yeoldbanjoguy - Posted - 12/15/2018:  14:03:48

Quest for perfection? All the luck in the world with that one

Bruce

banjoak - Posted - 12/15/2018:  16:55:57

Another great book is Helmholtz "Sensation of Tone" - especially for it's reference calculations for intonations and temperaments.

No evidence that Pythagoras was adjusting intonation, developing a temperament (nor concerned with modulation); rather just studying how sound waves and harmonics work, looking for explanation*. The pursuit of understanding sound, harmony, scale notes, and why things sound good, goes back further than Pythagoras. 

But even back then most likely something like either low ratio Just intervals (5, 7 or 11 limit), or harmonic series were what folks used.  Mostly they just had ears to guide them.  Just simple easy to perceive aspects of acoustical physics; found in many cultures around world; and which still exist, as well ears ability to hear the effects.  Still often used and preferred over ET.

Tempering is about making adaptations... to solve issues, like playing in different keys, modulation, or instrument issues like frets; but is tradeoffs both direct and indirect to what sounds good (and subjective).

Ears have ability to short term adapt (to a degree) to different tuning schemes (India music is good example). That's not to say listeners can't notice the differences; even while they might not be perceiving "out of tune", they might notice overall effects of intonation or temperaments (richer, fuller, tighter, brighter).  How much is dependent on the music. 

*A lot of the older pursuit of understanding the math and physics of music (from Greeks to Kepler) was not really just music, but pursuit to explaining the universe tied to spirituality, astrology...  how everything must be harmonically related. A few books I recall reading about this were  "Music of the Spheres" - and "Harmony of the Spheres"

Rawhide Creek - Posted - 12/15/2018:  18:25:18

quote:

---

Originally posted by banjoak

 . . .

No evidence that Pythagoras was adjusting intonation, developing a temperament (nor concerned with modulation); rather just studying how sound waves and harmonics work, looking for explanation*. The pursuit of understanding sound, harmony, scale notes, and why things sound good, goes back further than Pythagoras. 

 . . .

---

Also, it must be recognized that much that is labeled “Pythagorean” was in fact unknown to Pythagoras.  The name became a label for a school of thought.

G Edward Porgie - Posted - 12/15/2018:  18:57:31

Pythagorean tuning, whether or not he invented it, was still a very early attempt to devise a workable tuning system. It basically involves tuning in a series of perfect fifths. Let's say C to G to G to D to A to E to B to F# to C# etc. around the fifths and back to the C. Unfortunately, this tuning is is still an "intonation adjustment," because by the time one gets back to that C (from what would be the F) the interval is no longer a perfect fifth, but closer to a diminished fifth. Early on, this tuning was used despite that obvious flaw, and led to the term "Diablos en Musica, or "the Devil in music." It may also have been a reason why early harmonis theory considered thirds to be dissonant intervals (tuniong by perfect fifths ignores those intervals, and they'd certainly be mistuned because they were ignored. Because Pythagorean tuning does not follow the overtone series (excepting for one particular interval) it should rightfully be called a "temperament."

Certainly philosophy, religion, astrology, and spiritualism figures in to all music. One instructor I had who had studied Polynesian culture told classes that in those cultures, the belief was that everyone had a particular pitch they responded to more than other pitches. Most music of the Dark Ages was religious in nature, and most all rituals and rites feature music of some kind, be it simple chants or rhythms, or more complex "call-response" forms. I'm not sure how relevant any of that is to actual intonation adjustments, though.

Rawhide Creek - Posted - 12/15/2018:  19:54:10

And your typical, classically-trained player of bowed strings (which includes me) will tune adjacent pairs of strings by ear to the sound of the perfect fifth—except, of course, for the bass.

Edited by - Rawhide Creek on 12/15/2018 19:57:03

banjoak - Posted - 12/15/2018:  20:49:30

quote:

---

Originally posted by Rawhide Creek

quote:

---

Originally posted by steve davis

The 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?

---

"History" of tuning is sometimes funny... lot's of interesting and differing stories, (based on who wrote history?)... some  skeptical. 

------------------

Steve's comment is IMO essentially what it's all always been about... the listening sensory experience, what sounds good. That has always been the guide. Historically probably closer to reality... especially considering ALL cultures music, folks relied on their ears... to if it sounded good or not.  (lacking great precise math calculation, physics and technology to measure, electronic tuners). Ears are still a good way.  

He makes a point in discussion. Listening is the end, more important than prescriptive hypothesis, or scientific explanation about about what should sound better. Especially with effect of temperaments. The part science plays in music is more descriptive, to understand and explain why it might sound good; but not be determinate of "if"  it sounds good to a human.  (there are some aspects science has tough time explaining). I think Steve is right that historically, most musicians/singers (esp folk oriented) generally ignore the prescriptive theory authorities and whatever "history" they might claim; folks just adjust to what they think sounds good.

----

From what I gather, Steve listens, has done a lot of actual experimenting with the sound(s); sensory aware of temperament effect he hears. (not just read in a book concepts).  Might disagree with his idea of perfect; it's still a tradeoff with shortcomings; but rather one which his opinion offers he best overall for what he wants to play. Perhaps not concerned with ever playing Cb... or ever needing a B# note. His tuning works for him. 

Actual hands on practical experience, listening... let ears be guide, still pretty valid. Steve has written a bit on and shares his actual hands on experience working with sound. 

But just out of curiosity; what's the name of your book? How well does it sell?  What exactly is it about? Simply regurgitating what you've read from others have written in books? Does it offer some actual experience, discovery and insight and practical use?

banjoak - Posted - 12/15/2018:  21:00:36

quote:

---

Originally posted by Rawhide Creek

And your typical, classically-trained player of bowed strings (which includes me) will tune adjacent pairs of strings by ear to the sound of the perfect fifth—except, of course, for the bass.

---

Your typical non-formal trained fiddler will use perfect fifths, as well as 5-limit just intervals' and many will sometimes comfortably use other non-equal tempered intonation (like neutral thirds and sevenths, and more). 

Ironically I find "typical" more formal or classically trained folks of the last 60 years; almost always default to 12TET. (and can struggle with hearing some others, or think they are out of tune). 

