----- Original Message ----- From: "Taco Walstra" <[EMAIL PROTECTED]> To: "lutelist" <[EMAIL PROTECTED]>; "Jon Murphy" <[EMAIL PROTECTED]> Sent: 30. januar 2004 09:26 Subject: Re: Fw: Equal Temperament
| On Friday 30 January 2004 06:50, Jon Murphy wrote: | Dear Jon, | I wonder if this Catherine is helped by your explanation because you do not | explain anything of the background of differences between temperaments in | your long e-mail. For example meantone has pure thirds etc. If you want the | explain temperaments you need to refer to the differences of how the octave | is divided, i.e. the differences in ratio often expressed in cents. | It would be better if you give her some website links with explanations. | Perhaps you can forward her the following links which I saved on my | webbrowser a long time ago: | | http://www.microtonal.co.uk/xtra.htm | http://home.planet.nl/~d.v.ooijen/lgs/meantone.html | and the following more technical links: | http://www.b0b.com/infoedu/science.html | http://www.jimloy.com/physics/scale.htm | http://home.swipnet.se/~w-37192/eng/handbook/Tuning/history.html | | About electronic tuners you are wrong. I have two of these things, one is a | cheapo with ofcourse only equal temperament and only a=440 Hz. The other Korg | OT-12) can be calibrated to any frequency you like and also many temperaments | (valotti, meantone, etc. etc.). that's certainly not a cheap thing. This was | also written on this list by the way if I remember well. | Best | taco Catherine, Jon, Taco, All Here's also a bibliography, for those masochistically inclined: http://www.xs4all.nl/~huygensf/doc/bib.html and FWIW I forward the following mail from the Yahoo group on tuning: Both the above link and Margo's mail are nothing less than overkill, but someone might find it useful, esp. M. Lindley's books (which I haven't read), just acting as a conduit here! Regards Göran. From: "M. Schulter" <http://groups.yahoo.com/group/tuning/post?protectID=17410722201706608914313 3102248163237053159035046044127169> Hello, there, and thanks to Bill Alves for sharing a post originally made to the Society for Music Theory (SMT) list by Jeffrey Dean, on which I would have a number of comments, inviting a repost of what follows or any portion thereof to the SMT list if Bill or another subscriber finds it appropriate and helpful. > There is evidence that fretted instruments had been tuned (to a > close approximation) to equal temperament from early in the 16th > century; Mark Lindley has written a great deal about this and other > practical tuning and temperament systems, and I won't single out a > particular essay of his. Here the main qualification might be that while 12-tone equal temperament (12-tET) with equal semitones does appear to become the "standard" tuning for lute by around the middle of the century, Lindley notes that some lute pieces by composers such as Milan around the 1530's seem ideally to fit a meantone tuning.[1] Also, as Lindley notes, it happens that because of the physics of lute playing with the factor of pressure applied to the frets in stopping them, Vincenzo Galilei's "18 rule" of frets spaced by a repeated rational factor of 18:17 (~98.95 cents) in practice give a better approximation of 12-tET than the "correct" logarithmic spacing. > It *may* be pertinent that in 1482 Bartolomeus Ramis de Pareia > argued that the tritone is identical to the diminished 5th; this is > strictly true only in equal temperament, but he may simply have been > counting keys (he often cited the keyboard, sometimes specifically > the organ, to illustrate his points). While the views of Ramis (or Ramos) on the tritone are of great interest, I would emphasize that whatever his views on its size in relation to the diminished fifth, his treatse of 1482 clearly points to some tuning for keyboards using _unequal_ semitones, which Lindley persuasively argues is likely some shade of meantone temperament.[2] In his treatise, in discussing how to find "good" and "bad" thirds and other intervals on a keyboard instrument, Ramos gets into a discussion of the relative merits of having Ab or G# in a 12-note tuning -- that is, Ab-C# vs. Eb-G# as the chain of fifths. In a 12-tET tuning where G# and Ab are acoustically equivalent, this debate (in which Ramos finds Ab the more "provident" choice) would seem rather beside the point. In the course of this discussion, Ramos argues that the utility of G# in an Eb-G# tuning is limited because there is no "good" fourth D#-G#, stating that Eb-G# does not form a proper fourth, as it would, of course, in 12-tET. Further, he observes that some people like to satisfy both sides of the question by providing a keyboard instrument with keys for both Ab and G# -- the "split-key accidentals" of