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Please note this is an archived topic, so it is locked and unable to be replied to. You may, however, start a new topic and refer to this topic with a link: http://www.banjohangout.org/archive/341664/2
janolov - Posted - 05/04/2018: 11:30:25
Another joke with some relevance to this topic (I think I heard Bruce Molsky tell this on a Youtube clip):
Q: How long does it take to tune a banjo?
A: Nobody knows, it has never been done.
BrooksMT - Posted - 08/07/2018: 09:48:29
Universal offsets to obtain Just Intonation (JI) from any Equal Temperment (ET) electronic tuner
Good for any key, any tuning
Note offset,cents Scale Notes examples
1 0 C D G F
2 +3 D E A G
3 -12 E F# B A
4 -2 F G C Bb
5 +2 G A D C
6 -18 A B E D
7 -15 B C# F# E
1. Write down scale in your key. Scales for keys of C, D, G,and F are given as examples.
2. Choose notes for your tuning and tune strings to Equal Temperment using electronic tuner.
3. Consult table to obtain offsets from Equal Temperment.
4. Adjust tuning pegs to obtain approximate offsets, using your ears (-flatter than ET, +sharper than ET)
5. Adjust JI results to improve harmonics at 19th fret (or whatever fret you prefer to test harmonics)
6. Adjust tuning to get good-to-your-ear melody notes and chords.
Example: Sandy River Belle tuning fCFCD key of F according to Art Rosenbaum's "Old Time Banjo" book pg 100.
string offset
1st D -18 (about 20% flatter than ET)
2nd C +2 (slightly sharper than ET)
3rd F 0 (same as ET)
4th C +2
5th f 0
When I tune to this JI F tuning, my Sandy River Belle song sounds noticeably better, to my ear. This tuning uses the 6 note of the scale, D, which is the most different of the lot from ET. I used my fancy StroboPlus tuner so as to get exact offsets (did not need to approximate them by ear). I've always had trouble getting this song in this tuning to sound sweet. But with this JI, it does sounds sweet :-) I did not need to make any adjustments to the JI offsets. I also tried "She'll be comin around the mountain" in SRB tuning, and it also sounded sweet.
Hope you find this useful.
Edited by - BrooksMT on 08/07/2018 09:59:09
Rawhide Creek - Posted - 08/07/2018: 12:14:38
7. If you’re going to embark on lengthy discussions about temperament, use the correct spelling. (Some of us actually pronounce the third syllable: tem-per-a-ment.)
JoeDownes - Posted - 08/07/2018: 13:40:22
If you want to play in just intonation you need a fretless banjo or one with crooked frets. Just tuning the open strings in just intonation won't work for obvious reasons.
This fretboard is a compromise to play intervals closer to just intonation in the keys of E, A and D.
If you make a crooked fret fingerboard that's perfect for just intonation you can only play it in one key without changing the intervals. Equal temperament is the best you can get with an ET spaced fingerboard, assuming the intonation is correct to begin with. All other temperaments will have unisons on different stings sounding out of tune.
Edited by - JoeDownes on 08/07/2018 13:55:38
BrooksMT - Posted - 08/07/2018: 17:15:16
Joe, your comments were addressed earlier in the thread, I believe.
Just Intonation is a process directed towards a goal, namely, better intonation. I believe, or at least my ears tell me, that the process is worth the effort. If you feel otherwise, that's fine, I have no quarrel with you.
--------------
Not everyone, at least among those BHO members who write about intonation, can tell the difference between ET and JI. tuning. That's ok, we are all different :-) I wrote this thread for the musicians who want to explore other tuning methods. Ultimately, only your own ears can tell you whether other methods sound better or worse than ET. For banjoists who like to explore the plethora of alternate banjo tunings, JI may be helpful in making these alternate tunings sound sweeter. I struggled with Sandy River Belle tuning last year; it seemed to take a long time to get the banjo tuned to sound good; I'd tweek this then tweek that. Then, I tried setting up SRB using JI techniques, and was pleasantly surprized at how nice it sounded, with very little twiddling of the peghead knobs :-)
-------------------
Sorry Rawhide, I never could spell. I guess I just don't have the Temperment for spelling Temperament. Sorry for the spelling Dissonance.
Edited by - BrooksMT on 08/07/2018 17:26:57
dr4dpet - Posted - 08/09/2018: 01:09:42
On a somewhat related note:
I was in the forums and the main web site for Musescore, an alternative to TablEdit. I noticed there is a plugin titled Tunings and Temperaments. The description reads "Alter the tuning of a selection to one of a predefined list of available tunings and temperaments." Checking the readme file I see that just and equal are two of seventeen options. This would seem to be an easy way to compare the two if you are using a soundfont that is better than the standard midi sounds. I would guess, but don't know, that TablEdit has a similar option.
BrooksMT - Posted - 08/09/2018: 07:14:11
Thanks Dr4dpet, very interesting readme file. Obviously there are a lot of people who have tinkered with Temperament, more than I knew. I liked the thought, by the file author, that you could alter every tuning to put the wolfs in places where they would have less effect on the song.
G Edward Porgie - Posted - 08/09/2018: 19:55:35
17 temperaments doesn't surprise me at all. The most common, of course, are equal temperament, just intonation, mean-tone temperament, and Pythagorean tuning. There have been more than one kind of mean-tone temperaments. banjo players probably have their own temperaments; some do tune so that they achieve a G scale third that's closer to J.I, but might not touch the other notes.
People are still trying new, "improved" tunings. I know of a piano tuner in the S.F. Bay area who has set up his own tuning system, and has been tweaking it ever since he heard some of his original temperament thoughts actually recorded in a concert setting. If he's still with us, I'm sure he's probably still rejecting what, to many, is normal.
I've never given it much thought, myself. Were I a member of a Renaissance consort, then I'd worry about it more, but most of what I've encountered has been fairly contemporary and in multiple--and distant--keys, which are generally best served with equal temperament. And back when I tuned pianos, in over thirty years, I was never, ever asked to tune to anything other than equal temperament.
BrooksMT - Posted - 08/09/2018: 22:52:53
George, thanks for writing. It's my understanding that ET was designed for keyboard instruments. Retuning a piano with every key change is, to say the least, impractical :-) But for instruments with only 5 strings, retuning with key change is not only practical, but common with old time banjo, though not so much with bluegrass. So, if you are retuning anyway, choosing a temperament more friendly to the song becomes a possibility to consider.