Rawhide Creek - Posted - 12/15/2018:  22:51:03

quote:

---

Originally posted by banjoak

quote:

---

Originally posted by Rawhide Creek

quote:

---

Originally posted by steve davis

The 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?

---

"History" of tuning is sometimes funny... lot's of interesting and differing stories, (based on who wrote history?)... some  skeptical. 

------------------

Steve's comment is IMO essentially what it's all always been about... the listening sensory experience, what sounds good. That has always been the guide. Historically probably closer to reality... especially considering ALL cultures music, folks relied on their ears... to if it sounded good or not.  (lacking great precise math calculation, physics and technology to measure, electronic tuners). Ears are still a good way.  

He makes a point in discussion. Listening is the end, more important than prescriptive hypothesis, or scientific explanation about about what should sound better. Especially with effect of temperaments. The part science plays in music is more descriptive, to understand and explain why it might sound good; but not be determinate of "if"  it sounds good to a human.  (there are some aspects science has tough time explaining). I think Steve is right that historically, most musicians/singers (esp folk oriented) generally ignore the prescriptive theory authorities and whatever "history" they might claim; folks just adjust to what they think sounds good.

----

From what I gather, Steve listens, has done a lot of actual experimenting with the sound(s); sensory aware of temperament effect he hears. (not just read in a book concepts).  Might disagree with his idea of perfect; it's still a tradeoff with shortcomings; but rather one which his opinion offers he best overall for what he wants to play. Perhaps not concerned with ever playing Cb... or ever needing a B# note. His tuning works for him. 

Actual hands on practical experience, listening... let ears be guide, still pretty valid. Steve has written a bit on and shares his actual hands on experience working with sound. 

But just out of curiosity; what's the name of your book? How well does it sell?  What exactly is it about? Simply regurgitating what you've read from others have written in books? Does it offer some actual experience, discovery and insight and practical use?

---

As I indicated several weeks ago, my thesis, with additions, has been optioned by a publisher.  It will be a textbook.  Under terms of contract, I don’t get to choose the title.  As a textbook, it will (a) be expensive and hence (b) will not sell well.  One of the chapters is on temperment.

But it’s certainly reassuring to know that I can come to the BHO for your snotty remarks about my years of education, playing experience, and teaching experience.

What are your qualifications to judge?  You’re hiding behind a screen name and scant information.  Why should I (or anyone else) take your opinions on music theory seriously?

Edited by - Rawhide Creek on 12/15/2018 22:58:25

Rawhide Creek - Posted - 12/15/2018:  23:35:29

Sorry:  I meant to type >temperament< at the end of the first ¶.

Mooooo - Posted - 12/16/2018:  00:12:55

quote:

---

Originally posted by Rawhide Creek

But it’s certainly reassuring to know that I can come to the BHO for your snotty remarks about my years of education, playing experience, and teaching experience.

What are your qualifications to judge?  You’re hiding behind a screen name and scant information.  Why should I (or anyone else) take your opinions on music theory seriously?

---

Russ, I respect what you say, and believe most of it usually, not because you use your real name or because of your education. Educated people give opinions that aren't true all the time, even in their area of expertise. The reason I trust your opinions is  because they make sense, and are confirmable, you don't make wild claims. Your education and real name don't prove anything. It seems strange that you ask BanjoAK to identify himself for your approval, his name or education says nothing about whether he is making sense or not.

G Edward Porgie - Posted - 12/16/2018:  07:59:10

Uh-oh. This thread is now in danger of becoming a p***ing contest. I hope we can all settle down with our opinions and remarks about others, whether or not we think they're incorrect in their opinions/facts. 



Let's have a little more Christmas hospitality and good will to men. Please!

steve davis - Posted - 12/16/2018:  11:16:59

Luck has nothing to do with a quest for perfection.It's simply a nobel effort.
You seem to be a tad negative,Bruce.

BrooksMT - Posted - 12/16/2018:  13:13:50

My thoughts on online arguments and "piss..." matches:



I used to get in online arguments (RC sailboats: squareriggers and schooners topics). At one point, I asked the moderators to ban a guy. They didn't. At one point, they threatened to ban me....*rueful grin*.



I try to avoid online arguments now, not always successfully, sigh. The reasons for my avoidance:



1) Impossible to tell the mental state and emotional state of the "opponent". Words don't convey the emotional state, and thus, insults can easily be implied when none are intended. Written with a smile, written to offend....hard to say.



2) In a debate in front of a live audience, the goal of winning becomes paramount. Honor must be defended to avoid looking like a coward/whimp/dummy. But online, the audience reaction is missing. Maybe the audience booed the opponent, thus no response needed. Maybe the audience applauded the opponent, thus counterattack "necessary." But, really, "necessary"? My friends will support me regardless, my enemies will not, regardless. So, what's the point of getting nasty....none for me, at least at age 67...I wish I knew at 47 what I know now *smiles*.

----------------

For this thread, I ask that the participants respond to perceived insults by personal message to the offender. Remember, great writing skills are not universal. Sometimes things are written poorly in the sense that the words don't really transmit what the writer intended. When I mess up, I try to apologize, seems to help. It certainly shows honor, which is a goal I strive for.

---------

Please, all of you, keep writing if you have something to add or expand on. I've learned from all the posts here, thank you for taking time out of your life to help me expand my knowledge of intonation and temperaments.

Edited by - BrooksMT on 12/16/2018 13:15:58

yeoldbanjoguy - Posted - 12/16/2018:  13:55:19

Brooks, my oldest daughter was a speech & debate runner up at state her senior year. It was a joy to watch her play the audience. Live reactions didn’t phase her. I’ve only been on here a short while, and have seen quite a few adults arguing like little kids. It’s funny to a degree, then it’s just annoying. I think deep down they would like to help, but their ego seems to override common sense response. I’ve seen Russ explain himself in a most professional style, then be ridiculed for his knowledge. This baffles me

Bruce

G Edward Porgie - Posted - 12/16/2018:  17:41:16

Nice thoughts, Brooks. I will add, though, that many people don't understand what a person is trying to express even when they are standing live in front of him.  (Of course, sometimes that person isn't making himself clear enough to actually be understood.)  It does seem, however, that there are quite a number of people who don't always understand satirical comments, playful sarcasm, and good natured teasing, and I try to avoid any of that unless I know the audience well. I am not always successful, probably because those sorts of humor have always been a staple in my family. 



And Bruce, I'm happy for your daughter, and I, too, do not like to see adults arguing like children. I am also baffled by some of the responses to well explained and well researched comments, not only here, but in other forums.

 

Edited by - G Edward Porgie on 12/16/2018 17:51:28

steve davis - Posted - 12/16/2018:  21:22:19

A good old-fashioned argument has nothing to do with childishness...it's just different points of view with no "one right way."



Nice to speak one's opinion,freely and equally with no ranking system or chain of command.

Edited by - steve davis on 12/16/2018 21:23:56

yeoldbanjoguy - Posted - 12/17/2018:  08:27:23

On a banjo forum? A good old fashioned argument? I thought you were here to teach, and help,or so says your profile. Is that a typo?

Bruce

steve davis - Posted - 12/17/2018:  11:06:19

A good old argument is a great way to teach and help others see differing points of view,Bruce...then the readers can make a more complete decision about what they believe.
You seem to have a very narrow point of view about what teaching and helping mean,here.
I'll continue to teach and help in the same way as I have been for a few years,now.

Texasbanjo - Posted - 12/17/2018:  11:11:07

Okay, let's play nice, okay? We don't need any pissing contests on this thread or on the Hangout. Agree to disagree but don't get snarky or it'll get a thread locked and/or a time out for those who continue to cause problems.

It's Christmas time, let's be good to one another. Maybe it'll last until way into the next year.

yeoldbanjoguy - Posted - 12/17/2018:  11:33:47

I’m all for that sherry. I sure hate being berated during the holidays

Bruce

steve davis - Posted - 12/17/2018:  11:46:57

I don't get the "berated" part.

Texasbanjo - Posted - 12/17/2018:  12:45:55

quote:

---

Originally posted by yeoldbanjoguy

I’m all for that sherry. I sure hate being berated during the holidays



Bruce

---

I did not intend to "berate" anyone, just ask that we agree to disagree and be nice because it's the season to enjoy family, friends and be thankful for what we have. 

yeoldbanjoguy - Posted - 12/17/2018:  13:17:25

I know sherry, and I wasn’t speaking of your berating me. Merry Christmas!

steve davis - Posted - 12/17/2018:  15:55:59

I hope you can recover from your beratement,Bruce.

banjoak - Posted - 12/18/2018:  06:14:10

quote:

---

Originally posted by G Edward Porgie

Pythagorean tuning, whether or not he invented it, was still a very early attempt to devise a workable tuning system. It basically involves tuning in a series of perfect fifths. Let's say C to G to G to D to A to E to B to F# to C# etc. around the fifths and back to the C. Unfortunately, this tuning is is still an "intonation adjustment," because by the time one gets back to that C (from what would be the F) the interval is no longer a perfect fifth, but closer to a diminished fifth. Early on, this tuning was used despite that obvious flaw, and led to the term "Diablos en Musica, or "the Devil in music." It may also have been a reason why early harmonis theory considered thirds to be dissonant intervals (tuniong by perfect fifths ignores those intervals, and they'd certainly be mistuned because they were ignored. Because Pythagorean tuning does not follow the overtone series (excepting for one particular interval) it should rightfully be called a "temperament."

 

---

The basic core of Pythagorean tuning is not a tuning adjustment. It conforms to a 3-limit Just Intonation scheme to make a diatonic scale. The fourth is perfect; a 4:3 ratio (factors of 2 and 3). But as well Pythagorean has been expressed as way to calculate the size of a tone defined as fifth of fifth (9/8), using the single size tone in scalular construction of the octave. (this is similar to many other scale type systems of same size steps).

The Diablos en Musica refers to tritone. 

The diminished fifth is 610 cents. The augmented fourth is 590 cents. The Pythagorean tritone is 612 cents.  Circle of fifths (process you describe) would give would only be 520 cents. 

I'm not aware of the Pythagorean thirds was considered dissonant, or that they were ignored or avoided. Seems evidence they were used. Still are by some... they especially in linear horizontal context... there seems to be an appeal for some to use Pythagorean thirds, sixths and sevenths. In the right context IMO they can sound quite nice. (they can also show up as linear differentials in 5-limit Just Intonation modal schemes). 

Related to the OP... Pythagorean would also be similar problematic on straight fretted banjo or guitar.

-----------

5-limit Just intonation does not follow the overtone series, nor calculated from it. It does however share up to the 6th, and the 4,5,6 makes tonic, third and fifth. Overtone schemes do exist but are a bit different.

---------------

Some of the stories about Diablos en Musica, and forbidden, might be a little myth than reality. As well...keep in mind, in speaking intonations and theory... that these histories only represent a very small rather elitist part compared to the world of music. Other music existed then as it does now.

G Edward Porgie - Posted - 12/18/2018:  11:50:16

Tritone instead of diminished fifth is nitpicking, as they are basically the same interval (at least in modern temperament). I also only indicated that the final interval in the Pythagorean system was "closer to a diminished fifth;" I didn't say that it was one.



I cite now the New Harvard Dictionary of Music: "Tritone:" An interval consisting of three whole tones; hence, the augmented fourth, or because in equal temperament the inversion of that interval yields an interval of the same same size, the diminished fifth. It has been regarded as a dissonance since the Middle Ages, when it was nicknamed the diabolus in musica (the devil in music) and was the object of prohibitions by theorists..." 

Your characterization of using the single siz tone to construct an octave is also incomplete. There is actually a dieses (difference) that occurs in two places. Harvard: "...the diatonic scale from c to c' would consist of five whole tones, each with the ratio 9:8, and two semitones (e-f and b-c), each with the ratio 256:243."

I haven't done the actual calculations, but because I said "closer," and not "exactly," they could be considered irrelevant points.  I also don't know what process you've used to derive those figures. Again from "Harvard:" Pythagorean scale. A diatonic scale characterized by pure fifths (3:2). pure fourths (4:3), and whole tones defined as the difference between a fifth and a fourth (3:2-4:3=9.8)" They go on to say "...the earliest complete presentation occurs in Plato's Timaeus..." and this: "The same scale can be derived by assuming a series of perfect fifths beginning with F. If this series, F c g d' a' e" b", is collapsed into a single octave, the Pythagorean scale is produced," and further, "...this scale formed the basis of ancient and medieval divisions of the monochord."

As far  as dissonances, I was conjecturing about why thirds weren't used much in early harmony. It's been pretty well established by music historians that early harmonies consisted primarily of fourths and fifths. It is true, though, that some thirds naturally occurred or were used as dissonances, much as a thirteenth chord would be called dissonant by many, but might still be used for effect.

As far as your thoughts about Pythagorean not being a tuning adjustment" I have to say that because it doesn't follow the entire overtone series that it definitely produces a tempered, or adjusted scale. It doesn't line up completely with J.I.

Histories, I think we all know, only represent a very small rather elitist (that "elitist" remark is debatable) part compared to the world of music, and that other music existed then and now, so it's not really important to point that out.

Personally, I think much of this discussion has devolved to semantics and trivial misunderstandings of one another. I am not going to say any more.

banjoak - Posted - 12/18/2018:  12:36:15

quote:

---

Originally posted by Rawhide Creek

But it’s certainly reassuring to know that I can come to the BHO for your snotty remarks about my years of education, playing experience, and teaching experience.

---

I made no remark about how many years of education, playing experience, and teaching experience you have.

Nor do I care... I simply don't find it necessary in order to evaluate information. Rather I can just evaluate from the merits of what a post provides to the discussion, shares, communicates relevant observations, info, interest, concepts, insight... most important explanation of why.

Those that can and do actually engage contribute in discussion in that manner... helps informs me some about their interest and actual relevant experience; those folks that choose to do something else, put focus on other... certainly doesn't provide evidence.

quote:

---

Originally posted by Rawhide Creek

What are your qualifications to judge?  You’re hiding behind a screen name and scant information.  Why should I (or anyone else) take your opinions on music theory seriously?

I know my actual life experiences, observations, knowledge, research, experiments... use that to evaluate what I read, comprehend concepts; that qualifies form opinion for myself.  I have no qualification to judge for other people, nor responsibility.

People can read what I post, explain discuss; whether they take me serious if up to them... I make no demand.  Need to do a background check, investigation,... seems  appeal to authority, or argumentum ad verecundiam, if that is important to what learning is about for that person....  no problem, I have no interest in figuring out what meets their criteria, metrics; proving, persuading or winning the top authority contest of someone else's criteria.  So by all means find the top authority that meets your criteria, metrics. (Piece of paper in frame? title? trophy?). You decide what's important to you, do what fits your need or goal.   So no need to take me serious, fine to assume I know nothing, just hick banjo player... it's all made up reject it. 

banjoak - Posted - 12/20/2018:  16:14:30

quote:

---

Originally posted by G Edward Porgie

Your characterization of using the single siz tone to construct an octave is also incomplete. There is actually a dieses (difference) that occurs in two places. Harvard: "...the diatonic scale from c to c' would consist of five whole tones, each with the ratio 9:8, and two semitones (e-f and b-c), each with the ratio 256:243."

I also don't know what process you've used to derive those figures. Again from "Harvard:" Pythagorean scale. A diatonic scale characterized by pure fifths (3:2). pure fourths (4:3), and whole tones defined as the difference between a fifth and a fourth (3:2-4:3=9.8)" They go on to say "...the earliest complete presentation occurs in Plato's Timaeus..." and this: "The same scale can be derived by assuming a series of perfect fifths beginning with F. If this series, F c g d' a' e" b", is collapsed into a single octave, the Pythagorean scale is produced," and further, "...this scale formed the basis of ancient and medieval divisions of the monochord."

---

Here is what I stated previously post

The basic core of Pythagorean tuning is not a tuning adjustment. It conforms to a 3-limit Just Intonation scheme to make a diatonic scale. The fourth is perfect; a 4:3 ratio (factors of 2 and 3). But as well Pythagorean has been expressed as way to calculate the size of a tone defined as fifth of fifth (9/8), using the single size tone in scalular construction of the octave.

 

I was pointing out that your previous calculation of F note (the a fourth); was in error; and that it uses a 4:3 (as seems your fact check confirms?). A fourth is simply the inverse of a fifth; and taking 4/3 x 3/2 = octave of 2/1.  The process I always used... is mostly based on Helmholtz, pretty straightforward, easy to remember (for basic tones and intervals)... but has handy tables to look it all up and check for more complex if needed (and of course the explanation, logs and math.   As a fifth is 3:2, as I mentioned if you take 3/2 x 3/2 = 9/8. (a tone)  You can use this then to calculate and construct the Pythagorean scales from tones of fifths. However using multiplication generates large ratios;  It's easy to do via addition using cents. To keep it in one octave subtract 1200.

So starting with a pitch... a fifth (702) of fifth; 702 + 702 = 1404 (-1200) = 204; to continue 204 + 702 = 906; 906 + 702 = 1608 (-1200) = 408; 408 + 204 = 1110. The fourth is inverse 1200 - 702 = 498. 

Which gives tetrachords of 0 204 408 498 and 702 906 1110 1200 as such gives

Ionian - 0 204 408 498 702 906 1110 1200

The single size tone I referenced earlier; and yep there are 5 of those in the Ionian scale (seems to agree with your fact check?). 2 tones make mediant; Fifth and tone make submediant and so on.  Similar methods of fifths and fourth (inverse) make for other modes such as Aeolian - 0 204 294 498 702 792 996 1200.

Since they are all mulitples of 3/2, then will conform to 3-limit factors of 2 and 3. Seems elegantly simple and clean.

So I'm not understanding what your methodology you use.

quote:

---

Originally posted by G Edward Porgie

There is actually a dieses (difference) that occurs in two places.

....and two semitones (e-f and b-c), each with the ratio 256:243."

