Archicembalo in meantone 24: Renaissance fifthtone music (4 of 4)

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An archicembalo in 24-note meantone:
Renaissance fifthtone music on two 12-note keyboards
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(Part IV of IV)

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Notes
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1. For a complete translation of Vicentino's treatise, see Nicola
Vicentino, _Ancient Music Adapted to Modern Practice_, tr. Maria Rika
Maniates, ed. Claude V. Palisca (New Haven: Yale University Press,
1996), ISBN 0-300-06601-5. A fascimile of the 1555 edition is
available: _L'antica musica ridotta alla modern prattica_, ed. Edward
L. Lowinsky, Association Internale des Biblioteques Musicales,
Documenta Musicologica, Erste Reihe: Druckschriften-Faksimiles 17
(Basel and New York: Barenreiter Kassel, 1959). On Vicentino's
instrument and its tuning, see also Bill Alves, originally appearing
in _1/1: Journal of the Just Intonation Network 5(No.2):8-13 (Spring
1989), available at http://www2.hmc.edu/~alves/vicentino.html, with a
helpful biography; Henry W. Kaufmann, "More on the Tuning of the
_Archicembalo_," _Journal of the American Musicological Society_
23:84-94 (1970); and Marco Tiella, _L'Archicembalo_, available at
http://www.infosys.it/pamparato/ima/ma/ma81/Tiella.html.

2. The term "fifthtone" may be more specific than "diesis," which can
refer among other things to a Pythagorean diatonic semitone at 256:243
(the usual limma). At the same time, it is more accurately descriptive
than "quartertone" for Renaissance intervals equal to about 1/5-tone.

3. This 128:125 interval is sometimes known more specifically as the
"lesser diesis," the "greater diesis" being the difference between
four pure 6:5 minor thirds and a 2:1 octave, 648:625 or ~62.57 cents.
In the Greek enharmonic genus, a semitone is divided into two dieses,
~45.11 cents each if we take the semitone as a Pythagorean limma of
256:243 or ~90.22 cents.

4. See, for example, Mark Lindley, "Temperaments," _New Grove
Dictionary of Music and Musicians_ 18:660-674, ed. Stanley Sadie,
(Washington, DC: Grove's Dictionaries of Music, 1980), ISBN
0333231112, at 666. In the standard 16th-century modal system, G#
serves for example as a major third above the final of E Phrygian,
while Eb permits a fluid degree E/Eb in G Dorian with Bb signature, a
transposed equivalent of B/Bb in D Dorian.

5. Transcribed in Maniates and Palisca, n. 1 above, at pp. 218-222,
mm. 30-31; and facsimile, Lowinsky, n. 1 above, at 69v-70v.

6. Transcribed in Henry Expert, ed., _Anthoine de Bertrand, Second
livre des Amours de Pierre de Ronsard_, Monuments de la Musique
Francaise au temps de la Renaissance_ 6 (New York, Broude Brothers,
n.d.), 27-30, at p. 30, 3rd system, m. 4, at text _Plus il est
contraint_.

7. Transcribed in Maniates and Palisca, n. 1 above, at p. 208. For
Vicentino's approximate ratio of 11:9, see ibid. p. 437; for fascimile
of musical examples, see Lowinsky, n. 1 above, at 66v.

8. Maniates and Palisca, ibid., pp. 337, 436-437.

9. Expert, n. 6 above, at p. 30, second system, mm. 2-3, at text
_navre a` tort_.

10. From a modern perspective oriented to medieval as well as
Renaissance music, this use of a small cadential semitone might
suggest the Pythagorean tuning of the 13th-14th centuries, where
relatively concordant but active and unstable thirds and sixths
"strive" toward stable intervals such as fifths and octaves. Combining
such compact semitones with pure or near-pure thirds, however,
requires "unusual" intervals such as the 6/5-tone steps in this
example.

11. Fabio Colonna, _La Sambuca Lincea, overo Dell'Istromento Musico
Perfetto, con annotazioni critiche manoscritte di Scipione Stella
(1618-1622)_, ed. Patrizio Barbieri, Musurgiana 24 (Lucca: Libreria
Musicale Italiana, 1991), ISSN 1121-0508, ISBN 88-7096-026-9. This
fascimile edition includes a very helpful commentary in Italian and
English.

