Is a# the same as bb?

[groveland]

These are the 'legit' major and minor key signatures. There are zillions of theoretical key signatures and modes that aren't conducive to a key signature. It's my understanding that Bartok would occasionally mix flats and sharps in key signatures (Levine).

In a piece of modal software I am particularly familiar with, the key signatures are really troublesome. (So I can understand the BIAB challenge.) When attempting to describe ALL scales in ALL keys, it becomes apparent pretty quickly that 100% accurate use of accidentals (double sharps, double flats, no repeats of note names) can easily obscure the lessons in intervals, music, repeated patterns and relationships, and the meaning from the largest audience. IMHO.

[Richard H]

"By the way, if you play just temperament instruments, as Apk said, there is a big difference; A# is noticeably sharper than Bb." Glauber

Since this is so, there must be a measurable difference in frequency.

On the sites I've checked, where A=440, Bb/A# (just above it)is given as 466.16 hz.

So is this Bb, A# or a compromise?

[EdSherry]

Richard -- Welcome to the world of "well tempered" and "equal tempered" scales.

If one were to start with (say) an F note and play the 4th (Bb) of a "just tempered" scale (one that takes advantages of the natural Pythagorean relationships between notes) starting on F, it would be a slightly different pitch than the fifth note (A#) of a "just tempered" scale starting on D#. #Instruments tuned so that they sounded "right" in one key would be "off" in another key.

The decision was made back several centuries ago to "fix" this "problem" by moving to a "well tempered" scale (and later an "equal tempered" scale), in which all intervals (other than octaves) are adjusted slightly.

Bach wrote "The Well Tempered Clavier" to show off the fact that the new-fangled instrument could play equally well in all keys.

The result is that (nowadays) there is no difference between A# and Bb. #

See
http://en.wikipedia.org/wiki/Musical_temperament

[jmcgann]

The result is that (nowadays) there is no difference between A# and Bb. #

Nowadays in orchestras and among non-fretted instruments, there is VERY MUCH a difference, as those folks are VERY picky about intonation in context of the music. they are not equal temperment fans by and large!

This was news to me until I started working with orchestras- them folks are a might picky about their tuning, and any professional classical fiddler/violist/cellist/bassist/clarinetist/horn/oboe/bassoon/trumpet etc. will tell you the difference between A# and Bb is very real in their world.

Piano is another world altogether, and lots of orchestra players sniff at it the way they sniff at fretted instruments

[EdSherry]

John -- I stand corrected. #Live and learn. #

(Then again, I don't hang around symphony players much. #Somehow, fitting a symphony into a Celtic or gypsy jazz session or a bluegrass or swing jam doesn't strike me as practicable.)

I agree that, when playing in a particular key, it sounds "sweeter" to use just temperament -- which, as I suspect, is why the orchestral types like it.

But I learned a long time ago that, if I try to tune a fretted instrument to get that "sweet" just-tempered sound in one key, it is hopelessly out of tune in other keys.

Fiddlers can adjust their finger placement ever-so-slightly to capture the differences. #But for those of us unable to make such micro-intonation-adjustments on our fretted instruments, I fear we're stuck with equal temperament and all it implies.

[Richard H]

http://www.phy.mtu.edu/~suits/scales.html

has some interesting info on this.

[jmcgann]

Ed- it's true, I am learning about this stuff via steel guitar as well. Those guys almost all tune to a form of JI rather than ET, which makes the triads sound beautiful, but as soon as you leave them, all bets are off, to my ears. The gains in "sweetness" make the dissonances sound bad by contrast- and I'm a guy who loves sweet dissonance.

The steel players tend to tune the "beats" out of the major thirds (which are really sharp in ET). Of course, once THAT note functions as something else, it's just flat...but the way the steel works, most players tune to the proscribed functions of the pedals and levers and then fudge the bar to make little corrections. It's a beast to play already- then the whole "playing in tune" thing- makes you want to take up something easy like subatomic physics!

We'd need an 84 fret octave to play "in tune" that way. Equal temperment is a system that is out of tune in order to split the out of tuneness across the spectrum so we can play in any of the keys...and it doesn't bother most of us. But I am friends with the Boston Pops guitarist, and he tells me no matter how "in tune" he is, he gets dirty looks from the section players (who are mostly Boston Symphony types) and admonishions to "tune it up!".

Pianos are not tuned straight up 440 the way we tune- the pitch is "stretched" so the bottom and top registers are either higher or lower than 440 (I forget which is which, but I think the high end gets around 442 or higher).

This spring, I wrote 4 arrangements for orchestra that we (The Boston Edge- me, Seamus Connolly on fiddle and Joe Derrane on accordion) played with a local symphony (The New Philharmonia in Newton, MA). The difference between working with the Boston Pops and the locals was that there were a lot of obviously bored to the gills players in the Boston Pops- the players in the local orchestra were very enthusiastic about playing Irish music with us, and actually APPLAUDED the arrangements when they read through them! They weren't worried that the instruments weren't JI- they were playing music for the love of it and not as hired mercenaries.

