[LUTE] Re: Temperament wondering...
-Original Message- From: Sam Chapman [mailto:[EMAIL PROTECTED] Sent: Saturday, October 04, 2008 12:40 AM To: Andrew Gibbs Cc: Lute List Subject: [LUTE] Re: Temperament wondering... In any tempered fretting system that's been worked out properly you need to first set the frets, then tune the strings to each other in perfect octaves or unisons, since these intervals must be pure in all schemes. If you insist on all unisons and all octaves being pure you have no choice - you must use equal temperament. This is a straight forward calculation in linear algebra. Best wishes, Rainer aus dem Spring IT Business Solutions Division CONFIDENTIALITY DISCLAIMER The information in this email and in any attachments is confidential and may be privileged. If you are not the intended recipient, please destroy this message, delete any copies held on your systems and notify the sender immediately. You should not retain, copy or use this email for any purpose outside of any NDA currently existing between Toshiba Electronics Europe GmbH and yourselves. Toshiba Electronics Europe GmbH Hansaallee 181 - 40549 Duesseldorf - Germany Phone: +49 (211) 5296-0 - Fax: +49 (211) 5296-400 Handelsregister Duesseldorf HRB 22487 Geschaeftsfuehrer: Hitoshi Otsuka Amtsgericht Duesseldorf To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Temperament wondering...
You're right, Rainer - but just in case there's any misunderstanding: In a meantone temperament you don't expect all the apparent octaves to be pure, for example the Gb on the first fret (high position) of the 4th course with the F# on the fourth fret (low position) of the 2nd course - this is just a consequence of having frets which are straight and cannot be in different positions on different courses. You still expect the proper octaves to be pure, such as 2nd fret 4th course with open 1st course. Anyone using meantone fretting has to be aware of the limitations and test only some octaves and not others (and move frets according to the notes required by the piece). Best wishes, Martin Spring, aus dem, Rainer wrote: -Original Message- From: Sam Chapman [mailto:[EMAIL PROTECTED] Sent: Saturday, October 04, 2008 12:40 AM To: Andrew Gibbs Cc: Lute List Subject: [LUTE] Re: Temperament wondering... In any tempered fretting system that's been worked out properly you need to first set the frets, then tune the strings to each other in perfect octaves or unisons, since these intervals must be pure in all schemes. If you insist on all unisons and all octaves being pure you have no choice - you must use equal temperament. This is a straight forward calculation in linear algebra. Best wishes, Rainer aus dem Spring IT Business Solutions Division CONFIDENTIALITY DISCLAIMER The information in this email and in any attachments is confidential and may be privileged. If you are not the intended recipient, please destroy this message, delete any copies held on your systems and notify the sender immediately. You should not retain, copy or use this email for any purpose outside of any NDA currently existing between Toshiba Electronics Europe GmbH and yourselves. Toshiba Electronics Europe GmbH Hansaallee 181 - 40549 Duesseldorf - Germany Phone: +49 (211) 5296-0 - Fax: +49 (211) 5296-400 Handelsregister Duesseldorf HRB 22487 Geschaeftsfuehrer: Hitoshi Otsuka Amtsgericht Duesseldorf To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Temperament wondering...
Just so Martin. The principal problem with meantone on fretted instruments has often been raised before but it's always as well to repeat it for those new to the issue: If the diatonic and chromatic sequence between frets as one ascends the fingerboard were the same on each string then meantone fretting could indeed by applied, but since this is not the case then, as you say, a number of significant compromises have to be made. These compromises are, of course, less if one stays in certain positions and and the music does not modulate very far from the tonic. Martyn --- On Sat, 4/10/08, Martin Shepherd [EMAIL PROTECTED] wrote: From: Martin Shepherd [EMAIL PROTECTED] Subject: [LUTE] Re: Temperament wondering... To: Lute List lute@cs.dartmouth.edu Date: Saturday, 4 October, 2008, 11:12 AM You're right, Rainer - but just in case there's any misunderstanding: In a meantone temperament you don't expect all the apparent octaves to be pure, for example the Gb on the first fret (high position) of the 4th course with the F# on the fourth fret (low position) of the 2nd course - this is just a consequence of having frets which are straight and cannot be in different positions on different courses. You still expect the proper octaves to be pure, such as 2nd fret 4th course with open 1st course. Anyone using meantone fretting has to be aware of the limitations and test only some octaves and not others (and move frets according to the notes required by the piece). Best wishes, Martin Spring, aus dem, Rainer wrote: -Original Message- From: Sam Chapman [mailto:[EMAIL PROTECTED] Sent: Saturday, October 04, 2008 12:40 AM To: Andrew Gibbs Cc: Lute List Subject: [LUTE] Re: Temperament wondering... In any tempered fretting system that's been worked out properly you need to first set the frets, then tune the strings to each other in perfect octaves or unisons, since these intervals must be pure in all schemes. If you insist on all unisons and all octaves being pure you have no choice - you must use equal temperament. This is a straight forward calculation in linear algebra. Best wishes, Rainer aus dem Spring IT Business Solutions Division CONFIDENTIALITY DISCLAIMER The information in this email and in any attachments is confidential and may be privileged. If you are not the intended recipient, please destroy this message, delete any copies held on your systems and notify the sender immediately. You should not retain, copy or use this email for any purpose outside of any NDA currently existing between Toshiba Electronics Europe GmbH and yourselves. Toshiba Electronics Europe GmbH Hansaallee 181 - 40549 Duesseldorf - Germany Phone: +49 (211) 5296-0 - Fax: +49 (211) 5296-400 Handelsregister Duesseldorf HRB 22487 Geschaeftsfuehrer: Hitoshi Otsuka Amtsgericht Duesseldorf To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Temperament wondering...
