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Thread: Sweetened tuning

  1. #26
    Mandolin user MontanaMatt's Avatar
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    Default Re: Sweetened tunning

    So, my experience is that the sweetened tuning is the real deal. My four piece switched to stroboclips. Our sound gelled. When we play in b and e, the guitar and the banjo use the capo function to correct for the key...I use it for my mando, and a new level of intonation happens. I recommend doubters read about the interval inaccuracy of the 12tet system. That being said, it does take extra time to retune for key changes, but we listen to in ear hi-fidelity monitors, so the dry signal of the monitors is very noticeable to me.
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    Default Re: Sweetened tunning

    Quote Originally Posted by MontanaMatt View Post
    So, my experience is that the sweetened tuning is the real deal. My four piece switched to stroboclips. Our sound gelled. When we play in b and e, the guitar and the banjo use the capo function to correct for the key...I use it for my mando, and a new level of intonation happens. I recommend doubters read about the interval inaccuracy of the 12tet system. That being said, it does take extra time to retune for key changes, but we listen to in ear hi-fidelity monitors, so the dry signal of the monitors is very noticeable to me.
    Happy pickin
    Thanks Matt, I couldn't remember who had posted this experience. So you guys re-tune between numbers during performances?
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  3. #28
    Mandolin user MontanaMatt's Avatar
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    Default Re: Sweetened tunning

    Quote Originally Posted by Mark Gunter View Post
    Thanks Matt, I couldn't remember who had posted this experience. So you guys re-tune between numbers during performances?
    Not every tune, but when the guitar adds a capo, he hits the capo button and retunes, same with the banjo. I've been doing it for bmaj, using capo 4 setting. My understanding is it centers the turnings for the native key's frequently used notes. I don't play much open strings in b so it's detuning of open fifths is only noticeable when we get back to g or d. We usually play a few songs in b in a row when we all go through the retuning. We all mute so our audience doesn't hear what's going on.
    The bass doesn't bother to retune as he's fret less and using his ear to match our pitch.

    If you have a stroboclip, check out what I'm talking about with chords in b...standard tuned, and capo 4 tuned, it becomes noticeable.

    This is all under the standard mandolin sweetener tuning
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  5. #29
    The Amateur Mandolinist Mark Gunter's Avatar
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    Default Re: Sweetened tunning

    Quote Originally Posted by foldedpath View Post
    It's not about the quoted accuracy of all these tuners, Snark, Peterson, or whatever. They all have quartz crystal circuits that are incredibly accurate on an electronic level.

    It's about how good the analog front-end is with the pickup, and how good the back-end design is for the analog display that tells you when you're "in tune" with an LED or LCD display. And also about how wide the margin of acceptance is for what the tuner considers to be in-tune. Any manufacturer can design a tuner that seems to "lock on" quickly by having a wide acceptance margin.

    I know some folks get frustrated by tuners that show upper harmonics like the Peterson tuners, but that lets you decide how close you want to get -- how close is "good enough" for the situation -- instead of a basic tuner with a wider margin and a more basic display.
    Actually, I think the quoted accuracy is an important aspect. Non-strobe tuners are generally accurate to +/-3 cents. That gives a worst-case 6 cent possible spread on a reading of "accurate" or "in-tune", and the difference is enough for your ears to hear the beats. This is why collective wisdom says to tune one string in a course by the tuner, and its twin by ear. A true strobe tuner is far more accurate.

    Some "regular" tuners have a so-called "strobe mode" that uses an LED display that mimics the appearance of a strobe tuner, but uses the same, regular circuitry and method with a +/-3 cent margin of error. This is the reason I bought a strobe tuner. You don't need a strobe tuner, or any electronic tuner to tune your instrument well - see Norman Blake videos above - electronic tuners are newfangled things. But if you want a highly accurate tuner for setting intonation on instruments, a strobe tuner is a practical necessity. It has nothing to do with the fact that all these tuners use solid state chips, but everything to do with the method behind the circuitry and programming. Regular tuners suffer from inherent limitations in their methodology.