I admire people who obsess about that tuning stuff, but it's not my world either. I love my A=440 tuner! I am a guitarist and mandolinist, and just dabble at a few other things, but it's fun to see how the other half lives and what they get into. You should see the posts about tuning on the Steel Guitar Forum!

[groveland]

I've had this book on my shelf collecting dust, "Harmonic Experience" by W. A. Mathieu. Anybody read it? I blew the dust off it this morning at breakfast... Seems like a wonderful wild ride for the ears! #I wonder if these old R&R ears are up to the task.

Are there certain selected ET intervals that will exhibit JI characteristics? #Probably shouldn't start posting before the coffee's on...

<span style='font-size:7pt;line-height:100%'>Edit: #The "Harmonic Experience" deals with the difference between A# and Bb, Just Intonation, Equal Temperment, what we hear, why we hear it, etc. #I was certain someone here had read it and could shed more light on the topic at hand. Apparently no takers...</span>

[Strange1]

Speaking of sad. This whole thread went from sad to pitiful in just a short while. I hope the originator was able to glean the info needed from all the chaff. BTW, hence I will tune my mando to the fridge. I just wish it was a mite smaller. My current one won't fit in the back of my 4 runner.

Jack

[JimD]

f one were to start with (say) an F note and play the 4th (Bb) of a "just tempered" scale (one that takes advantages of the natural Pythagorean relationships between notes) starting on F, it would be a slightly different pitch than the fifth note (A#) of a "just tempered" scale starting on D#.

You mean "just intoned" -- by definition just intervals are not tempered.

Also, "Pythagorean" refers to all of the fifths being tuned purely -- this leaves us with troublesome thirds etc. Just intonation is a tuning in which all of the intevals are tuned purely.

Bach wrote "The Well Tempered Clavier" to show off the fact that the new-fangled instrument could play equally well in all keys.

More precisely -- old instrument, new tuning (well-temperament) -- many musicians of Bach's time used tunings that hid the worst intervals in the least played keys. Since Bach used all the keys in this set, there was no place to hide...

By the way, I read the Wikipedia article. Be careful with that one. There are some strange things in it. You might want to read the tuning articles in the Grove's Dictionary of Music instead.

[jmcgann]

Speaking of sad. This whole thread went from sad to pitiful in #just a short while.

WELLLLL EXCUUUUUUUSE ME! JACK!!

On behalf of all the chaff artists...I guess we post because we might be sharing information that someone might find useful. We wrote about tuning and notation issues that happen to actual musicians. If it's not your cup of tea, don't read it. This IS the theory and technique tips section, right?!?!

[groveland]

What is the difference between A# and Bb?

hope the originator was able to glean the info needed from all the chaff.

I think the question was answered to the poster's satisfaction in the first response.

But there's so much fun to be had beyond the stock answer. "What is the difference between A# and Bb" opens the door to tunings and the history of our system and the science. Hence the rest of the posts. It happens a lot here, and I like it. Some of the best discussions come out of rabbit trails. No disrespect intended. It's just hard to tell when it all deserves a new thread - You don't want to break up the momentum...

[EdSherry]

John -- I agree that subatomic physics is simple compared to pedal steel. #

At least I think I understand subatomic physics as well as any layman can [a consequence of two years as an undergraduate physics major before I saw the light, a solid grounding in differential equations and probability theory, and a lot of reading since]. #Pedal steel theory is beyond me, though I've been trying to play steel for 20+ years [for the last 6 years under the tutelage of Bobby Black, who I was fortunate enough to play with in a band several years ago]. #Those steel players THINK differently!

JimD -- You may well be right technically. But I used the terminology I'm familiar with. #To my knowledge, plenty of people use the term "just tempered" to refer to what I was referring to. #"Just intoned" may be the preferred language, but I don't think that I was misusing the terminology. #Similarly with "Pythagorean." #I'm sure that Wikipedia has limitations, but I don't own a copy of Grove (not at $2,500+!). #I acknowledge your point about the distinction between a "new instrument" and a "new tuning." #My mistake.

[JimD]

Ed -- I beg to differ. The correct term is Just Intonation. The definition of temperament is "a system of tuning in which the intervals deviate from the pure (acoustically correct) intervals".

If you have heard plenty of people use the term incorrectly, that doesn't make them right -- except perhaps in a "wikipedia" sense.

[JimD]

Some good references on Just Intonation:

Just Intonation Primer

Kyle Gann on Just Intonation

History of Tuning

[EdSherry]

Jim -- I think we are in agreement. #People may use terminology "incorrectly." #That is a fact of how people use language. #I used the language I'm familiar with. #It may well be wrong as a conceptual matter.

