Talk:Archicembalo

Spelling
Both arcicembalo and archicembalo is in use, but as far as I can make out the latter is more correct. Gene Ward Smith 08:18, 20 November 2005 (UTC)


 * I believe that arcicembalo was Vicentino's own spelling, but archi- is the standard anglicization. The New Grove has it under arci- which is why i spelled it that way in the Vicentino article.  I'll fix any redirects.  Thanks for starting this article!  I've had a note to myself on my to-do list to make a drawing of the keyboard for a while now ... maybe I'll add it to the article soon.  Antandrus  (talk) 15:55, 20 November 2005 (UTC)


 * Archicembalo is definitely preffered in English writings. I suppose the difference came out as a clarification of its pronounciation. It might not have worked out though... shouldn't "arcicembalo" in Italian sound as "ar-chee-chem-ba-lo"? Everyone I've ever heard say it says "ar-kee-chem-ba-lo" though. Archipelago is another word that comes to mind... Rainwarrior 23:18, 31 March 2006 (UTC)


 * Either the given English spelling, or the pronunciation, or both, don't make sense. The Vicentino spelling in Italian gives the pronunciation /tʃ/ not /k/. If one wishes to anglicize then "archicembalo" is fine, but should be pronounced like "archbishop" or "archfiend" (same as the Italian). The pronunciation "arkicembalo" makes no sense in Italian. "Archipelago" is not really analogous since it is a fully naturalized English word, whereas arc(h)icembalo is a specialized technical term loaned from Italian. As such there is no good reason to anglicize the spelling unless it is to preserve the Italian pronunciation! If the word is spelt "arci-" as in Italian then /tʃ/ is undoubtedly correct (and one should also use italics). I would vote for at least giving two alternative pronunciations. --Tdent 10:57, 26 April 2006 (UTC)


 * I asked around a bit, and it seems that a lot of North American musicologists say "ar-kee-chem-ba-lo". I agree that it doesn't make sense given the Italian root of the word, but it's still the pronounciation one is most likely (in my opinion) to encounter from an English speaker. I don't know the etymology, but it's reasonable to speculate that this word might have been in the English language, albeit in a "specialist" repertoire, for a couple hundred years, which can certainly account for the pronunciation shift. (The confusion might stem from the similarity of certain Greek-rooted words such as architect, and archaic.)
 * Would you mind if I changed "the English spelling might also be taken to denote [arkiˈtʃɛmbalo] as in archipelago." to read "though by English speakers it is more frequently pronounced [arkiˈtʃɛmbalo], as in arcipelago." Or does your experience with the spoken term differ from my own? Rainwarrior 02:14, 27 April 2006 (UTC)


 * I have no direct experience: 'asking around' yields contradictory responses. Whatever North American musicologists say now, I think the article ought to contain the original Italian spelling and pronunciation (so far as it can be determined). The question of when it started to be used in English is an interesting one - I would guess, about the time people started doing Renaissance musicology, i.e. 1900. --Tdent 11:46, 27 April 2006 (UTC)


 * Well, it's not worth changing solely based on my personal experience, of course. Perhaps a concensus may be gathered... has anyone else ever used "archicembalo" in conversation? Rainwarrior 00:07, 28 April 2006 (UTC)

Vicentino named his instrument the arcicembalo (pronounced [artʃiˈtʃɛmbalo]), but in English texts it is more often spelt archicembalo (play /ɑrkiˈtʃɛmbəloʊ/), possibly confused with similarly spelled words having Greek origin, such as architect.

This is not true. Vicentino spelled his instrument only as 'archicembalo', most likely having in mind the Greek ἀρχι- ("major", "senior") and not Ital. archi ("strings") at all (compare his 'archiorgano', what has the pipe organ with strings to do?) For authentic usage of Vicentino see (folio numbers are given by the facsimile of his treatise issued by Lowinsky), e.g. and many other entries. New Grove also gives archicembalo. Also, I have no idea, where 'arcicembalo' comes from (sources would be appreciated). Olorulus (talk) 06:03, 14 October 2012 (UTC)
 * f.11v: il nostro instrumento, detto Archicembalo,
 * f.16v: nel trattato del quinto libro sopra lo stormento, da me detto Archicembalo
 * f.17v: come è l'Archicembalo nostro

Tuning
I'm not sure it's correct to say that the Archicembalo tuned 31 equal divisions of the octave. The accounts I have read suggest that for the most part it would have been tuned to an adapted form of Meantone temperament. Does anyone have a source for this assertion? (In my hands I have a copy of Henry Kaufmann's article from the Journal of the American Musicological Society, vol. 23, 1970, entitled "More on the Tuning of the Archicembalo" which certainly doesn't suggest an equal temperament at all.) Rainwarrior 23:18, 31 March 2006 (UTC)


 * I would say 31-equal is an adapted form of meantone temperament. If you tuned it to quarter-comma meantone, the pitches separated by 31 fifths would be very close, almost indistinguishable, so the distinction is mostly academic. —Keenan Pepper 23:38, 31 March 2006 (UTC)


 * That's an interesting point. I do think the theoretical distinction is important, though, even if the practical one isn't. Rainwarrior 00:05, 1 April 2006 (UTC)


 * The link  says Huygens described the traditional meantone tuning, in good approximation, by a selection from 31-ET. Haberg (talk) 22:27, 4 May 2008 (UTC)

Hah! Now it's pretty confusing as to why there might be five "near-duplicates" in something that's almost an EDO tuning. I'll do some reading and try and make this a bit more explanatory later. Rainwarrior 00:34, 1 April 2006 (UTC)


 * Okay, hopefully that's a good start on the article. Rainwarrior 20:51, 1 April 2006 (UTC)


 * The link  says the reason is to provide some provide pure fifths (rational interval 3/2) - in 31-ET, those are 5.18 cents off. If those are excluded (approximating 31-ET keys 5, 10, 18, 23 and 28), and the cent values in the article are correct, the others are 31-ET within 3.3 cents. Haberg (talk) 22:27, 4 May 2008 (UTC)


 * I've just added a new para saying that Huygens recognized that extended quartercomma meantone almost exactly approximates 31-et and that he says he came up with the idea independently but knew of an earlier cite by Salinas reporting on the Archicembalo. That doesn't prove that Vincento himself thought of it as 31-et of course. Have just presented it "as is" in the source I found. I think it's good to make clear what was understood historically by the authors we mention and what we now know in hindsight was the case. Anyway with 31-et it goes back to before 1661 at least. I'm not sure what date the Salinas reference is, someone might be interested to follow that up. Robert Walker (talk) 10:19, 14 July 2016 (UTC)


 * That would have to be the seventh book of Salinas's De musica, published 1577. Whether Salinas actually describes 31-equal temperament is another question, though. As you say, interpretation in hindsight is a different thing from the source actually stating something. This will require some further investigation.—Jerome Kohl (talk) 21:06, 14 July 2016 (UTC)


 * Okay thanks! I'll be interested to hear what anyone finds out. Have added this page to my watch list. Robert Walker (talk) 22:14, 14 July 2016 (UTC)


 * It looks like that ought to be book 3 rather than book 7, but a preliminary scan of the Latin text at the Thesaurus Musicarum Latinarum does not turn up any mention of Vicen[tino], archi[cembalo], or the numeral "31". The Fokker Foundation site insists that Salinas does discuss Vicentino specifically, so maybe I am just not finding the right keywords. Also according to that site, Salinas sought to simplify Vicentino's 31-note scale (NB: there is no mention of 31-equal tuning, just a scale with 31 notes in the octave) to a keyboard with just 19 keys to the octave.—Jerome Kohl (talk) 22:45, 14 July 2016 (UTC)


 * Oh, interesting. Sorry about the Vicentino / Vicento - I think I'm slightly dislexic, often do things like that. Fixed it in the article now. Just found this article, the author Karol Berger is rather skeptical of the idea that Vincentino intended 31 equal, he thinks from remarks he makes about his tuning that the major thirds were smaller than pure by an amount comparable to the amount by which the 5ths were tempered because Vicentino says that if you combine the back keyboard's slightly higher E with the front keyboard's slightly lower C you get a purer third, concluding his discussion there "This degree of variety among the 5ths and 3rds would not deprive the tuning of its euphony, but it would render Vicentino's thirty-one dieses somewhat unequal: Chromatic systems (or non-systems) from Vicentino to Monteverdi - that's from 1980 - so - a lot could have happened in the understanding of this in the last 35 years, but back then anyway we can see that at least one theorist thought it was unlikely that Vicentino himself thought of his tuning as being in 31 equal.


