Pythagorean Tuning….(?)

This topic contains 22 replies, has 5 voices, and was last updated by  John Cockman 3 months ago.

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  • #58874
    rodger
    rodger
    Participant

    John,  well..it’s late winter & too early for spring…so it’s the ideal time to go crazy & this is sending me there.

    I recently saw a sight I never, ever expected to see.  I’ve never seen a high level, pro violin/fiddler have a really bad day, but I did see this the other day.  I was kind of obsessed to understand how it happened.  He was playing a fiddle that had been given to him by a hobby type violin maker that has made nearly 20 fiddles.  I came to the conclusion that this fiddle had some peculiar harmonic characteristics that messed with the weird world of musical tonal complexities that simply devastated his acquired handle on these complex interactions of tones.  I came to this conclusion by the look on this guys face.

    Last night I was looking at tuners, and one tuner had a comment by a reviewer that it was set for Equal Temperament and violins have to be tuned with Pythagorean tuning!  On no…I had no idea what this meant, but I sensed it would be the final door to insanity for me.

    Here are three links that truly opens up the world of musical lunacy for the rest of my life:

    https://en.wikipedia.org/wiki/Pythagorean_tuning

    http://www.soundfromtheheart.com/2013/10/pythagorean-tuning-compared-to.html

    http://www.soundfromtheheart.com/2012/12/432-hz-compared-to-440-hz.html

    So according to the last one, when we hear Bach’s music played on modern instruments, it sounds nothing like what Bach wrote and was played in his day!!  And you should have a warning disclaimer on your homepage that music harbors this dark, secret dungeon of practical  madness that can capture weak minded people like me and eat them for breakfast.

    If you read the comments at the bottom of the last link you will never return to the world of sanity ever again…

    #58879
    cricket
    cricket
    Participant

    From what I understand, Pythagorean tuning, or some Pythagorean- like tuning, was used early on…described by early physicists by observing the overtone series in tones.  The perfect fifths are exact, physics- wise.  This eventually caused tonality problems if you moved around too much in keys…like, you’d 3ventually run into a wolf fifth…one that screached so far off pitch from other tones that even the most tone deaf audience would cringe…it pretty much kept all chord progression imprisoned within just a limited range of motion.  Now, Bach comes along one day, tired of havin* to get keyboard instruments retuned for this or that…he embraces a newer type of tuning, called equal temperament, because the exactness of tonal interval used in Zpythagorean is abandoned by mak8ng every time slightly off pitch from the overtone series…but, by doing this, a keyboard can move through chord progressions and keys without having to be returned, and avoiding tonal clashes, like the wolf fifth.  He demonstrated the new tuning in his work, The Well Tempered Clavier, which worked its way through all of the keys.  But unfretted string instruments, not being fixed in pitch, are tuned Pythagorean, because the player of the instrument can micromanage the exact pitch as they play.  That’s my understanding, anyway.  I once used this subject as a letter of intent to enter a masters program in liberal studies, and wanted to research all this stuff eventually getting into stuff like dulcimer, fiddles, fretless and fretted banjos, guitar, etc.  But I wasn’t accepted into the program…lol.  They took my husband on his social science paper, but not me on my tonalities of the western world paper…lol.  Oh well…what do ya do with that kinda degree anyway?  But that’s my understanding in a concise nutshell…a fiddle is Pythagorean tuning.  To me, in my own thinking, that’s one reason why Black Mountain Rag tuning sounds so weird on the fiddle…it has that major 3rd that sounds funny…but perfect fifths or fourths sound more true together, to my ear.  If you wanna hear the overtone series, find a piano, hold the sustain pedal down, and hit a buncha Cs at the same time and just listen…youlll definitely hear the perfect intervals, fifths and fourths, ringing out sympathetically…the thirds oughta be in there somewhere, but harder to hear, if you can actually hear them at all.  This third problem is weird on guitar tuning….on the guitar, like bass fiddle, you have perfect fourths, EADG….just backwards from the perfect fifths of the fiddle…then, wham, they throw in a third…major third…B…for a guitarist, getting that doggone string to sound in tune is always a hassle…it’s a third…just makes it not wanna ring true with the perfect intervals, and from the B, you get a perfect fifth, E, also an octave of the first E.  Besides being fretted, the weird third thrown in that tuning allows for some interesting chords and chordal progressions on the guitar, and I often marvel at the absolute genius of tha5 tuning…however…it forces the guitar to be more of an equal tempered instrument…so, it just makes it easy to play all kinds of stuff, yet, hard to sound true to pitch.  Banjo tuning has the same issue, if you go with gDGBD, the standard tuning. Anyway…dulcimer is another interesting thing here…it’s all very interesting and fascinating, I think!