It's sort of a shame that old time fretted instruments are stuck with a temperament designed for the piano. Going fretless for the first 5 frets or so is done by several professionals I respect, breaking the piano deadlock for at least that part of the neck. I have a fretless mountain banjo, I just don't play it much for some reason. When I do, am always pleasantly surprized at how sweet the fretless sounds; consonance is built in :-)
The Turkish musician and professor I referenced earlier, along with others in the microtonal world, have adjustable fret guitars and Turkish instruments. Someday, maybe banjoists will have the same *hopeful smile*. The western scale of 12 semitones in an octave will never be fully consonant, but it sure can be sweeter than we are used to with the piano fretting of our banjos and guitars.
G Edward Porgie - Posted - 08/10/2018: 07:15:34
Equal temperament was not designed because of the piano. It was developed primarily because composers were beginning to write pieces with more complex key changes within one movement or one score. It would have been extremely inconvenient to stop in the middle of a modulation in order to retune the entire orchestra to sound right for the new key.
Folk music, of course, generally doesn't change keys in such dramatic fashion, so just intonation could be more practical. I can easily see its use for "Sandy River Belle" and other tunes, but even on a banjo, it won't work well with a jazz number that Bill Keith might play, or some of that tunes of Bela Fleck. To the average ear (brought up with E.T.) it will simply sound sour. I also note that guitars are also fretted in E.T., so playing a J.I. banjo with one could sound rather odd.
While there are some very nice arguments for just intonation, and I am not arguing with your own choices about its use, I also think that perhaps you are not giving equal temperamemnt its proper respect for its service to modern western music. We have certainly given up some "sweetness," but we've gained a helluva lot of variety and flexibility with the use of equal temperament.
rudy - Posted - 11/19/2018: 09:56:53
Brooks,
Thanks for putting the effort into tackling such a mis-understood (and very often contentious) subject. It's a subject that is NOT easily understood and certainly is difficult to explain in a simple and easy to understand format. I wrote bluestemstrings.com/pageBanjoC...ips3.html">"Why Can't I Get This Thing To Play In Tune?" for my old website, even including a simple demonstration of a tri-tone chord played in both ET and then JI with the third lowered in pitch by 14 cents. The page is available at the internet archive link posted, although the tri-tone demo file might not be archived.
It was done to relate to banjo specifically, but tuning systems obviously apply to a wide range of instruments, and any fretted instrument is going to have problems trying to adapt to instruments that are designed to play in Just tuning, such as the Cajun accordion.
I played in a Cajun band for many years and built a few Cajun diatonic single row accordions. I also worked a bit with a prominent maker of accordions in Louisiana and re-tuned sets of Binci #1 reeds to Just tuning.
I do sometimes chuckle when I see the "crooked fret" photo, since the "inventor" obviously went to a LOT of work to try to "correct" ET, without the understanding that it's not "note values", but how the human ear perceives pitch relationships that is the real "elephant in the room".
BrooksMT - Posted - 11/20/2018: 08:33:29
Nice explanation of ET vs JI intervals on your site, Rudy. Thanks for posting the url. The sound file is, as you suspected, missing, even from the Wayback machine.
I'm blessed/cursed with semi-perfect pitch :-) From a young age I could hum an A whenever I wanted, but that's about it. There are many levels of "perfect pitch" Some people can name any pitch they hear, for instance (not me).
I also can tell when my banjo is playing in harmonious chords and intervals and when it's not. So Just Intonation, to the extent I can manage, i.e. to the extent I can make JI open tunings on ET frets work for me, is a partial solution. What is strange is that my ability to hear (and tune for) harmonious chords varies day to day. On a bad ear day, I can't get it right, and have learned to simply set the banjo down till my perception returns. With unlimited $ and space (we live in a small house), I'd get a set of moveable fret banjos, and leave them JI tuned in different keys...ah..bliss . Or I guess I could take up Cajun accordion, or harmonica :-)
The Turkish musician/scholar, Tolgahan Ço?ulu, will build a moveable fret guitar for customers, I think. In one of his videos, he simply uses double side tape to place short segments of fret wire flat on the fingerboard. That might be something for me to investigate. Several great banjo players use brass sheet on the nut to 7th fret portion of the neck, converting to partial fretless - their intonation is very good.
Tolgahan taped-on short frets:
youtube.com/watch?v=XT4oOYj4SwQ
Hunter Roberson - Lonesome John on partial fretless banjo
youtube.com/watch?v=2Kka9npO064
Edited by - BrooksMT on 11/20/2018 08:52:35
G Edward Porgie - Posted - 11/20/2018: 12:04:57
I have a recording of some Lou Harrison guitar pieces written with alternate temperaments involved (mostly just intonation, but if I recall, a Pythagorean temperament on one or two along with one or two in E.T.). The guitarist used a guitar with removable fingerboards each with fret spacings for each desired temperament. These were held in place to the neck with rare earth magnets. That would seem to me the most logical way to approach changing the fret spacing. It would be far more difficult to lose an entire fingerboard than it would be to lose a single partial fret, and the player wouldn't have to worry about tape residue when he/she changed the fret spacing for different temperaments. Just pop off the E.T board and replace it with the J.I.
JoeDownes - Posted - 11/21/2018: 02:49:20
quote:
Originally posted by rudyBrooks,
(...) I do sometimes chuckle when I see the "crooked fret" photo, since the "inventor" obviously went to a LOT of work to try to "correct" ET, without the understanding that it's not "note values", but how the human ear perceives pitch relationships that is the real "elephant in the room".
I don't get what you're saying here, Rudy.
rudy - Posted - 11/21/2018: 06:31:51
quote:
Originally posted by JoeDownesquote:
Originally posted by rudyBrooks,
(...) I do sometimes chuckle when I see the "crooked fret" photo, since the "inventor" obviously went to a LOT of work to try to "correct" ET, without the understanding that it's not "note values", but how the human ear perceives pitch relationships that is the real "elephant in the room".I don't get what you're saying here, Rudy.
Usually when the "crooked fret guitar" is posted it's someone who is reading a topic related to intonation problems and is sure the "solution" has been invented and is now available in the form of the crooked fret instrument.