 * It might be interesting to have something on this. Of course Salinas might still have thought it was 31 equal, indeed even Vicentino might have thought it was in 31 equal, people sometimes think contradictory things that they don't know are contradictory. That's a matter for more research, meanwhile not quite sure what to do about the article itself, what we have so far is that Huygens thought that Sallinas thought that Vicentino's tuning was 31-et. From which also I think it's also likely that Huygens himself thought that Vicentino's tuning was 31 et. But we don't know what Salinas or Vicentino themselves thought yet. Robert Walker (talk) 23:23, 14 July 2016 (UTC)


 * For now I've just added an extra para:


 * "Vicentino's description of his first tuning, has some puzzling statements if it is understood as 31 equal. He says that the major third from C to E is made closer to pure if it uses the slightly lower pitched C on the front keyboard with the slightly higher pitched E from the back keyboard. This is puzzling because in pure 31 equal all the major thirds should have been almost exactly pure already. Karol Berger's analysis of this suggests that he may actually have used a somewhat unequal tuning for his extended meantone system, varying perhaps from 0.2 comma smaller than pure to 1/3 comma larger than pure."


 * Robert Walker (talk) 23:41, 14 July 2016 (UTC)


 * So far as I remember from reading these authors in a previous life (say, 25 years ago), Huygens didn't know about Vicentino; Salinas neither, but he did know of an Italian harpsichord with 31 notes in the octave. Vicentino's tuning indications are far from clear. His first tuning may be a 1/4-comma meantone extended to 31 notes. The second tuning has the two keyboards some interval apart, but the interval may not have beem 1/4 comma as stated in the article.
 * In any case, Vicentino's purpose does not appear to have been "modulation to a wide range of keys", because that made no sense in the 16th century, when pitch standards were not fixed. 12-note meantone allows playing in C, D, F, G, A and B♭ [major], keys at most a minor third apart. 17-note meantone (all black keys split in two) allows the keys of C, D♭, D, E♭, E, F, G, A♭, A, B♭ and B, all keys a semitone apart, but all with exactly the same interval. (One may remind that the main argument against ET in the 18th century was that it would make all keys sound the same: this is true of any meantone temperament.) Even today, the possibility to play a fraction of a semitone higher or lower than these would serve no purpose at all.
 * To the extent that the Archicembalo may have played in just intonation, the purpose might have been to extend this possibility; but extended just intonation does not lead to a wider range of keys, only to a wider range of chords (within the same keys), with the inconvenience of shifts in pitch that were condemned in Vicentino's time (see the well known correspondence between Benedetti and Rore).
 * Vicentino's purpose appears to have been the playing of microtones, namely 1/2 chromatic semitones ("quarter tones"?) and 1/3 diatonic ones – his 31 division indeed consisted in that the tone is divided in 5 equal parts ("dieses"), 2 for the chromatic semitone and 3 for the diatonic one. The problem that remains is the precise definition of the tone, which may not have been exactly 5/31 of the octave. (Similarly, in my Conservatoire years, I did learn that the tone consisted in 9 "commas", but I was never told that the octave amounted to 53 [or 55] such commas.)
 * Hucbald.SaintAmand (talk) 20:49, 15 July 2016 (UTC)


 * Yes I think you are right that his aim wasn't particularly to explore a wider range of keys, but rather to explore microtonal shifts of pitch. I just found a page that goes into his compositional technique in detail. Here: Wild, Vicentino’s 31-tone Compositional Theory Haven't read it just skimmed through, but it says that he was aware that it was a circulating system of 31 keys, saying that it's “the foremost and perfect instrument, in that none of the keys lacks any consonances” so he did know that you can play in any of the 31 keys, but that wasn't his objective from his compositions.


 * Note though that though he, and Zarlino also. were using unequal systems (unequal 19 note keyboard based on 2/7 comma in case of Zarlino), according to Mark Lindlay, some of their contemporaries used equal systems. This is for a 19 tone keyboard which becomes almost exactly equal temperament tuned to extended 1/3 comma meantone. He says that Costely (1570) and Salinas (1577) as well as Praetorius in 1619 describe keyboards of similar design tuned with an equal spacing between the keys. I've actually written up a short answer on quora summarizing some of the things I've found out in the process of these conversations with you here + talking about the ideas off wiki with my microtonal friends / colleagues here: My answer to "To be totally unconventional, should a piano with keys of E# and B# be produced? Would it be more versatile and more interesting?" might interest you.


 * As for changing key - well you could say that changing key in 12 equal also serves no purpose at all as the music is in the same relative pitches, but you have the relationships between the keys which drives the music,rather than the absolute pitch of the keys (apart from things like instruments having different ranges and apart from people with absolute pitch of course). Actually I find microtonal shifts of pitch rather intriguing at times, can be as striking as larger changes, e.g. if you have a whole chord shift up or down by a microtone in some way that makes musical sense. Or indeed sometimes just an individual note, shift just by some perceptible comma, but that tiny comma shift in context can be a striking moment in the piece. I do that from time to time in my own short compositions, I'm an amateur composer and do short compositions, not elaborate long pieces, to try out ideas. And that is something that Vicentino did do, deliberate comma type shifts. Margo Schulter wrote about that in a message to the tuning group years ago and I remember the context that either she had shared one of her own compositions that used the technique or one of Vicentino's I can't remember now. But I do remember it was very striking. I have the quote from her here: Adaptive puzzle "This can be startling to listeners in the 16th century or 21st century, definitely "xenharmonic," and something that got Vicentino very mixed reviews.".  :) Robert Walker (talk) 00:38, 16 July 2016 (UTC)

Robert, you write:
 * ... changing key in 12 equal also serves no purpose at all as the music is in the same relative pitches, but you have the relationships between the keys which drives the music ...

No, the situation today is quite different for several reasons.

The first is that, even without having absolute pitch, we do expect keys to sound at specific pitches, and they usually do because modern musicians usually play at a more or less stable pitch, A4=440Hz. It goes so far that "Baroque" musicians of the second half of the 20th century invented another pitch standard, A4=415Hz (an exact tempered semitone below 440Hz), that would mark their music as different. Musicians in the time of Vicentino could not have thought in this way because the key in which a piece was written by no means indicated its pitch: the key was dictated mainly by the constraints of notation and the resulting pitch depended on the instrument(s) used. What would be the point to write a piece of music, say, a quarter tone higher than another, when the played pitch could vary from occasion to occasion by way more than that? As a matter of fact, in Vicentino's time, transposed keys hardly were used. Keyboardists often were unable to transpose, but for the transposition involving a signature of one flat which at times was required by the constraints of notation. (On the constraints of notation, see for instance this article [in French]).

The second reason is that circulating through keys is quite foreign to the music of the 16th century. Modes did not differ from each other by their pitch level, only by their internal organization. The idea of "modulating" from one mode to another was totally unknown by then. The chord shifts that you describe happen within a given piece, and this may well be what Vicentino tried to do, but his contemporaries probably hardly understood it. Add to this the difficulty of playing the instrument (a difficulty lessened today by the use of electronic devices), and the reasons of Vicentino's lack of success become evident.

