Re: [abcusers] intonation - Fomula for determining a half step in MgHz...
Hello, John Walsh wrote: In fact, the even tempered scale hasn't completely taken over. The uilleann pipes are usually tuned against the drones, and I imagine that is also true of the highland pipes and other instruments like the vielle which have drones. (...) To my understanding, there are two groups of tuning systems which both are forming the basis of western music: 1) tempered intonation scales Including everything from pythagorean to equal tempered. In this system some or all intervals are made gradually imperfect to open a wider range of chromatic changes more "playable" scales on a twelve key instrument (like the piano). The common idea starts at one specific point of the musical system: dealing with the difference between the octave and the accumulation of twelve fifths. The dominance of the twelve keys per octave instrument, which is in fact one of the major reasons for this kind of tonal system, has historical reasons not entirely musical. These tempered scales, in their notation system, note names, temper relations, even the twelve tone system of semi tones still refer to the other group of scale intonations the 2) just intonation scales (I do not really know if this is the right term in english the german term is "Skalen mit reiner Intonation") In this intonation the scale is assembled out of "perfect" simple ratio intervals the specific characteristic of a scale based on the relations of the used numbers. As an example two common scales of this type: the scale used by the Alphorn which just uses the harmonics of one basic note is constructed on the numbers 7 :8 :9 :10:11:12:13 b :c :d :e :f :g :a as one can see these numbers differ strongly against equal temperament. It is used today by traditional music, singers, fiddle players, not just Alphorn players! in many european regions. The scale most drone based instruments use (not just those): 24:27:30:32:36:40:45 c :d :e :f :g :a :b this proportions are based on the ratios of only three numbers, the first three indivisible numbers 2,3,5. This makes the scale more usefull for music which contains harmonies because there are less beat-notes (ger:interferenz-tne) than in the alphorn scale wich includes ratios of many numbers such as 7:11 (...)This effectively means that they are in some kind of just tuning: the ratio of the frequency of each note to the drone frequency is a simple fraction with fairly low denominator. (...) It's close to the even tempered scale for the fifth and third, not so close with the second, for instance. (15-17 cents I disagree strongly! the just third is quite far from the equal tempered. and the fifth is really different too. not so close with the second, for instance. In fact in those just intonation scales I know the perfect second is a very stable nearly consonant sound, seen as fifth of the fifth. Laura Conrad wrote: "Phil" == Phil Taylor [EMAIL PROTECTED] writes: Phil Yes and no. the expression "well-tempered" comes from the Phil title of Bach's two volumes of preludes and fugues. (...) No, I think most people these days believe that Bach's Well-tempered keyboard was not equal tempered. as far as I know it was well tempered following a system developed by a man called werckmeister. In systems like this you chose a number of consecutive fifths wich are about just intonation and divide the divergence between 12 just intonated fifths and the octave between the other fifths. As I remember, this specific system also includes a correction for the thirds. Simon Wascher - Vienna, Austria To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] intonation - Fomula for determining a half step in MgHz...
Simon Wascher wrote: To my understanding, there are two groups of tuning systems which both are forming the basis of western music: 1) tempered intonation scales ... 2) just intonation scales (I do not really know if this is the right term in english the german term is "Skalen mit reiner Intonation") Yes, it's the same in English. ... Laura Conrad wrote: "Phil" == Phil Taylor [EMAIL PROTECTED] writes: Phil Yes and no. the expression "well-tempered" comes from the Phil title of Bach's two volumes of preludes and fugues. (...) No, I think most people these days believe that Bach's Well-tempered keyboard was not equal tempered. as far as I know it was well tempered following a system developed by a man called werckmeister. In systems like this you chose a number of consecutive fifths wich are about just intonation and divide the divergence between 12 just intonated fifths and the octave between the other fifths. As I remember, this specific system also includes a correction for the thirds. I stand corrected. However, if the system used involved distributing the accumulated error from twelve perfect fifths among all the notes, the result will surely be an equally-tempered scale, even though it's mathematical basis is different? Phil Taylor To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] intonation - Fomula for determining a half step inMgHz...