You're right - it's not a circular process if the fretting system has been worked out properly. As I said, I've been using David van Ooijen's instructions for tuning in 1/6 comma and it's a straight- forward process. But I was referring to the historical instructions found on the LSA Fret Placement Chart, which (no disrespect to the Ancients) haven't been passed down to us 100% accurately. So there's some to-ing and fro-ing between frets and open strings to figure out that Gerle, for instance, was aiming at approx. 1/6 comma. Obviously, having established this, I don't need to repeat the process - I can just tune straight to 1/6 comma... On 3 Oct 2008, at 23:39, Sam Chapman wrote: In any tempered fretting system that's been worked out properly you need to first set the frets, then tune the strings to each other in perfect octaves or unisons, since these intervals must be pure in all schemes. If this doesn't work and your lute sounds out of tune, then the fret placement has been wrongly calculated. There should be no need for a circular process (unless you're interested in inventing a new temperament by trial and error). -- To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Temperament wondering...
Ah...I see what you mean Andrew! In reply to Rainer, Martin and Martyn: perhaps I'm being incredibly naive, but I've always managed to tune octaves and unisons on my theorbo with no beating, whether or not I set the frets equal or to some variety of meantone. Of course I don't count, for example, g-sharp to a-flat as an octave or unison. I simply stick on tastino if I need a different note, or use alternate fingerings if I'm playing continuo. Do you really suggest that one should tune, for example, the 6th course so that it beats with the 1st and 13th when using temperaments other than equal? Perhaps we misunderstood each other? All the best, Sam 2008/10/4 Andrew Gibbs [EMAIL PROTECTED]: You're right - it's not a circular process if the fretting system has been worked out properly. As I said, I've been using David van Ooijen's instructions for tuning in 1/6 comma and it's a straight- forward process. But I was referring to the historical instructions found on the LSA Fret Placement Chart, which (no disrespect to the Ancients) haven't been passed down to us 100% accurately. So there's some to-ing and fro-ing between frets and open strings to figure out that Gerle, for instance, was aiming at approx. 1/6 comma. Obviously, having established this, I don't need to repeat the process - I can just tune straight to 1/6 comma... On 3 Oct 2008, at 23:39, Sam Chapman wrote: In any tempered fretting system that's been worked out properly you need to first set the frets, then tune the strings to each other in perfect octaves or unisons, since these intervals must be pure in all schemes. If this doesn't work and your lute sounds out of tune, then the fret placement has been wrongly calculated. There should be no need for a circular process (unless you're interested in inventing a new temperament by trial and error). -- To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html -- Sam Chapman Oetlingerstrasse 65 4057 Basel (0041) 79 530 39 91
[LUTE] Re: Temperament wondering...