The part about how we perceive pitch relationships relates to the fact that some people are more sensitive to reacting to harmonious pitch relationships than others. The OP here obviously is one of those folks who have difficulty ignoring "off pitch" note relationships. I've posted the link to my explanation of the "problem" as relating to ET and fretted instruments and how we should address it many times in the past, so I'm sure you've read it before.
Since I'm spent a lot of time designing and making fretted (as well as fretless) banjos it's a subject I spent considerable time wrapping my head around. In my day job I spent a lot of time working with complex waveforms and filters to isolate the frequencies contained within, so it gave me an excellent understanding of exactly why we find some note relationships harmonious vs. inharmonious as well as how simply combining those notes have unintended consequences that then influence our perception and response to what we hear.
Other than the website link that's about as simplified as I can make it, so hopefully that clears up any misunderstanding you might have about what I stated.
JoeDownes - Posted - 11/22/2018: 03:03:01
But the 'note value' (the frequency of the notes) is what determines the pitch relationship (intervals). The crooked frets move the 'note value' (frequency) closer to just intonation. In a way a crooked fretboard visualizes the difference between ET and the mean tone temperament of the fretboard. It also visualizes all the intervals that are not pure intervals when you tune your open strings to just intonation on a straight fret instrument. Here some fretboards you would need to play a guitar in just intonation in different keys. The same goes for banjo, of course.
Edited by - JoeDownes on 11/22/2018 03:06:02
G Edward Porgie - Posted - 11/22/2018: 07:47:53
This is a very good illustration of one reason why equal temperament was devised. One can readily see the problem of having to switch fretboards whenever a new key was introduced. The same happens with other instruments. In Mozart's day, the french horn players had to be ready to add or subtract tubing in the form of removable crooks when drastic key changes occurred, and it's also why trumpets were labeled "trumpet in C" or some other key for a specific piece. One might really cringe if attempting to play an organ or harpsichord with enough keys to cover all the notes needed for just intonation, or even to stop midway and re-tune an organ with the standard keyboard layout. Just imagine trying hurriedly to retune 100 or more pipes!
Rawhide Creek - Posted - 11/22/2018: 22:36:18
quote:
Originally posted by G Edward PorgieThis is a very good illustration of one reason why equal temperament was devised. One can readily see the problem of having to switch fretboards whenever a new key was introduced. The same happens with other instruments. In Mozart's day, the french horn players had to be ready to add or subtract tubing in the form of removable crooks when drastic key changes occurred, and it's also why trumpets were labeled "trumpet in C" or some other key for a specific piece. One might really cringe if attempting to play an organ or harpsichord with enough keys to cover all the notes needed for just intonation, or even to stop midway and re-tune an organ with the standard keyboard layout. Just imagine trying hurriedly to retune 100 or more pipes!
100 pipes is a very small organ. (I put myself through engineering school tuning pipe organs and rebuilding consoles.)
Here is an organ keyboard with “split” black keys, an early attempt to address the problem:
banjoak - Posted - 11/23/2018: 15:05:47
quote:
Originally posted by BrooksMTUniversal offsets to obtain Just Intonation (JI) from any Equal Temperment (ET) electronic tuner
Good for any key, any tuning
Note offset,cents Scale Notes examples
1 0 C D G F
2 +3 D E A G
3 -12 E F# B A
4 -2 F G C Bb
5 +2 G A D C
6 -18 A B E D
7 -15 B C# F# E1. Write down scale in your key. Scales for keys of C, D, G,and F are given as examples.
2. Choose notes for your tuning and tune strings to Equal Temperment using electronic tuner.
3. Consult table to obtain offsets from Equal Temperment.
4. Adjust tuning pegs to obtain approximate offsets, using your ears (-flatter than ET, +sharper than ET)
5. Adjust JI results to improve harmonics at 19th fret (or whatever fret you prefer to test harmonics)
6. Adjust tuning to get good-to-your-ear melody notes and chords.
Example: Sandy River Belle tuning fCFCD key of F according to Art Rosenbaum's "Old Time Banjo" book pg 100.
string offset
1st D -18 (about 20% flatter than ET)
2nd C +2 (slightly sharper than ET)
3rd F 0 (same as ET)
4th C +2
5th f 0
Your offsets are not quite right by a few cents. Major scale in cents = 0 - 204 - 386 - 498 - 702 - 884 - 1088 - 1200. (ET is in even 100 cent).
Sandy River Belle tuning fCFCD - shows issue on straight fret ET instrument. (even on 6 note limit). Getting open strings correct... the frets are not. Most problematic...
1st string third fret, (F note, tonic) will be 18 cents flat. The fifth fret (G note) is 22 cents flat. The other strings are not going to be significantly different than ET; 3rd string - fourth fret (A note) is still an ET third. The 2nd string second fret (D note) is 20 cents sharper than the adjacent open D note. (Note, in this tuning and context, moving the bridge to shorten the scale; might make it work better, but will still have then other note/fret issues; limited, not work in other context). Other tunings will have other fret issues.
If trying to achieve these results, some solutions. The examples of fingerboards (crooked or staggered) with individual note fret layout, designed for specific tunings, keys, intonation layouts. Adding more straight frets is another; gives more choices for notes.
Moveable frets idea can achieve some solutions. It's an old idea.. gut frets tied around neck. Adjustable for different specific tunings, scales, intonations. I've played with that idea on a banjo, similar to the tied on ones. Another DIY way is gluing a wire (paper clip) to thin plastic.. then using double sided tape to place where needed. These of course don't necessarily require full layouts, just adding few frets between existing, for notes you need for certain tunings and intonations. There is a bit of tradeoff between simple, close (and limited); vs more accurate but complex. (ET frets is sometimes just better tradeoff choice, for many reasons).
Of course if not needing complex chord fingering - fretless gives unlimited choice and flexibility.
------------
FWIW, offsets should not require electronic tuner, but done by ear.
Edited by - banjoak on 11/23/2018 15:14:37
banjoak - Posted - 11/23/2018: 17:53:56
The Cajun accordion, (single row diatonic melodion); quickly illustrates some aspects with JI.
Certainly can have it perfect in one diatonic key... for example C major. (typical accordion key) And plays C tunes great. But... those are push tunes.