---

Can't speak for your book... but do you perhaps mean the Great Diesis (42 cent) -   I believe only used in meantone (and double flat/sharp stuff) or diminished second? Never seen it in Pythagorean, nor understand how it would fit? (128:125 , does not conform 3-limit and way small). Can you give an example of a piece you play with that... or how you would use that?

But the 256:243 as I know it is the Limma, (90 cents); and yes I left it out.  It is not generally considered the principle concept. (tones via fifths)... considered as direct calculated musical interval in itself (nor in Pythagorean generally referred as a semitone), but rather the defect from the assembly of tones (calculated from the fifths.) As noticed in defect from 2 tones, mediant (408) and the fourth (498). It does play a part (as do other defect tones in just) in calculations. But unlike tones would never add 2 defects 90 and 90, or arive at those thru 3:2 or 4:3 alone?

But please clarify if this not the concept... and show me the right formula.

-------------

quote:

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Originally posted by G Edward Porgie

....because by the time one gets back to that C (from what would be the F) the interval is no longer a perfect fifth, but closer to a diminished fifth. 

---

So I simply was clarified...for the F when I wrote

quote:

---

Originally posted by banjoak

The fourth is perfect; a 4:3 ratio

Circle of fifths (process you describe) would give would only be 520 cents. 

---

In reference to your original understanding it was simply going around a spiral of fifths would give an F note of 520 cents, or 22 cents wider than the 4:3 or 498.  This 22 cent is 81:80 comma; and occurs in other intonation schema. As well notice each fifth is making a 2 cents larger than 12TET; so 11 times around = 22.

Thus taking that 520 by 3/2; the octave (12x4) would end up as 24 cents wide; (called Pythagorean Comma); or an Octave of 1224.  - as noted though, NOT how Pythagorean Octave is done... it's simply 2/1... and is a perfect fifth 702 of the the F (498) - as I originally said, and as far as I can tell per the book you read. Please clarify my misunderstanding.

quote:

---

Originally posted by G Edward Porgie

this tuning is is still an "intonation adjustment," because by the time one gets back to that C (from what would be the F) the interval is no longer a perfect fifth, but closer to a diminished fifth. Early on, this tuning was used despite that obvious flaw, and led to the term "Diablos en Musica

---

The book you read seems to agree with what I stated "The Diablos en Musica refers to tritone" NOT the comma you seemed to be referring. No?

I just  simply don't see how any of this is closer to a diminished fifth (nor tritone) any  or what intonational adjustment that a diminished fifth would make to actual Pythagorean tuning. Please explain if you would.

quote:

---

Originally posted by G Edward Porgie

Tritone instead of diminished fifth is nitpicking, as they are basically the same interval (at least in modern temperament). I also only indicated that the final interval in the Pythagorean system was "closer to a diminished fifth;" I didn't say that it was one.

---

Nitpicking comment is interesting you make. I just don't understand your explanation. I did provide the different definitions and calculations of tritone... for comparison and none of them seem relate to what you are saying; nor understand how would add up to anything. But again my understanding of the concept and experience using of Pythagorean is that it is method using 3:2; 3-limit; and most often to single size of a tone (and then arrangement of 5 tones). Seems to work pretty good for that. 

But while we are here...since we are talking Pythagorean (not Equal) and to the OP about non-ET tuning concepts...  in my experience Pythagorean tuning is not just "semantics" but considered a very specific concept (and pure); just 3-limit, as explained in previous post only using factors of  2 and 3.  Pythagorean tritone has specific calculation. I am unaware of any diminished fifth or augmented fourth in Pythagorean, it would seem a bit antithetical.

quote:

---

Originally posted by banjoak

The Pythagorean tritone is 612 cents. 

---

If you took where we left off in the sequence of fifths (generating the 5 tones); it was 1110. Add 702 = 1802 (-1200) = 612 cents. Doing the rations = 729:512. (since it's 3/2 to the 6th... will qualify for factors of 2 and 3).  Note as above each time gets additional 2 cents from 12TET, 6x2=12... so 12 cents more than the ET 600 cent tritone. Also notice it is 90 cents less than the fifth of 702. However, it is 114 cents more than the fourth 498. Thus 114 represents another defect space (Apotome). 

The diminished fifth and augmented fourth are different concepts in other tunings (and temperaments). But that's another post. 

quote:

---

Originally posted by G Edward Porgie

 

As far as your thoughts about Pythagorean not being a tuning adjustment" I have to say that because it doesn't follow the entire overtone series that it definitely produces a tempered, or adjusted scale. It doesn't line up completely with J.I.

---

These are not really just "my" thoughts... many who put to practical use, concept of Pythagorean is 3-limit Just Intonation (as explained, only to get 3:2 and 4:3). What most simply refer to as JI is 5 limit factor of up to 5 (so still includes the 3:2 and 4:3 combination of 3-limit); which gives all low ratios folks quote to get intervals 5:3, 5:4, 6:5, 8:5, 10:9 (a second size tone), 16:15. Similar to 3-limit being fifth fourth based, 5 limit becomes more thirds, sixths and sevenths. Can be extended to many other chromatic notes... such as 45:32 aug4 (590) and 64:45 dim5 (610). For math geeks, the ratios are interesting fun, note certain inverting  relationships (both have 45 and 32 is half 64); which give clues about balance within octaves and fifths, what secondary harmonic relationships.  Just also extends to 7 limit, 11 limit (which open up Septimal and Unidecimal); and various others. These are not for us consider temperaments as no notes are tempered, deviate from the correct tones. (there are other different non-tempered possibilities like EDOs). That's are the concepts I am familiar with, and put to great use... and as every one I know who uses JI. Concept works great.  I have no idea what the Authority Rule masters have, or to pass their tests? Be interested to know. Certainly want to know where I stand if to those who adamantly insist folks teach it "right".

As I pointed out - the overtone series and tunings I am familiar with and have used, (like overblown flutes) is slightly different concept; and alone could easily generate 5 limit ratios (just does not line up either noticeable the 7th and 11th harmonic. Nor how 3-limit as subset of 5 limit can not be? Can you give the explanation, process and cents you use to tune and play? 

quote:

---

Originally posted by G Edward Porgie

Personally, I think much of this discussion has devolved to semantics and trivial misunderstandings of one another. I am not going to say any more.