Thanks andrew, but i have a problem with LSA file, i see every thing as 0, beside the english... i used both office 2008 and Neoofice, and it showed me the same thing. might be becuase I'm a mac user... On Oct 2, 2008, at 1:48 PM, Andrew Gibbs wrote: Hello Omer I've been tackling this issue myself recently. I started by trying some historical instructions for fret placement (found on the The Lute Society of America Fret Placement Spreadsheet): http://www.cs.dartmouth.edu/~lsa/download/index.html I found, after a lot of trial and error, that Gerle's instructions led to more-or-less 1/6 comma, which is more-or-less what I wanted. An easier way of achieving 1/6 comma (and 1/4 comma) is very clearly explained on David Van Ooijen's site: http://home.planet.nl/~ooije006/david/writings/meantone_f.html Andrew On 2 Oct 2008, at 11:00, Omer katzir wrote: i guess any one already have his favorite, and i want to discover my own... sssoo Any recommendation? i want it for my nice little 7c...but i might try something new with my guitar :-D thank you again Omer -- To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Temperament wondering...
On Fri, Oct 3, 2008 at 8:22 AM, Omer katzir [EMAIL PROTECTED] wrote: Thanks andrew, but i have a problem with LSA file, i see every thing as 0, beside the english... More than you'll ever need: http://www.netcat.li/instrument-tuner/TemperamentTables.html -- *** David van Ooijen [EMAIL PROTECTED] www.davidvanooijen.nl *** To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Temperament wondering...
The LSA file works on my mac - but I found those historical instructions for placing frets weren't really that useful - I think some are inaccurate (Dowland's doesn't seem to make much sense). And there's no instructions on how to tune the open strings - so if you don't know what temperament you're aiming for, it makes the process a bit circular - tweak the frets, tweak the open strings, tweak the frets etc My basic understanding is that 16th c lute players would have used some kind of meantone - ranging from 1/4 to 1/8 - but of course wouldn't have used that terminology as the fine maths weren't worked out until later when meantone was on the point of becoming obsolete. This is my basic understanding - I'm sure someone on this list will know better/more... Andrew On 3 Oct 2008, at 07:22, Omer katzir wrote: Thanks andrew, but i have a problem with LSA file, i see every thing as 0, beside the english... i used both office 2008 and Neoofice, and it showed me the same thing. might be becuase I'm a mac user... -- To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Temperament wondering...
Actually, Dowland's tuning is quite sensible. The rule of 18 sets a lute (in theory, neglecting string stretch caused by sideways displacement at the finger and fret) to very-nearly equal temperament. Apparently, the stretch added by actually fingering the strings brings it very very close. This isn't too hard to understand if you look at the math. ET12 is based on each higher semitone frequency being in a ratio of the 12th root of 2 to the previous frequency. From A=440, this is about 440*1.0594631 =466.163761 (using 20 digits for the multiplication and throwing away the seventh decimal on: even still, with 7 decimals, the answer to six decimals is .03 higher!) The rule of 18 uses a ratio of 1+1/18 =.055keep repeating 5's forever, and the result of multiplying this times 440 is 464.4repeating 4's. The percentage of error here is on the order of -.36%. It is not hard to raise the pitch of a string by 1/300th of its current frequency with sidestretching. The error is cumulative, because each subsequent fret is set to (1+1/18)^fret#, but the string is not parallel to the frets (unless you are very lucky) which probably adds stretch, but also the side-stretch caused frequency increase decreases as you approach the middle of the string, which probably nullifies the effect, so the highest frets will be off by as much as 7*-.36, or about 2.4%. This is worth a bit of fudging, but the fifths are already flat from pure, and this amount of difference may not be significant. The rule-of-18 ratio for the fifth is 1.45005 (rounded to five decimals) while the ET12 fifth ratio is 1.49831 (again, to rounded to five decimals.) The just intonated fifth is 1/5. This makes rule-of-18 fifths over A=220, before figuring string stretch modifications, 321.211Hz, ET12 is 329.62Hz, and just is 330Hz. Does anyone have good data on frequency deviation caused by string stretch on a Dowland-era 8-course (for instance) lute? As I have mentioned before, at least to my ear, Dowland's and Holborne's music sounds very good with rule-of-18 fret placement, even without modification. (Then again, the lutes I have been able to play have all had the action a bit too high.) It doesn't seem to work so well for other composers, though. Ray On Fri, Oct 3, 2008 at 5:19 AM, Andrew Gibbs [EMAIL PROTECTED] wrote: The LSA file works on my mac - but I found those historical instructions for placing frets weren't really that useful - I think some are inaccurate (Dowland's doesn't seem to make much sense). And there's no instructions on how to tune the open strings - so if you don't know what temperament you're aiming for, it makes the process a bit circular - tweak the frets, tweak the open strings, tweak the frets etc My basic understanding is that 16th c lute players would have used some kind of meantone - ranging from 1/4 to 1/8 - but of course wouldn't have used that terminology as the fine maths weren't worked out until later when meantone was on the point of becoming obsolete. This is my basic understanding - I'm sure someone on this list will know better/more... Andrew On 3 Oct 2008, at 07:22, Omer katzir wrote: Thanks andrew, but i have a problem with LSA file, i see every thing as 0, beside the english... i used both office 2008 and Neoofice, and it showed me the same thing. might be becuase I'm a mac user... -- To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Temperament wondering...
That does sound sensible - and ingenious - but from recollection, the measurements given by the LSA chart for Dowland's lute gave a narrow distance between the second and third frets, which didn't sound much like ET to me - and generally didn't seem to produce a pattern of proportionally reduced distances between the frets that I imagine you would get from such a system. Any ideas where I went wrong? Andrew On 3 Oct 2008, at 13:45, William Brohinsky wrote: Actually, Dowland's tuning is quite sensible. The rule of 18 sets a lute (in theory, neglecting string stretch caused by sideways displacement at the finger and fret) to very-nearly equal temperament. Apparently, the stretch added by actually fingering the strings brings it very very close. .. -- To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Temperament wondering...
OK, I'm stupid this week. Sorry. Rule of 18 is from Vincenzo Galilei and predates the Varietie of Lute lessons. I'll check dowland's tuning when I get home and see if I can make sense of it as well. Interestingly, Doctor Oakroot remarked on possible inaccuracies in Dowland's tuning instructions in this list in April of 2006: it might be instructive to pursue that thread, in the mean time! Ray On Fri, Oct 3, 2008 at 9:32 AM, Andrew Gibbs [EMAIL PROTECTED] wrote: That does sound sensible - and ingenious - but from recollection, the measurements given by the LSA chart for Dowland's lute gave a narrow distance between the second and third frets, which didn't sound much like ET to me - and generally didn't seem to produce a pattern of proportionally reduced distances between the frets that I imagine you would get from such a system. Any ideas where I went wrong? Andrew On 3 Oct 2008, at 13:45, William Brohinsky wrote: Actually, Dowland's tuning is quite sensible. The rule of 18 sets a lute (in theory, neglecting string stretch caused by sideways displacement at the finger and fret) to very-nearly equal temperament. Apparently, the stretch added by actually fingering the strings brings it very very close. .. -- To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
[LUTE] Re: Temperament wondering...
In any tempered fretting system that's been worked out properly you need to first set the frets, then tune the strings to each other in perfect octaves or unisons, since these intervals must be pure in all schemes. If this doesn't work and your lute sounds out of tune, then the fret placement has been wrongly calculated. There should be no need for a circular process (unless you're interested in inventing a new temperament by trial and error). 2008/10/3 Andrew Gibbs [EMAIL PROTECTED]: The LSA file works on my mac - but I found those historical instructions for placing frets weren't really that useful - I think some are inaccurate (Dowland's doesn't seem to make much sense). And there's no instructions on how to tune the open strings - so if you don't know what temperament you're aiming for, it makes the process a bit circular - tweak the frets, tweak the open strings, tweak the frets etc My basic understanding is that 16th c lute players would have used some kind of meantone - ranging from 1/4 to 1/8 - but of course wouldn't have used that terminology as the fine maths weren't worked out until later when meantone was on the point of becoming obsolete. This is my basic understanding - I'm sure someone on this list will know better/more... Andrew On 3 Oct 2008, at 07:22, Omer katzir wrote: Thanks andrew, but i have a problem with LSA file, i see every thing as 0, beside the english... i used both office 2008 and Neoofice, and it showed me the same thing. might be becuase I'm a mac user... -- To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html -- Sam Chapman Oetlingerstrasse 65 4057 Basel (0041) 79 530 39 91
[LUTE] Re: Temperament wondering...
Hello Omer I've been tackling this issue myself recently. I started by trying some historical instructions for fret placement (found on the The Lute Society of America Fret Placement Spreadsheet): http://www.cs.dartmouth.edu/~lsa/download/index.html I found, after a lot of trial and error, that Gerle's instructions led to more-or-less 1/6 comma, which is more-or-less what I wanted. An easier way of achieving 1/6 comma (and 1/4 comma) is very clearly explained on David Van Ooijen's site: http://home.planet.nl/~ooije006/david/writings/meantone_f.html Andrew On 2 Oct 2008, at 11:00, Omer katzir wrote: i guess any one already have his favorite, and i want to discover my own... sssoo Any recommendation? i want it for my nice little 7c...but i might try something new with my guitar :-D thank you again Omer -- To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