Many tunes are pull tunes (it's like cross harp) - play in the key of G (or G mixolydian). The issue becomes the A note. As JI major sixth in C it makes solid 6/5 interval, 884 cents... and with F, makes solid IV chord. But in key of G the A serves as a fifth to the V (D chord), the D/A fifth would be 680 cent fifth. Sounds really bad. And as the V is usually more prominent in tunes, sustained, it is more noticeable. But rather than just use ET, they can temper some to have a balance of both. Usually making the A sharper, and might use some other tweaks. Often it's just about making certain choices, to what is more important.
Note, they often play with guitars, tuned in ET; but is not a problem. Similarly fiddles and singers also might tend to use JI, with ET guitars (or pianos). There are some various reasons why is not generally a problem.
G Edward Porgie - Posted - 11/23/2018: 21:26:16
quote:
Originally posted by banjoakquote:
Originally posted by BrooksMTUniversal offsets to obtain Just Intonation (JI) from any Equal Temperment (ET) electronic tuner
Good for any key, any tuning
Note offset,cents Scale Notes examples
1 0 C D G F
2 +3 D E A G
3 -12 E F# B A
4 -2 F G C Bb
5 +2 G A D C
6 -18 A B E D
7 -15 B C# F# E1. Write down scale in your key. Scales for keys of C, D, G,and F are given as examples.
2. Choose notes for your tuning and tune strings to Equal Temperment using electronic tuner.
3. Consult table to obtain offsets from Equal Temperment.
4. Adjust tuning pegs to obtain approximate offsets, using your ears (-flatter than ET, +sharper than ET)
5. Adjust JI results to improve harmonics at 19th fret (or whatever fret you prefer to test harmonics)
6. Adjust tuning to get good-to-your-ear melody notes and chords.
Example: Sandy River Belle tuning fCFCD key of F according to Art Rosenbaum's "Old Time Banjo" book pg 100.
string offset
1st D -18 (about 20% flatter than ET)
2nd C +2 (slightly sharper than ET)
3rd F 0 (same as ET)
4th C +2
5th f 0Your offsets are not quite right by a few cents. Major scale in cents = 0 - 204 - 386 - 498 - 702 - 884 - 1088 - 1200. (ET is in even 100 cent).
Sandy River Belle tuning fCFCD - shows issue on straight fret ET instrument. (even on 6 note limit). Getting open strings correct... the frets are not. Most problematic...
1st string third fret, (F note, tonic) will be 18 cents flat. The fifth fret (G note) is 22 cents flat. The other strings are not going to be significantly different than ET; 3rd string - fourth fret (A note) is still an ET third. The 2nd string second fret (D note) is 20 cents sharper than the adjacent open D note. (Note, in this tuning and context, moving the bridge to shorten the scale; might make it work better, but will still have then other note/fret issues; limited, not work in other context). Other tunings will have other fret issues.If trying to achieve these results, some solutions. The examples of fingerboards (crooked or staggered) with individual note fret layout, designed for specific tunings, keys, intonation layouts. Adding more straight frets is another; gives more choices for notes.
Moveable frets idea can achieve some solutions. It's an old idea.. gut frets tied around neck. Adjustable for different specific tunings, scales, intonations. I've played with that idea on a banjo, similar to the tied on ones. Another DIY way is gluing a wire (paper clip) to thin plastic.. then using double sided tape to place where needed. These of course don't necessarily require full layouts, just adding few frets between existing, for notes you need for certain tunings and intonations. There is a bit of tradeoff between simple, close (and limited); vs more accurate but complex. (ET frets is sometimes just better tradeoff choice, for many reasons).
Of course if not needing complex chord fingering - fretless gives unlimited choice and flexibility.
------------
FWIW, offsets should not require electronic tuner, but done by ear.
If this is supposed to bring a person to just intonation, by your own statement (the one that I've emphasized with bold type) this is not just intonation at all. When you claim that the "offsets" are off by even a few cents, you are not getting the pure overtones of JI. This is merely a different temperament; one of your own devising, and probably similar to some of the "mean tone" and other tunings used a couple of centuries ago--somewhere between J.I and E.T.
People who really want to play in true JI should by a fretless banjo and tune it properly for the desired key. Offsets from the ET layout of frets simply don't do the job accurately. I will add, however, that one of the things that distinguishes true J.I is that one can get a different "edge" should one switch to a closely related key, because the intervals will not be quite the same. The problem, though, is that when one tries to change immediately to a distant key without retuning the intervals sound too different and it's perceived as "sour," "discordant," or "just plain noise."
BrooksMT - Posted - 11/24/2018: 10:27:27
Sigh, I guess I should feel some joy that people are even interested in JI on BHO. Bashing my numbers, fine, go ahead.
If you (by this I mean *anyone*, not just the posters here) want to use different numbers, I have no problem with that. If you want to study the history of frets, intonation, and how to correct instruments for each key, I think you will find that there are many different ways to calculate the offsets. I chose one way, and if you chose another way, fine. It's your ear you have to please, after all, and if my numbers are not as pleasing as your numbers, then you should use your numbers!
If you want to use your ears to adjust string tensions to achieve good sounding intervals and chords, instead of offset numbers and an ET electronic tuner, that's fine also. For thousands of years, humans have used ears; electronic tuners were not available to Bach or Pythagoras :-) In the interest in meshing well with ET players in a group setting, I suggest you use your electronic tuner to set the string tension in whatever string(s) play the root note of the key, then use your ears to set the tensions in the rest of the strings.
Or, if there is a designated leader in the group, use his/her root tone to set your root tone; if you do it this way, you will by necessity have to use your own ears to set the rest of the strings to either the leader's non-root tones (which will be ~ ET if leader tunes with electronic tuner), or your own JI-by-ear tones. At this point, you will have to wrestle with the philosophic question: Is it better for the group to have off-tone pitches that exactly match the off-tone pitches of the leader, or will the band's sound be perceived by the audience as better if only the leader's pitches are off? Only you can answer that one :-) You might consider that sound engineers will record snippets of songs with the instruments retuned to sweeten just that snippet; the engineer then cuts and pastes the replacement sweet bits into the original track. In other words, sweetness (consonance) is important to people who deal with sound and pitch for a living, and by implication, is important to those who shell out $$ for a CD or for an individual .mp3.
As always, I hope my thoughts help you achieve whatever you want to achieve with your own music.
Edited by - BrooksMT on 11/24/2018 10:30:04
JoeDownes - Posted - 11/25/2018: 04:31:37
It's a good thing that folks reading this thread are aware that you don't get to play in just intonation by retuning the open string on a conventional banjo. You need to move the frets, too.
I wonder if a banjo tuned in just intonation would sound any good in a bluegrass context. Consider the 5th between A and E when playing in JI in G. It's tuned to 27:16, which sounds really unstable in a chord. So if there's a II chord in the piece you would need an extra fret to compensate. It's just not very practical.
Edited by - JoeDownes on 11/25/2018 04:37:06
JoeDownes - Posted - 11/25/2018: 06:29:27
Correction: the A to E fifth is tuned to 40:27, that is about 21 cent below where a perfect fifth ought to be.
Edited by - JoeDownes on 11/25/2018 06:34:29
banjoak - Posted - 11/25/2018: 08:04:59
quote:
Originally posted by G Edward Porgiequote:
Originally posted by banjoakYour offsets are not quite right by a few cents. Major scale in cents = 0 - 204 - 386 - 498 - 702 - 884 - 1088 - 1200. (ET is in even 100 cent)....
....Of course if not needing complex chord fingering - fretless gives unlimited choice and flexibility.If this is supposed to bring a person to just intonation, by your own statement (the one that I've emphasized with bold type) this is not just intonation at all. When you claim that the "offsets" are off by even a few cents, you are not getting the pure overtones of JI. This is merely a different temperament; one of your own devising, and probably similar to some of the "mean tone" and other tunings used a couple of centuries ago--somewhere between J.I and E.T.
People who really want to play in true JI should by a fretless banjo and tune it properly for the desired key. Offsets from the ET layout of frets simply don't do the job accurately. I will add, however, that one of the things that distinguishes true J.I is that one can get a different "edge" should one switch to a closely related key, because the intervals will not be quite the same. The problem, though, is that when one tries to change immediately to a distant key without retuning the intervals sound too different and it's perceived as "sour," "discordant," or "just plain noise."
I didn't actually devise those; just passing on the correct info. Those are the mathematical calculations to cents of 1/1; 9/8; 5/4; 4/3; 3/2; 5/3; 15/8; 2/1 - this is the basic 5-limit JI Diatonic scale. There is no more pure can get. There is no temperament, nor is any meantone; quite the opposite.
Just intonation is all about math and physics foundation of these low ratios, (and others... 6/5, 8/5, 16/15, 10/9). Very specific math calculations, the physics of how sound works, and relationships. Literal and not subjective.
If one note is vibrating at 440Hz another at 660 make 3/2 relation a perfect fifth; likewise 440 and 550 is 5/4 - a Just major third; 330 and 550 is 5/3 a Just major sixth. The lower the ratio, the less complex, stronger and more consonant node; harmonic locking. Easier it is for our brains to perceive.
This is very integrated... and a lot of mathematical congruency when you delve into it. Thus in making a single diatonic scale/mode layout using these, (it's only from a single tonic) it automatically includes a lot of the same exact relations (not different ones); which serve to give the scale a very consonant interlocked harmonic integrity. And then creating for triads, using a 5/4 (or 6/5) third and 3/2 fifth; not only from the tonic I; but same in the IV, V, and vi chords. True JI hallmark is incredible solid feel consonance. (not edge).
These explain why folks (esp singers/fiddlers) might naturally gravitate towards Just Intonation; and why folks consider it eay to hear and so powerful. (as compared to ET).
True JI basic 5-limit foundation is all about great solid harmonic relation, simply not designed for nor good at key modulation or chromaticism.
Edited by - banjoak on 11/25/2018 08:06:56
G Edward Porgie - Posted - 11/25/2018: 09:12:09
I'm not faulting your numbers. I'm simply saying that you still can't get JI in every key due to the spacing of the frets. I may have misunderstood your remarks about offsets, thinking that you were adjusting the JI intervals, but there is still no way to achieve these offsets as soon as a finger is placed behind an immovable fret. Even if your "D" string is tuned so it's the correct fifth (in cents) above the G tonic, as soon as you note at the second fret on that string, you are no longer in perfect J.I.
While it's certainly true that J.I. is based on solid math and physics, all of it goes out the window when one adds in the inevitable inharmonicity of a vibrating string. One can talk forever about these ratios, but in truth they only happen when all the notes are achieved on one string and no other strings are added to the harmonic mix. The overtones of, say, a G string can not be matched perfectly against the fundamental of a B string, because that G string cannot in reality vibrate in segments that are the correct ratio. Due to its stiffness, each and every harmonic it produces will be a tiny bit sharp. It's not much of a problem on the low numbered partials, but get up a bit and this inharmonicity can be really noticeable. One should not cite the physics and math of vibrating strings without also including the physical properties of the strings themselves.
BrooksMT - Posted - 11/25/2018: 11:46:03
George, see if I understand your post. I think you are talking about the difference between perfect string theory (also perfect JI theory), and the non-linear properties of materials (real string behavior):
1) The thicker the string, or the more tightly it's tensioned, the stiffer the string will be.
2)Stiffness alterers the vibration properties of a string, with more stiffness leading to sharper pitch (i.e.faster vibration than perfect string theory would predict).
In that case, I conclude 3) if harmonics of sympathetic vibration are important to you (as they are to me), then thicker strings should be loosened a bit (tuned flat comparted to the designated pitch, whatever the temperament chosen).
-------------
If the above conclusion is correct, then perhaps JI offsets to ET should be ignored if they suggest sharpening the pitch of any open string. And only the offsets that suggest flatting the pitch should be used when tuning a string. In my Aug 7,2018 post, those notes of the scale that JI suggest flatting are 3,4,6,7 (-12,-2,-18,-15 cents). Ignore offsets for notes 2,5 (+3,+2 cents).
--------------
I've noticed that I flat-tune the D string about 6 cents from JI when tuning double C. JI says the D note should be sharpened +3 cents according to my table. So my D string is really 9cents flat compared to ET. I tune flat to get a better sounding E (2nd fret) in the root chord. Since JI wants E to be -12cents offset anyway, my ears like the flatted D string to get a nicer, more JI-like, CEG root chord. I'd put it all down to wrong fret position for JI, but it's also possibly due to shortening the D tuned 1st (to make the E) makes the string stiffer, and thus play sharper. So I kill the D to enliven the E...the Dr. Frankenstein of Banjo :-) What it means to me is that adjusting your strings away from Any tuning scheme is probably necessary to get better sounding music.
banjoak - Posted - 11/25/2018: 12:09:29
quote:
Originally posted by BrooksMTSigh, I guess I should feel some joy that people are even interested in JI on BHO. Bashing my numbers, fine, go ahead.
Bashing?? I was just sharing information. I have had great interest in JI, from growing up with it to 45 years of exploring sound and intonations... combines many of my interests of music, math, science, acoustical physics, modal music and theory; - how sound works, what explains why things sound good. Among other instruments, I play fiddle, like most, quite a bit utilizing JI intervals... (it is fairly obvious a fiddle). JI is often a great match for lot's of traditional and (older) modal based music.
One thing I find very useful with JI... is to teach folks (esp fiddlers) about developing strong understanding of scales, intervals, harmonic understand and good intonation; show how is much easier to hear JI; (than their trying to swim around in ET).
quote:
Originally posted by BrooksMT
If you (by this I mean *anyone*, not just the posters here) want to use different numbers, I have no problem with that. If you want to study the history of frets, intonation, and how to correct instruments for each key, I think you will find that there are many different ways to calculate the offsets. I chose one way, and if you chose another way, fine. It's your ear you have to please, after all, and if my numbers are not as pleasing as your numbers, then you should use your numbers!
As in my previous post... Just Intonation 5-limit intervals are very specific... a major third is 5/4 (386 cents), period. Same as a perfect fifth is always 3/2. There is not really other numbers nor ways to calculate and still achieve Just intervals. It's not subjective about whose ear to please.
You of course can use any note you want and decide if it's more pleasing or not... but if it's not 3/2 then it's not a perfect fifth. It's tempered.
As I had mentioned previously, in playing, a few cents off on a note might not be that important, especially on a banjo (for some other reasons, some that Rudy briefly alluded to). What is more valuable is understanding target intonation and system... this is especially true when you need to make decisions about the layout of notes in say a scale. Otherwise it's easy to get off, drift, have errors accumulate; not recognize potential problems. Very important for fretless players, fiddlers... they have little to guide them other than good sense of what intonation should be. As well anyone needing to make fixed pitches, whether frets, free reeds, or electronically. And playing with others, really understanding the intonation system (whatever one you choose) can be useful, make a difference in the final result.
The reason I mentioned by ear, rather then electronic tuner... is similar to issues of fiddlers learning, by ear is far superior. (as well, for banjo, the point of JI is that it sounds better to the ear; so dependent on being able to hear it.)
FWIW - I find ET does have it's use as well, incredibly useful but in different context.
JoeDownes - Posted - 11/25/2018: 12:10:47
(...) What it means to me is that adjusting your strings away from Any tuning scheme is probably necessary to get better sounding music. (...)
So the solution to the century old tuning system problem is not to use a tuning system at all?
Banjoak, when you play fiddle tunes on the violin with lots of seconds, do you play them closer to JI or ET? I once heard a classical violin player say that most of them prefer the more even spacing of ET for most melodies and the sweetness of JI for harmonies.
Edited by - JoeDownes on 11/25/2018 12:22:45
G Edward Porgie - Posted - 11/25/2018: 13:34:43
quote:
Originally posted by BrooksMTGeorge, see if I understand your post. I think you are talking about the difference between perfect string theory (also perfect JI theory), and the non-linear properties of materials (real string behavior):
1) The thicker the string, or the more tightly it's tensioned, the stiffer the string will be.
2)Stiffness alterers the vibration properties of a string, with more stiffness leading to sharper pitch (i.e.faster vibration than perfect string theory would predict).
In that case, I conclude 3) if harmonics of sympathetic vibration are important to you (as they are to me), then thicker strings should be loosened a bit (tuned flat comparted to the designated pitch, whatever the temperament chosen).
-------------
If the above conclusion is correct, then perhaps JI offsets to ET should be ignored if they suggest sharpening the pitch of any open string. And only the offsets that suggest flatting the pitch should be used when tuning a string. In my Aug 7,2018 post, those notes of the scale that JI suggest flatting are 3,4,6,7 (-12,-2,-18,-15 cents). Ignore offsets for notes 2,5 (+3,+2 cents).
--------------
I've noticed that I flat-tune the D string about 6 cents from JI when tuning double C. JI says the D note should be sharpened +3 cents according to my table. So my D string is really 9cents flat compared to ET. I tune flat to get a better sounding E (2nd fret) in the root chord. Since JI wants E to be -12cents offset anyway, my ears like the flatted D string to get a nicer, more JI-like, CEG root chord. I'd put it all down to wrong fret position for JI, but it's also possibly due to shortening the D tuned 1st (to make the E) makes the string stiffer, and thus play sharper. So I kill the D to enliven the E...the Dr. Frankenstein of Banjo :-) What it means to me is that adjusting your strings away from Any tuning scheme is probably necessary to get better sounding music.
The problem arises mostly when the intervals of one string conflict with those of another. There are really no good adjustments to fix that. If an open string is flatted slightly, it still may not match with the notes on the second string playing harmony because both strings will produce more than one overtone and they will all deviate from more and more from one another in a greater fashion as one reaches the higher overtones.
Part of the reason for all of the various temperaments that have been used over the centuries is that people do hear some of the odd things that happen with vibrating strings and tried to get a more harmonious sound by tuning differently. Obviously, this is still happening, and particularly in folk realms where even those who play primarily in equal temperament sometimes retune their B string so the key of G sounds better (to them, anyway!)
Personally, I'm not against temperaments other than equal. I do think, however, that people should be aware of the fact that there is absolutely no tuning that will ever be completely perfect. I happen to prefer E.T, because I'm originally from the world of western classical and modern music which runs through every key known to man, many modes, chromatic modulations and oddities like whole tone scales. For others' purposes, JI, or mean tone, or Pythagorean is fine and important to each particular sound and style. I will add that equal temperament, just as with JI, is only accurate in theory, and the stiffness factor is still an issue. It's why octaves on a piano are stretched--the higher note doesn't match the overtone of the lower, but it's more acceptable to the ear to hear a smooth interval rather than the wah-wah-wah produced when a perfectly tuned octave is sounded. Because perfect tunings don't really exist due to mechanical limitations that interfere with the perfection of physics and math, I can't complain about anybody using whatever tuning they wish to use. I just hope they do it with some understanding of what they are changing and it's overall effects, rather than simply changing a note or two because they like how it sounds. Here in the western world, most every music we hear is ET and we're pretty much used to that sound, so it pays to be aware that what one individual is doing may sound screwy to others. It also pays to be aware when playing in a group of just how the others are tuning. Different temperaments don't always mix well.