12. On such 19-note instruments and their music around 1600, see
Barbieri's commentary, ibid. pp. XLIX-L. In this music based on a
range of Gb-B#, an occasional enharmonic note may arise at either end
of the chain. Thus Gesualdo, in one of his vocal madrigals, uses a Cb
(Vicentino's B*), while a keyboard composition by Giovanni Maria
Trabaci from the same era has an optional F## as a major third to D#,
with the performer invited to substitute a minor third F# on a usual
"chromatic" instrument. On Gesualdo's accidentals, see Glenn Watkins,
_Gesualdo: The Man and His Music_ (Chapel Hill: University of North
Carolina Press, 1973), pp. 194-196. Stella entered Gesualdo's service
in 1594, see Barbieri, ibid. p. XXXIV.

13. If this is the correct interpretation, then Vicentino's use of
these keys, or of all 17 keys of the second manual in an alternate
tuning based on "just fifths" with the basic 19 notes of the first
manual (e.g. Maniates and Palisca, n. 1 above, 333-334 and commentary
at xlix-l, and Tiella, n. 1 above, Fig. 5), might fit the concept of
"adaptive just intonation" discussed by modern theorists such as Paul
Erlich. In such a system, the melodic steps of the gamut are tuned in
a scheme such as meantone, but concords with pure ratios are placed
above these steps.

14. Colonna, n. 12 above, Barbieri's commentary at XXXV.

15. Colonna, ibid., at 103-110 (110 numbered as 100), and
transcription at LVII-LXII.

16. Ibid. at 72, and Barbieri's interpretation at XLVI-XLVII and
Fig. 2; my diagram is based on ranks consistently 1/5-tone apart, with
Eh (E+4/5) equivalent to Vicentino's F*, and Bh to C*. If Colonna's Cb
and Fb on Rank 4 are emended to C and F, as Barbieri and I have done,
this keeps the symmetry of the ranks.

17. J. Murray Barbour, _Tuning and Temperament: A Historical
Survey_ (East Lansing: Michigan State College Press, 1953), p. 119.

18. E.g. C-C*-C#-Db-D (LF-SF-LF-CS); G*-G#-Ab-A-A* (SF-LF-CS-LF);
E-E*-F-F*-F# (LF-CS-LF-SF); and Gb-G-G*-G#-Ab (CS-LF-SF-LF).

19. Colonna, n. 12 above, at 101-102, and Barbieri's commentary at LI
and transcription at LXVI-LXVII.

20. Ibid., XL-XLIII, where Barbieri explains Colonna's principle that
a ratio is admissable if its smaller term forms an acceptable concord
with the difference of the two terms, e.g. 17:12, 12:(17-12) = 12:5 (a
just minor tenth); prime factors include "3, 5, 7, 11, 13 and 17."

21. See Maniates and Palisca, n. 1 above, pp. 336-340, where Vicentino
expresses the viewpoint that while the proximate minor thirds and
sixths (here E4-C*5) are acceptable concords, proximate major thirds
and sixths (here E4-Db5) are "less tolerable" or even "harsh,"
although he does not categorically exclude them. In his partial
madrigal _Madonna, il poco dolce_, he has a passing sonority of minim
or half-note duration B3-F#3-B4-Eb4, ibid. at 214-217 at 216 m. 31,
discussed at lv; facsimile in Lowinsky, n. 1 above, 68v-69r. This
sonority includes both the proximate major third or tenth B3-Eb4 and
the proximate major sixth F#3-Eb4, and occurs at the word _pianger_,
"to weep." Colonna's G-C*, a diesis wider than a usual fourth, does
seem to me a vertical interval uncharacteristic of Vicentino.

22. While I find this example pleasant, and milder than Colonna's (the
fourths between the upper voices remaining unaltered), Vicentino says
that the "minimal third" a diesis smaller than minor (here Gb-A, first
sonority) is generally "discordant" and should be "set aside" like the
proximate major sixth, pp. 339-340. To my ears, this interval (~269.21
cents) near 7:6 (~266.87 cents) is rather concordant; here it is
combined with the augmented fifth Gb-D, a not too unusual interval in
14th-century music. Since the LF-SF-LF motion in the lowest part
(Gb-F#-F*-F) leads to the diatonic semitone F-E, the total descent
Gb-E is a curious 6/5-tone, used as a direct melodic interval in
Bertrand's cadence cited in Section 1 and n. 9.