    When I use a strobe tuner and get accurate readings of in-tune on a pair of strings, my ears tell me that the strings are in unison without further tweaking. So by that experience, and what I've been told for years, and what I've read on the accuracy of different types of tuners, I believe it. You may be right that "any manufacturer can design a tuner that seems to "lock on" quickly by having a wide acceptance margin" - I won't try to dispute that - but I do believe that the accuracy of strobe tuners vs. other designs is generally accepted fact. I haven't found any literature that indicates otherwise.
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  7. #30
    Registered User Ivan Kelsall's Avatar
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    Default Re: Sweetened tunning

    Olaf - Many thanks. So - it's the stringed instrument version of 'The well tempered clavier' ?. I fully understand that fretted instrument intonation is a clever compromise,but a compromise nevertheless.

    The way i tune my mandolins is to tune 1 string in each course to an elec.tuner,then the second string to the first string by ear = 'tuning the unisons'. I then check them 'course to course',fretted at the 7th fret. Usually D matches G / A matches D (so closely that they sound perfectly ok) but the E strings on my Weber & Lebeda are a tiny fraction flat,so i tune 'em up to suit that A at the 7th & they sound fine. Only my Ellis is ''almost'' perfectly spot on A to E,possibly due to Tom Ellis making his own custom compensated bridges for his mandolins.

    Here's how piano tuners do it :- Click image for larger version. 

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  8. #31
    Registered User grassrootphilosopher's Avatar
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    Default Re: Sweetened tunning

    Quote Originally Posted by DavidKOS View Post
    Ah, the guitar "sweetened" tuning debate now in mandolin form.

    "Basically all fretted instruments are out of tune all of the time"

    Only if you assume that "pure" just intonation tuning is the only tuning. Our fretted instruments are in tune, to a system called 12 tone equal temperament.

    ...
    Well ain´t that some kind of a sweetened tuning? ... just saying...

    Your reference to the different tuning approaches shows that we do "sweeten" the tuning whichever approach we are using.

    I took Ivan´s question as a general question and not just as related to the mandolin. Therefore specific tuning topics that arise in other instruments (guitar) are ok to bring up, no?

    Also, tuning has to do something with our ears, namely how we accept intervals. The setup of the instrument is crucial.

    Listen to Tony Rice:



    I agree that it has to do with the individual instrument (Clarence White D-28). I also agree that with an instrument that is tuned in fifth the interval thingy is not as crucial. Yet listen to this:



    The adjustments made by the violin is also a way of "sweetening".

    Further elaborated here:



    What I´m saying is, that we use a certain way of tuning that already takes into consideration our hearing/listening habits.

    As this thread has derailed somewhat by strongly discussing different tuning approaches I would like to come back to the Peterson HD tuner and its sweetening modes.

    I see that the sweetening modes on the Peterson HD tuner deals with the different types of music that the customers play. I think that the sweetened tunings of mandolin, banjo, "fiddle" and acoustic guitar have the bluegrass customer in mind. Therefore the sweetener focuses on G and C shapes on the mandolin, the typical B-string tuning topic on a guitar and for the fiddle probably on blending it into the guitar and mandolin sweetened tuning.

    I found out that with the wider acceptance range of tuners such as a Korg (I have some older ... but quite ok ... ones) the intonation is quite less acurate. In this case you do not hear a "sweetening" as pronounced (probably not at all).

    After having used (the old) Peterson stroboclip for some time (in various modes, EQ, ACOU, MAN, BJO etc. on various instruments, guitar, mandolin, banjo, dog house bass) I found out that my hearing got sensitive to a point where I strongly started to notice the different modes, their strong points and their drawbacks. I still "tweak" by ear. But the Peterson stroboclip makes tuning a lot easier.
    Olaf

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  10. #32
    Registered User grassrootphilosopher's Avatar
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    Default Re: Sweetened tunning

    Quote Originally Posted by Ivan Kelsall View Post
    Olaf - Many thanks. So - it's the stringed instrument version of 'The well tempered clavier' ?. I fully understand that fretted instrument intonation is a clever compromise,but a compromise nevertheless.
    You could probably call it that. The "compromise" is what I would call the sweetening.

    My beautiful Strad-O-Lin does need a lot of compromise when it comes to setup. I once was fool enough to take the bridge off. I could not get the instrument set up properly. So I thought I´d take it to some (gifted) violin makers. They put the bridge back on. They did not change the bridge height or anything else. The open strings and the twelfth fret were perfectly in tune. The harmonics were there. Yet all the notes inbetween were off. So I had to drive my 350 km to my nearest mandolin maker of choice to have him set up the instrument well. Lesson learned.