    #58883
    cricket
    cricket
    Participant

    Oh, wait…we’re you talking about 440 as opposed to 432?  Oh yeah, there’s that too.  I think some of the old German pipe organs are still set to eithe4 432 or something else, but not 440.  We tune higher now because of the d3velopment of equal temperament tuning.  I t7ned 3verything Down to 432 several years back, but somebody mentioned to me they ha$ wanted to play along with some YouTube of mine and couldn’t because of m6 tuning, so I went back…s3veral years ago.  I played at an outdoor event at 432 tuning once and did notice a pair of young does hiding behind the trees and cranking their necks out to watch…lol.  I didn’t kniw if it was the tuning or if the6 would’ve just wa5ched anyway.

    #58890

    John Cockman
    Keymaster

    Haha Rodger you’ve definitely ventured into the dark side. And Cricket, that was some interesting information!

    Modern instruments, including fiddle, banjo, etc., are tuned with equal temperament. This is why you can’t tune your open strings to perfect fifths; you have to make them all a little flat or you’ll sound awful when accompanied by piano or guitar.

    If you are writing music for Pythagorean tuning, you can’t build double stops with thirds or sixths because it sounds terrible. However, the fourths and fifths sound fantastic.

    440 Hz vs. 432 Hz? That is some crazy stuff. I will say that the lowest resonant frequncy of water around 26 octaves above an E4. A plucked string doesn’t have any harmonics high enough to drive a water molecule.

    Here is a neat video I show every year in my Science of Sound class, comparing just to equal temperament (originally an ad for Justonic Tuning, Inc).

    #58899
    cricket
    cricket
    Participant

    Nice video, John.  From what I understand, the early church approved of Gregorian Chant as the only church music…because of the human voice plus pure intervals…mainly only fifths, fourths, and octaves.  It took a long time for them to finally get around to approving chordal stuff with complicated progressions, fixed tonal instruments, etc.  Realky, one of the most pleasant sounds to me is getting the perf3ct fifths l8ned up so true on the fiddle…I love tunings where if you can get it right…the ring of the drone is so nice to hear.  I love dulcimer for the same reason….fixed with frets but the drones are sweet.

    #58906
    fiddliferous1950
    fiddliferous1950
    Participant

    Cricket and John and others, very interesting and informative discussion.

     

    Speaking of tuning; I had a nightmare last night: I dreamed I had a Martin guitar with six “B” strings! lol

    #58910
    cricket
    cricket
    Participant

    What a nightmare that would be!

    #58918
    rodger
    rodger
    Participant

    OK John…so where’s that insanity disclaimer.

    Some of my music books say specifically to tune to perfect fifths for that book!  So this is hopeless…

    Stay tuned?…….ha ha…stay tuned for the nuthouse..

    #58920
    Nancy Parker
    Nancy Parker
    Participant

    A little more about Pythagorean tuning and when to use it:

     

    #58921
    rodger
    rodger
    Participant

    Nancy…that confirms my worst fear..I couldn’t believe it was that bad, but now I know it’s even much worse…OH NO!!  (excellent video)

    One thing I read (on the internet) is if your tuner tunes in equal temperament, and you want to tune Pythagorean, tune the A right on to 440, then tune the E slightly higher, the D slightly lower, and the G a little more slightly lower.   Obviously guys like Randy Howard & others who had such a special sound had this figured out how to make whatever necessary adjustments to get it with their double stops.

    #58923
    cricket
    cricket
    Participant

    This is why I never liked electronic tuners…I use my tuning fork for A, then sound other strings agains5 each other until they sugary sweet together.  Using a tuner leaves you slightly off pitch for playing in equal temperament. Also, on the guitar, I still use the tuning fork, because to my ear, whatever chords I’ll be playing need tuning adjustments or it just sounds sour, to me.

    #58924
    rodger
    rodger
    Participant

    But if you tune the strings to a sweet open string double stop, starting from a 440 A, that is perfect fifths & Pythagorean not equal temperament….right(?)

