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septendecimal en · ADJ · etymology 1

Etymology

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

Meanings

1. (not-comparable) Relating to or based on the number 17.

septendecimal en · ADJ · etymology 2

Etymology

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

Meanings

1. (not-comparable) Of or relating to a seventeenth.
   • 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. 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:
   • 17/8 septendecimal minor ninth / 17/12 2nd septendecimal tritone […] 24/17 1st septendecimal tritone 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:
   • I am sorry I cannot illustrate septendecimal harmony on this instrument as it is now tuned. It does not go beyond septimal harmony. 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: