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Pythagorean tuning or equal temperment?
Topic Rating: 3.5 Topic Rating: 3.5 Topic Rating: 3.5 Topic Rating: 3.5 Topic Rating: 3.5 Topic Rating: 3.5 (2 votes) 
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Uzi
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July 14, 2014 - 10:28 pm
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Don't know if ya'll have seen this, but it is interesting to note.

 

A positive attitude may not solve all your problems, but it will annoy enough people to make it worth the effort. ~Herm Albright

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DanielB
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Some of us have definitely seen it before.   It is a pretty good explanation of the different temperings and how that are usually used.

One of the many neat things about violin and the other fretless bowed strings is that you have that sort of flexibility. 

"This young wine may have a lot of tannins now, but in 5 or 10 years it is going to be spectacular, despite the fact that right now it tastes like crude oil. You know this is how it is supposed to taste at this stage of development." ~ Itzhak Perlman

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RosinedUp
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I saw that video recently and have been meaning to ask about it. 

I've been able to think of some questions to begin to understand it.

1) Is this issue of Just vs. Pythagorean partly, mostly, or completely outside of the context of Bluegrass, Country, and other popular genres that have heavy involvement of equal-tempered instruments such as mandolin and guitar?

2) In the first fifteen seconds he states, "Most of the time we use the Pythagorean system.  Any scale, melody, or passage with one line of music will sound cleaner with large whole steps, narrow half steps, large major thirds, narrow minor thirds, and high seventh or leading tones."   In this context, is the pitch of each note always considered in terms of its interval with the tonic?  Or maybe its interval with the root of the current chord?  Or its interval with one or more of its neighbors?  Or something else?  Do those answers change when considering segments longer than one line?

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DanielB
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July 15, 2014 - 5:09 am
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I think "one line of music" refers to a melodic line for a single instrument, and not one line as in the few bars we see in one pass from left to right on a page of score.

"This young wine may have a lot of tannins now, but in 5 or 10 years it is going to be spectacular, despite the fact that right now it tastes like crude oil. You know this is how it is supposed to taste at this stage of development." ~ Itzhak Perlman

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Ferret
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July 15, 2014 - 8:10 am
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Hi Uzi

Yes, have seen it before and I'm sure it is a good explanation of the differences.

But I'm equally sure, that being the 'late starter' that I am, unfortunately I will not be able to put it to good use. Darn

And it's a beautiful piece of music, but I think that I'm doomed to playing solo by the campfire.

Not a bad fate but....... :)

A good post

Seen it all. Done it all. Can't remember most of dunno ..... What was I saying???? facepalm

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coolpinkone
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July 15, 2014 - 12:51 pm
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Very interesting.  I hope to play those pieces in my life time. :)    I guess I have the bar high.  🙂

Vibrato Desperato.... Desperately seeking vibrato

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ratvn
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July 15, 2014 - 4:12 pm
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Thank you @Uzi for the link.

Indeed, it's interesting and it's also the beauty and power of the instrument.

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RosinedUp
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July 16, 2014 - 1:46 am
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My ear is trained enough and I can hear sympathetic vibrations well enough that if I concentrate, I am able to play the most-used scales (G, D, C, F, etc.) pretty accurately, according to equal temperament, without the tuner, often hitting a green light on every note.  I can do the same with simple melodies.  I play perhaps half the time without the tuner.

When I am more relaxed and not keeping such close track of my points of reference, I find that I am hitting notes that sound good and sound right on---sound as good as or better than the equal-temperament pitches.  But the tuner tells me they aren't on the ET scale.  I'm pretty sure they aren't random pitches, pretty sure there is something natural about them.

So I seem to be coming up against the issues treated in the video.  I think I've been experiencing similar things for some time, so I don't consider this an issue only for advanced players.

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DanielB
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July 16, 2014 - 6:21 am
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Warning.. Long post.  Probably boring to most folks, if not also confusing. Feel free to skip it.  If you do decide to read it, might want to get a fresh cup of coffee, walk the dog, go to the bathroom and maybe even pack a lunch before reading it.  Don't say I didn't warn you..

-----

 

Personally, I think it is something quite natural, RosinedUp. 

Pythagorean tempering is what most people default to if they are singing or whistling a melody with no accompaniment.  Pythagoras didn't invent it, he noted some mathematical relationships in how people sung, and what sounded good to people.  One doesn't have to learn it to use it.   For the most part, it is how an unaccompanied singer will tend to sing, even if they have no training in music.

Just intonation, aside from complicated descriptions of the frequencies and etc is actually just "fine tuning" the harmony a bit when playing doublestops or chords.  The major or minor third from the root that is "dead on" by equal tempering (like your electronic tuner) doesn't sound quite as nice or "sweet" to the ear as when it is adjusted a little. 

I think that adjustment is just a natural reaction when one gets to the point in learning where they have been using doublestops and chords for a while.

Equal tempering also is good in it's way, and a player will naturally adjust to play with it when playing against something like piano accompaniment.

What was good about the invention of equal tempering, in my opinion, is that it allowed musical instruments like the piano to become more affordable and easier to play.  Do some research and you'll find some of the wild things that were done earlier to try and make harpsichords (and later the pianos) that could play in just intonation.  The keyboards were more complex, or they needed much more complex shifting tuning systems.  Fewer could afford to have one, and fewer could learn to play them. 

That simpler system involves some compromises, though.  No key or commonly used interval sounds terrible, but they also don't sound as good/sweet as they *could*.  Still, it is workable and sounds at least pretty good, and it allows more players to be able to afford something like a piano and learn how to play it.  Standardization is a mixed blessing.. It makes some things easier at the cost of making some things a bit less optimal.

The problem with the equal tempered system is that while the comparatively simple mathematics can seem appealing, few things in nature exactly follow a regular mathematical proportion.  The human ear is made of assorted organic materials and has a shape, it was not constructed as a mathematically precise measuring instrument.  It would be tempting to think of equal tempering as "more correct" because of it's mathematical regularity, but that is not exactly how the ear perceives things.   Still as a compromise, it is a very useful one in some ways.

Consider your electronic tuner, for example.. There are some on the market that can do the different temperings or offer 'sweetened' tunings.  But they cost more, because they have to be a bit more complex. So fewer people would have them if they weren't mostly standardized to equal tempering.  They'd also be less likely to come free with inexpensive violin or guitar beginner outfits.  LOL

Point of trivia.. Pianos, in real life, aren't actually tuned in perfect equal tempering either.  Since the human ear tends to perceive lower pitches as being a bit sharper than they actually are and perceive higher pitches as being a little flatter than they actually are, pianos are intentionally tuned a bit off the pure mathematical/theoretical perfect equal tempering to compensate for that.  As you go down from the middle C octave, the lower octaves are tuned progressively lower and as you go up from the middle C octave, the higher octaves are tuned progressively more sharp.  The difference, from one octave to the next is slight.  If my memory serves correctly, I think it is around 35 cents (since I know you prefer cents as the increment, rather than old hold-outs like me who insist on Hz..LOL), spread out over the entire range of over 7 octaves.  A little over a third of a half step. 

My point in mentioning it is that it is a concession to the properties of the human ear and human perception.  It is a concession made even in an "equal tempered" instrument like piano.  The Pythagorean and Just tempering systems are also concessions to the human ear and perception.  Doing what is necessary to make the music we play sound as good as possible.   All of the tempering systems have some degree of compromise, in that they do some things better than they do others.  With a flexible little instrument like the violin, we can adjust our playing slightly to do what works best for a given circumstance.

I can't claim to know how the different tempering systems are actually practised in classical musical training for violin.   But I can say from personal experience that the longer one plays, the more one tends to automatically incorporate whatever little adjustments it takes to make one's playing sound good.  We get increasingly more aware of "Is that 'in tune'?  Does it sound good?  Can I make it just a little better?"  I don't know if most players actually formally study it so much as becoming aware of it and allowing oneself to make the adjustments, in most cases. 

Personally, I think of it as something that mostly comes naturally over time, as a part of one's development as a musician.  Just part of what we learn to do in the process of learning to make things sound as good as we possibly can.  A listener most likely will just perceive it as skill, since it sounds better to their ears.

Perhaps you are correct, RU and it is not an "advanced only" topic.  But I would have to say that since it was only barely touched on in music theory classes when I was working on my 2 yr degree as a music major, it apparently isn't "basics that every beginner should worry about" either.

"This young wine may have a lot of tannins now, but in 5 or 10 years it is going to be spectacular, despite the fact that right now it tastes like crude oil. You know this is how it is supposed to taste at this stage of development." ~ Itzhak Perlman

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Ferret
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July 16, 2014 - 8:39 am
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@DanielB 

Dan

I read the whole thing. And then poured a glass of 'string cleaner'

I'm sure that I'll never understand all this stuff. Old dogs 'can' learn new tricks, but it seems there must be a limit. rofl

However, it may never be an issue as I don't actually know anyone that plays a piano or any other instrument for that matter :)

The way that I see it us if I'm playing solo, it doesn't really matter.

Am I right, or have I had a tad too much 'string cleaner'?

Seen it all. Done it all. Can't remember most of dunno ..... What was I saying???? facepalm

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suresh
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Thank you Daniel!.  The penultimate para sums it up all.  This topic took me to many sites and youtube videos.  But I could not understand anything, as music theory is not my cup of coffee.dazed

If music be the food of love, play on;
Give me excess of it ..(William Shakespeare in Twelfth Night)

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Hman
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I give up........pass the string cleaner.

 

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Uzi
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@DanielB you said:

Personally, I think of it as something that mostly comes naturally over time, as a part of one's development as a musician.  Just part of what we learn to do in the process of learning to make things sound as good as we possibly can.  A listener most likely will just perceive it as skill, since it sounds better to their ears.