Rawhide Creek - Posted - 11/25/2018: 18:55:30
Discussions of temperament, when applied to fretted instruments, frequently devolve to threads like this one: There is some very sound (no pun intended) information that does apply, more that does not, and then there is a large voodoo component that is entertaining but ranges from oversimplistic to misleading to absolute nonsense.
banjoak - Posted - 11/26/2018: 07:18:54
quote:
Originally posted by JoeDownes
Banjoak, when you play fiddle tunes on the violin with lots of seconds, do you play them closer to JI or ET? I once heard a classical violin player say that most of them prefer the more even spacing of ET for most melodies and the sweetness of JI for harmonies.
It really depends on context; the type of tune, the key, mode, tempo, how it lays out on fiddle and tuning, open strings, double stops, who I might be playing with. Mostly I just listen to what sounds better, but balancing with what's more important and/or pragmatic.
Mostly for JI diatonic the second tone of scale, will typically use a 9/8 (204 cent), for both melody and harmony; but might be times when 10/9 (182) might be better choice. As well I differentiate between Just fixed scales to then Just intervals and Just triads/chords; and moveability. There are times I might use a bit of hybrid system... that still uses lots of just intervals for double stops, or chords, but might also follow some ET as needed.
In your other question about the second with the sixth not being a fifth in a ii chord... can have more than one A note or E note; changed for context. (it's ike the old G# vs Ab, or even Abb). So if for a ii chord; the choice is 182 second, or use a 906 sixth. Pragmatically, probably the latter; if not just use ET; as tunes get more chordy complex... IMO looses its JI significance... so ET works better. There ae some other aspects about the type of tunes that likely make ET better.
G Edward Porgie - Posted - 11/26/2018: 08:15:23
quote:
Originally posted by Rawhide CreekDiscussions of temperament, when applied to fretted instruments, frequently devolve to threads like this one: There is some very sound (no pun intended) information that does apply, more that does not, and then there is a large voodoo component that is entertaining but ranges from oversimplistic to misleading to absolute nonsense.
That statement can be applied to almost any thread on any topic.
banjoak - Posted - 11/26/2018: 08:37:41
quote:
Originally posted by rudy
how the human ear perceives pitch relationships that is the real "elephant in the room".The part about how we perceive pitch relationships relates to the fact that some people are more sensitive to reacting to harmonious pitch relationships than others. The OP here obviously is one of those folks who have difficulty ignoring "off pitch" note relationships.
I agree that "perception" aspects are often ignored. Lot's of misinterpretation, myths, and then over rating the theory; which don't quite match real world observations. The role context plays and psychoacoustic effects, has been of interest to me, esp what explains why some things work that theoretically shouldn't. Things that should be problems don't actually seem to be. Things that are supposed to be very important, don't seem to be so much.
I don't think it's merely some people are more sensitive (nor anything to do with perfect pitch). But rather there are conditions that make these relationships more apparent or less apparent... or important; and how and what our brains perceive and are capable of perceiving. (including being fooled by illusion).
One aspect. How folks might obsess on getting "in-tune". What do we really mean? Many folks can quote some method or ideal exact number. (some rely on a tuner) - but it might be worth considering what makes it sound "out-of tune" - that is the point of divergence where target listener notices. With that gives a "window" of intonation. Then consider the window is not uniform on every note in a tune, in every tune, every environment, every context; and consider everything else about the music; some the window needs to be narrower than others.
For example; slow music, long notes, foreground, played on violin or voice, primary scale (1/3/5/6) solid tones, with full power sustain of over 250 milliseconds, esp against a strong tonic or drone. Compared to fast music, short notes, on more percussive notes, sharp noisy attack/little sustain, background, each note voiced maybe 40 milliseconds and a new note comes in every 110 milliseconds; and includes more complex, chromatic, passing, non-chord tones. Add to that if solo quiet, vs other instruments, lots of quick complex ET chord movement (III7, VI7, aug, dim, 13th, 9th-5); drums... strong rhythmic quality (groove); and in a noisy environment like dance or club. So in one might be easy to hear, think you have good ears... in some, kind of wonder if our ears have time or are really even capable to determine if in-tune. Yet the latter still sounds good. Maybe our brains use implied intent? Maybe if just enough info of intonation intent exists, it can fool the ear.
Related to this text, that when folks (myself included) are in their home, slowly tuning their guitar or banjo... can notice that pesky B note, and maybe other aspects with bridge and compensation, and (esp new discovered) love of JI intervals... heightened zoomed in focus and maybe concern. But it might be important to reminded to zoom out... and listen in context of music.
Might explain why playing JI lead/vocal with ET chords works... as long as zoom out and listen to the whole group.
And of course other aspects of music, articulation, rhythm, groove, expression, composition, arrangement... seems to override weakness/deficiencies. As reminded sometimes on fiddle... if you want to make better music maybe focus on these other things, more than if you are within a tenth of a cent of a tuner.
Edited by - banjoak on 11/26/2018 08:45:50
Rawhide Creek - Posted - 11/26/2018: 08:56:59
quote:
Originally posted by G Edward Porgiequote:
Originally posted by Rawhide CreekDiscussions of temperament, when applied to fretted instruments, frequently devolve to threads like this one: There is some very sound (no pun intended) information that does apply, more that does not, and then there is a large voodoo component that is entertaining but ranges from oversimplistic to misleading to absolute nonsense.
That statement can be applied to almost any thread on any topic.
Now that you mention it. . . .
G Edward Porgie - Posted - 11/27/2018: 08:33:00
The only other thing I'd like to add is that too many people don't know about Equal Temperament or Just Intonation. They seem to be using "Unjust Intonation" instead, and anyone with a good ear can tell. It's a temperament that punishes the listener unfairly.