    #58925
    cricket
    cricket
    Participant

    Yes, I think so, but, if you are playing with a band or something, your ear will cause you to adjust where your fingers go for the pitch to match up with how the other instruments are tuned…the guitars, banjos, etc., are fixed tuning, so they have to pretty much rely on equal temperament…unfretted instruments that tune in perfect intervals are not fixed tonalities, so they can tune Pythagorean and still play equal temperament…I think that’s why fiddlers would rather note most of the strings instead of playing on an open string….like if you’re playing a break with the band and you have a choice between an open string or a noted string, the noted string is gonna sound more in tune with the band, because your ear will try to make your fingers adjust to their pitch.  If you’re doing some kinda old timey stuff that realky works the drones, you might get away with it…better.   I guess most fiddlers in bands tune each string to electronic tubers, which means they are tuning in equal temperament…I’ve never tuned that way…as I said, I like a 440 A and just tune from there.  Even on the guitar I tune that way, but I’m always having to fiddle around with the tuning, because I can play one chord progression and to my ear have it sounding ok on pitch, then switch to another key or different chord shapes and have it sound all out of pitch to me…which means I’m always messin’ with my tuners on the guitar and banjo…lol.  This was something the band I was in was always kind of, well they didn’t like it…lol.  They even bought me a couple of electronic tuners, but…I just can’t stabd to tune that way…my ear fights it out with electronic tuners and it drives me batty…of course, I feel like 3verything seems out if tune most of the time anyway.  The precursor of guitar, the lute, was an interesting arrangement…having frets, but they were not fixed…the lute players had to retune AND move their frets around to play different kinds of things.

    #58926
    fiddliferous1950
    fiddliferous1950
    Participant

    And let’s remember what a gong show it can become when the fiddle plays in a key where the guitar and banjo pickers decide to use capos. Most (99%) of musicians (unless they’re approaching professional level) will place their capos in the middle of two frets and get them way too tight on the instrument neck, causing the strings to sound somewhat sharp. Below are a couple of concerns I had a while back and wrote about on my website:

    The Importance of Tuning
    The importance of tuning your instrument before entering a jam session is so necessary a step to a successful, meaningful musical experience; not only for one’s own satisfaction, but for the overall satisfaction of the group of assembled musicians.

    It isn’t enough to rely on the accuracy of inexpensive electronic tuners that can be off as much as a whole tone when batteries are weakened through use or age. Checking and replacing worn out batteries is an obvious “must”.

    Capo placement is critical, too. A poorly placed capo can raise the pitch a semi-semi tone on a guitar, banjo or mandolin (some players use capos on mandolins) creating a disturbing dissonance for fellow musicians and listeners alike.

    Of course, some inexperienced players are unable to detect when an instrument is out of proper tuning. Those persons should pay particular attention to replacing batteries in electronic tuners when necessary and check and re-check capo placements (with their tuners) to assure pitch accuracy. Not allowing an electronic tuner ample time to zero-in on a certain frequency is a common mistake inexperienced players make when attempting to tune for a jam session. Taking adequate time to ascertain that the pitch is correct is so important for the overall good of the group, yet so many musicians hurry through this most important step.

    Maintaining proper tuning throughout the entire jam session is also of utmost importance. It is never enough to only tune at the beginning of a session. Checking often is a better way to assure a jam session free from the din of instruments wildly out of tune.

     

    Creativity Using A Capo
    When considering the wise use of capos during musical sets for bands performing Bluegrass to minimize the fine-tuning and re-fine-tuning over and over again within musical set lists, it’s seems to me that careful selection of songs and instrumental tunes and their key signatures would be warranted.

    Let’s assume, for example that the first piece on set “A’s” list is an instrumental in the key of A and the instruments present in the band are guitar, banjo, mandolin, fiddle and upright bass. The guitar and banjo will most likely capo up two frets. Hopefully the instruments using capos will be tuned before beginning the set, using an electronic tuner to finely adjust the effects using a capo will have on the tuning of the instrument. Assuming all instruments are in tune as the tune begins, the music will be pleasing to the audience in so far as consonance is concerned.

    Now, for tune number two on the set list, perhaps we selected a song in the key signature of D. The guitar and banjo are in tune with the capo on the 2nd fret and simply choosing to play in the “C” position will guarantee a minimum, if any, tuning to prepare for this next piece.

    For tune number three, perhaps the band might select another song, this one in the key of E. The guitar might elect to play it in “D” position while remaining capoed on the second fret. No tuning necessary. In this example, the banjo might elect to remain at the 2nd fret and play in “D” position or if necessary, re-capo to the 4th fret, playing in “C” position causing a disruption in the continuity of the band’s program. At least there has been a minimum of tuning up to this point.

    Entire sets can be constructed using a minimum of re-tuning and re-capoing by a little thought as set lists are created. How creative can you be?