Hucbald.SaintAmand (talk) 08:09, 16 July 2016 (UTC)


 * Oh sorry, I thought you were talking more generally rather than in terms of the music practice of the day. Yes, see Margo Schulter's: When did modal music give way to the modern key system? - she talks about "modal fluidity", sounds like that's the most we can expect of Vicentino. So I suppose his chord shifts are an example of that. Though they did have the concept of a key, just not the idea of modulating between keys, and he does say that it's the  “the foremost and perfect instrument, in that none of the keys lacks any consonances” . So he saw the ability to play in any key as a perfection of his instrument. But that of course doesn't mean that he played in them, except perhaps experimentally to check that none of them lack any consonances. I wonder why he saw that as a perfection, given that it is unlikely he or anyone else would ever play in most of them? Maybe the answer is that he was on the cusp of a change of thinking towards modulation, but had not yet articulated it fully, was aware of the ability to play in any key as somehow an advantage of his instrument, but not sure how to take advantage of that ability or what it was good for? What do you think? And maybe his sudden chord shifts were a first stage of awakening towards that possibility? And it could possibly have moved him in a different direction, e.g. the modulation in maqams where the idea is not transposition, but rather, changing to a different system with different relationships between the notes and different expectations for melodic movement. Perhaps he was at some kind of a fork in musical history where it was possible to go many different directions, but later generations ended up going in the direction of modern key modulation which is usually based on ideas of transposition of the key structure keeping all the interval and chord relationships intact, except mainly for the variation of major and minor. I agree that it's not surprising that his music challenged his contemporaries. I think it's interesting because of the fluidity, that at the time, nobody knew where this was all going, and you can invent alternative histories from then on that could have taken modern Western music in totally different directions such as something more like maqams, or maybe other ideas we just don't have anywhere at present.


 * I think that somewhere wikipedia should say something about Vincentino's compositional approach. As there's quite a lot written about it out there and we also have surviving compositions by him, and if it did, then it should of course stress this fluidity and make it clear that he wasn't aiming for transposition of keys in the modern sense with his 36 notes per octave keyboard, but he was exploring a kind of modal fluidity that went way beyond what his contemporaries were doing and which challenged their ears and indeed can even challenge modern ears too. I don't know how to summarize all this but I think a short para in this article on the topic would be useful. It could be based on a summary of Wild, Vicentino’s 31-tone Compositional Theory, which is surely WP:RS, peer reviewed academic journal. The reader is bound to ask, "Why did Vicentino want so many keys to an octave". It would be interesting to have a summary of his own reasons for exploring it, and what he did with it, in his compositions. Robert Walker (talk) 09:06, 16 July 2016 (UTC)


 * Robert, when Vicentino wrote that "none of the keys lacks any consonances", he did not mean keys as tonalities, he merely refered to the keys of the keyboard: in ogni tasto no[n] li manca consonanza alcuna (p. 99 of the 1555 original). It is not even sure that Vicentino understood "consonances" as we do. Indeed Bermudo, in his Declaraciòn de instrumentos musicales of the same year, alludes to the fact that his own "perfect instrument" (unfortunately to be described in the 6th Book that was never published) had all six "voices" (bozes) on each key of the keyboard; the six voices probably were the notes of the hexachord: therefore the intervals available on all keys were the tone, the major 3d, the 4th, the 5th and the major 6th – these had been described in the Middle Ages, notably by Guido of Arezzo, as the ... consonances!
 * Margo Schulter unfortunately does not clearly define what she understands by mode and key system (nor, for that matter, by "modal fluidity"). Her mistake (a very common one) is to think that modality was replaced by ("gave way to") tonality, while modality more probably evolved towards, and gradually became tonality. This is a highly complex matter, which I won't discuss further because I would soon have to turn to the argument of authority, which I want to avoid here (in short, I directed several recent PhDs on this topic).
 * As to "modulation in maqams", I suggest that you read the page devoted to ajnas in the same website. The theory of moving through ajnas is today part of the doctrine taught in Oriental conservatoires, and Oriental musicians are used to perform in this way, but I doubt that it belongs to history. It is quite unlikely that Vicentino could have considered modes as formed of two tetrachords, as Oriental musicians view maqam today, and he could have moved from one tetrachord to another only in the sense that he may have passed from diatonic to chromatic or enharmonic.
 * You are right that the direction music eventually took is one among many, and that other directions may have been tried with less success. I'd like to know where Schulter got her idea of "modal fluidity": I can figure out what she may mean by this, but I would certainly not call it "fluidity" because similar terms have been used in tonal theory (see for instance the word "fluency", translating fließend, in Schenkerian analysis).
 * I'll reread Wild's paper in MTO – and Vicentino himself – but I am afraid we may never know what the guy really had in mind... Hucbald.SaintAmand (talk) 14:12, 16 July 2016 (UTC)


 * First, on the comparison with maqams, I didn't mean an exact one as in use of tetrachords. And the Arabic maqams are much more than a combination of tetrachords as I understand it from the way it's been described to me. I was just saying there that as in his day they didn't have the idea of changing key in our sense, could he have evolved some idea of changing to a different tuning in the same key or close to it, rather like the maqams, but not using tetrachords necessarily, just that general idea, like changing from major to minor but more variations on that, above the same tonic. Since he did do lots of microtonal shifts of notes, in his compositions, then you have to say he was moving out of the comfort zone of his contemporaries, and if not in the direction of modulation - where else was he going? So I was suggesting, if it's this "modal fluidity" maybe it was more of a direction something like the maqams in the sense of more variations than just major and minor including microtonal changes of pitch of the notes. Of course we can't know where it "would have lead" as his work was a bit of a dead end with nobody else taking it further. I can understand it is an intricate debate whether modality evolved into tonality or it was replaced by it. Might it not depend on your perspective and what you pay attention to? For instance if Vicentino is thought of as irrelevant to the history here, you can just find a straight line progression, while if you take account of him then he surely is exploring "modal fluidity" in a direction that is not on a straight line progression from modality to modulation. So, could it be that the more experimental modal work was just replaced while maybe you can say that other lines of research at the time evolved? That way both views could be just looking at the same material wearing different "spectacles" as it were. So both were happening at once in that case. As for the word, well is there any chance of confusion of modal fluidity with melodic fluency? The phrase made immediate sense to me as a phrase, seems some word is needed for whatever Vincentino and his contemporaries were doing. If it is not tonality and modulation, what do you call it? Modal fluidity seems like a good phrase for it to me.


 * I'm sorry, I don't understand, how could Vicentino have been referring to the keys as in individual notes, when talking about the consonance of his perfect instrument? For consonance you need two notes, not just one, e.g. to compare fourths, fifths, major and minor thirds based on different keys. So his "keys" there - how can it possibly mean individual notes? Wild gives that quote as a reason for saying that Vicentino thought of it as a circulating system in Wild, Vicentino’s 31-tone Compositional Theory so I was just repeating what he said and his interpretation of the quote. Robert Walker (talk) 04:21, 17 July 2016 (UTC)


 * On authority - I know you are an academic and expert in the topic area, is obvious from the way you write about it. But I also know that academics have views and often don't agree at all with each other. Sometimes you get big battles between academics who are expert in a topic area. And often you get a wide spectrum of academic views on a particular topic. So you can't accept the views of any particular academic as truth by authority. Rather when academics or professors, or other experts speak on a topic, I regard it as one academically respectable view on the subject. Also - when they talk about the views of other specialists, again, that's something too where their particular perspective is almost bound to colour what they say to some extent, not always, but often does. It just comes with the territory as it were. So when I challenge or question things that you say, I'm not questioning your authority in this topic area in any way. It's just recognizing you as one of probably many authorities who may have different views on these various topics. And so it is no surprise if sometimes I turn up articles that express different views on the topic. Indeed would be astonished if eveyone thought exactly the same way as you on everything here! :) 04:29, 17 July 2016 (UTC)