a kind advocated by certain early 15th-century theorists in a Pythagorean setting, and used in the Lucca organ of around 1480 (G#/Ab, and either Eb/D# or Bb/A# depending on which sources or interpretations one favors). Like Lindley, I find his remarks very much in line with the hypothesis of the widespread use of meantone temperament by 1482, a practice expressly described by Gafurius in 1496, although not precisely quantified in terms of fractions of a syntonic comma until Zarlino (1558 and later). At any rate, he is evidently describing some tuning other than 12-tET. A quick aside: the fine distinction between tritone and diminished fifth might or might not be made at various eras. Thus a typical 13th-century reckoning based on Pythagorean intonation recognized a diatonic set of 13 simple intervals ranging from unison to octave, with a single category of tritone (_tritonus_). Around 1325, however, Jacobus of Liege pointed out that there were actually 14 such intervals, since the _semitritonus_ or diminished fifth had a different and smaller size of 1024:729 (~588.27 cents) than the _tritonus_ or augmented fourth at 729:512 (~611.73 cents). > I want to comment specifically on the issue of "chromaticism". This > meant something entirely different in Lassus's time from what we > normally understand today. When we talk about chromaticism we mean > the 12-note semitonal octave. When Lassus's contemporaries (we don't > have any verbal testimony from Lassus himself, only the music) > referred to "chromaticism" they meant the chromatic genus of ancient > Greek music, in which the octave is constituted from two chromatic > tetrachords (semitone-semitone-semiditone) separated by a tone > [1132113]. Certainly the Greek chromatic genus was one defining concept in the 16th century, but not necessarily the only one. As Thomas Morley observes in 1597, musicians such as organists often regarded a "chromatic" figure as one alternating diatonic and chromatic semitones in stepwise motion, giving the example in semibreves or whole-notes of E-F-F#-G-G#-A. Since the chromatic semitone might be considered the distinctive interval defining the chromatic genus, this looser sense has some connection to the stricter one. Morley himself remarks that a theme such as that he states "is not right Chromatica, but ... patched up of half Chromatic, and half Diatonic."[3] > When Claude Le Jeune wrote "Quelle eau" (1585), "Qu'est devenu ce > bel oeil" (1608), and "Hellas, mon Dieu" (1612) he exemplified > chromaticism *not* by saturating his pitch space with semitones but > by expressing the chromatic tetrachord specifically. For Nicolo > Vicentino, the minor 3rd was as much a diagnostic interval for > chromaticism as the semitone, and this was the thrust of his famous > (losing) debate with Vicente Lusitano in 1551 over whether the music > of the time was diatonic or not. Yes, Vicentino's thesis was that whenever a melodic minor third appeared, it marked a use of the chromatic genus, causing him to describe music of the common practice as _participata & mista_, or "tempered and mixed," featuring both the slight narrowing or "blunting" of the fifth characteristic of meantone, and the mixing of the genera. Zarlino (1558) condemned this opinion of the "chromaticists," asserting that the chromatic semitone and enharmonic diesis rather than the minor and major third were the defining intervals of these two genera, with steps of a major or minor third belonging equally to the diatonic. Vicentino also maintained that a strictly "diatonic" composition could not use _any_ accidental inflections such as sharps applied by composer or performer to obtain major sixths before octaves, etc. In contrast, Zarlino took for granted the use of "justifiable" and indeed necessary accidentals as a feature of normal diatonic style. > In Pythagorean or just intonation the diatonic semitone is smaller > than the chromatic; in meantone temperament it is larger. Indeed in Pythagorean intonation, the diatonic semitone or limma (256:243, ~90.22 cents) is smaller than the chromatic semitone or apotome (2187:2048, ~113.69 cents), while in meantone, e.g. 1/4-comma with pure 5:4 major thirds, the diatonic semitone (~117.11 cents) is larger than the chromatic (~76.05 cents). However, for "just intonation" taken in the sense of a system based on pure ratios of 3 and 5 (as in the systems of Fogliano in 1529 and Zarlino in 1558), as for meantone, the diatonic semitone is larger, most typically 16:15 (~111.73 cents), than the chromatic semitone, most typically 25:24 (~70.67 cents). These semitone sizes vary, because of the use of differently sized whole-tones at 9:8 and 10:9, but with the diatonic semitone characteristically larger. > Lusitano's winning argument against Vicentino was that in normal > music the chromatic semitone is never used, therefore music is > diatonic. Composers immediately (if they hadn't already) proved him > wrong, as they usually do with overgeneral theoretical > pronouncements. Interestingly, the first bold use of what is sometimes termed "direct chromaticism" -- the use of a chromatic semitone as a melodic step -- in Western European polyphonic music may be the practice of Marchettus of Padua and some of his colleagues during the early 14th century, described and advocated in his _Lucidarium_ of 1318, and also documented in some compositions from this epoch cited by Jan Herlinger.