---

I agree this devolved from what I tried to simply state...(certainly never my goal, quite opposite) and certainly not interested in semantics, nor nits; but just actual understanding of concepts.  Music theory, and intonation, tuning is not just semantics... especially for those who first hand understand and use more than 12TET  (It's certainly not trivial nor just semantics to me and others I know) -  But you've presents what made me very confused... (and perhaps many others).  I would think based on what you've stated here and on many other theory posts, you have a responsibility to say more, no?, let us be in the know. Let's clear up misunderstanding discuss, explain; isn't that the point of music theory forum? (Unless wasn't point of involvement on the discussions, some other reason?)

I'm not interested in the history... nor in what sounds dissonant/consonant (I can test and listen for myself)...  but in the actual concept of how you have been tuning and putting it to actual practical use.

I think it will be enlightening, look forward to it.

---------

FWIW - Somewhere I have an old copy of Harvard Brief Dictionary of Music; IIRC it is a bit thin on actual theory... just more a book for terminology, maybe history... maybe to help pass a test for like a music appreciation class, (those who need a class to learn how to listen to music), maybe helps get a piece of paper to frame.   I do recall it saying something about - Just intonation as theoretical, not of practical use for making actual music. 

Your Harvard book seems to be different, curious how it better explains the theory, the applicable concepts? I'll have to try and pop over to the library. 

Edited by - banjoak on 12/20/2018 16:21:54

banjoak - Posted - 12/20/2018:  19:31:02

quote:

---

Originally posted by steve davis

Luck has nothing to do with a quest for perfection.It's simply a nobel effort.

You seem to be a tad negativej,Bruce.

---

Sorry I forgot to send this earlier... 

But I noticed and want to cheer you on.  I had no idea they even had a banjo related category. But agree it's not luck, (nor false authority)... but determined effort, focused goal, quest for perfection seems to be the ticket to Oslo! 

I am surprised the typical grammar police didn't issue a warning and correction? But I got what you meant and yes, "technically" you should have used a capital "N" to describe your effort  .

yeoldbanjoguy - Posted - 12/21/2018:  08:24:53

Just fly.com has $297 tickets to Oslo. Actually not too bad

Bruce

jblue - Posted - 12/26/2018:  07:33:24

Hello,

Thanks to @BrooksMT for starting this forum and his posts. There's a researcher/professor who I think may be of interest to contact about microtonal possibilities on banjo. His name is Michael Kudirka at Arkansas State University. I bring it up because he has a patent on removable microtonal fretboards for guitar. He uses rare earth metals as a magnet and literally pulls the fretboard off the guitar and slides on a new one. He has quarter comma meantone, Rameau tuning, Bach (it wasn't quite equal temperament), and others as well as developing new ones for modern composition. He's quite friendly and helpful to contact and I'm sure he'd be very curious to hear from others about building and adapting a removable fretboard for banjo in a collaborative project.

G Edward Porgie - Posted - 12/26/2018:  13:15:14

quote:

---

Originally posted by banjoak

quote:

---

Originally posted by G Edward Porgie

Your characterization of using the single siz tone to construct an octave is also incomplete. There is actually a dieses (difference) that occurs in two places. Harvard: "...the diatonic scale from c to c' would consist of five whole tones, each with the ratio 9:8, and two semitones (e-f and b-c), each with the ratio 256:243."

I also don't know what process you've used to derive those figures. Again from "Harvard:" Pythagorean scale. A diatonic scale characterized by pure fifths (3:2). pure fourths (4:3), and whole tones defined as the difference between a fifth and a fourth (3:2-4:3=9.8)" They go on to say "...the earliest complete presentation occurs in Plato's Timaeus..." and this: "The same scale can be derived by assuming a series of perfect fifths beginning with F. If this series, F c g d' a' e" b", is collapsed into a single octave, the Pythagorean scale is produced," and further, "...this scale formed the basis of ancient and medieval divisions of the monochord."

---

Here is what I stated previously post

The basic core of Pythagorean tuning is not a tuning adjustment. It conforms to a 3-limit Just Intonation scheme to make a diatonic scale. The fourth is perfect; a 4:3 ratio (factors of 2 and 3). But as well Pythagorean has been expressed as way to calculate the size of a tone defined as fifth of fifth (9/8), using the single size tone in scalular construction of the octave.

 

I was pointing out that your previous calculation of F note (the a fourth); was in error; and that it uses a 4:3 (as seems your fact check confirms?). A fourth is simply the inverse of a fifth; and taking 4/3 x 3/2 = octave of 2/1.  The process I always used... is mostly based on Helmholtz, pretty straightforward, easy to remember (for basic tones and intervals)... but has handy tables to look it all up and check for more complex if needed (and of course the explanation, logs and math.   As a fifth is 3:2, as I mentioned if you take 3/2 x 3/2 = 9/8. (a tone)  You can use this then to calculate and construct the Pythagorean scales from tones of fifths. However using multiplication generates large ratios;  It's easy to do via addition using cents. To keep it in one octave subtract 1200.

So starting with a pitch... a fifth (702) of fifth; 702 + 702 = 1404 (-1200) = 204; to continue 204 + 702 = 906; 906 + 702 = 1608 (-1200) = 408; 408 + 204 = 1110. The fourth is inverse 1200 - 702 = 498. 

Which gives tetrachords of 0 204 408 498 and 702 906 1110 1200 as such gives

Ionian - 0 204 408 498 702 906 1110 1200

The single size tone I referenced earlier; and yep there are 5 of those in the Ionian scale (seems to agree with your fact check?). 2 tones make mediant; Fifth and tone make submediant and so on.  Similar methods of fifths and fourth (inverse) make for other modes such as Aeolian - 0 204 294 498 702 792 996 1200.

Since they are all mulitples of 3/2, then will conform to 3-limit factors of 2 and 3. Seems elegantly simple and clean.

So I'm not understanding what your methodology you use.

quote:

---

Originally posted by G Edward Porgie

There is actually a dieses (difference) that occurs in two places.