 * At the risk of incorrectly anticipating Hucbald's response to the question of "key", his point is that Vicentino uses the Italian word tasto, which means "key" only in the sense of one of those wooden things forming part of a keyboard. You seem to be assuming the sense of tonalità or, as I believe Vicentino would have said in 16th-century Italian, tuono. It may seem impossible that a single "key"/lever on a harpisichord could be anything but "consonant", unless you consider Bermudo's remark about tuning other notes above a particular reference tone. Then all becomes clear, I think.—Jerome Kohl (talk) 07:03, 17 July 2016 (UTC)


 * Robert, and Jerome, it is even more difficult than that. What Bermudo says, in 1555, is this: "in my [perfect] organ all semitones can be played and each white and black key possesses all six voices" (...mi organo: enel qual se tañen todos los semitonos, y cada vna delas teclas blancas y negras tiene todas seys bozes..., Declaraciòn, vol. 13 v°). "Playable" semitones are diatonic semitones: Bermudo means that on his keyboard there are diatonic semitones everywhere. There is little doubt that the bozes are the solmization syllables, because there is a long (medieval) tradition of calling them voces in Latin. But to "possess" all six syllables may mean either to have them above the key, or to have notes that allow each key to be called any of the six syllables, ut re mi fa sol la. Take the C key: if it is ut, then the keyboard has C D E F G A; if it is re, the keyboard has B♭ C D E♭ F G; mi, A♭ B♭ C D♭ E F; fa, G A B C D E; sol, F G A B♭ C D; and la, E♭ F G A♭ B♭ C. That is that if C has the six syllables, the keyboard has notes for C, D♭, D, E♭, E, F, G, A♭, A, B♭ and B. Repeat the same reasoning for the twelve note of the chromatic scale, and you would come to an overall scale of 17 notes in the octave (including 5 flats and 5 sharps). There is a flaw in the reasoning, however, because if the keyboard has 17 keys, not 12, then the same reasoning should be applied to the additional keys as well, producing new keys, to which... etc. In short, Bermudo's keyboard (which unfortunately is not further described) must have had between 17 and an infinity of keys.
 * I can understand Robert's puzzlement at seeing a single note being called a "consonance", while a consonance (or a dissonance) obviously involves (at least) two notes. This, however, is a tradition in music theory since at least the time of my pre-incarnation Hucbald in the 9th century, and probably long before. A dissonance, to us, is a single note (dissonant with another), and the identification of this particular note makes no problem – in a 7th chord, it is the 7 that is the dissonance, not the fundamental. It is this note (and not the other) that needs a resolution, often by descending conjunct movement. In Renaissance counterpoint, the dissonance received the nice name of "patient", and the other note, that which rendered the first dissonant, was the "agent". "Consonances" (phthongos) are notes able to enter a melody, "discrete and determined by a rational quantity, apt at any melody" (rationabili discretos ac determinatos quantitate, quique melodiae apti existerent, Hucbald, Musica, GS I p. 107). This all must be kept in mind when reading Vicentino because otherwise one might reach into misunderstangings, all the more dangerous that they'd remain unnoticed.
 * Tonality is a matter of directionality. There is a pre-tonal harmony in which the direction of the harmonic progressions is almost free (it never is entirely free, though: as early as one can go back, there always existed some asymmetry). The asymmetry (e.g. between descending and ascending 5ths) may reach 90/10% and more in common practice tonality. The phenomenon apparently is due to an increase in the usage of dissonances from about 1550 to 1650 (linked to a desire of expressing emotions, e.g. in madrigals and early operas): the need to prepare and resolve the dissonances favored descending 5ths and other similar progressions. The usage of dissonances later diminished, but the asymmetry remained or even increased (without any other clear cause than an established usage). What Margo Schulter apparently means with "modal fluidity" is the relative indifference to the direction of progressions in modal music. However, fließender Gesang ("fluid, flowing song") is an important concept in 18th-century German counterpoint (including Fux, who spoke of flexibili motu), later taken over by Schenker and probably pointing at an asymmetry in the voice-leading. What I mean, in short, is that Schulter's (and your) usage of "fluidity" is too vague to be of real use: the word should at least be better defined.
 * Hucbald.SaintAmand (talk) 09:15, 17 July 2016 (UTC)

Margo Schulter's ideas of modal fluidity
Hi Hucbald, I've been having a long conversation with Margo about her ideas of modal fluidity, over the last few days. Here is a short summary of some of the main points:


 * She agrees that the 16th century compositions show relative indifference to movement by fifths. But that's because they are using intensive cadences (upper ascend by semitone, lower descend by tone) and remissive (upper voice ascend by tone, lower voice descend by semitone) intensive cadences (one voice ascends by semitone, the other descends by a tone) and remissive (one voice ascends by tone, the other voice descends by a semitone)
 * These have a strong sense of directionality once you understand the compositions in those terms, based on principles other than those of late 17th-19th century tonality. So by modal fluidity she doesn't mean lacking in directionality.
 * She makes an interesting comparision with 12 tone rows, that to talk about relative indifference to chain of fifths progressions in the 16th century is rather like talking about relative indifference to 12 tone rows in 18th to 19th century composers. She thinks they are best analysed and understood in their own terms.
 * She sees a transition from the earlier resolution to trines in the 14th century, with many dissonances resolving to the 2:3:4 sonority, to a much smoother texture in the sixteenth century with 4:5:6 sonorities throughout, but still based on intense and remissive cadences..
 * By modal fluidity she means a flexibility of accidental inflections and contrasts, and gave examples of intriguing accidental contrasts outside any one diatonic mode, following their own vertical logic:
 * "all intervals are available from all tasti" means from all intervals are available from each note on the instrument, without any implication of either "modal centers," ( Thomas Morley's "keys" in 1597) or the later major or minor key. Vicentino has a section on how to find each type of interval on the keyboard. He is saying that one is free to transpose or circulate as desired, in whatever approach one is using.
 * Circulation here doesn't necessarily mean to circulate by fifths, she says that the idea you have to circulate by fifths is an anachronism in the sixteenth century. They often used small steps such as chromatic steps, which in meantone is seven steps up, so they can move about in the gamut quickly. However they did explore n circulation by fifths as well, in Colonna's 1618 "example of circulation" cadencing on all 31 steps of the instrument (used by Colonna but he doesn't say who wrote it, could be by him, could for example be by Ascanio Mayone). The score is here LA SAMBUCA LINCEA DI FABIO COLONNA E IL TRICEMBALO DI SCIPIONE STELLA by Patrizio Barbieri on pages 194-196. I'm author of a microtonal retuning program and I plan to do a microtonal realization of his score when I get time :).
 * The result is that the modes can be transposed to any of the 31 notes in the mentone circle.
 * Vicentino's main innovation was to arrive at some extraordinary progressions with intensive or remissive cadances with one or the other part of the cadence raised by a fifth tone, whicn leads to many new intervals and sonorities.

She has an article on these diesis jumps here: An archicembalo in 24-note meantone: Renaissance fifthtone music on two 12-note keyboards Strictly speaking a diesis shift up is equivalent to 12 meantone fifths down, but she finds it better to treat the diesis as an interval or dimension of motion in its own right.

She also has some interesting sidelights on our discussion of Salinas' discussion of Vicentino. He thought Vicentino was talking in terms of a justly tuned diesis of 128:125, major semitone of 16:15 and minor semitone of 25:24 and says his instrument can't realize those intervals. But of course Vicentino agrees as he recognizes that the intervals on his instrument are irrational and that they approximately realize ratios.