In any case, I don't think we're in disagreement about the fundamental point -- namely, that "just temperament" (and/or "just intonation") differs from "equal temperament," in the sense that A# and Bb are "the same note" in the context of "equal temperament" but are different when one considers "just temperament/intonation."

Indeed, my (limited) understanting is that the concept of "just intonation/temperament" is inherently tied to the reference pitch. #If you start at F, then Bb (the fourth of an F scale) is one pitch. #If you start at Eb, then Bb (the fifth of an Eb scale) is a different pitch if one uses just temperament/intonation. #If you start at C, then Bb (the flatted seventh of the C scale) is still another pitch. #Which of these is "the" "correct" pitch for Bb? #Beats the hell out of me.

[JimD]

OK -- Your point about the pitches is correct.

What is the point you are trying to make now by continuing to use incorrect terminology?

[EdSherry]

Jim -- I've looked into the matter more, and you're right. #

I'm certainly not trying to perpetuate incorrect terminology. #(I make my living by drawing fine distinctions.) #In future, I'll use the "just intonation" terminology that you suggest. #Thanks for the "heads up."

But you seem to be acknowledging that others use the terminology that I used, though you suggest that it is "incorrect terminology." #That's fine. #

As I see it, language is a tool. #If my usage is within the range of what others use, then I'd suggest that it is not "incorrect" other than in a pedantic sense. #I'm all for drawing pedantic distinctions. but that does not detract from my basic point -- that equal temperament is different from just intonation. #On that, we seem to agree.

[JimD]

Actually. I wasn't acknowledging that others use that terminology. Since you kept insisting that you've heard it used that way, I wasn't going to contradict you.

[Shana Aisenberg]

[QUOTE]I've had this book on my shelf collecting dust, "Harmonic Experience" by W. A. Mathieu. Anybody read it?

Yes, I read it and worked through it. If you wish to learn to actually use just intonation as opposed to only theorizing, this is a very good workbook with plenty of hands on exercises.

For anyone who plays fiddle or steel guitar, having working knowledge of these temperaments is highly useful. And regarding pedal steel (and sub atomic physics), I prefer playing lap steel. We don't need no stinkin' pedals

Seth

[jmcgann]

Thanks JimD! The Kyle Gann site is really mind bending; I can't wrap my mind around the math, but it is some crazy ear training.

Most people are gonna say "shut up, use a tuner and you are in tune". But as the Firesign Theater so aptly pointed out in the '60's:

Everything you know is wrong!

Since mandolin can never truly be "perfectly in tune" by most concepts of tuning, we are safe

[groveland]

Whoa, having started the Mathieu book and worked through the Kyle site a bit - Now I know you guys are completely familiar with this stuff, but I have been able to maintain a blissful ignorance of the subject. Some personal epiphanies today:

It occurs to me that our well-tempered system of tuning, which so many of us take for granted, is synthetic in the sense that we had to trump up some rules and a myriad of adjustments to get around the physical laws and make the notes in a given single octave "portable" to other ranges.

Jazz is totally dependent on that synthetic system. #It seems that it would follow that jazz harmony can only exist "naturally" within a single octave. And even within a single octave different combinations of notes produce varying degrees of "harmonic success", if I might call it that.

So I propose that jazz has no more right to exist in the world than polyester or nylon.

This is somehow unsettling. #Somebody, please tell me I'm wrong!

[JimD]

It occurs to me that our well-tempered system of tuning, which so many of us take for granted, is synthetic in the sense that we had to trump up some rules and a myriad of adjustments to get around the physical laws and make the notes in a given single octave "portable" to other ranges.

Our equal-tempered tuning (well-temperament is a historical family of tunings that predate the current "ET") is artificail in that compromises were made in order to approximate pure tuning (just intonation) in a way that causes all keys to be usable by making them all equally out of tune.

Our whole harmonic system grew out of this premise. If jazz would have no right to exist, neither would classical music or anything else that has a harmonic basis.

The earlier Pythagorean tuning (i.e. all 5ths pure) was beautiful for Medieval chant and such but impractical for much else. All tuning is a compromise of sorts.

One interesting thing about the Mathieu book is the way he takes just intonation (which works well for the Indian music that he references) and reconciles it with equal temperament so that we can hear the compromises and the approximations -- hearing equal temperament in terms of just intonation, so to speak.

[Shana Aisenberg]

[QUOTE]So I propose that jazz has no more right to exist in the world than polyester or nylon.

This is somehow unsettling. Somebody, please tell me I'm wrong!

I think that just intonation is best suited to playing music over a drone like classical Indian ragas or that is mostly diatonic. I tend ot incorporate just intonation in playing folk styles such as Celtic, blues, Appalachian, klezmer, Scandinavian, etc. Music composed in equal temperament such as jazz or classical tends to be more harmonically complex and I believe is well suited to it. Both temperaments have their strengths and limitations.

Seth

[jmcgann]

Yeah, drones JI and modulations ET. Polyester or bust