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Sharps and Flats


Greta Schmidt
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Sort of. On the piano, they are the same note. But recently (this past summer) I was told for the first time that they are not the same note. a D# is somehow different than an Eb. Though I posted on the subject, asking for an explanation, it was never explained to my satisfaction. Either I automatically adjust or I don't at all (because I certainly don't consciously adjust between the "same" notes). For all intents and purposes, they are the same note, but technically they're not. Ach... it's such an annoying topic.

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I'll write what I think I know about it - someone correct me if it is incomplete or incorrect.

The intervals in a key are defined (there is a choice behind this definition) by unique ratios (rational numbers, which are in the form: integer/(non-0 integer)).

If C is 1 (frequency-wise), then within C major:

D is 9/8

E is 5/4

F is 4/3

G is 3/2 (fifth)

A is 5/3

B is 15/8

next C is 2

But you realize that those ratios are attached to the intervals, and not the notes themselves:

9/8 = major 2nd (eg C-D)

5/4 = major 3rd (eg C-E)

4/3 = perfect 4th (eg C-F)

3/2 = perfect 5th (etc...)

on the piano, the interval between D and E is the same (frequency-wise) as the interval between G and A (one tone). Equal temperament divides an octave into (*almost*) 12 equal (frequency-wise) semi-tone intervals.

If you check the D-E and G-A intervals in just temperament with the ratios I wrote, you already see that:

D-E = 9/8 to 10/8

is not equal to

G-A = 9/6 to 10/6

That shows more explicitly the difference between equal and just temperaments.

Now, why could you have to play 2 different notes from the same note symbol on your partition? The answer lies in the asymmetry of the distribution of the intervals I gave out. It depends in which key you are playing and in which interval that note is contained.

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Greta, here's the fast 'n' dirty explanation that I received when I posted a similar question on Maestronet a few years ago:

In melodic passages, string players usually play the leading tones in the scale (the thirds and the sevenths, or E and B in the key of C) a little bit sharper than they would be on the piano to emphasize their "leading" quality. If you're playing in E, for instance, that means your D# is going to be a little sharper than usual. Unless, however, you're playing in a key that has leading tones on open strings, in which case you play the notes you're leading to somewhat flat. For instance, if you're playing in Eb you would want to make the Eb low enough so that the open D would lead to it properly.

There's a good explanation of this in many of the standard works on violin pedagogy--check out the intonation discussions in Fischer's _Basics_ or Flesch's _Art of Violin Playing, Bk. 1_.

It is a basic--and confusing--issue.

Trent

[This message has been edited by Trent_Hill (edited 02-22-2001).]

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They are not the same note, which is part of the magic of the violin.

According to theory they are the same note but if you think about how they are played it becomes obvious that they are not. I'll use F# and Gb in 1st position on the D string for example. When you play a F# you push your second finger right behind your third finger on G to get the half step down. To play a Gb you put the third finger up tight against the second finger on F to get the half step.

What is really fun is when you're playing some note say C# and the the composer switches to Db. Does the composer really want a slightly different note or is it just to make the chords lines up right in the score?

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I play a lot in ensembles - some with a piano, some orchestras with harp - sometimes piano, with fixed intonation percusion instruments, etc. In all of these settings an A# = B-flat, etc. Sometimes a little bit of "enhancement" of intonation higher or lower by the strings (or even the winds) may better engage the intent of the composer without creating a sense of being out of tune. After all, when 20 violinists vibrato at the same time the intonation spreads - sometimes beyond the tolerable - and a general fuzz results.

I like the experience of playing in smaller ensembles with piano because it eliminates all arguments like this one about intonation. After all, if the sharps and flats are to be tempered differently, so must all the notes - so that all the intervals (chords) come out close to proper.

Andy

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  • 3 weeks later...

It has to do with the harmonic series as Mu0n suggested.

A neat trick to do to prove that a enharmonic notes are actually different is to (first make sure your violin is perfectly in tune) then on the d string play an E in 1st position against an open A. Get the notes so that they are perfectly in tune with each other (a perfect 4th). Then without moving your left had at all play the E on the d string against your open G string. You'll find that the notes (major 6th) are out of tune and you'll have to adjust your finger to get in tune. This is just a neat way of explaining the difference between well temepered tuning and non-tempered tuning. smile.gif

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