    Even my new (now 11 years old) F-5 needs (a little) compromise. I sincerely doubt that there is anyone out there who could say that there is no compromise in tuning.

    When I started to learn how to tune an instrument I checked the harmonics (guitar at the 5th, 7th and 12th fret, mandolin 7th and 12th fret). Now I do all sorts of things, the afore mentioned harmonics, the Norman Blake thing on guitar (guitar: listen to the interval of the adjacent strings one played open the other fretted at the 2nd fret 3rd fret on the B-string in reference to the G-string) and most of all listening to the intervals while playing the strings open (see Tony Rice). I learned this while tuning with the Stroboclip. I got quite good at it so far. It´s all tweaking.
    Olaf

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    Default Re: Sweetened tunning

    Quote Originally Posted by Mark Gunter View Post
    ... collective wisdom says to tune one string in a course by the tuner, and its twin by ear. ...
    .
    Overall, the thread linked in Post #7 does not appear to support the idea that this is in fact collective wisdom.

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    Default Re: Sweetened tunning

    I find Norman Blake's videos very interesting.

    I rarely am happy with a guitar tuned to a tuner, certainly using the open strings, although I get on a bit better by tuning the D note (third fret) of the second string to the tuner rather than the open B.

    I usually find it's ok for a mandolin, however.
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  14. #35

    Default Re: Sweetened tunning

    Good point.. and in the promo video's for the StroboClip HD their reasoning is exactly that.

    The human ear can detect variances of 2 cents or more. So if you have a Snark tuned ensemble with +- 5 cents these instruments can potentially be 10 cents apart and easily sound off pitch.

    For my own use, I'm considering the 'sweetened tuning' for strictly my solo recording work for the moment. I consider the value of the StroboClip HD to be that if I begin the set spot on, then it should hold there reasonably through the end of the set.
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  16. #36
    Registered User Hendrik Ahrend's Avatar
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    Default Re: Sweetened tuning

    A tuning is also called "temperament", a term derived from the latin "temperare", which means something like "to temper", "to milden", "to soften" and, if you will, "to sweeten". So "sweetened tuning" is a pleonamus, doesn't make much sense to begin with. David is spot on with his explanation of modern equal temperament. Ideas of that equal temperament have been around since at least 1511 (Arnold Schlick), but wasn't generally adopted (for pipe organs and pianos) until the mid 18th century, especially because super artists like Bach more and more wanted to compose in all keys. The price, however, was high: In equal temperament, all major thirds sound 13.7 cents (of a tempered halfnote) out of tune, "too wide", so to speak. All fifths, a less important interval since after the middle ages, are too narrow. Out of tune thirds are a major problem with instruments that generate lots of overtones, such as a harpsichord. But it not so much a problem with modern pianos. Their strings are moved by felt hammers - overtone killers. Now, pianos sound comparatively boring (as compared to harpsichords and other "historical instruments with complex overtone structures; the most boring - to name the opposite - would be a tuning fork with just a sinus curve). When it comes to dynamics however, piano is king. Not for nothing the instrument is being called "piano forte". Still, equal temperament is so boring on the piano that piano tuners have developed a method of "stretching" the temperament over the whole keyboard compass, that is tuning the notes a bit "too high" the higher they are on the keyboard. So, only on the overtone-poor piano, the octaves are not tuned pure, they beat a bit. Those beat-frequencies make a piano sound more colorful and interesting, an approach called "sweetening", at which every piano tuner has his own art. In this sense, only on the piano tuning can be an artistic approach. On all other instruments, tuning is merely technical, especially when you rely on a tuner. (Just for the record, there are lots of keyboard instrument tunings like "Werckmeister", that are called "well-tempered": The idea is to favor several more frequent major thirds at the cost of some more rare major thirds, the latter typically the ones with more bs and #es.) Fretted instruments are usually made for equal temperament, although in reality and merely due to individual differences and basic problems (e.g. frets generally straight, strings differ in tension), not all notes obey exactly to equal temperament on each and every note and instrument, technical issues, if you will. That said, in my view and to my experience (I do own a Peterson) a "sweetened tuning" for mandolins is just a sales pitch, appearing like some advanced and highly sophisticated artistic development in temperament, some sort of progress. Any temperament remains a compromise. Of course, if you tune your strings in pure fifths, all your fifths (and fourths) should sound nice and pure, the major third for instance on the note A however (7th fret on the D-string, 4th fret on the A-string) becomes even wider than the already false sounding 13.7 cents, thus almost unbearable. Such trade-offs just can't be avoided with sweetening. Which doesn't make sense at all to me. (It should be clear that mandolins shouldn't be tuned after the violin.) The sweetening of the piano cannot be transferred to the mandolin, because a whole string, all possible notes on that string, are tuned higher (or lower for that matter). Doesn't seem like delicate approach to me, but instead one put on with a shovel. Not only that, I like the display on the Peterson, but I find the many possibilities and the need to keep the owner's manual within reach quite annoying.

