al (after English seventeenth[2] and decimal), from septendecim (“seventeen”), after decimus (“tenth”).[2] Compare Latin septimusdecimus (“seventeenth”). By surface analysis, septen- +‎ decimal. Coined by English mathematician, philologist and musician Alexander John Ellis in 1885 (see the quotation).

Adjective

septendecimal (not comparable)

  1. (music) Of or relating to a seventeenth.
    • 1885, Alexander J[ohn] Ellis, “Introduction of the Seventh and Seventeenth Harmonics”, in Hermann L[udwig] F[erdinand] Helmholtz, translated by Alexander J. Ellis, On the Sensations of Tone as a Physiological Basis for the Theory of Music, 2nd English edition, London: Longmans, Green, and Co., →OCLC, appendix XX (Additions by the Translator), section E (On Musical Duodenes or the Development of Just Intonation for Harmony), page 464, columns 1–2:
      If it is desired to proceed beyond tertian to septimal harmony to introduce the harmonic form of the phord of the dominant Seventh, with the ratios 4 : 5 : 6 : 7 as Mr. Poole has done (see sect. F. No. 7), or even to septendecimal harmony to introduce the harmonic form of the chord of the minor Ninth 8 : 10 : 12 : 14 : 17 (see p. 346c, note *), the number of the notes will be nearly tripled. […] The cents in the tertian chord of the minor Ninth C E, G B♭ D1♭ are 0, 386, 702, 996, 1200 + 112. Hence the cents in the harmonic septimal chord of tiie dominant Seventh, or C E1 G B♭, are 0, 386, 702, 969, and the cents in the septendecimal chord of the minor Ninth, or C E1 G 7B 17D1♭, are 0, 386, 702, 969, 1200 + 105.
    • 1932 April 26, Wilfrid Perrett, “The Heritage of Greece in Music”, in Proceedings of the Musical Association, 58th session, [London]: Oxford University Press, →ISSN, →OCLC, page 94:
      I am sorry I cannot illustrate septendecimal harmony on this instrument as it is now tuned. It does not go beyond septimal harmony.
    • 2003 December 19 (indicated as 2004), Ján Haluška, “List of intervals”, in The Mathematical Theory of Tone Systems (Pure and Applied Mathematics), New York, N.Y.; Basel: Marcel Dekker; Bratislava: Ister Science, →ISBN, page xxiv:
      17/8 septendecimal minor ninth / 17/12 2nd septendecimal tritone […] 24/17 1st septendecimal tritone

References

  1. ^ “septendecimal, adj.”, in Merriam-Webster Online Dictionary, Springfield, Mass.: Merriam-Webster, 1996–present.
  2. ↑ 2.0 2.1 “septendecimal, adj.”, in OED Online ⁠, Oxford: Oxford University Press, launched 2000.
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