....and two semitones (e-f and b-c), each with the ratio 256:243."

---

Can't speak for your book... but do you perhaps mean the Great Diesis (42 cent) -   I believe only used in meantone (and double flat/sharp stuff) or diminished second? Never seen it in Pythagorean, nor understand how it would fit? (128:125 , does not conform 3-limit and way small). Can you give an example of a piece you play with that... or how you would use that?

But the 256:243 as I know it is the Limma, (90 cents); and yes I left it out.  It is not generally considered the principle concept. (tones via fifths)... considered as direct calculated musical interval in itself (nor in Pythagorean generally referred as a semitone), but rather the defect from the assembly of tones (calculated from the fifths.) As noticed in defect from 2 tones, mediant (408) and the fourth (498). It does play a part (as do other defect tones in just) in calculations. But unlike tones would never add 2 defects 90 and 90, or arive at those thru 3:2 or 4:3 alone?

But please clarify if this not the concept... and show me the right formula.

-------------

quote:

---

Originally posted by G Edward Porgie

....because by the time one gets back to that C (from what would be the F) the interval is no longer a perfect fifth, but closer to a diminished fifth. 

---

So I simply was clarified...for the F when I wrote

quote:

---

Originally posted by banjoak

The fourth is perfect; a 4:3 ratio

Circle of fifths (process you describe) would give would only be 520 cents. 

---

In reference to your original understanding it was simply going around a spiral of fifths would give an F note of 520 cents, or 22 cents wider than the 4:3 or 498.  This 22 cent is 81:80 comma; and occurs in other intonation schema. As well notice each fifth is making a 2 cents larger than 12TET; so 11 times around = 22.

Thus taking that 520 by 3/2; the octave (12x4) would end up as 24 cents wide; (called Pythagorean Comma); or an Octave of 1224.  - as noted though, NOT how Pythagorean Octave is done... it's simply 2/1... and is a perfect fifth 702 of the the F (498) - as I originally said, and as far as I can tell per the book you read. Please clarify my misunderstanding.

quote:

---

Originally posted by G Edward Porgie

this tuning is is still an "intonation adjustment," because by the time one gets back to that C (from what would be the F) the interval is no longer a perfect fifth, but closer to a diminished fifth. Early on, this tuning was used despite that obvious flaw, and led to the term "Diablos en Musica

---

The book you read seems to agree with what I stated "The Diablos en Musica refers to tritone" NOT the comma you seemed to be referring. No?

I just  simply don't see how any of this is closer to a diminished fifth (nor tritone) any  or what intonational adjustment that a diminished fifth would make to actual Pythagorean tuning. Please explain if you would.

quote:

---

Originally posted by G Edward Porgie

Tritone instead of diminished fifth is nitpicking, as they are basically the same interval (at least in modern temperament). I also only indicated that the final interval in the Pythagorean system was "closer to a diminished fifth;" I didn't say that it was one.

---

Nitpicking comment is interesting you make. I just don't understand your explanation. I did provide the different definitions and calculations of tritone... for comparison and none of them seem relate to what you are saying; nor understand how would add up to anything. But again my understanding of the concept and experience using of Pythagorean is that it is method using 3:2; 3-limit; and most often to single size of a tone (and then arrangement of 5 tones). Seems to work pretty good for that. 

But while we are here...since we are talking Pythagorean (not Equal) and to the OP about non-ET tuning concepts...  in my experience Pythagorean tuning is not just "semantics" but considered a very specific concept (and pure); just 3-limit, as explained in previous post only using factors of  2 and 3.  Pythagorean tritone has specific calculation. I am unaware of any diminished fifth or augmented fourth in Pythagorean, it would seem a bit antithetical.

quote:

---

Originally posted by banjoak

The Pythagorean tritone is 612 cents. 

---

If you took where we left off in the sequence of fifths (generating the 5 tones); it was 1110. Add 702 = 1802 (-1200) = 612 cents. Doing the rations = 729:512. (since it's 3/2 to the 6th... will qualify for factors of 2 and 3).  Note as above each time gets additional 2 cents from 12TET, 6x2=12... so 12 cents more than the ET 600 cent tritone. Also notice it is 90 cents less than the fifth of 702. However, it is 114 cents more than the fourth 498. Thus 114 represents another defect space (Apotome). 

The diminished fifth and augmented fourth are different concepts in other tunings (and temperaments). But that's another post. 

quote:

---

Originally posted by G Edward Porgie

 

As far as your thoughts about Pythagorean not being a tuning adjustment" I have to say that because it doesn't follow the entire overtone series that it definitely produces a tempered, or adjusted scale. It doesn't line up completely with J.I.

---

These are not really just "my" thoughts... many who put to practical use, concept of Pythagorean is 3-limit Just Intonation (as explained, only to get 3:2 and 4:3). What most simply refer to as JI is 5 limit factor of up to 5 (so still includes the 3:2 and 4:3 combination of 3-limit); which gives all low ratios folks quote to get intervals 5:3, 5:4, 6:5, 8:5, 10:9 (a second size tone), 16:15. Similar to 3-limit being fifth fourth based, 5 limit becomes more thirds, sixths and sevenths. Can be extended to many other chromatic notes... such as 45:32 aug4 (590) and 64:45 dim5 (610). For math geeks, the ratios are interesting fun, note certain inverting  relationships (both have 45 and 32 is half 64); which give clues about balance within octaves and fifths, what secondary harmonic relationships.  Just also extends to 7 limit, 11 limit (which open up Septimal and Unidecimal); and various others. These are not for us consider temperaments as no notes are tempered, deviate from the correct tones. (there are other different non-tempered possibilities like EDOs). That's are the concepts I am familiar with, and put to great use... and as every one I know who uses JI. Concept works great.  I have no idea what the Authority Rule masters have, or to pass their tests? Be interested to know. Certainly want to know where I stand if to those who adamantly insist folks teach it "right".