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    The Amateur Mandolinist Mark Gunter's Avatar
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    Default Re: Sweetened tuning

    Quote Originally Posted by Henry Eagle View Post
    That said, in my view and to my experience (I do own a Peterson) a "sweetened tuning" for mandolins is just a sales pitch, appearing like some advanced and highly sophisticated artistic development in temperament, some sort of progress.
    +1 on that

    Quote Originally Posted by Henry Eagle View Post
    Such trade-offs just can't be avoided with sweetening. Which doesn't make sense at all to me.
    See Mandoplumb, post #20: "but if I play BG guitar I’m playing the G shape and the D shape so much more than the E shape so why shouldn’t my guitar be tuned to sound better in G and D. That is where the personal sweeting comes in. Sweeten it for what your ear and your music needs."

    And repeating from post #18: 'I don't "argue" for any kind of "sweetened" tunings - but I would say that two things logically make "sweetened" tunings popular and desirable to some. One would be the characteristics of any individual instrument, and another would be the personal tastes of an individual player.'


    Quote Originally Posted by Henry Eagle View Post
    I like the display on the Peterson, but I find the many possibilities and the need to keep the owner's manual within reach quite annoying.
    Just think how annoying you'd find the early mechanical strobe tuners.
    Last edited by Mark Gunter; Nov-24-2017 at 1:21pm. Reason: emphasis added in quotes
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    Registered User Timbofood's Avatar
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    Default Re: Sweetened tuning

    I wonder what Carlton Haney might say about this.....
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  22. #39
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    Default Re: Sweetened tunning

    Perfect tuning bothers me a little. An extreme example would be electronic sounds with perfect wave forms vs. any acoustic instrument. Which sounds better: mathematical perfection or hand made imperfection? I’ve said this before but i quickly grew tired of the band “Boston” due to their perfect tuning and harmony. It’s boring and impersonal. I prefer live recordings over studio perfection.
    I hope you get my drift here. No offense to the discussion above, which is very interesting
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    Registered User foldedpath's Avatar
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    Default Re: Sweetened tunning

    Quote Originally Posted by MontanaMatt View Post
    Not every tune, but when the guitar adds a capo, he hits the capo button and retunes, same with the banjo. I've been doing it for bmaj, using capo 4 setting. My understanding is it centers the turnings for the native key's frequently used notes. I don't play much open strings in b so it's detuning of open fifths is only noticeable when we get back to g or d. We usually play a few songs in b in a row when we all go through the retuning. We all mute so our audience doesn't hear what's going on.
    The bass doesn't bother to retune as he's fret less and using his ear to match our pitch.

    If you have a stroboclip, check out what I'm talking about with chords in b...standard tuned, and capo 4 tuned, it becomes noticeable.
    I can see where this might work for a Bluegrass or other Americana style band, where you stay in one key for a while. But man, that really would NOT work for Irish music!


    It's slippery stuff. Three tunes played in a continuous set might not be in the same keys/modes. Some tunes will even shift different keys/modes back and forth within the same tune like "Kid on the Mountain," "Knocknagow," etc. And then there are tunes are in gapped scales where you can't even tell if they're supposed to be a major or minor feel. Irish trad isn't the only music that does this. You hear it in Jazz and Pop music too. But it's one of the distinctive features of the music that keys aren't as locked-down as they are in Americana styles.

    Another wrinkle is that certain diatonic melody instruments will play C natural a bit sharp -- the "piper's C," or "C supernatural." I have to be careful when backing a Dmix tune on guitar, avoiding a full C chord that clashes with the melody instruments. This is one case where I could use a sweetened tuning, but then it wouldn't work if the next tune in a set is in a different key. In this style of music at least, keeping my Peterson in bog standard 12TET is a least common denominator approach that seems to work best.