I think that's the major point. It is an advanced topic, from the perspective of mathematical elegance of frequency distributions or the physics of harmonics, or from the perspective of how humans differentiate and distinguish musical tones as distinct from noise, but not from the perspective of how one plays. The practice of shifting between equal temperament and just or pythagorean happens automatically and subliminally, whether or not one understands the theory, the mathematics or the physics -- which is a pretty interesting topic in its own right.   

A positive attitude may not solve all your problems, but it will annoy enough people to make it worth the effort. ~Herm Albright

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coolpinkone
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whoa Dan.. that was good. I read it this morning in bed.. and at my desk with coffee. Nice writing.  Nice article.  🙂

Vibrato Desperato.... Desperately seeking vibrato

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DanielB
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@Uzi: Exactly!   The terminology and mathematical models were developed to talk about what sounds good and how it happens.. But the actual shift between the different temperings is something that one learns to do automatically, even if one never learned the terms or equations, never looked at the tables of numbers.

 

@coolpinkone:  You're lucky it didn't put you right back to sleep, Toni.  LOL

 

@Ferret: You want a good laugh?  You're already using this stuff.  I hear it when you play Skye Boat Song, for example, you're settling right into that Pythagorean system.  When you use doublestops more, you'll slide right into Just tempering, and when you get around to playing against a guitar or piano backing track, you'll ease right into Equal tempering.  Your ears and fingers know more than you think.  LOL  Trust your ears and let your fingers do what they need to to make it sound good, and it'll come to you.

 

One of the things I have learned about this stuff in the past couple years with hearing different players here develop, is that it does come naturally.  They never mentioned that in classes, but it would have been nice if they had. 

That's one of the reasons I feel the original post was a really good video on it.  It is not more technical than it needs to be, and it shows it as something pretty easy and explains that it is just what we do to make the music sound good when we're playing in different situations.  Definitely easier to understand and "get" than the explanations I got when I asked questions in college. LOL

"This young wine may have a lot of tannins now, but in 5 or 10 years it is going to be spectacular, despite the fact that right now it tastes like crude oil. You know this is how it is supposed to taste at this stage of development." ~ Itzhak Perlman

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coolpinkone
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@DanielB I totally did not fall asleep.  Because I was trying to get this.  I know that there was a class this past semester when good old Pythagorus  stuff was mentioned. More than anything I recall a young woman arguing with the professor on how to correctly pronoun his name.  I recall the Professor not agreeing with her.  I recall a part of the class where everyone was in a coma... I took vigorous notes and I was only able to gather the gist of what he was saying. We were not tested on it, and if I had been, I would have surely failed.  ha ha It is nice to have the forum and good conversations like this so slowly put this "theory" stuff back in to my brain. I always appreciate the information, even if I don't have any "brainy" words to add. :)

Vibrato Desperato.... Desperately seeking vibrato

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DanielB
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Your thoughts are always plenty "brainy", Toni. 

And the notion of a prof and one of the other students arguing over how to pronounce Pythagoras is hilarious!   Neither of them were alive back then, so neither of them can actually know if for a certain fact.  And since it wouldn't actually matter anyway, a great example of how people can get sidetracked by a detail and miss some of the actual lesson they could have had.  LOL

1st-place

"This young wine may have a lot of tannins now, but in 5 or 10 years it is going to be spectacular, despite the fact that right now it tastes like crude oil. You know this is how it is supposed to taste at this stage of development." ~ Itzhak Perlman

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ratvn
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Thanks, @DanielB.

Great posts, great information.

Violin is an amazing instrument, able to use different temperings at will, combination of them or even two of them at the same time.

Thanks for the posts.

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Ferret
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DanielB said
Your thoughts are always plenty "brainy", Toni. 

And the notion of a prof and one of the other students arguing over how to pronounce Pythagoras is hilarious!   Neither of them were alive back then, so neither of them can actually know if for a certain fact.  And since it wouldn't actually matter anyway, a great example of how people can get sidetracked by a detail and miss some of the actual lesson they could have had.  LOL

1st-place

@DanielB

That is sooooooo true Dan. 

I used to fly paragliders, and while I do understand the basics of aerodynamics, I really know nothing of the mathematics of it. Lift/drag coefficient just didn't come into it while you where doing it. They just took care of themselves.

I would fly by the 'feel' of my butt in my harness. I could feel every slight turbulence and change in lift as it was transmitted by my wing, through the 'lines' to my harness.

If things started to go 'pear shaped' you just fixed it. You really didn't have time to think about it. But I would learn from it and be less likely to make that particular mistake again

I approach playing the fiddle in much the same way. The thing that the fiddle has over the paraglider it that the fiddle is no where near as dangerous when you get it wrong. rofl

Seen it all. Done it all. Can't remember most of dunno ..... What was I saying???? facepalm

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