Is a# the same as bb?

[groveland]

Thanks guys. I'll be okay now.

[Peter Hackman]

Some good references on Just Intonation:

Just Intonation Primer

Kyle Gann on Just Intonation

History of Tuning

I looked at kylegann and found something very puzzling. Among
all these simple rational intervals, like fifth=3/2, there's the
tritone, given as 45/32. How did they arrive at that complex interval?
My guess: the only tritone in the C major scale is
from f to b. f to c #is 3/2, b to c is 16/15, and the quotient
is 45/32.

However, if we accept the theory that the ear approves primarily
of simple rational relationships one should look at the overtone series.
Let the fundamental c be no. 1; then e is no. 5, and b flat
is no.7 (that's a flat b flat), so the first tritone appearing
is the interval 7/5. The inverse interval would be
10/7, which is larger. Another tritone relationship is
from no. 12, a g, to no. 17, a c sharp (of sorts), giving the interval
17/12. (oh, yes, there is 8 to 11, an f#, but that's a really bad one)

Now the perfect symmetry/ambiguity tritone is the tempered one,
exactly half an octave,
the square root of 2. It turns out that 17/12 is closer
to that #than
the more complex interval 45/32!

Actually, in math (I'm a retired math lecturer)
there is a technique, called continued fractions,
for producing rational approximations, and it turns out that
the first three approximations obtained in this manner are 3/2 (but that's a pure fifth!), 7/5, and 17/12 !!

If the perceived relationship between f and b, in Pythagorean c, is
45/32, no wonder it longs to be resolved!

What do we hear, and what do, e.g., #singers produce? I once read about an investigation, trying to decide whether trained singers intonate
Pythagorean or tempered. It turned out their intonation
wasn't good enough to settle the issue.

[ApK]

[QUOTE= (Peter Hackman @ Nov. 13 2006, 09:36)]

It turned out their intonation
wasn't good enough to settle the issue.

"Good" enough or "consistant" enough?
Seems like if they sound good enough, then they are good enough, but is it perhaps they modulate a bit more dynamically and variably than a study like that could make use of?

Isn't that part the reason violin has a "voice-like" quality, because the violinist can make microtonal adjustments as they play?

[Peter Hackman]

[QUOTE= (ApK @ Nov. 13 2006, 10:18)]

It turned out their intonation
wasn't good enough to settle the issue.

"Good" enough or "consistant" enough?
Seems like if they sound good enough, then they are good enough, but is it perhaps they modulate a bit more dynamically and variably than a study like that could make use of?

Isn't that part the reason violin has a "voice-like" quality, because the violinist can make microtonal adjustments as they play?

I interpreted the statement as ''not close enough to either alternative'';.
Maybe your interpretation is more to the point; I may have to look it up again.

[Richard H]

Wow! When we start using quarter tones like I understand they do in African music, someone's gonna have a lot of fun with this intonation thing.

What do they call those notes anyway? Is the note between A and Bb called A1/2# or Bb1/2b?

[mandocrucian]

List of microtonal intervals

Microtonal notation


B half sharp; B#; B sharp&1/2 |B half flat; Bb; Bb & 1/2

B half-flat is halfway between B and Bb; Bb1/2 is halfway between Bb and A and enharmonically equivalent to A‡ (half sharp)

NH

[Richard H]

Mandocrucian,
You're joking, right?

Why don't we scrap frets and notes altogether and write music in Hz? Unlimited variation.

But then again music is already being used as a form of torture and we don't want to make it any worse.

[Shana Aisenberg]

Some composers use ratios instead of conventional notation for pieces using just intonation.

Seth

[ApK]

The standard notation we speak of is standard only to the western 12-tone system of music. #Other musical cultures have other forms of notation expressing different things.

Hz is a viable one...didn;t the aliens in Close Encounters use that? #:-)

[Ted Eschliman]

That just Hz to even think about...

[mandolin123]

theory,

no flats or sharps between E&F of B&C.

everything else has a fret between it.

My way of thinking.

[jmcgann]

Richard H- if you go beyond mandolin and listen to music from, say, any non-western country, you'll hear notes you didn't know existed. It's very cool out there, and they've been doing it that way for even longer than old time music in the USA. Some of them ferinners don't even use chords

Just because we don't (intentionally) get 'em on the mandolin doesn't mean they aren't valid, real, or worth considering.

[hepcat mando]

In trying to decipher the difference between A# and Bb you guys have overlooked(much to your chagrin) the obvious. If you look at them sideways the A# looks like a birds beak with profanity coming out of it while the Bb looks like an angry person sticking their tongue out, making them both equally offensive. They don't teach that in college...you have to learn it in the real world.