[4] However, according to much conventional theory, the apotome or chromatic semitone was "unsingable," and this view is expressed as late as 1565 by Tomas de Santa Maria in a treatise on four-voice keyboard textures and the art of _fantasia_ or improvisation, where he further cautions that "what cannot be sung cannot be played." As you rightly note, the experimental compositions of Lasso, Rore, and others of this same era might serve as counterexamples. As far as the Vicentino-Lusitano debate goes, I might award the formal and narrow issue of the disputation to Lusitano (a melodic leap of a minor third as tone-plus-diatonic-semitone, or of a major third as a "ditone" or tone-plus-tone, seems routinely diatonic to me). However, I would emphatically join Vicentino in celebrating the artistic merits and possibilities of polyphonic music using the steps of the chromatic semitone and enharmonic diesis -- the latter fortuitously and felicitously realized by the usual meantone diesis of 128:125 (~41.06 cents), about 1/5-tone. Based on my own experience with a 24-note archicembalo (or the synthesizer equivalent) in 1/4-comma meantone as a subset of Vicentino's full instrument with 36 or 38 notes per octave, I would say that his germinal contributions leave immense scope for further exploration. Maybe the Vicentino-Lusitano affair is an example of how great aesthetic controversies can focus on issues not always so happily defined. > I don't disagree with the harmonically-based analyses that have been > posted before this, but I think they ought to be supplemented by > attention to what the composers thought their "chromaticism" meant. As someone looking at 16th-century music from something of a medievalist perspective (which means maybe that my 14th-century biases and other people's 18th-century biases may average out to a balanced analysis <grin>), I would focus on such things as the theme of "closest approach" progressions by contrary motion such as m3-1, M3-5, M6-8 as they guide motion between the pervasive tertian sonorities of the newer style. Scholars such as Richard Crocker and Carl Dahlhaus have emphasized this point, and I might describe the 13th-16th century approach as one of "combinative verticality," with two-voice intervals as the elementary particles, but with a three-note unit of complete sonority. In Gothic music, this unit is Johannes de Grocheio's _trina harmoniae perfectio_ or "threefold perfection of harmony" expressed by the combination of outer octave, lower fifth, and upper fourth (e.g. d-a-d' or D3-A3-D4 in MIDI notation), which another theorist writing in the same era around 1300 derives from the series of ratios 2-3-4. Interestingly, this "natural" series with 2:3 fifth below 4:3 fourth coincides with the modern frequency ratio of 2:3:4; the medieval string ratio is 12:8:6 or 6:4:3. By the second quarter of the 16th century, it is clearly what Zarlino terms _harmonia perfetta_, "the third plus fifth or sixth," ideally outer fifth, lower major third, and upper minor third, with a string ratio of 15:12:10 and a frequency ratio of 4:5:6. In my view, an analysis of 16th-century music, chromatic or otherwise, should approach the vertical dimension in terms of directed two-voice progressions (some borrowed from earlier Gothic practice and theory, others new) and in terms of the different combinations and arrangements of _harmonia perfetta_, with Zarlino's remarks on these points providing one valuable outlook. Also, Vicentino and Santa Maria bring their own vital perspectives to this question, and I've found that the latter's four-voice patterns and progressions can be relevant for analyzing a range of 16th-century pieces, especially those involving note-against-note textures. > *The real problem alluded to here is that there is evidence that > singers (and players of instruments with flexible tuning) did not > hold strictly to the basic tuning they were following. (The evidence > that singers used an essentially just tuning rather than the > Pythagorean goes back to Ramis in 1482 again, and is probably valid > for about a