Hello Phil, Phil Taylor wrote: However, if the system used involved distributing the accumulated error from twelve perfect fifths among all the notes, the result will surely be an equally-tempered scale, even though it's mathematical basis is different? 'xcuse I think I got the point of your question just in the second reading: The twelve fifths not only cumulate to meet the octav (more precise: five octaves) but also represent each by each one single note on the keyboard: B-E-A-D-G-C-F-Bb(=A#)-Eb(=D#)-Ab(=G#)-Db(=C#)-Gb(=F#)-Cb(=B*) , so making them smaller or larger means to change these notes (their equation on the keyboard) Simon Wascher - Vienna, Austria To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] intonation - Fomula for determining a half step inMgHz...
hello, I wrote: consecutive fifths wich are about just intonation and divide the divergence between 12 just intonated fifths and the octave between the other fifths. As I remember, this specific system also includes a correction for the thirds. Phil Taylor wrote: I stand corrected. However, if the system used involved distributing the accumulated error from twelve perfect fifths among all the notes, the result will surely be an equally-tempered scale, even though it's mathematical basis is different? I think I was not quite clear in my writing. what I wanted to describe is a intonation system based on 12 fifths which are from two (or more) different sizes. All 12 together have the same size as in an equal temperament but inside there are bigger and smaller fifths what makes it possible to have perfect fifths (and thirds) in favorised keys and such that are not so good at the far end of the circle of fifths. In case of Werckmeister the circle of the fifths is "closed" not only because thelve fifths equal the octave but also because all fifths are of musically usable size. For example there are no fifths which are to big, what would sound very bad (there are tonal systems wich include such fifths, meaning that one cannot play in all keys, but in the range of four or five keys these tuning systems sound very brilliant - these systems are very usefull for music from the sixtenth and sevententh century europe). So the kind of tunings people like Werckmeister worked out made it possible to play music like the "welltempered piano" because all the scales starting from all 12 (piano) keys are well sounding and even better, each has an individual coulor because of their different distance to the more brilliant center of tonalities arround these four or five perfect fifths. for music which does not use a 12 key (piano) keyboard there is no real need to use those intonation compromises. The color (intonation) of every interval, step or harmony can be choosen more freely and the A bevore the modulation must not be the same as after . Typical example: The A wich is the sixth of C is lower in many just intonation systems than the A as secund of G if C and G are common to and a perfect fifth in both keys. For computer generated music it should be possible to give up the equal tempered intonation and to calculate the intonation outgoing from the tonic center, maybe even when using a twelve key piano keyboard for input. Back to abc and traditional music this would for example mean that the K: signature should influence the intonation. Simon Wascher - Vienna, Austria To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] Fomula for determining a half step in MgHz...
Mike Whitaker wrote: cb 278.43 277.2 d# 274.69 277.2 You mean C# and Db, surely? Of course. Sorry. I had some font convertion problems. The flat and sharp signs actually were * and * (that's how they're mapped in MetTimes) and I messed up the search-and-replace routines. Here's the correct table: Pythagorean Equal c260.74 261.6 c# 278.43 277.2 db 274.69 277.2 d293.33 293.7 d# 313.24 311.1 eb 309.03 311.1 e330 329.6 f347.65 349.2 f# 371.25 370 gb 366.25 370 g391.11 392 g# 417.66 415.3 ab 412.03 415.3 a440 440 a# 469.86 466.2 bb 463.54 466.2 #495 493.9 Phil Taylor wrote: That's not what I understand as a Pythagorean scale. Yes and no. Your description of the Pythagorean system is the correct one, but I chose to leave out a couple of intermediate steps to simplify things a bit. If you go through the cycle of fifths (dividing with two every now and then to stay in the same octave) you end up with the ratios I gave for semitones. These two temperements have two things in common, they are simple to define mathematically and they are pretty useless musically. It is indeed a pretty useless scale for any music which wanders very far away round the circle of fifths. We wouldn't get very far without the equal-temperament scale though would we? The equally-tempered scale distributes the comma of Pythagoras around all twelve intervals so all intervals are very slightly wrong. It's the only way you can tune an instrument with fixed tunings and have it sound reasonably OK in all keys. This only applies to keyboard instruments. All other insruments are to some degree intonated on the spot - whether the player is concious about it or not. A for keyboards - well, any decent piano tuner will tell you that he or she does not use strict equal temperament. You have to adjust the intonation slightly to get a good result. John Henckel wrote: Is "well-tempered" and "equal-tempered" the same thing? By coincidence, I aked that question at the smt maillist (where all the high-browers in music meet) a week or so ago. The answer seemed to be a rather clear "No". There's nothing to suggest that Bach used or tried to use equal temperament, and he didn't seem to have any problems writing in all major and minor keys. Laura Conrad wrote: John One time I watched a professional piano tuner and was John surprised to see that he didn't use any electronic pitch John measuring device. Yes, but he still tuned the piano to an equal tempered scale. Piano tuning is an art because piano strings are stiff, so the harmonics of the string are not the same as the mathematical overtones. Also, the tone sounds better if the 2 or three strings that are struck for one note aren't exactly in tune. There are a number of factors a piano tuner have to take into account, the overtones are never completely pure, unison strings should be slightly detuned for a fuller sound, bas strings has to be tuned slightly sharp... One of the important factors is that he has to somehow compensate for the shortcomings of the equal temperament system. Bruce Olson wrote: Can anyone tell me where to find out what Pythagoras said in a reliable translation? Unfortunately not. It's important to remember that Pythagoras lived quite a bit earlier than the other famous Greek philosophers and most of our information about him is based on myths. Platon seems to be one of our main sources, and he was born more than sixty years after Pythagoras died. Simon Wascher wrote: To my understanding, there are two groups of tuning systems which both are forming the basis of western music: 1) tempered intonation scales Including everything from pythagorean to equal tempered... 2) just intonation scales... Right except that Pythagorean isn't a tempered scale. It firmly belongs to the just intonation group. Phil Taylor wrote: I stand corrected. However, if the system used involved distributing the accumulated error from twelve perfect fifths among all the notes, the result will surely be an equally-tempered scale, even though it's mathematical basis is different? Not at all. The art of temperament is all about evening out the "deficiency" of the original fifth based system. There are literally thousands of ways to do this, all producing quite different results. John Walsh wrote: In fact, the even tempered scale hasn't completely taken over. I'll go further than that. Equal temperament is only used by electronic instruments. That's one of the main reason (perhaps *the* main reason) why a musical piece played by a computer sounds "unnatural" and "synthetic". Frank Nordberg To subscribe/unsubscribe, point your browser to:
Re: [abcusers] intonation - Fomula for determining a half step inMgHz...
On Thu, Apr 05, 2001 at 01:27:08PM +0200, Simon Wascher wrote:
for music which does not use a 12 key (piano) keyboard there is no real
need to use those intonation compromises. The color (intonation) of
every interval, step or harmony can be choosen more freely and the A
bevore the modulation must not be the same as after . Typical example:
The A wich is the sixth of C is lower in many just intonation systems
than the A as secund of G if C and G are common to and a perfect fifth
in both keys. For computer generated music it should be possible to give
up the equal tempered intonation and to calculate the intonation
outgoing from the tonic center, maybe even when using a twelve key piano
keyboard for input.
I would not be at all surprised to discover that most guitarists who
tune to DADGAD ('modal D' tuning) do so in a manner which is not in
the least even-tempered, too. And not necessarily consciously.
--
Mike Whitaker | Work: +44 1733 766619 | Work: [EMAIL PROTECTED]
System Architect | Fax: +44 1733 348287 | Home: [EMAIL PROTECTED]
CricInfo Ltd | GSM: +44 7971 977375 | Web: http://www.cricinfo.com/
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[abcusers] Re: abcusers-digest V1 #473
John Henckel wrote: Date: Wed, 04 Apr 2001 10:23:20 -0500 From: John Henckel [EMAIL PROTECTED] Subject: Re: [abcusers] Fomula for determining a half step in MgHz... . One time I watched a professional piano tuner and was surprised to see that he didn't use any electronic pitch measuring device. He only used ONE tuning fork for middle C, and he tuned all the other notes from there! I said, "why don't you just tune each note separately to its correct frequency" and he said that would sound awful. He said it is impossible to tune any piano perfectly, but it is always a compromise of many different factors. In other words, it is an art. A discussion of the practical art of piano tuning is way beyond any reasonable amount of space most people on this list would tolerate. But there are two basic reasons piano tuners do not use electronic tuners: (1) On any stringed instrument, but especially the piano, octaves are "stretched" (wider than an exact frequency ratio of 2:1), due to the way the harmonic series is produced in a vibrating string. Electronic tuners do not, and can not take this into effect, since the amount of "stretch" varies with the thickness and tension of the strings. (2) Once properly informed on what to listen for, the human ear is much more accurate than the electronic tuners. This does *NOT* make tuning a piano an "art" in the sense everyone does it whichever way feels right to them. There is a standard reference pitch and scale which should apply to any instrument. I call it a "practical art" like woodworking -- there is a great deal of science involved, but since you're also dealing with imperfect materials, a fair amount of practical experience is necessary to achieve the scientifically correct result on an actual piano. Alan S. Watt [EMAIL PROTECTED] 770-469-7544 (USA) [Voice/FAX] http://www.mindspring.com/~alan.watt To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] intonation - Fomula for determining a half stepinMgHz...
