septendecimal

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

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