23. See nn. 7-8.

24. This term is borrowed from physics and chemistry. As used here,
"chirality" in 1/4-comma meantone involves a distinction equal to that
between 31 tempered fifths and a pure 2:1 octave, or between the large
and small fifthtones, ~6.07 cents. The "handedness" metaphor may
suggest the relationship between pairs of intervals such as the large
fifthtone (12 fifths down) and the small fifthtone (19 fifths up); or
the larger proximate minor third (15 fifths down) and the smaller one
(16 fifths up).

25. My special thanks to Ed Foote, musician, advocate, and tuner
extraordinaire, for inspiring this section.

26. On Vicentino's archicembalo tuning, views have varied. Barbour,
n. 17 above, pp. 117-119, describes this tuning as "a clever method of
extending the usual meantone temperament of 1/4 comma," and asserts
that this temperament, the "common practice" of the time, "is
undoubtedly what Vicentino used." Tiella also takes this view, and
gives values in cents for the notes of the instrument based on this
tuning. However, Maniates and Palisca, n. 1 above, Appendix VII,
pp. 452-453, give rounded values in cents for 31-tet, and Kaufmann,
n. 1 above, pp. 87-88, 93-94, and Tables I and II, adopts the view of
Lemme Rossi, _Sistema musico_ (1666), that Vicentino's tuning is
31-tet rather than the very closely related 1/4-comma. The scale file
vicentino1.scl from scales.zip, an archive of scale data for Manuel op
de Coul's Scala computer program, likewise gives the tuning as 31-tet.
Among those favoring 1/4-comma, views of chirality vary, although
Vicentino's own tuning procedure, Maniates and Palisca, pp. 332-333,
specifies Cb-D###, with B* tuned a fifth down from Gb, but all other
notes of the enharmonic fifth and fourth ranks up from B# (Gb*-E*),
the fifth rank (Gb*-Bb*=F##-A##) being tuned _before_ the remaining
notes of the fourth (F*-E*=E##-D###). Barbour, p. 118, says that the
fourth rank adds flats (i.e. B*-F*=Cb-Gbb), while the fifth rank adds
sharps (i.e. Gb*-Bb*=F##-A##), for a tuning of Gbb-A## -- following
Vicentino's scheme for the fifth rank and for B*=Cb, but not for the
other notes of the fourth rank. Tiella, in his Fig. 4, shows values in
rounded cents which would define a 1/4-comma tuning with all 12 notes
of the fourth and fifth ranks tuned as flats (Gb*-B*=Abbb-Cb), or
Abbb-B#. This scheme would be identical to the 24-note tuning Eb*-G#
described here plus Gb*-Ab*(Abbb-Bbbb) and D#-B# to complete a 31-note
division; corresponding notes on the two manuals, as Tiella's diagram
shows, are consistently a 128:125 diesis or large fifthtone apart (a
rounded 41 cents). While it is gratifying to find an earlier precedent
for my 24-note scheme with its flat chirality, Vicentino's scheme is
different.

27. Fifths are tempered by ~5.38 cents in 1/4-comma, and ~5.18 cents
in 31-tet. This excellent approximation is noted, for example, by
Barbour, n. 17 above, pp. 117-119, citing also the calculations of the
17th-century Netherlands theorist Christian Huyghens that the two
tunings differ by no more than "1/110 comma." Kaufmann, n. 1 above,
pp. 87-88 and 93-94, cites Lemme Rossi on the similarities, and noting
"how closely the two tunings are related," states at p. 87: "The 1/4
comma temperament will thus be used for the tuning of the fifths in
the remaining orders of the _archicembalo_" (although values in cents
are given for 31-tet). Barbieri's commentary in Colonna, n. 12 above,
at XLVII and XLIX, refers to 1/4-comma as "the most common tuning in
the early seventeenth century" and notes that 31-tet is "excellently
approximated" by this tuning.