Mike Whitaker wrote:
I would not be at all surprised to discover that most guitarists who
tune to DADGAD ('modal D' tuning) do so in a manner which is not in
the least even-tempered, too. And not necessarily consciously.
Indeed. I don't think it's limited to DADGAD either. I am aware
that if I intend to play in D Major in standard tuning I always tune
the top E a little flat to make the F# sound good. It's a compromise,
because if I make it too flat the A and the top D will be off. But
then I can compensate by pulling those notes sharp on the fly.
I think you will find that everybody makes these kinds of compromises,
whether they are aware of it or not.
Phil Taylor
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Re: [abcusers] Fomula for determining a half step in MgHz...
"Frank" == Frank Nordberg [EMAIL PROTECTED] writes: Frank A for keyboards - well, any decent piano tuner will tell Frank you that he or she does not use strict equal Frank temperament. You have to adjust the intonation slightly to Frank get a good result. Frank There are a number of factors a piano tuner have to take Frank into account, the overtones are never completely pure, Frank unison strings should be slightly detuned for a fuller Frank sound, bas strings has to be tuned slightly sharp... One Frank of the important factors is that he has to somehow Frank compensate for the shortcomings of the equal temperament Frank system. The American piano tuners I know believe that they are trying to approximate equal temperament, although certainly not by tuning each string to the mathematical frequency calculated for that note. This was apparently not true as recently as 100 years ago, so it could be that Norwegian piano tuners are using a different theory from the American ones. As far as electronic piano tuners go, there are electronic tuners which are designed for piano tuning, and which take into account the "stretch factor" and allow you to select the harmonic you're tuning for, and count the beats between the strings for you. There is a snobbery common among piano tuners about being able to do a better job than these sophisticated electronic instruments. This is undoubtedly true in an ideal setting, but any tuner who claims to be able to tune better than the box in a noisy restaurant while the dishes are being washed is deluded. -- Laura (mailto:[EMAIL PROTECTED]) http://www.laymusic.org : Putting live music back in the living room. To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] Fomula for determining a half step in MgHz...
When tuning a fiddle, I use an electronic tuner for the A string, then tune the other strings by ear to the fifth. Seems to me that ends up a little sharp on E and a little flat on the D, according to the tuner. Laura Conrad wrote: [snip] As far as electronic piano tuners go, there are electronic tuners which are designed for piano tuning, and which take into account the "stretch factor" and allow you to select the harmonic you're tuning for, and count the beats between the strings for you. There is a snobbery common among piano tuners about being able to do a better job than these sophisticated electronic instruments. This is undoubtedly true in an ideal setting, but any tuner who claims to be able to tune better than the box in a noisy restaurant while the dishes are being washed is deluded. -- Laura (mailto:[EMAIL PROTECTED]) http://www.laymusic.org : Putting live music back in the living room. To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html -- Wil Macaulay email: [EMAIL PROTECTED] voice: +1-(905)-886-7818 xt2253FAX: +1-(905)-886-7824 Syndesis Ltd. 28 Fulton Way Richmond Hill, Ont Canada L4B 1J5 "... pay no attention to the man behind the curtain ..." To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] intonation - Fomula for determining a half step inMgHz...