Incidentally, I was interested to learn from her that the intervals he mentions as approximated by ratio include the 11/9 which he expresses as 5.5/4.5 for the "proximate minor", which nowadays we refer to as a "neutral third" between 6/5 and 5/4, and his "minimal third" at an approximate 7:6, which we call the septimal minor nowadays.

She's done a reply for you here, which goes into some of this in detail: Margo's reply to my question about what she means by "modal fluidity"

Robert Walker (talk) 12:54, 19 July 2016 (UTC)


 * @Robert Walker Robert, I am afraid I won't be able to answer all this for several reasons, among which:
 * 1) I won't have enough time to digest all that and find the needed references for an answer;
 * 2) This is no more a discussion of general interest for Wikipedia and we should find somewhere else to go on;
 * 3) It becomes more and more difficult for me to answer without quoting my own publications on the topic, which I could not do under a pseudonym. I begin to realize that my choosing anonymity may not have been a good idea, but it would still be an important step to change that. My publications usually ain't in English, which I am sorry to have to acknowledge makes them largely unknown in the US and even the UK – the reverse usually being not true, or not to the same extent. [I mean by this: Margo S. probably does not know me, but she should... ;–)) ]
 * I'll keep to your points made here, and suggest that for the rest we find another forum where Margo S. could join us: why not SMT Discuss? Or my own public forum, but of which I will not give the adress here, again for reasons of anonymity.
 * • She agrees that the 16th century compositions show relative indifference to movement by fifths. I mentioned root movements by fifths only as an example, and never claimed that they would be more important than others (altough I do admit that they would in some tonal styles). I only meant that the ratio of descending vs ascending fifths could reach 90/10% and more in some tonal styles, and that they always shew some asymmetry; I did not say that they formed the majority.
 * • intensive cadences and remissive cadences have a strong sense of directionality. An interesting remark. Are the expressions "intensive" and "remissive" cadences her own? Note that if ascending semitone + descending tone is the "intensive" cadence and ascending tone + descending semitone the "remissive" one, it must be added that the remissive one is equal to the intensive one taken in the other direction. So, indeed, there is a stong sense of directionality here. Would the Phrygian cadence be an inversion of those of other modes?
 * • to talk about relative indifference to chain of fifths progressions in the 16th century is rather like talking about relative indifference to 12 tone rows in 18th to 19th century composers. Did I ever speak of "chain of fifths"? I don't think so, and I would believe that such chains are as rare in common-practice tonality as in the 16th century. (There are very long such chains, I think, in some of Lassus' compositions, very rare and exceptional, probably, but certainly longer than any that I know in later repertoires.)
 * • She sees a transition from the earlier resolution to trines.... My own and my students' extensive statistics are based on triadic roots and I don't think they can easily compare to earlier "trines". I do not mean that there is no relation, there may be one in the intensive vs remissive cadences, I merely mean that our present tools do not easily allow such comparison. (But I trust that she will agree that considering 16th-century harmony in terms of roots is not really an anachronism.)
 * • By modal fluidity she means a flexibility of accidental inflections and contrasts. I am not sure this is much clearer to me. In my view, the kind of chromatic inflections she may have in mind is usually linked, in the 16th century, to root progressions by third from major to major (or, more rarely, from minor to minor). This is rather more frequent in the 16th century than later, but not so frequent either, unless in quite specific chromatic styles (some of Lassus works).
 * • "all intervals are available from all tasti" means all intervals are available from each note on the instrument, without any implication of either "modal centers," or the later major or minor key. I don't see, indeed, how "modal centers" or "keys" could be concerned here, but I do think that some limitation must be given to "all intervals". This may mean "all diatonic intervals", but then it boils down to Bermudo's description of all bozes. "Intervals" must mean "singable intervals", which excludes the apotome which is not strictly speaking an interval, only a rest. Otherwise, one would necessarily end with an infinite number of keys.
 * • Circulation here doesn't necessarily mean to circulate by fifths. Once again, did I ever say that? I never mentioned circulating by fifths. There is a famous Fantasy by Bull on the hexachord, in the Fitzwilliam virginal book (vol. I n. 51), which circulates through the full cycle: the problem is that such a circulation necessarily requires an enharmony (in this case, if my memory does not fail, an A major chord with the third spelled as D♭ instead of C♯), which in turn either requires that enharmonic notes are the same, or irremediately leads away from the starting point.
 * I do not enough remember Vicentino's pieces, which I studied more than 25 years ago. But I remain convinced that if his aim was circulating in just intonation or even in meantone, the kind of shifts he performed through the various intonations always would have involved a "wolf" harmony in the end (because his number of keyboard keys was finite), as in Bull's Fantasy, and that this therefore cannot have been his main purpose. His purpose must primarily have been the playing of microtones (which he believed belonged to the Ancient Greek enharmonic genus).
 * But such considerations, you will admit with me, are way too technical for Wikipedia.

Hucbald.SaintAmand (talk) 20:35, 19 July 2016 (UTC)


 * Hi Hucbald, Just a few immediate responses. First, on intensive and remissive, the actual terms are her own but describe concepts in works by medieval theorists. It's similar to Tomas de Santa Maria (1565), who speaks of cadences as sostenida or "sharp" with ascending semitones, and remissa or "flat" with descending semitones. They are not normally reversible. That's especially so in early medieval music where they resolve by outwards motion to a trine. In sixteenth century she has one example which is approximately time reversed, but that's unusual, and it is not exactly time reversed, the Bass motions are E - A time reversed to A - E but the sonorities above them are different.


 * Anyway you'd better ask her for the details and I agree this sort of thing is probably best off wiki. Especially as it will be easier for you to share your own academic papers for clarification as well. I wonder what you think about joining our discussions on the Xenharmonic Alliance? It's where all the microtonalists seem to be nowadays, the ones who used to post to the Mills tuning list and then to Yahoogroups tuning - that's still going on I think but most of the action for some reason is now in facebook in the Xenharmonic Alliance II.


 * With the 31 equal circulation, yes you can circulate all the way through the cycle of fifths without any wolf fifths as Colonna's example shows. Yes, as you circle around at some point you'll use the enharmonic equivalences such as Dx=Fbb etc. The wolf firths are there if you want them, for instance G#-Eb will be a wolf fifth, but you don't need to play that to complete the cycle. G# - D# is fine, also Gx to Dx which is the same as Bbbb to Fbb and so on. In his circulating example it progresses through sharps first, then you get enharmonic transitions to the flats and then back to the unaccented notes at the end.


 * It's the same for extended meantone, that you need enharmonic equivalences, but with 31 tones the enharmonic equivalences there are so close to identical that again, all the keys are close to identical,and you don't get any wolf keys. Indeed in 31-note 1/4-comma tuning, the "odd" 31st fifth is actually purer than the others, which are 5.377 cents narrow, since it's wider by a small difference between 31 meantone fifths and 18 2:1 octaves at 6.069 cents, making it slightly wide of pure.


 * On the technical nature of this conversation, the wikipedia guidelines say that highly technical subject matter still belongs here and that making articles more understandable doesn't mean that technical matter should be removed. See the guidelines on WP:TECH-CONTENT. And as you observed some of the tuning maths here is highly technical.


 * If you go to the more advanced pure maths articles here on wikipedia, most of them can only be read by experts in that particular topic area. I'm a maths graduate and did postgraduate maths too, yet many of the maths articles here in wikipedia are too technical for me to read at all, because they are for different areas of maths from the ones I specialized in. That's just normal in the maths topic area for all mathematicians - the days of mathematicians who can read technical articles and papers throughout the entire field of maths, like Leonhard Euler, are long gone now.