28. Maniates and Palisca, n. 1 above, pp. 331-332.

29. Colonna, n. 12 above, e.g. at 69, and Barbieri's commentary at
XLIX.

30. Lindley, n. 4 above, at 662, and his "Early Sixteenth-century
Keyboard Temperaments, _Musica Disciplina_ 28:129-151 (1974), with
pp. 139-144 on Aaron, and a statement at p. 150 and n. 23 that "one
should not assume _a priori_ that it was 1/4-comma meantone in
particular that Nicola Vicentino necessarily had in mind" for the
standard tuning of the first two ranks of his instrument. In my view,
one can propose 1/4-comma as an historically likely realization of
Vicentino's 31-note division while joining Lindley in recognizing the
variety of Renaissance meantone tunings. Incidentally, at 150 n. 23,
Lindley cites Barber's puzzlement with part of Vicentino's scheme;
Barber's perplexity may have resulted from a confusion in his sources
of Vicentino's tuning based on a 31-note division of the octave and
his alternative tuning with the notes of the second manual providing
just fifths to those of the first (see n. 13 above).

31. Vicentino describes intervals of a "minor diesis" (1/5-tone),
"major diesis" (2/5-tone, a chromatic semitone), and "major semitone"
(3/5-tone, a diatonic semitone); and Colonna, n. 12 above, at 103,
prefaces the music for his "example of circulation" with a statement
that this composition demonstrates that "our division of the tone into
five intervals" is true. In fact, Vicentino's model can be as useful
in extended 1/4-comma as in 31-tet for many purposes (e.g. counting a
"proximate minor third" such as C-Eb or C*-E as 9/5 of a tone); and
either tuning permits Colonna's full circulation. Playing Colonna's
piece on his instrument or Vicentino's in 1/4-comma, we would
encounter a few sonorities of the kind described near the end of
Section 3, with thirds of "opposite chirality" (major thirds 27 fifths
down instead of four fifths up, ~392.38 cents; minor thirds 28 fifths
up instead of three fifths down, ~304.20 cents). Intriguingly, we
would also encounter one fifth of opposite chirality (30 fifths down
rather than one fifth up), an almost pure interval of ~702.65 cents,
wider than a just 3:2 (~701.955 cents) by the difference between the
almost perfectly balanced factors of chirality and usual tempering,
(~6.07 - ~5.38) or ~.69 cents. With Vicentino's tuning scheme of
Cb-D###, for example, we would encounter this near-pure fifth
D###3-Cb4, and likewise the near-pure fourth Cb4-D###4, at the
sonority E*3-B*3-E*4-Ab4 (Colonna, ibid. at 105, m.2 of this page),
realized as D###3-Cb4-D###4-Ab4, with the major tenth and third
D###3-Ab4 and D###4-Ab4 also of opposite chirality, but the major
sixth Cb4-Ab4 a usual meantone interval (as the spelling suggests).
How noticeable these variations of chirality would be among those of
the tuning process over 31 notes remains an interesting question, but
in any case they seem no barrier to Colonna's full "circulation."

32. For Bernard's piece, see n. 6 above; since this piece does not use
G#, one could also play it in Ab-C#/Ab*-Db. For Vicentino's example,
see Maniates and Palisca, n. 1 above, pp. 209-210, with commentary at
lii-liii, and fascimile, Lowinsky, n. 1 above, 67r.; this excerpt
likewise does not use G#.

33. Maniates and Palisca, ibid., pp. 211-213, with commentary at
liii-lv, and facsimile, Lowinsky, ibid., 67v-68r. In a pinch, one
might attempt this piece in Eb-G#/Eb*-Ab by disregarding the
enharmonic inflections in all parts at m. 14 of the transcription,
changing Ab*2-Ab*3-Eb*4-C*4 to Ab2-Ab3-Eb4-C4 (upper voices crossed).
Vicentino's own remarks about optionally performing in "mixed" genera
would seem to permit such an expedient, and here I see no obvious
vertical or melodic contraindications.

34. For _Madonna, il poco dolce_, see Maniates and Palisca, ibid.,
pp. 214-217, and fascimile, Lowinsky, n. 1 above, 68v-69r; for _Musica
prisca caput_, see n. 5 above. Commentary on both pieces appears in
Maniates and Palisca, lv-lviii.

Most respectfully,

Margo Schulter
mschulter@value.net