[mandocrucian]

But it's not just non-western music. Listen to any string bending guitarist with an incredible sweet sound (Mark Knopfler, Richard Thompson, BB King etc.) and when they do doublestop bending (especially), it's to just intonated inervals. And the blues guys are (intuitiontially) all over the microtonal map!

Ever notice when a fiddler and a mandolinist play the exact same tune (especially when doublestops are involved), the fiddle version is likely to sound better, sweeter.... #It's because of the microtonal adjustments to the notes on the fiddle. #Vassar Clements is playing something other than the 12-tone-equal-tempered (12TET) scale. And so are all those old-time and Cajun fiddlers.

(When these fiddle players say that you can't really get it off the printed page, a big part of what they mean has to do with intonation. The notation is an approximation, and except for the neutral 3rds, 7ths, etc - more-or-less quarter-tone intervals - rarely notated.) You've got to listen to the records if you are going play those adjustments of pitch.)

Listen to Curley Ray Cline play "the notes between the notes". Ralph Stanley doesn't sing restricted to the pitches on the piano, and neither does Etta James and hundreds and hundreds of other singers. And Doyle and every other great vocal harmony outfit (Golden Gate Quartet, Sons Of The Pioneers, etc. etc.) are not in 12TET; if they were, it wouldn't sound nearly as magical.

And anything said about string bending guitarists and fiddle players applies in spades to any of the slide instruments: slide guitar, steel guitar, pedal steel, dobro.

Bagpipes are not pitched to 12TET. Flute players can bend notes by rolling the flute back or forward against the lip. Autoharpists don't tune to 12TET; that's why they always have 3 or 4 instruments onstage. An instrument will sound great in 2 or 3 keys, but if they want to play in some different key, they'll pick up the instrument which has been tuned for optimal consonance in that particular key.

I was on a workshop panel a few years ago with a couple big name acoustic players. I brought up the subject of microtonal adjustments to intonation as it related to a sweet "tone" (but it's really non-12TET intonation rather than timbre), and to my astonishment, it became apparent that neither of those guys knew what I was talking about.

With the overwhelming dominance of 12TET music here in the west, especially in mainstream music, listeners are programmed to hear and expect that intonation. And they register non-western (or folk based) music and players as being out-of-tune. #But it's not "out of tune"; it's just a different way of carving up the octave.

But once you start to "hear it" (and having someone demonstrate the differences between, say, just-3rds vs 12TET-3rds will speed up the process), you won't/can't turn back. I couldn't stand to go back to playing strictly 12TET pitches; if I couldn't microtonally tweak my notes with bending, I think I'd just put down the mandolin for good and switch over all the way to a non-fretted instrument.

Niles H

PS: Come to the blues mando bootcamp and we will get into the use of non-12TET intonation. If you don't start using them, you'll sound like Pat Boone instead of Little Richard (metaphorically)!

[ApK]

But it's not just non-western music. Listen to any string bending guitarist with an incredible sweet sound (Mark Knopfler, Richard Thompson, BB King etc.) and when they do doublestop bending (especially), it's to just intonated inervals. And the blues guys are (intuitiontially) all over the microtonal map!

Yeah, that's true, and while you're unlikely to see those blues bends represented in standard notation using those half-sharp and half-flat symbols very often, you will often see them in tab with notations to bend or slide a fraction of a half step.

[mandocrucian]

Yeah, that's true, and while you're unlikely to see those blues bends represented in standard notation using those half-sharp and half-flat symbols very often, you will often see them in tab with notations to bend or slide a fraction of a half step.

Electric guitar notation and tab has developed it's own way of denoting the partial step bends and such. But it's different in one sense - the notated note is where the finger is placed, while the arrow tells how much to stretch the string. #It could be 1/4 step, or a 1/2 step, a full tone, or even a minor 3rd (1.5 steps). If it is going to another diatonic or chromatic pitch (more-or-less) that target pitch may be notated with a note head within a set of () rather than "1/2 step" above the bend symbol. For a fretted instrument, this is very effective, especially in conjuntion with a tablature stave.

Now if it is only a stave of standard notation, you'll find slurrings, bendings or (glissandi)slides notated conventionally. And with old-time fiddle transcriptions (say in Fiddler Magazine), you will see the half-sharp and half-flat symbols being used to notate quarter-tone neutrals.

When you get into the area of notated music or transcriptions of Turkish and Middle Eastern music, you'll see these half-sharps and half-flats being used as part of the key signatures, as well as accidentals. The Arabic maqamat (scales) have quarter-tone intervals in them.