generation earlier.) As Bill Alves has aptly emphasized on the Tuning list, flexible intonation is indeed flexible, so that a tuning for fixed-pitch instruments is a model rather than a definition of what an ensemble may actually do. Here I would agree that "about a generation" before the treatise of Ramos, or around 1450, is a very reasonable date for a shift from Pythagorean to meantone tuning for keyboards, and to some approximation of just intonation based on ratios of 3 and 5 (i.e. 5:4 and 6:5 thirds) for singers and players of flexible-pitch instruments. The problem of intonation in the era of the Gothic-Renaissance transition, arguably making up most of the 15th century, is an intriguing one. For the era of the young Dufay (say 1420-1450), I would be inclined with Mark Lindley to posit some kind of modified Pythagorean tuning with smoother "schisma thirds" (diminished fourths and augmented seconds with ratios very close to 5:4 and 6:5) used for certain sonorities, especially prolonged noncadential ones. Experimenting with a 15-16 note Pythagorean tuning on two synthesizer manuals (one in the likely typical Eb-G# of the 14th century, or Bb-D#, the other in the popular Gb-B tuning of the early 15th century), I've found myself agreeing with Prosdocimus de Beldemandis (1413) and Ugolino of Orvieto (c. 1425-1440?) in favoring regular and active Pythagorean thirds and sixths for cadences in the "classic" 14th-century manner combining M6-8 and M3-5 (e.g. E-G#-C# to D-A-D). At the same time, noncadential schisma third sonorities like E-Ab-B (written E-G#-B) can have a beguiling effect which to my ears very much evokes the fresh new aura of the Dufay era. Lindley suggests 1450 as an approximate date for the transition to meantone, with the compositions of Conrad Paumann for keyboard and the vocal works of the later Dufay and Ockeghem favoring such a system with a consistent use of pure or near-pure thirds. However, some scholars lean toward the view that singers may have still often favored a somewhat "Pythagorean" approach in the middle to late 15th century, so that the kind of theoretical disarray discussed by Lindley may reflect the transitional nature of practice as well as conceptual models. For example, singers may have at times leaned toward the compact diatonic semitones of the Pythagorean tradition, and at other times toward smoother vertical thirds and sixths, for example in resolving the suspension dissonances playing a central role in the new style. > But there are other witnesses from the beginning of the 14th century > (Marchettus of Padua) well into the 16th (the preface to a French > chanson publication of Lassus's time; I'm afraid I've mislaid the > precise reference) that the supposedly diatonic semitone between a > sharped note and the note above was narrower than the proper > semitone (solmized fa-mi) between a flatted note and the note below, > or between F and E or C and B. The expression of such views by Renaissance theorists is very interesting, and I'd love to learn more about this. What you describe is a very apt summary of Marchettus, who indeed advocates the use of an extra-narrow cadential semitone or "diesis" in certain directed vertical progressions from an unstable to a stable interval by stepwise contrary motion (specifically M3-5, M6-8, or M10-12). In his fivefold division of the tone -- with at least one passage suggesting to both Jan Herlinger and me that he may have meant a division into five _equal_ dieses -- a usual mi-fa semitone such as E-F or B-C is "two parts" of the tone, possibly 2/5-tone, and the usual apotome (e.g. Bb-B, or German B-H) "three parts," possibly 3/5-tone. In contrast, a cadential diesis such as G#-A is only "one part" of the tone, possibly 1/5-tone, or about half the size of a usual semitone step. The complementary "chroma" or "chromatic semitone," e.g. G-G#, is thus equal to the remaining "four parts," possibly 4/5-tone. Note that Marchettus is addressing vocalists, who could made small adjustments to achieve these different step sizes while maintaining or closely approximating the pure Pythagorean ratios which Marchettus makes part of his system (2:1 octave, 3:2 fifth, 4:3 fourth, 9:8 whole-tone). In a keyboard tuning system, one must make some compromises one way or another -- this is not a theoretical flaw, only a limitation of modelling vocal intonation on a fixed-pitch instrument. One moot question may be whether Marchettus, in advocating his extra-narrow diesis specifically for progressions with _ascending_ semitones involving _musica ficta_ (mi-signs or sharps outside the Guidonian gamut of the diatonic notes plus Bb), may in part be reflecting notational concerns. He advocates a distinction between the usual "square-B" sign (like a modern natural sign) showing a note below a normal semitone step such as B-C, and a special diesis sign (somewhat like a modern sharp) showing at once a semitone alteration and his special division of the tone into _chroma_ and diesis (e.g. G-G#-A). In usual practice, both types of signs are often used interchangeably as "mi-signs" showing a note below a semitone. Marchettus proposes that the diesis sign be reserved specifically to show his special chroma/diesis division. Thus his system permits a notated distinction between regular semitones and special cadential ones using signs already familiar. To show a similar chroma/diesis division for _descending_ semitones, he would have had to invent a new kind of "fa-sign" in addition to the established "round-B" sign (the source of the modern flat). Of course, one could reply, "If he wanted his special semitones in cadences with descending semitonal inflections (e.g. Eb-D), or in such progressions within the regular or _musica recta_ gamut, he could have invented appropriate signs, or at least described such a practice." The Berkeley Manuscript or Paris Anonymous of around 1375 -- part of it dated to that year -- includes one treatise advocating that singers intone a usual mi-fa semitone as 2/3-tone, but a cadential semitone as 1/3-tone. Oliver Ellsworth has interpreted this statement, directly addressing only the finding of semitones for singers, not polyphony or vertical intervals, as suggesting 19-tone equal temperament (19-tET), the system used and described about two centuries later by Costeley (1570).[5] However one interprets these 14th-century statements and systems -- another topic -- they do suggest a distinction for some musicians between cadential and other semitones. Here I should emphasize that I use "cadential" (from _cadentia_) in the medieval sense of Jacobus of Liege: a progression from a more tense or unstable interval to a stable one, not necessarily limited to the end of a phrase or the like. While accentuated cadential progressions with narrower-than-usual semitones seem to me a not-unlikely practice in various eras and places, I'm not sure about any consistent tendency to make ascending cadential semitones narrower than descending ones. For theorists such as Prosdocimus and Ugolino in the earlier 15th century, these semitones should be the same size in either direction, and I have heard reports that performers may tend to narrow certain semitones in _either_ direction (e.g. either C#-D or Eb-D). ----- Notes ----- 1. Mark Lindley, _Lute, viols, and temperaments_ (Cambridge University Press, Cambridge, 1984), for example pp. 52-55 on Milan. 2. Mark Lindley, "Fifteenth-Century Evidence for Meantone Temperament," _Proceedings of the Royal Musical Association_ 102 (1976), 37-51. 3. Thomas Morley, _A Plain & Easy Introduction to Practical Music_, Alec Harman, ed., 2nd ed. (W. W. Norton, 1973), p. 103. 4. See Marchettus of Padua, _The Lucidarium of Marchetto of Padua_, Jan W. Herlinger, ed. (University of Chicago Press, 1985); and Jan W. Herlinger, "Marchetto's Division of the Whole Tone," _Journal of the American Musicological Society_ 34 (1981), pp. 193-216. 5. Oliver B. Ellsworth, "A Fourteenth-Century Proposal for Equal Temperament," _Viator_ 5 (1974), pp. 445-453. For Costeley's tuning, see Kenneth J. Levy, "Costeley's Chromatic Chanson," _Annales Musicologues: Moyen-Age et Renaissance_, Tome III (1955), pp. 213-261. Most respectfully, Margo Schulter From: "M. Schulter" <http://groups.yahoo.com/group/tuning/post?protectID=17410722201706608914313 3102248163237053159035046044127169> Date: Tue May 30, 2000 11:44 pm Subject: Re: TD 656: New keyboard technologies and tuning arrays ADVERTISEMENT Hello, there, and in Tuning Digest 656, Arthur W. Green wrote: > While, I will try not step into this realm of unattractive cynicism > for now, it is clear to me that whether or not Mr. Duringer's > invention enables more sophisticated solo performance may be > negligible at this time. The public will probably never view this > invention as anything more than an oddity, as it is an unwaivering > belief at the moment by the public that the synthesizer does not > require the same kind of skill, prowess and stellar musicianship > that a "real instrument played by a real musician does". Until this > changes, I am not sure what can be said, since it seems to me the > "problem" with electronic instruments isn't the instruments > themselves. Here I'm tempted to reply that in a medieval or Renaissance European perspective, all instruments other than the human voice (the ideal) are "artificial instruments" of different kinds. In the 16th century, polyphonic instruments such as keyboards are also known as "perfect instruments" -- that