Phil Taylor writes: | Indeed. I don't think it's limited to DADGAD either. I am aware | that if I intend to play in D Major in standard tuning I always tune | the top E a little flat to make the F# sound good. It's a compromise, | because if I make it too flat the A and the top D will be off. But | then I can compensate by pulling those notes sharp on the fly. | | I think you will find that everybody makes these kinds of compromises, | whether they are aware of it or not. I've learned to tune the e string of my fiddle a tiny bit sharp. The reason is that pressure of the bow tends to drive the pitch a bit flat, and this effect is stronger on the lighter strings. It's also a function of how loud you're playing. Since you usually tune quietly, when you start playing, the notes will come out flat. You can't correct for this on the open strings, so it's best if the e and possibly the A are tuned slightly sharp. This is one of the reasons that classical violinists usually don't use open strings. But a lot of "fiddle" styles require using open strings, so you learn what you have to do to make them play in tune. People who play fretless stringed instruments are usually quite aware of their intonation, and can usually hear the difference between the equal tuning of keyboards and the tuning that they prefer to use. (The latter is commonly called "playing in tune". ;-) For yet another reason for using a harmonic sort of tuning rather than equal half steps, try some flute (or recorder) duets. In a quiet environment, something that flute players eventually notice that they can hear a quiet "ghost" note that us usually a lower pitch. The frequency is the difference of the frequencies of the two notes. It's fun to try to get this third part to play in tune. This can take a bit of practice. To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
[abcusers] multiple verses in abc2ps and relatives
I wrote: Attached is a file of a tune with several verses. But then I forgot to attach it: X:1 T:VI. Now, O now, I needs must part, C: John Dowland O: From The First Booke of songs or Ayres of foure parts, with Tableture for the Lute T:Cantus M:3/2 L:1/2 N:Original clef, C on first line K:Gmix %%MIDI nobarlines %1 |: B2 A | G2 ^F | E2 G | A2 z | B2 d | c2 B | A2 B w:1.~Now, O now, I needs must part, part- ing though I ab- sent w:While I live I needs must love, love lives not when hope is w:2.~Deare, when I from thee am gone, Gone are all my joyes at w:And al- though your sight I leave, Sight where in my joyes doe w:3.~Deare, If I do not re- turne, Love and I shall die to- w:Part we must though now I die, Die I do to part with %2 A2 z |B2 A |G2 ^F | E2 G | A2 z | B d c c B A | G6 :| w:mourn. Ab- sence can no joy im- part: joy once fled can- not re- turne. w:gone. Now at last de- spaire doth prove, love di- vi- ded lov- eth none. w:once. I loved thee and thee a- lone, In whose love I joy- ed once. w:lie, Till that death doth sence be- reave, Ne- ver shall af- fec- tion die. w:gether. For my ab- sence ne- ver mourne, Whom you might have joy- ed ever: w:you. Him des- paire doth cause to lie, Who both lived and di- eth true. %3 |:c2 c | c2 e | d2 e | d2 z | c c B | A c B | A6 | B2 A | w:Sad de- spair doth drive me hence, this des- paire un- kind- nes sends. If that %4 G2 ^F | E2 G | A2 z | B d c c B A G6 :| w:part- ing bee of- fence, it is shee which then of- fends. -- Laura (mailto:[EMAIL PROTECTED]) http://www.laymusic.org : Putting live music back in the living room.