 * So, just as it is acceptable to have highly technical articles on maths and on tuning maths, I think it should also be acceptable to have highly technical articles on the intricacies of medieval tuning systems, including this fascinating period when Vicentino and his contemporaries were exploring many experiments including a fair fiw that seem xentonal even to us today.


 * I agree that it's best to go off wiki for some of this discussion, especially detailed discussions of yours and Margo'os ideas.


 * At some point it would be good to continue a conversation here focused on how to improve this and other articles to take account of how the medieval composers themselves worked with their archicembalos and other instruments. And in that sense I think our discussion here so far has been highly relevant to improving wikipedia. As groundwork that may be very useful later on.


 * Also, I'm not sure this article is the best place for it, but I think it would be good if at some point we had some more technical sections in wikipedia about medieval harmony. So in my mind this is still to do with improving wikipedia, In the case of this particular article, I would like to suggest that at some point it needs a short section on the way that Vicentino himself used / intended to use his keyboard perhaps linking to a more technical article elsewhere for the details. Though for now maybe it's best just to note that as a wish / project for the future.


 * If you want to join in the discussion on facebook then I could link to one of our many conversations there on the Archicembalo and Vicentino, can do it here. Or, you can contact me via email. As a software developer my address is displayed publicly, in many places on the web, but Gmail's spam filter seems to handle it fine, so just send an email to support at robertinventor.com and I'll then have your email address and can reply with a link to the conversation.


 * Margo is looking forward to the discussion, in the Xenharmonic Alliance or a related group, and I must say I'm looking forward to it too. Robert Walker (talk) 00:09, 20 July 2016 (UTC)


 * Robert, even if as I suspect Margo may be reading this above your shoulder, we cannot continue the discussion in such conditions. I cannot answer her bestii.com document because I cannot access its server. I like her opposition between "intensive" and "remissive" cadences, but I am not convinced that it is found in medieval theory – even Santa Maria's sostenidas and remissas clausulas may not convey the same opposition, he may merely have meant that a sostenida cadence involved a sostenida note (sharp), etc. In addition, when speaking of asymmetry, I did not think of cadences particularly, I meant progressions at large: it is for this reason that I don't think my ideas to be "tononormative" – they remain fully independent of the particular key the work is in. Of course, tonal cadences usually are by descending fifth; but that may not prevent the rest of the piece to be more, or less, asymmetric. Even in some of the Renaissance chromatic pieces, the chromaticism results from a more intensive use of third progressions, which may evidence the same kind of asymmetry as progressions by fifths (e.g. descending thirds being more frequent than ascending ones – I am speaking in terms of roots). This, of course, has very little if anything to do with tuning.


 * I admit that 31-note meantone allows circulating through the enharmonic modulation, a fact that I may have overlooked, and that this apparently was what Colonna had in mind. It doesn't tell us what Vicentino aimed at, however. From my now distant recollections, I'd say that he was more interested in playing (multiples of) fifths of tone than in circulating through a slowly shifting diatony. We have very few elements on which to judge. I think however that to view this from the standpoint of modern "xenharmonicity", and to consider the evolution taken by music at large an unfortunate accident that prevented, for three or four centuries, microtonality to arise, is an unduly biased point of view. Vicentino's archicembalo must have been hardly playable – and that also needs be said. Electronic instruments today allow pitch to derive in real time, but this must have been quite problematic in the Renaissance. And much of the Renaissance music was not for keyboard.
 * Hucbald.SaintAmand (talk) 20:23, 20 July 2016 (UTC)


 * Hucbald, first, if you post here of course anyone can read what you say. It was natural to ask her I think, as a friend, and because you were saying various things about what you thought her ideas of modal fluidity meant. Did you see my offer above to continue this discussion on facebook on the Xenharmonic wiki? I gave my public email address here it is again support at robertinventor.com. Both Margo and I are looking forward to continuing this discussion off wiki.


 * One minor point on the above. First, yes, Vicentino used diesis shifts a lot, and chromatic semitone shifts and so on. When you do that, just as for the ciruclation through fifths, the internal structure of the chord remains unchnanged. It's just like moving all the notes of a chord up a semitone in twelve equal. This is a mathematical feature of any equal temperament, that if you move all the notes of a chord up in pitch by any number of steps you like, the result is always again a chord with exactly the same relative tunings of the notes in that same equal temperament. There are modern reconstructions of the Archicembalo and they are emininently playable and they have been used to play Vicentino's own pieces. They are quite xenharmonic sounding especially the diesis shifts. But it's clear that this is what he intended them to sound like. Judge for yourself, here is a recording played on a modern Archicembalo of Vicentino's music. Vicentino's enharmonic madrigals. There are several other recordings of Vicentino's music around nowadays played on authentic reconstructions of archicembalos of 31 tones and other numbers of keys. I give another example on my quora answer, with a video of one of them played on a 24 key archicembalo - i.e. tuned to 24 out of the 31 total notes of extended meantone. As for the rest, I leave it to Margo to explain her ideas in detail and to discuss medieval theory with you, off wiki, where she can do it at length. Do email me if you want to continue this discussion off wiki. We both look forward to discussing it with you in a relaxed situation where we can learn about your academic papers and where we can talk about any of these questions at length and without being limited to the conventions and expectations for a wikipedia talk page. Thanks! Robert Walker (talk) 21:06, 20 July 2016 (UTC)


 * Robert, I don't mind discussing in public, I merely meant that the discussion we might have on modality/tonality is of little concerns to those reading an article on the Archicembalo. I won't joint the Xenharmonic Facebook page because I find Facebook way too intrusive and I am not interested enough in microtonality to consent to the flood of messages that this would occasion.


 * I had been interested in Vicentino in a former life, when I was working in one of the major museums of musical instruments. But my interests shifted, I am now more interested in tonal theories (mainly Schenker), in modal theory (which I thaught in a new life in a major university), and in musical analysis at large. I have read many of Margo Schulter's papers, they often interested me, but I often found them biased toward a consideration of tuning that seems to me out of place or, at least, excessive (say, for instance, in the case of "systematist Burzug"; but this is a bias of the systematic school itself; I have had a PhD student who devoted his thesis to works that followed, the so called école praticienne).


 * I have a tendency never to refuse a good discussion. But now, really, I have too many other things on the fire that become urgent. Yet, and do consider it a challenge, if you or Margo find me on Internet (there are enough clues in the above), I'll find the time for a discussion, and I'll invite you on my own forum – where others will join us.


 * Hucbald.SaintAmand (talk) 21:43, 20 July 2016 (UTC)

Sorry to hear you don't want to join a discussion on the Xenharmonic Alliance. I know a few people don't like to use facebook, unfortunately that's where nearly all the microtonal discussions happen these days. There's the yahoogroups tuning which used to be very active but there has been no activity for several months. But that was just a suggestion, I gave you my email address so you can just send us the information about how to take part in your preferred location if you have somewhere else. Or for that matter we could just continue via email. Both Margo and I are on email and I'm sure she'd be happy to join in a private email discussion if that was preferable to you, I could check if you are interested.