As I pointed out - the overtone series and tunings I am familiar with and have used, (like overblown flutes) is slightly different concept; and alone could easily generate 5 limit ratios (just does not line up either noticeable the 7th and 11th harmonic. Nor how 3-limit as subset of 5 limit can not be? Can you give the explanation, process and cents you use to tune and play? 

quote:

---

Originally posted by G Edward Porgie

Personally, I think much of this discussion has devolved to semantics and trivial misunderstandings of one another. I am not going to say any more.

---

I agree this devolved from what I tried to simply state...(certainly never my goal, quite opposite) and certainly not interested in semantics, nor nits; but just actual understanding of concepts.  Music theory, and intonation, tuning is not just semantics... especially for those who first hand understand and use more than 12TET  (It's certainly not trivial nor just semantics to me and others I know) -  But you've presents what made me very confused... (and perhaps many others).  I would think based on what you've stated here and on many other theory posts, you have a responsibility to say more, no?, let us be in the know. Let's clear up misunderstanding discuss, explain; isn't that the point of music theory forum? (Unless wasn't point of involvement on the discussions, some other reason?)

I'm not interested in the history... nor in what sounds dissonant/consonant (I can test and listen for myself)...  but in the actual concept of how you have been tuning and putting it to actual practical use.

I think it will be enlightening, look forward to it.

---------

FWIW - Somewhere I have an old copy of Harvard Brief Dictionary of Music; IIRC it is a bit thin on actual theory... just more a book for terminology, maybe history... maybe to help pass a test for like a music appreciation class, (those who need a class to learn how to listen to music), maybe helps get a piece of paper to frame.   I do recall it saying something about - Just intonation as theoretical, not of practical use for making actual music. 

Your Harvard book seems to be different, curious how it better explains the theory, the applicable concepts? I'll have to try and pop over to the library. 

---

the semantics becomes a problem when two people are making basically the same argument, but using different words, which only make it seem as though they are not on the same page.

Also, I am not quoting from any "brief" dictionary. I think you should check the actual source I quoted from before making claims of it being "thin on actual theory."

I have no idea what you could possibly be insinuating with your comment about my "having a responsibility to say more." That seems rather snide to me, as if I am deliberately attempting to obfuscate the issues here, and I do not appreciate it. I really don't know what else I can say without inviting more argument from such a self-proclaimed expert as yourself.  Maybe you have some knowledge, but I honestly think you are confusing things by claiming that Pythagorean is not a tuning adjustment. (It should be obvious that anything that deviates even in just one or two intervals from J.I. is an adjustment from what is a natural occurrence.) My main point is to say that Pythagorean is a form of a temperament, but you have proceeded to argue otherwise with claims that don't really address my original statement. 

G Edward Porgie - Posted - 12/26/2018:  13:35:30

quote:

---

Originally posted by jblue

Hello,



Thanks to @BrooksMT for starting this forum and his posts. There's a researcher/professor who I think may be of interest to contact about microtonal possibilities on banjo. His name is Michael Kudirka at Arkansas State University. I bring it up because he has a patent on removable microtonal fretboards for guitar. He uses rare earth metals as a magnet and literally pulls the fretboard off the guitar and slides on a new one. He has quarter comma meantone, Rameau tuning, Bach (it wasn't quite equal temperament), and others as well as developing new ones for modern composition. He's quite friendly and helpful to contact and I'm sure he'd be very curious to hear from others about building and adapting a removable fretboard for banjo in a collaborative project.

---

I have often read that Bach possibly did not use ET when he composed "The well Tempered Clavier" (the word "well" is often cited as having a different connotation than "Equal," but which may be just have been a simple and somewhat meaningless word choice). I do wonder, though, that if he were using a different tuning system, why he only composed 24 pieces. 24 pieces fits better into the concept of E.T. with its enharmonic spellings (F# minor but no Gb minor, for one example) than it does with any other temperament. While it's certainly possible, or even probably that there are other temperaments which would produce only 24 keys, or that Back simply chose to use 24 keys and not all the ones available in some other altered temperaments, it seems to me that it's possible that his ideas were based on a system such as ET which completely eliminates the need for some of those difficult keys like Gb minor or B#.

I have heard of those rare earth fingerboards, and have mentioned them in the past. Unfortunately, I couldn't remember the name "Michael Kudirka." I have a recording of some Lou Harrison guitar pieces which makes use of them.

Rawhide Creek - Posted - 12/26/2018:  16:48:43

quote:

---

Originally posted by G Edward Porgie

quote:

---

Originally posted by jblue

Hello,



Thanks to @BrooksMT for starting this forum and his posts. There's a researcher/professor who I think may be of interest to contact about microtonal possibilities on banjo. His name is Michael Kudirka at Arkansas State University. I bring it up because he has a patent on removable microtonal fretboards for guitar. He uses rare earth metals as a magnet and literally pulls the fretboard off the guitar and slides on a new one. He has quarter comma meantone, Rameau tuning, Bach (it wasn't quite equal temperament), and others as well as developing new ones for modern composition. He's quite friendly and helpful to contact and I'm sure he'd be very curious to hear from others about building and adapting a removable fretboard for banjo in a collaborative project.

---

I have often read that Bach possibly did not use ET when he composed "The well Tempered Clavier" (the word "well" is often cited as having a different connotation than "Equal," but which may be just have been a simple and somewhat meaningless word choice). I do wonder, though, that if he were using a different tuning system, why he only composed 24 pieces. 24 pieces fits better into the concept of E.T. with its enharmonic spellings (F# minor but no Gb minor, for one example) than it does with any other temperament. While it's certainly possible, or even probably that there are other temperaments which would produce only 24 keys, or that Back simply chose to use 24 keys and not all the ones available in some other altered temperaments, it seems to me that it's possible that his ideas were based on a system such as ET which completely eliminates the need for some of those difficult keys like Gb minor or B#.

I have heard of those rare earth fingerboards, and have mentioned them in the past. Unfortunately, I couldn't remember the name "Michael Kudirka." I have a recording of some Lou Harrison guitar pieces which makes use of them.

 

---

And how do you fit Werckmeister (late 1600s) into your thesis?

I tune my harpsichord myself, as did Bach, and as do most players of the instrument that I know do, also.

Edited by - Rawhide Creek on 12/26/2018 16:56:49