is, instruments capable in themselves of supplying a "perfect" (or complete) harmony of three or more voices and intervals at the same time. Interestingly, in 1565, Tomas de Santa Maria's treatise on the art of composition or improvisation for such instruments was written for "keyboards, vihuela, harp, and other instruments capable of playing three, four, or more voices." >From this perspective, a polyphonic electronic synthesizer is simply another form of "perfect instrument." I tend to consider it a variant on an organ or harpsichord. Generally, playing medieval and Renaissance music on such an instrument calls for the same kinds of musical decisions as using an acoustical organ or harpsichord. For example, I ask myself, "Does this sixth want to be made major before an octave -- and, if so, should I use Eb or C#?" Whether one is playing on a period instrument or a microtunable synthesizer, the answer might be different from performance to performance, and depends on the performer. This is also true for a more specialized question of the kind especially appropriate for this Tuning List: "For this early 15th-century piece, should I play this interval in a 15-note Pythagorean tuning as A-C# or A-Db?" While Ugolino of Orvieto tells us that an "intelligent organist" can use a 17-note keyboard to realize cadences more aptly, how one would use such a keyboard in the stylistic ambience of this epoch remains an open question. It's an area for imagination and the artist's taste. What microtunable synthesizer technology does is to provide a more accessible basis for such artistic judgment. [On tunings with multiple manuals or "ranks" of keys] > It would be nice perhaps to be able to figure out some "reliable" > way to implement it in respect to each tuning by rank in respect to > an adjacent ranks' tunings, rather then merely taking potshots in > the manual mapping of the tuning of each rank in the synthesizer or > the controller instrument. Perhaps, then it would seem so much less > arbitrary in nature. At the risk of being labelled a "7+5 chauvinist," I might suggest that the topic of such keyboard designs also may have it's "x/y" parameters. In the y-dimension, we have "generalizability," the idea that each keyboard has the same intervals in the same arrangement. In the x-dimension, we have "familiarity" -- or, more specifically, familiarity for people used to a 12-note keyboard, and more particularly yet one in the 7+5 arrangement which apparently came into vogue sometime around the early to middle 14th century. A "Xeno-Gothic" 24-note archicembalo with two identical Pythagorean keyboards a Pythagorean comma apart, and likewise a 24-note meantone archicembalo with two identical keyboards in 1/4-comma meantone a diesis apart (128:125, or more generically a "fifthtone"), maximize both advantages. Each keyboard in itself is ideally familiar -- especially to those of us used to Pythagorean or meantone tunings in something like Eb-G# -- and the relationship between the two keyboards is consistent and easy to grasp (at least for me). Thus if we want both generalizability (symmetry between keyboards) and familiarity (a familiar layout for each keyboard), then a "12 x 2" array or 24 notes in all would seem an attractive choice. >From some people, of course, circularity is an important consideration calling for larger arrays of notes: 53 for Pythagorean, or 31 for 1/4-comma meantone (real mathematical purists might insist on 31-tet or 53-tet, evening out some variations in more remote intervals which make a simple Pythagorean 53 or 1/4-comma meantone 31 actually a kind of subtly unequal "well-temperament"). For the meantone situation, both historical precedent and certain recent reports on this Tuning List about patent proposals lead me to suspect that two 19-note keyboards might be a logical choice. Of course, there would be two obvious applications for two such keyboards tuned in unison: either a 19-tet system of the kind proposed by Guillaume Costeley in 1570 (and endorsed in the 20th century by such theorists as Joseph Yasser), or a 19-note set of 1/4-comma meantone (or 31-tet if you prefer). However, we could additionally use these keyboards to implement a 31-note meantone tuning. For a circulating 31-note meantone with completely generalized keyboards (and a bit of redundancy), we can use the 19 notes of the first manual plus 12 of the second, with the others replicating some notes on the first manual, but maintaining the consistent layout: Db* Eb* Gb* Ab* Bb* Db Eb F Gb Ab Bb C C* D* E* F* G* A* B* C* -------------------------------------------------------------------- Db Eb E# Gb Ab Bb B# C# D# F# G# A# C D E F G A B C Note that in this tuning, both keyboards have an identical pattern: major and minor