You suggested we continue this discussion off wiki and I'm confused now, have you changed your mind? I have never attempted to figure out someone's real identity from clues in their conversations on wikipedia, and don't want to find out how to do that either (if it is possible), for privacy reasons. If you want to continue this conversation off wiki, please send me an email, thanks! Robert Walker (talk) 22:13, 20 July 2016 (UTC)

Bull?
What is the source / evidence for John Bull having been an archicembalo player? He would probably have met keyboards with more than 12 notes per octave in the Low Countries, but I don't know of any verifiable archicembalo sightings that far north. --Tdent 11:15, 26 April 2006 (UTC)


 * Sorry, I don't have the reference on hand, but I believe it was Gustav Reese's "Music in the Renaissance" where it was suggested that John Bull played an archicembalo (I think if you check the index for archicembalo you might find it). However, Reese's usage of archicembalo might actually extend to all microtonal harpsichords, so under the current definition it might actually be a minor stretch to get Bull in there. (Or might update this page with a mention of this alternate definition?) I can't get to a library at the moment, so I can't gather all of the information together myself for a little while. Do you know of any other composers who came into contact with archicembali? I didn't want to have just one listed. Rainwarrior 01:56, 27 April 2006 (UTC)


 * It's on Reese page 861, in reference to a chromatic composition of Bull which uses the notes C# and Db, as well as G# and Ab, in the context of a contrapuntal piece in which a subject appears on each chromatic scale degree. "the presence in a single composition of [these notes] ... suggests that the piece may well have been written for some instrument like the arcicembalo."  Antandrus  (talk) 02:00, 27 April 2006 (UTC)


 * Wow, you looked it up in under 5 minutes! That's impressive. (I take it you have Music in the Renaissance on your own bookshelf?) Rainwarrior 02:16, 27 April 2006 (UTC)


 * Actually, considering I usually work on early music articles, it was open next to my computer, LOL... I didn't even have to move. ;-) Antandrus  (talk) 02:18, 27 April 2006 (UTC)


 * Okay, I removed the reference to Bull, but it might be worth sticking him back in there somewhere. At least, I think it's interesting that Reese would speculate that his particular chromatic style /suggests/ the use of an instrument that might have been inspired by the Archicembalo. Rainwarrior 03:07, 27 April 2006 (UTC)


 * Some points here. I know this particular composition (Ut Re Mi fantasia) which is preserved in the Fitzwilliam Virginal Book, and it is highly debatable what instrument or tuning it was intended for. The problem is that it seems to require enharmonic *equivalence*, i.e. a closed circle of fifths, since it shifts from sharps to flats within a single bar; whereas with enharmonic instruments one cannot do that without a sudden shift in pitch by about a quarter tone and probably also having some chords out of tune. The purpose of the archicembalo was to play as many chords as possible in tune, so it would not help for this part of the piece. There is an article of Annette Otterstedt that points out that English viol music might well be based on equal temperament (standard 17:18 fretting) and gives some examples of enharmonic equivalence implying a closed circle of fifths - also mentioning that some viol pieces were transcribed for keyboard. Finally, it is a long stretch from an enharmonic keyboard, which might only have G#/Ab and D#/Eb for instance, to an archicembalo. Might be worth mentioning that the archicembalo was somehow an extreme case of a more common practice of providing a few 'extra' notes. --Tdent 11:35, 27 April 2006 (UTC)


 * It's been a little while since I've looked at the works of Bull, though I recall the tied enharmonics you're talking about. As I said before, though, I no longer live near a good library (as of a few days ago), so I'll leave it to your discretion. After Antandrus' quote jogged my memory, the John Bull connection has begun to feel gradually more tenuous as I have been thinking about it; it was basically a misremembered reference in the first place on my part.


 * As far as the required equivalence, the Archicembalo's tunning was specifically designed to be capable of such things (albeit with some unusual looking fingerings), though certainly a keyboard that has merely enharmonic black keys would not (so unless Reese was referring to something ). What requires a "closed circle of fifths"? (And do you mean circle of 12 fifths by this? Vicentino's tuning was basically a closing of the meantone fifth cycle.) I suppose an enharmonic shift followed by a return to the original key via a new route would do this if it is decided that the return must be at the exact same pitch, which is a reasonable enough to decide...


 * I've read some things about lutes being among the first instruments to have (more or less) equal temperament, though I don't know much about viols. What is 17:18 fretting? I'll take a look for Otterstedt's book once I find myself a new library. (Thanks for the reference.) Rainwarrior 00:45, 28 April 2006 (UTC)


 * $$\left({18\over17}\right)^{12}$$ is 13 cents short of an octave, so 17:18 was used as a rule of thumb for measuring frets for equal temperament. Hmm, we should probably mention that in the Equal temperament article... —Keenan Pepper 10:19, 28 April 2006 (UTC)


 * Maybe we are slightly at cross purposes here. The Archie had different keys and pitches for (say) G# and Ab, whereas a piece written with a sudden shift from (say) G# minor to Ab major would need the pitches to be equal if there was not to be a sudden lurch. The Bull has a C# in A major right next to a Db in the key of Gb and the simplest interpretation is (IMO) that they were different spellings of the same pitch. By "closed circle of fifths" I mean twelve fifths which return to the starting pitch with an enharmonic shift in notation at some point - as Bull's piece contains. Vicentino's 31-equal tuning only returns to the start after 31 fifths and some really bizarre equivalences such as D##=Fbb... which I expect do not find a use in any music. You could play the Bull on an Archie, but only if you can accept the sudden lurch in pitch which goes with the switch from C# to Db (and F# to Gb etc. etc.) in the middle of a phrase.


 * The Otterstedt I read was in conference proceedings (Michaelstein) but I would expect some of the same points to appear in the book. Lutes and viols have almost exactly the same principles of tuning, just plucked or bowed respectively. - User:Tdent 17:04, 28 April 2006 (UTC)


 * (Pardon me for moving your comments around, but you put yours right in the middle of mine, and it made the threading difficult to follow. ...and you didn't sign them.) What I was saying is that if you don't actually require the piece to end on the same pitch as it started, the Archicembalo can do it without the sudden discontinuity (lurch) that you're talking about. (The actual fingering for this on the archicembalo would involve placing your hand across both manuals at once.) But even beyond that, if this modulation by a comma (which occurs at the enharmonic tie) is allowed to operate in reverse later on in the piece, you actually can recover the starting pitch at that later point. If it does not, and the original key is returned to by another route, you cannot without travelling the whole circle of fifths. Actual written note names can be considered to have a more local tuning when an archicembalo is being used, because you simply can't account for all of them with just flats and sharps: if there is a finer pitch distinction to be made in practice, some names would have to be reused or the notation would have to be augmented to accomodate. (I can't comment on this particular piece right now though because I don't have it in front of me; please don't take me to be arguing about it directly. I do find both sides of the argument interesting though, the case for equal temperament, and the case for an archicembalo. I might actually like to write an article about this; not for wikipedia though.) Rainwarrior 05:42, 29 April 2006 (UTC)

Picture
I thought theirs was a reproduction of Trasuntino's 1606 |"Clavemusicum Omnitonum". According to Denzil Wraight's list Lewis Jones made one too, it was at London Guildhall University a few years ago. Mireut 20:50, 3 September 2006 (UTC)

Pronunciation and anglicisation
—Preceding unsigned comment added by 194.74.1.82 (talk) 26 April 2011
 * 1) Pronunciation: /r/ is used in both the Italian and the English pronunciations; this is fine if the pronunciation is phonemic, but should the English pronunciation use /ɾ/ to distinguish it from the Italian /r/?
 * 2) The article is inconsistent about whether "archicembalo" is anglicised; presumably it is, because its spelling is different from the Italian "arcicembalo". In that case, should the plural not be "archicembalos" rather than the sham Italian "archicembali"?