    #58927
    cricket
    cricket
    Participant

    Good points, Fred…capos can drive 3verybody crazy,..lol.  I don’t like them, but they’re necessary for guitar playing, at least for me they have been, but I despise them…lol…still, I have many and I use them.  I was thinking about all this tuning stuff, and, we’ll its very mathematical and hard to understand, or to u derstand in a practical way for a musician to utilize.  So I h7nted around @ little on the net for s9me practical info, and I think I found it here.  So I’ll link it, in the hopes it might help clarify all this stuff.  First, a couple of my own self-taught, I might add, observations…I think it’s important to realize that whether you choose 440 or 432…what makes your tuning Pythagorean, just intonation, equal temperament, or whatever else is actually determined by the distance between fifths along the circle of fifths…so I think they use the middle fifth, then calculate distances from there.  So, equal temperament, whichever tone they calculated mathematically from to set intervals from each other ended up with the A to 440…and I think it was Pythagorean, but coulda been some ithe4 temperament, tha5 the calulations to determine the mathematical measurements between tones, ended up setting the A lower, at 432.  I know from my daughter’s opera studies that today’s singers have a lot harder jobs because they are singing written notes that now are actually higher than the tones in the da6 they were originally written.  But the othe4 observation is that circle of fifths…it’s just a circle, like artists color wheel…except instead of colors along the circle, it’s fifths…for 8nstance…we know part of the order of fifths from tuning a fiddle…GDAE…if you get a five string fiddle you can start out with one fifth lower…CGDAE…if you add a fifth to both ends, you have them all…FCGDAEB…anyway, like the color wheel, where an artist looks at the placement of one color against the placement of another in order to see how colors act together, so the6 know how to mix them.  Like, complementary colors are opposite each other on the color wheel, and the artist might see blue across from orange on the color wheel, and know s/he can put those two together to make brown…and make adjustments of what kind of brown by observing more about placements of colors and how they interact.  Same with the circle of fifths…you can see a circle with fifths laying along it and figure out how they behave…what will their minor key be…how many sharps or flats do they have…etc.  Anyway, I’m saying the circle of fifths just to say that from my homespun understanding of this whole thing, how they cane up with 432 or 440 was because of which fifth they started doing their math from.  Ok…’nuff of that blabbering….I could be wrong, but at least I’m on topic…lol.  But here is a link that might tell this stuff in plain English…

    The Secret to Tuning Your Acoustic Guitar Perfectly

    #58928
    cricket
    cricket
    Participant

    Well let me say one more thing, then I’m gonna eat taters chips and get the dogs ready for bed…I want taters chips…lol.  Anyway…one of the frustrating things in tuning a guitar…you have backwards fiddle tuning to start with…EADG…since they are upside down fifths, they are fourths apart from each other.  Easy to get them tuned together.  To know a fifth…just sing Twinkle Twinkle, Little Star…the first two Twinkles are a perfect fifth.  To know the sound of a perf3ct fourth, sing Here Comes the Bride…the first two notes are a perfect fourth.  Now, the first four notes on the guitar can sound perfect and sweet…then you get to that nightmare string…B!  That’s a major third away from the G, and if you concentrate on getting that third sound good , then move on and you get another perfect 4th…easy, right?  Nope…either the third sounds sweet and the fourth sounds sour, or else 3ven the octave, the high E and the low E don’t sound like a perfect octave…I’m gonna eat tater chips.

    #58951
    cricket
    cricket
    Participant

    We gotta keep on talking about this…I was staying on topic so good, Great Scott would be so proud! I only veered off to eat the tater chips!

    #58953
    rodger
    rodger
    Participant

    Just so you let us know if they are equal temperament chips or some strange Pythagorean tater whatevers….

    #58957
    cricket
    cricket
    Participant

    In our modern world of gmos…you just never know about your tater chips!

    #58962
    cricket
    cricket
    Participant

    Uh-oh…I think…I’m………….off…….topic, or possibly just off my rocker…lol. Now, wha5 was it we were talkin’ about?

    • This reply was modified 3 months ago by cricket cricket.
    #58964
    cricket
    cricket
    Participant

    Oh well, who cares?  Now I’m taking a coffee/ and ice cream break…yes, I’m playin’ the spoons!  The coffee and ice cream are both organic, so I guess that makes them safely Pythagorean…the spoons, probably still mainly annoying….lol.

    #58993
    cricket
    cricket
    Participant

    More of that good ol Pythagorean coffee…I’m sorry to see our topic dissolve into caffeinated muck…lol.

    #59056

    John Cockman
    Keymaster

    Great video, Nancy! And Fred, I enjoyeed your entry on tuning and capos. It is irritating when someone puts on a capo and it shifts the pitch up a few cents.

    Fiddles sound very nice in Pythagorean tuning, and I think a lot of people tune that way “accidentally” when they don’t have to play in a band. Pythagorean really does sound harmonious. However, if you are used to playing Pythagorean notes, and if you are tuned to the key of A, then you are going to beat with a band tuned to equal temperament.

    The keys of Bb and F are hard enough as it is, but if you are used to Pythagorean tuning then your Bb is going to be too flat and your F is going to be too sharp when playing with a band.

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