semitones (about 3/5-tone and 2/5-tone respectively in meantone 31) appear in the same places on either keyboard, and corresponding notes on the two keyboards are always a diesis or fifthtone apart. Here I envision split keys on each keyboard for dividing the whole-tones, e.g. C#/Db, with the front portion of the key giving C# and the back Db (or whatever the user chooses to program, of course), and a single small key between E and F or B and C. > With the flexibility of MIDI and modern synthesizers, and of course > the assignment of X/Y 'matrices' on the instrument itself, it seems > to me that any sort of scheme can be left up the "performer". I > rather like this idea, despite its lack of any sort available > standard that I can recall. This is a very important point, and one of the advantages of a synthesizer: the hardware can permit many types of "software" settings, with the performer free to choose between them. > I will definitely agree that it is certainly not the first time this > concept has been seen in practice. But, I do think with the level of > technology we have today with electronic instruments, perhaps it > might be wise to try this concept yet again, as I think it might be > more promising this time around. Certainly it should be more easily accessible. Now, as then, overcoming psychological as well as technical barriers may be important. We are told that many keyboardists of the late 16th century were "frightened" by the multitude of keys on Vicentino's instrument, and also can read the views of a theorist such as Vincenzo Galilei who argued that intervals such as dieses or fifthtones were "ill-proportioned" to the nature of the human ear! One minor but not insignificant point might be the ergonomics of a keyboard array. Using two 12-note controllers, I find that my main problem can be in moving quickly from one manual to the other, especially when using an organ-like sound and striving for legato. The keyboards have to be at least around 3" apart vertically, a bit more than the depth of each keyboard, and this is a bit of a "jump" for my hands. I use a shelf permitting the upper manual to slide forward so that it overlaps the lower one, a partial solution, but hardly an ideal or comprehensive one. Maybe a design deliberately combining two 12-note or 19-note keyboards into a single package could emphasize making it easy to shift between the keyboards, and also to play notes on different keyboards with the fingers of one hand (something which a 16th-century observer remarks is often called for on Vicentino's instrument). Most appreciatively, Margo Schulter | | > Ladies and gentlemen,=20 | >0 | I ask your indulgence in reviewing this message that I have forwarded to = | the Lute List. The question comes from the Harp List, and my response = | has been sent. I'd like to know if I've made any gross errors (the = | object was to answer in principle, not in detail). Do remember that = | accomplished musicians on intruments that have fixed temperament may not = | have knowledge of temperament.=20 | | I solicit your comments,=20 | > | > I did see a letter a bit ago on the Lute List on electronic tuning, and = | > it made me wonder if the electronic tuner used equal temperament. Been = | > planning to repair my occilliscope and look at the freqencies, but I = | > think is a good assumption that the electronic tuner uses equal = | > temperament.=20 | > | > | > Best, Jon | > | > ----- Original Message -----=20 | > From: Catherine Hicks=20 | > To: [EMAIL PROTECTED] | > Sent: Thursday, January 29, 2004 4:12 PM | > Subject: Equal Temperament | > | > | > | > Dear Jon,=20 | > | > Hello, my name is Catherine and I am a harp student (just beginning!) = | > of Eala Clarke's. She said that you would be willing to maybe answer = | > some of my questions? | > My music theory isn't the grandest and this may be rather confusing, I = | > hope you can get at what I'm asking. I play piano as well as harp, and I = | > was reading a book on pianos, their construction and philosophy and = | > history, and it described the methods of tuning that they used. Equal = | > temperament, they called it, saying that the intervals are not tuned to = | > the same pitches all the way up the piano because it would then end up = | > sharp. So they divide the octave up into twelve tones and tune with = | > that. Then a friend of mine asked me if my harp was tuned in equal = | > temperament, like a piano. I use an electronic tuner and just tune it to = | > that. | > So what exactly is equal temperament? Would it not be true for other = | > instruments as well? Are electronic tuners based on that system? | > | > Thank you very much! | > | > | > Catherine Hicks | > ~ In Corde Mariae | > | > [EMAIL PROTECTED] | | |