 * Vicentino’s spelling in the original 1555 publication (I am looking at a facsimile now) is clearly Archicembalo (contrary to the discussion up the page back in 2006!), so I suppose the matter of pluralisation rests on whether it has entered English as a loan word. In addition, Vicentino always employs capitalisation, apparently. As for the question of pronunciation, wouldn’t the different character be presuming too much about particular English speakers? Philip User Talk Email 03:17, 23 May 2011 (UTC)

Etymology of archicembalo

 * with possible reference to Greek prefix ἀρχι- which means 'major', 'principal' (as in the word architect).
 * Vicentino does not mention this possible derivation. Who does so? (Comment and 'citation needed' template added by Jerome Kohl)

At present I can't find an external 'authoritative source' to support this, so it is mine. I deduce the opinion from the Latinized form 'Archicymbalum' found on the frontispiece of the Vicentino's treatise. Any student who can read Latin would connect 'archi-' with the described Greek (routinely Latinized in hundreds of examples of literature) prefix, and not with 'strings' or whatever. Moreover, I am pretty sure that 'arciorgano' found in the public announcement known as 'Descrizione' (1561; compared to the treatise, I doubt its provenience from 'Vicentino himself', btw; no other contemporary source of Vicentino's 'arciorgano' survived) means the same 'grando' or 'huge' or alike, because pipe organ has nothing to do with 'strings'. However, if you can offer another etymological explanation, I will highly appreciate that. Olorulus (talk) 07:42, 22 October 2012 (UTC)
 * Well, I have already added Garzanti on the Italian prefixes archi- and arci-. Although this does not specifically address Vicentino's intentions, the Musikforschung article by Volker Rippe does, so I should have removed that tag when I added the Rippe citation. The real answer to the terminological problem is undoubtedly the parallelism to other similarly formed organological terms, such as "arciliuto", "arcicetera", and "arciorgano", none of which (as far as I am aware) have ever used the "archi-" variant. However, it is perfectly true that the several articles in New Grove that opt for "arcicembalo" over Vicentino's spelling do not explain the reasoning behind their choices, nor do the other articles explain why they have chosen to go with Vicentino's spelling as opposed to their colleagues' entries in the same reference source. Vicentino himself reflects the Italian ambivalence about this prefix, in that six years after publishing L'antica musica he wrote a shorter treatise describing the "arciorgano", and spelled it just that way. (Vicentino's inconsistency is also discussed by Rippe, though he does not consider the possibilty that you have suggested, namely that in 1555 Vicentino intended to emphasize the Latin connection of the etymology, whereas by 1561 he had relaxed a bit into the vernacular.) We should be thankful that the Italian ambivalence over how to transcribe the Greek letter χ is restricted in this case just to the vacillation between chi and ci. Gerhard Rohlfs, in the first volume, "Lautlehre", of his Historische Grammatik der italienischen Sprache und ihrer Mundarten (1949), describes at least half a dozen different pronunciations and nearly as many spelling variants for Greek loan words involving that letter.—Jerome Kohl (talk) 16:46, 22 October 2012 (UTC)
 * The fist question is eventually not about arci- / archi- vacillation in the 16th century Italian language, it is more about (a) different kinds of transmission of one and the same historical term in the different lexicological traditions and (b) inconsistency of the New Grove, the editorial team of which didn't care enough about controlling terminological entries in their texts (mostly 'arcicembalo', very rarely 'archicembalo'). The second issue is that the English-speaking lexicological tradition 'arcicembalo' gives rise to the 'natural inclination' to read 'arci-' in the dicussed term as [artshi] (and not [arki]) which results to another (not orthographical, but pronunciation) problem (the pronunciation [artshitshembalo] of the word spelled archicembalo is inconceivable).
 * As for etymology ('derivation'), I think, there are lexical cases which are self-evident (arcimusico and archicembalo as examples) which belong to so called 'common sense' and should not be verified by any 'authoritative source'. In short, I repeat my question: if you have some other opinion (different from mine), what 'archi-' prefix could mean, I am eager to know it. Olorulus (talk) 05:03, 23 October 2012 (UTC)
 * I have not until now included the Garzanti entries, which make it plain that both prefixes have the same origin, namely the Greek particle ἀρχι-. Since there seems to be some confusion about what I am trying to say, here are the Garzanti entries:
 * archi-, dal gr. archi-, tema del verbo arco = essere il primo, a capo] prefisso che indica superiorità, comando (archiatro, archinginasio)
 * arci-, per l’etimo V. archi-] prefisso usato in parole di tradizione o di origine popolare per indicare superiorità, primato, abbondanza, eccesso (arcivescovo, arcivecchio).
 * Rippe confirms this derivation (as I have already said), offering the German equivalent "Erz-" (as in Erzbischof, Erzengel, Erzvater). There is absolutely no doubt in my mind that this is the correct interpretation. In fact, I would be astounded if anyone were to come up with a competing one. As for the pronunciation, there is also absolutely no doubt that, when spelt "archi-" the sound of the consonant is hard, similar to English or German K, and when spelled "arci-" the sound is soft, like English CH or German TSCH. The Italian arciliuto cannot be pronounced with the hard K sound, and neither can arcicembalo, which has two "soft" (affricate) Cs. I think it should be emphasized here that there is no anglicization involved in the variants of Vicentino's instrument name found in English-language sources like New Grove—they are simply the borrowed Italian variant words—unlike the case with arciliuto, which is anglicized as "archlute" (never spelled or pronounced "arklute"). Rohlfs goes into the phonetic variations of borrowed Greek χ at great length but, as I have already said, we do not need to investigate the possibilities beyond these two. (The others involve initial consonants, and various medial consonants and consonant clusters that do not include "-ρχ-".)—Jerome Kohl (talk) 06:06, 23 October 2012 (UTC)
 * Thank you for explanations. The last thing to do is to supply pronunciation (transcription) to the discussed term (in both variants) -- exactly in a form which is appropriate for English-speaking world (because English pronunciation can differ from Italian one, and you, as a native speaker, know it definitely better than I do). I would be glad if you insert the appropriate transcriptions side by side.
 * As for Erz- prefix, you might see that I've given it in a comment where your 'citation needed' template has been originally placed, according to the 'Sachteil' RML-12 (published in 1967). (talk) 11:33, 23 October 2012 (UTC)
 * You are very welcome. English pronunciation is an interesting problem in a case where the word is perceived as a foreign term, and the intention may be to pronounce it as is done in the source language. Differences invariably occur, but may vary according to region and the nature of the speaker's education (the famous example of Wagner's first name comes to mind). My expertise with the IPA is limited, but I imagine the best thing is to take a stab at it, and let better-informed editors have a good laugh before fixing my clumsy attempt. And, yes, the reference you added concerning German Erz- is just as good as citing Rippe.—Jerome Kohl (talk) 16:04, 23 October 2012 (UTC)

cycle of 31 quarter-comma-tempered fifths
The article states that "after a cycle of 31 quarter-comma-tempered fifths, the 32nd pitch will be remarkably close to a pitch already existing in the system". Actually, this is not the case, there is an error of 6 cent: $${\sqrt[4]{5}}^{31} / 2^{18} = 6.07\,\mathrm{cent}$$. This is not particularly close: If you take multiples of any irrational number, you will inevitably get close to a multiple of 100 at some point. Statistically speaking, an "error" of 6 % after 31 tries is not too impressive.

What I would guess was observed instead, is the fact that with 30 quarter-comma-tempered fifths, the remaining wolf fifth is very close to a just fifth: $${\sqrt[4]{5}}^{30}\cdot \tfrac{3}{2} / 2^{18} = -0.69\,\mathrm{cent}$$. In other words the error cancels the quarter comma correction for this particular interval.

However, it breaks the perfect symmetry as is to be expected from any tuning that is not 31-ED. In certain keys, a major third which should be just will be off by 1/4 of a comma. --Cebus (talk) 02:44, 27 February 2017 (UTC)

To add to article
To add to this article: mention of the reconstruction, in 2017, of an archicembalo designed by Carlo Gesualdo. Source 173.88.246.138 (talk) 07:29, 27 January 2021 (UTC)

Image
The image included with the article, which shows the tuning of the archicembalo in cents, appears to be following the analysis, referred to in the article, of Karol Berger, because keys in successive steps of the cycle of 31 notes often differ by 41 cents instead of 39 cents. This makes sense if even the basic tuning included modifications to allow better perfect fifths to be played in many cases. Quadibloc (talk) 07:22, 22 February 2021 (UTC)