For example, the "freygish" scale (I'm using the Klezmer name) which is found all over the middle-east as well as eastern europe and the Balkans - in the west (on 12-TET instruments) would be: D Eb F# G A Bb C D ; or by scale degree: 1 b2 3 4 5 b6 b7 8
(5th mode of the harmonic minor scale; in this case G harmonic minor, played from D to D)

but in its more authentic form it is:
D Ed F# G A Bd C‡ D (ascending) || D C Bb A G F# Ed D (descending)
1 2d(half-flat) 3 4 5 6d(half flat) d7(half-flat)* 8 || 8 b7 b6 5 4 3 2d 1

<span style='font-size:8pt;line-height:100%'>*Relating to a D major scale C# is the 7th, so C‡ is actually a 1/4 tone down from that making the maj 7th half-flatted".
(If I had used C Major with no sharps in the key signature, there would not be this possible confusion: i.e. #&#124;&#124; C Dd E F G Ad Bd C &#124; C Bb Ab G F E Dd C &#124;&#124;)</span>

The difference bewteen guitar and oud/violin is how you get to those quarter-tones - bending up to them from a fretted note on a guitar vs. placing the finger down on the string right at that quarter-tone pitch on a fretless instrument.

But the Turks and Arabs use different amounts of sharpness and flatness for various interval for what we might consider to be the 'same' scale. It gets pretty complicated. I had started getting more into the Middle-East/North African stuff (via Greek music, which is a good, transitional doorway from west to east), but after 9/11 and all that, I got disgusted with the entire region and said "screw all that" and put those Cds back on the shelves. I figure I can get plenty of quarter-tones from Norway and Sweden, not to mention good ol' American gutbucket blues. Ah-hawh-haw-haw

NH

[Peter Hackman]

Nobody has mentioned Harry Partch?

[johnhgayjr]

A friend recently told me how he trips up harmonica players who can't look at the guitar and figure out the key. #Tell 'em you're in E sharp. #Even those guys with all the harmonicas on their harmonica belt can't figure that one out. #Or you could use the key that Frank Wakefield uses on a tune on the Bluegrass Mandolin Extravaganza disk - K flat sharp!!

John Gay
Memphis

[Richard H]

Richard H- if you go beyond mandolin and listen to music from, say, any non-western country, you'll hear notes you didn't know existed. It's very cool out there, and they've been doing it that way for even longer than old time music in the USA. Some of them ferinners don't even use chords

- I get the impression even the Celtics didn't use chords.
- I sometimes get invited to play along at parties where Indians (from India) beat their drums and play the harmonium (?) It features a lot in their music and surely must be tempered like a piano. I don't know. Maybe the singers bend the notes.
- "Foreign" music always seems harder when you read it. For instance, Steve Mullins (Mando Mag.) says that in Venezuelan music, the mandolin and cuatro music is really in 5/8 but the drum is playing "a steady 2/4 rhythm beneath the melodic quintuplets."

Most of the music I'm playing nowadays is Venezuelan and I have no problem as long as I don't try to analyse it.

- Of course, on this site all that should really matter is whether Big Mon was even-tempered, mean-tempered or just tempered.

[jmcgann]

Notating folk music is like taking home a plastic bag of mountain air and putting it in a terrarium.

[EdSherry]

John -- and your point is? #I do that every time I go to the mountains. #Doesn't everyone? #(Hee, hee ...)

Seriously, "traditional" Western notation was developed in the context of "traditional" Western European music. #Not surprisingly, it has to be augmented to deal with other musical idioms that don't share the Western European major/minor framework.

[jmcgann]

That's what I meant to say, Ed!

Really, notation has little to do with music (as a performance art) at all. It's fabulous as a tool for expressing theory, but too many people try to get a concept of "style" from a page, and it just ain't happening. Without the ear and soul, the page is a drawing of a beautiful place-not the actual place itself.

What I mean (for example) is people using O'Neills Music of Ireland to learn Irish music without steeping in recordings/sessions etc.

[EdSherry]

John -- I couldn't agree more. #

I was recently asked to play rhythm guitar on a recording of a classically-trained violinist who wanted to play Irish fiddle tunes. #

He had great classical technique, and could sight-read like nobody's business, but my gosh he was clueless as to what the music should sound like!

[JeffD]

There is no music on the page. Just dots and lines. I noticed that when you take a piece of sheet music, roll it up and stick it in your ear, the sounds it makes are not the musical at all.

[EdSherry]

JeffD -- Pete Seeger had a book entitled "Henscratches and Flyspecks" on reading standard notation. Sounds about right to me. Lines like a chicken scratching in the dust, and dots like flyspecs on the paper.