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    Default Re: Sweetened tunning

    Quote Originally Posted by Cochiti Don View Post
    Perfect tuning bothers me a little. An extreme example would be electronic sounds with perfect wave forms vs. any acoustic instrument. Which sounds better: mathematical perfection or hand made imperfection? I’ve said this before but i quickly grew tired of the band “Boston” due to their perfect tuning and harmony. It’s boring and impersonal. I prefer live recordings over studio perfection.
    I hope you get my drift here. No offense to the discussion above, which is very interesting
    Don, I'm sorry to say it, but there is no perfect tuning, even if all notes were electronically measured true to equal temperament. Only the octaves are pure. I'm quite sure you mean something completely different.

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    Default Re: Sweetened tunning

    Quote Originally Posted by Henry Eagle View Post
    Don, I'm sorry to say it, but there is no perfect tuning, even if all notes were electronically measured true to equal temperament. Only the octaves are pure. I'm quite sure you mean something completely different.
    Thanks. I am fairly ignorant about these things
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    The Amateur Mandolinist Mark Gunter's Avatar
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    Default Re: Sweetened tunning

    Quote Originally Posted by Cochiti Don View Post
    Perfect tuning bothers me a little. An extreme example would be electronic sounds with perfect wave forms vs. any acoustic instrument. Which sounds better: mathematical perfection or hand made imperfection? I’ve said this before but i quickly grew tired of the band “Boston” due to their perfect tuning and harmony. It’s boring and impersonal. I prefer live recordings over studio perfection.
    I hope you get my drift here. No offense to the discussion above, which is very interesting
    Hey Don, I get your drift, but Henry's got a good point - and what you're talking about is personal taste there; obviously, there are Boston fans somewhere who love whatever it is you don't like about them. And, think about the other extreme - say, a live performance by someone on an instrument discordantly "out of tune" who can't carry a tune with vocals. Ouch.

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    Default Re: Sweetened tunning

    Quote Originally Posted by Cochiti Don View Post
    Perfect tuning bothers me a little. An extreme example would be electronic sounds with perfect wave forms vs. any acoustic instrument. Which sounds better: mathematical perfection or hand made imperfection? I’ve said this before but i quickly grew tired of the band “Boston” due to their perfect tuning and harmony. It’s boring and impersonal. I prefer live recordings over studio perfection.
    I hope you get my drift here. No offense to the discussion above, which is very interesting
    Totally off topic here but Boston's problem is they only have one song, lots of lyrics and titles but one song.

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    Default Re: Sweetened tuning

    If anyone wants to really geek out about intonation and temperament, there are two good books on my shelf (and probably more that aren't).

    Duffin, Ross W., How Equal Temperament Ruined Harmony (and Why You Should Care)

    Isacoff, Stuart, Temperament: How Music Became a Battleground for the Great Minds of Western Civilization

    Both are accessible to anyone who is a bit of a nerd, but neither requires a PhD to understand. As others have said, any system is full of compromises. The compromises you are used to sound best, at least until you start messing with others. Cajun music, for example, has its own tuning conventions. To me, it always sounds out-of-tune, but I'm sure people who hear a lot of it don't notice at all, and they probably find equal temperament equally grating.

    The whole point of Bach's well-tempering system, and our current use of equal temperament, is to allow the use of all key signatures. Old music (pre-Bach) rarely uses more that two or three sharps or flats. When they did, it was for effect: listen to Heinrich Biber's Rosary Sonatas sometime. They get progressively more and more tortured as he moves through scordatura—different tunings of the solo violin. Subsequent temperaments hoped to reduce the torture, although until the advent of equal temperament, different key signatures were presumed to have different emotional characters, caused by the tempering. It was a more interesting world.

    Any "sweetening" will come with benefits and drawbacks. Does one outweigh the other?

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    Default Re: Sweetened tuning

    Quote Originally Posted by Louise NM View Post
    ...Duffin, Ross W., How Equal Temperament Ruined Harmony (and Why You Should Care) ...
    I wonder if that's why some of the pre-Bach, and some Bach, pieces have occasional notes that, when played on modern instruments, sound horribly dissonant and clashy and harsh, like "Why would anyone write that, it sounds awful."

    I used to think they must have just liked clashy weird music back then, some sort of style or fashion of the times.

    But, if old composers were writing for different temperaments, that would explain a lot. They might be horrified to hear how their compositions sound on modern pianos etc.