BrooksMT - Posted - 11/27/2018: 08:50:55
Banjoak - When my ears go haywire, and I can't get instrument in tune, I am sitting in my usual practice place at home. So, I don't think acoustics are the source of the trouble. But...I never considered acoustics, so next time I'll change room and see if that helps. I've certainly noticed that different rooms yield a different feel/tone for the banjos and guitars I have (kitchen with lots of hard surfaces gives a ringy, sustained tone, while bedroom with cloth wall hangings and shelves of folded t-shirts gives a more subdued tone). Thanks for listing the many factors that go into acoustic perception.
George - "Unjust intonation".....I love it :-)
Russ - this thread has stayed remarkably intonated, compared to the tonal creep of other threads I follow :-). My thanks to all who have posted and continue to post.
banjoak - Posted - 11/27/2018: 09:08:08
I don't think i referred to room acoustics, although that could play a part. The main point I was trying to point out... is there are times when all is quiet, no distractions... and things like banjo resonance really ring... sustain to your ears... and you are playing a few notes slowly, it can be really easy to focus, zoom in and really notice a lot of very fine tune stuff (in very small cent). And perhaps overrate that; even get a bit OCD; assume that it should be noticeable in all contexts; and to others.
Similar, sometimes fiddlers read about perfect intonation in ET, over worry... told or believe it will sound "out of tune" if not within some perfect pitch standard. They themselves can't hear, but worry. I remind them they probably have average hearing, you can't intone better than you can notice; but just go for good, not perfect, it will naturally improve - and to think about potential listeners are probably less sensitive, so will the vast vast majority actually notice? But if you can't notice it probably won't matter much.
Edited by - banjoak on 11/27/2018 09:24:29
steve davis - Posted - 12/10/2018: 14:18:52
I stop adjusting when the G that's an octave lower than the open low G appears when the open strings are strummed down through.
A flattening of the B string brings this low G out.
Edited by - steve davis on 12/10/2018 14:20:37
steve davis - Posted - 12/14/2018: 06:46:51
The historic adjustments to intonation have hinged on the listening experience,imo.
Rawhide Creek - Posted - 12/14/2018: 23:55:22
quote:
Originally posted by steve davisThe historic adjustments to intonation have hinged on the listening experience,imo.
This is why the book, The Historic Adjustments to Intonation, by Stephen Davis, sells so well.
Who else knows more about the history of tuning?
Edited by - Rawhide Creek on 12/15/2018 00:02:15
steve davis - Posted - 12/15/2018: 09:11:48
We all have our own opinions,Russ.They don't have to pass your muster.
Maybe you should learn that lesson.
I'm thinking that intonation rules were first found working well with singers who were automatically adjusting intonation to sound sweeter.
Those that tuned instruments such as the harpsichord applied this sweeteness to the instrument they were setting up/building.
yeoldbanjoguy - Posted - 12/15/2018: 10:30:18
Russ. Is that book available on audiobooks? Or can I just order it through amazon.com
Bruce
G Edward Porgie - Posted - 12/15/2018: 12:27:26
For what it's worth, I believe Russ's inclusion of that devil's face indicates that he was mostly just joking around.
Actually, intonation adjustments go at least as far back as Pythagorus (yes, they had music and musical instruments back then) because the way humans hear didn't always make for a good tuning procedure.
It's pretty easy to sing in tune (for many people, anyway) and even early on, it was pretty easy to tune an instrument properly for a particular key. The trouble began when the key changed within the same piece. Due to the fact that Just intonation is based on the overtones of one given key note, but each note produces a different series of overtones, when the key was changed, the tuning would be slightly off and if the piece migrated too far from the home key, it began to sound bad. There were a number of attempts made to rectify this with adjustments to the intonation, which ultimately lead to equal temperament, where each interval was mis-tuned slightly to make all keys sound the same. It wasn't accepted at first, probably because some musicians thought it made everything sound out of tune, but our ears have managed to adjust and now ET is pretty much standard.
So even though one could say that intonation adjustments hinged on the listening experience, it's actually a bit more complex and subtle. If there hadn't been a step toward modulations within the same piece of music, no one would have felt the need to adjust anything. Also, due to the fact that ears do adjust to different temperaments (ET being the prime example) it could be said that it's the adjustments that have changed the listening experience, and not the other way around.
steve davis - Posted - 12/15/2018: 13:14:50
I didn't find it funny,George.I have no problem speaking my mind.
Rawhide Creek - Posted - 12/15/2018: 13:24:03
Yes, George, you’re right; I was being a smart-alec.
The excursion into different keys within a single work was indeed facilitated by 12TET; however, the “character” (or “flavor”, if you like) of different keys was certainly compromised, if/when not lost altogether.
A historical aspect you omit is the attempt to reconcile mathematics with music, of itself an entire philosophical pursuit off and on for centuries. As you yourself have pointed out, on more than one occasion, this physics (and physical consequences) of this is demonstrated in various ways, including the requisite and inevitable “stretching” of octaves low and high when tuning a piano.
And, as I have mentioned more than once, I have both my piano and my harpsichord tuned to Young’s #2 (1799, I think), not 12TET. I tune the harpsichord myself; but my piano technician/tuner is retiring next year (he’s 80-something) and I don’t know if I can find another. There’s a good one I’ve known for a long time from my two-plus decades in Kansas City; he’s just a kid (i.e., four years younger than I), but paying him to drive 2-1/2 hours each way, twice a year, is daunting.
Edited by - Rawhide Creek on 12/15/2018 13:31:24
steve davis - Posted - 12/15/2018: 13:34:46
My thoughts are based in an understanding of human nature and its quest for perfection.
Rawhide Creek - Posted - 12/15/2018: 13:45:08
quote:
Originally posted by yeoldbanjoguyRuss. Is that book available on audiobooks? Or can I just order it through amazon.com
Bruce
Bruce, the two books on intonation/tuning/temperament that I recommend often are:
Tuning and Temperament: A Historical Survey by J. Murray Barbour (1951). Dover has reprinted it for years. It began as Barbour’s thesis for his PhD; he subsequently expanded it into a book. He intended it to be a defense of 12TET but it outgrew that to become a standard reference work. It is sometimes tediously technical but nevertheless a worthy addition to your bookshelf.
How Equal Temperament Ruined Harmony (and Why You Should Care) by Ross W. Duffin (2007). This is a less technical and more reader-friendly book on tuning and temperament. It includes anecdotal material not found elsewhere and, despite the subject matter, is fun to read.
I believe both titles are available from Amazon, and they are not expensive.
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