Re: [abcusers] multiple verses in abc2ps and
Hello, if I looked well, abcm2ps 2.2.8 seems to print all of the words. Greetings Markus On 05 Apr 2001 16:30:47 -0400, Laura Conrad wrote: LC Attached is a file of a tune with several verses. The B section of LC the tune always has the same words, and in the A section for each LC verse the tune repeats but the words are different. LC LC All the versions of abc2ps and relatives that I've tried have lost LC some of these words. Does anyone know how to fix this, or better yet LC have a version that already has a fix? LC LC -- LC Laura (mailto:[EMAIL PROTECTED]) LC http://www.laymusic.org : Putting live music back in the living room. LC LC LC LC To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html LC To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
[abcusers] Re: scales and tuning
All the discussion on temperament, if peripheral, has certainly been interesting and, if I may, I would like to add my two cents. It is my understanding that it is only the extreme octaves (top and bottom) of a piano that are 'stretched' to accommodate the non-harmonic overtones of the (inflexible) strings. There is an implied assumption in the prior discussion that 'just' intonation, with small number ratios of the frequencies, is in tune, while other ratios, such as equal temperament, are slightly out of tune. That is not necessarily so. If two notes, about a major third apart, are compared, and one adjusted until it is 'in tune', the resulting frequency ratio depends very much on the nature of the comparison. In particular, it matters whether the two notes are sounded together, as a chord, or sequentially and, if the latter, on how long an interval exists between hearing the two notes. It also depends on whether the two notes are rich in harmonics or not. If rich in harmonics and sounded together, then the Pythogorean, or just, major third will sound in tune. But if a solo cello, say, plays one note and then the other a little later, we (anyone with a good ear) tend to settle on a smaller interval for the major third. [In another life I taught a course on the Physics of Music and, in the class lab, conducted a few experiments on this topic.] It is interesting that many diatonic African instruments, such as the Balanje (bush piano) in Sierra Leone, increase the interval between both semitones of the equivalent Western major scale, so to our ears the thirds and sevenths sound a bit flat, and the fourths and tonic sharp. I've noticed that some kids, learning the violin, tend to do the same thing! Derek Lane-Smith To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
[abcusers] Pythagoras
There have been various interpretations on what the Pythagorian scale is Can anyone tell me where to find out what Pythagoras said in a reliable translation? No text by Pythagoras survives. His ideas on music were documented much later by Archytas and Aristoxenus. As the New Grove entry points out, there were many tuning systems in the Middle Ages and later that were labelled as Pythagorean while being no such thing. Pythagoreanism fitted into so many other conceptual schemes (e.g. astrology) that dropping the label was inadvisable. The New Grove also points out that it is very unlikely that Pythagoras really invented anything musically new - practicing Greek lyre players didn't need a mathematician/philosopher to tell them how to tune up. === http://www.purr.demon.co.uk/jack/ === To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
Re: [abcusers] multiple verses in abc2ps and relatives
Laura wrote: | Attached is a file of a tune with several verses. | | But then I forgot to attach it: My clone of abc2ps had the same problem, and I found it pretty quickly. If you have the source, there's a 1-byte change that will fix it. In abc2ps.h there are the lines: #define NWLINE 5 /* max number of vocal lines per staff */ ... char *wordp[NWLINE];/* pointers to wpool for vocals */ This is a hard limit of 5 w: lines per staff, and there's no runtine feechur for upping the number. So just change NWLINE to be a larger number and recompile. The right solution would make this dynamically sized, of course. I'll add this to my TODO file ... Which reminds me: My abc2ps clone is at sourceforge, but I haven't been able to learn how to tell people where to get it. It sure seems like it oughta be simple. Anyone know where the clues are hidden? To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
[abcusers] how about 372 key/mode combos, then?
Apropos of Pythagorean and related tunings, I saved this article from rec.music.early a while ago. Margo is r.m.e's resident exotic-early- tunings wonk (she plays this way herself on a pitch-configurable electronic keyboard). I *dare* any of you to ask her to expand on this... From "M. Schulter" [EMAIL PROTECTED] Sun Feb 18 23:00:09 2001 Status: Subject: Re: temperament term??? From: "M. Schulter" [EMAIL PROTECTED] Date: 18 Feb 2001 23:00:09 GMT Organization: Value Net Internetwork Services Newsgroups: rec.music.early References: v04003a50b6add422bc5a@[128.173.232.136] [EMAIL PROTECTED] Path: purr!news.demon.co.uk!demon!dispose.news.demon.net!demon!newsfeed.gamma.ru!Gamma.RU!news.maxwell.syr.edu!feed2.news.rcn.net!rcn!news2.best.com!vnetnews.value.net!not-for-mail Message-ID: 96pk5p$1bu$[EMAIL PROTECTED] Lines: 130 Article 9424 Jonathan Addleman [EMAIL PROTECTED] wrote: : But it WAS done now and then, if only to accomodate the range of : various singers. Vicentino talks about this use of the archicembalo, : since you can play in meantone in any key. Frescobaldi at some point : mentioned that an organ tuned in equal temperament would be good for : this reason as well, though I don't know where that reference is.. : (I got it 2nd or third hand...) Hello, there, and I must admit to being a bit confused by parts of this thread, which is one reason that I've preferred simply to read rather than to post up until now -- but maybe I can comment usefully on certain points, at least. First of all, I haven't really previously heard the terms "base" or "focus" in describing a tuning, although I might speak of range, for example "a 12-note meantone tuning of Eb-G#," or "a 19-note tuning, likely 1/4-comma, of Gb-B#," or "a 17-note Pythagorean tuning of Gb-A#, evidently of the type described by Prosdocimus de Beldemandis and Ugolino of Orvieto in the earlier 15th century." In this thread, there seems to be a focus on two types of temperament: the regular meantone tunings of the late 15th to late 17th centuries, still in use in the 18th century, which might feature anything from 12 to 31 notes per octave; and the 12-note "well-temperaments" of the late 17th to 19th centuries, where the circle of fifths closes -- as it does, either precisely or "virtually" for musical purposes, also in a 19-note meantone tuning of around 1/3-comma, or in a 31-note meantone of around 1/4-comma. Indeed Vicentino promoted his _archicembalo_ and _arciorgano_ -- his superharpsichord and superorgan (the latter a kind of positive organ which could be disassembled, carried on a mule's back, and then reassembled at the next performance location -- as permitting free transposition. If we speak in "keys" in an Elizabethan sense as referring to the pitch level of a modal final, rather than to later major/minor concepts, then it is indeed correct that Vicentino's 31-note meantone tuning makes available all intervals on all 31 steps of the cycle. Basically Vicentino's tuning scheme of 1555 seems to combine two features which by the late 17th century were recognized to result in _very slightly_ different tunings. He describes a division of the whole-tone into five "minor dieses" of equal size, which would call for 31-tone equal temperament (31-tET), with major thirds very slightly larger than pure; he also suggests that major thirds are pure (1/4-comma meantone). In practice, the variations in a tuning by ear could be greater than the theoretical difference between these two models. Quite apart from accommodating singers, Vicentino's tuning makes available "enharmonic" steps inspired by those of Ancient Greek theory, about 1/5-tone in size, which this composer and theorist espouses for their subtlety and "gentleness." Indeed, these fifthtone steps have a remarkable effect, and add an expressive dimension to some more typical 16th-century chromatic progressions also. More conventional theorists also address the matter of transpositions to accommodate singers, but within an apparent framework of 12-note meantone, where transpositions by fifths or fourths, or by a major second up or down (two fifths on the tuning chain), are most typical. In 1570, Guillaume Costeley describes a 19-note keyboard arranged in thirdtones dividing the octave into equal parts -- this, like Vicentino's 31-note tuning in or around 1/4-comma, is a circular scheme, which would permit free transposition. In 1618, Fabio Colonna describes his 31-note meantone keyboard, with a tuning scheme similar to Vicentino's (likely 1/4-comma), but a keyboard arranged in five groups of seven notes, with each rank tuned 1/5-tone apart (resulting in some replications of notes). To demonstrate the closed nature of this system, he provides a composition giving an "Example of Circulation" which moves through a circle of cadences on all 31 steps of the instrument, each featuring motion of the bass by a fifth down or a fourth up. He also shows how various modes can be transposed to
Re: [abcusers] intonation - Fomula for determining a half step in
I wrote: (...)This effectively means that they are in some kind of just tuning: the ratio of the frequency of each note to the drone frequency is a simple fraction with fairly low denominator. (...) It's close to the even tempered ale for the fifth and third, not so close with the second, for instance. (15-17 cents And Simon Wascher replied: I disagree strongly! the just third is quite far from the equaltempered. and the fifth is really different too. Sorry, I was going from memory, and had the second and third reversed. Here is the table someone posted to the UP list. (Made up, I am sure, with a hand calculator, not a tuner on a set of real pipes.) Anyway, the second is reasonably close and the third is not, as you say, but the fifth on the other hand is quite close. (There's an interesting choice for the G#: the two possibilities differ by 35 cents.) NoteJust Ratio (to D)Equal tempered fraction Difference in cents ---- - D 1:1 1.00 0 D# 16:151.0595+12 E 9:8 1.1225+4 Fnat6:5 1.1892+16 (!) F# 5:4 1.2599-14 G 4:3 1.3348-2 G# 7:5 or 10:7 1.4142-17 or +18 A 3:2 1.4983+2 A# 8:5 1.5874+14 B 5:3 1.6818-16 Cnat9:5 1.7818+18 C# 15:8 1.8878-12 D 2:1 2.0 Cheers, John Walsh To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