    I did notice, early on in my piano lessons, that the major 3rds were so sharp as to be almost unlistenable.

    At least on a non-piano stringed instrument, you can do stuff to adjust the sound of a prominent note in a particular tune, if it becomes irritating. For instance, on banjo in 2C tuning, I intentionally de-tune the 1st string slightly so that the 3rd note of the scale (on the 2nd fret of 1st string) sounds sweet... however, I have to intentionally bend (sharpen) that same string's 5th-fret note (the fifth note of the scale) up a little bit to make it sharp enough to sound right, otherwise the 5th fret note is noticeably flat since I've detuned the open string slightly. In that tuning, the open 1st string is often just a passing note and doesn't seem to have as much emphasis, so it can get away with being a little out of tune. Anyway...

    I can see I have much reading to do.

    Thanks for the links!

  33. #47

    Default Re: Sweetened tunning

    Quote Originally Posted by Mark Gunter View Post
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    I see what you did there, adding the mandolin to the pic. Good job!

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  35. #48
    Registered User Ivan Kelsall's Avatar
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    Default Re: Sweetened tuning

    From Kip Carter - " The human ear can detect variances of 2 cents or more..". The human ear at it's best can distinguish between 440 Hz & 441Hz !!. There's a multitude of I/net articles to read up on 'tuning / hearing'.

    I've mentioned before on here,that compared to a 5-string banjo,mandolins are a cinch to tune. Getting a good compromise between the 3rd G string & the 2nd B & 1st D strings is a real PITA. Not only does the fretting innacuracy come into play,but the flexibility of the neck does as well. Ask any 5-string player & they'll tell you the same thing.

    Years back,i used to use several of the multitude of different banjo tunings to play 'Old Timey' tunes. That didn't last too long. Re-tuning to standard Bluegrass tuning D,G,B & D took way too long,& when you're playing to an audience,to have folk watching you tune up for 5 minutes or more,isn't really courteous - something that i wish all musicians would consider !,
    Ivan
    Weber F-5 'Fern'.
    Lebeda F-5 "Special".
    Stelling Bellflower BANJO
    Tokai - 'Tele-alike'.
    Ellis DeLuxe "A" style.

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  37. #49
    but that's just me Bertram Henze's Avatar
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    Default Re: Sweetened tunning

    Quote Originally Posted by Mark Gunter View Post
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    the scribbling on the blackboard seems to be a wild mixture of trigonometry and complex numbers, and yes, e is the connection between the two but if e = 2.9 in the US I totally understand why BG songs sound so out of tune...
    the world is better off without bad ideas, good ideas are better off without the world

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  39. #50
    poor excuse for anything Charlieshafer's Avatar
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    Default Re: Sweetened tuning

    Quote Originally Posted by JL277z View Post
    I wonder if that's why some of the pre-Bach, and some Bach, pieces have occasional notes that, when played on modern instruments, sound horribly dissonant and clashy and harsh, like "Why would anyone write that, it sounds awful."

    I used to think they must have just liked clashy weird music back then, some sort of style or fashion of the times.

    But, if old composers were writing for different temperaments, that would explain a lot. They might be horrified to hear how their compositions sound on modern pianos etc.
    )
    Well, possibly to some degree. Many of the compositions were written with odd intervals in mind, and they still are played and sound that way in a lot of the Bach Partitas and Sonatas. It was mentioned earlier that much of what our ears perceive as "pleasant intervals" are a function of our culture. As in: modern western European/U.S culture. A simple example of this would be to hit the streaming services and type in "Dzintars" or "Bulgarian Women's Choir." By using vocals as example instead of instruments, you eliminate any question of intent, tuning, weird instruments played in odd ways, etc. You'll find the chords and intervals and modes to be very unfamiliar to our ears, constantly shifting from discordant to sweet. It's what they want.

    When you're talking temperament, the cents between notes varies by an audible difference between the types of temperament, but not that much. There's a button box builder in Australia, Peter Hyde, who tunes all his boxes in Kellner tuning, as it sounds better when playing with fiddles. That tiny difference means everything to him. Anyway, there's a lifetime of study here, and many a post-doctoral professor are still hashing it out, so don't ever think there's a consensus in the air... 300 years later and there are still heated exchanges about exactly what tuning Bach was using.

    I was going to link an article or two, but so many came up it was pointless. Just google "Kellner Tuning" (what most think Bach was using) and get ready for many years of reading..

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