F# Scale

[thedontcarebear]

I am a noob when it comes to any theory, but why isn't the scale F# G# A# B C# D# F F#? Everywhere says its E# instead of F, I didn't think E# was in the chromatic scale? Haha.

[GreeneKing]

From what I know it's the norm to use all the letters alphabetically. Hence E sharp and not F.

[thedontcarebear]

But it would just be F being called E# then?

[Paul_C]

[quote name='thedontcarebear' post='155769' date='Mar 12 2008, 09:29 AM']I am a noob when it comes to any theory, but why isn't the scale F# G# A# B C# D# F F#? Everywhere says its E# instead of F, I didn't think E# was in the chromatic scale? Haha.[/quote]

scales are usually written out so that you have A B C D E F G every time, with marks to show any deviation from that, because the root F# is using the F, the E takes up the slack by being described as E#

[thedontcarebear]

Ahhh, good good, at least I understand now! Thanks.

[queenofthedepths]

If it bothers you, call it Gb and put a Cb in it!

[Paul_C]

another oddity for you..

a diminished 7th chord is written R b3 b5 bb7 (which is also a 6th)

[Broken Hero]

It's just a matter of convention. If you were playing a Bb scale then you would call the root Bb but an A# scale you would call it A#... but these would still be sonically the same scale.

Maybe a better example is if asked to play the scale of D (D E F# G A B C# D) and then asked to play a D# scale... you would want to be doing stuff relative to the note that is actually named... hence the scale of D# (D# E# F## G# A# B# C## D#). It's actually quite good to think of things like this <in my opinion> as it keeps your mind working and keeps your theory on the ball and I think makes you more versatile... that is if you ever come across a song written in such a key

Hope this helps > Si

[P-T-P]

Sounds like we could do with a "Circle of 5ths" diagram to explain the key signatures (which leads us to the scales that go with them).

I think the "D# scale" mentioned is just adding to the confusion as there is no key of D#, only Eb.

The term that needs to be brought up in reference to the E#/F and Cb/B issue, and indeed Ab/G#, Bb/A# etc. is "enharmonic."

The notes sound the same, but are named differently in order to maintain the integrity of the theory which usually results in a cleaner, easier to read, sheet music. For example, if the key was written as D#, you end up with 9 # symbols in the key signature whereas Eb has just 3 b symbols in the key signature, much easier to deal with.

Edited March 12, 2008 by P-T-P

[thedarxide]

Circle of fifths, it needs to have 6 sharps.

[P-T-P]

Going back to the original post...

[i]I didn't think E# was in the chromatic scale[/i]

There's no absolute way of writing the chromatic scale. The convention in music tends to be that if you're going up to a black key on a piano you use the sharp symbol and if you're going down to it you use a flat symbol.

So an ascending chromatic scale could be written C C# D D# E F F# G G# A A# B C

A descending chromatic scale could be written C B Bb A Ab G Gb F E Eb D Db C

But there's no right or wrong and where you get people who've not studied theory but still play music you can find a mixture. I'm sure the guitarist from my band would write a chromatic scale as being... C C# Eb E F F# G G# A Bb B C ... and use the same names for the notes whether ascending or descending.

As to the E# in an F# major scale. None of the major scales are built from the chromatic scale, they come about as the result of the way key signatures -the sharps or flats at the very beginning of a piece of music, just after the clef - are defined.

The easiest way to explain that is a thing called the cricle of fifths.



As the C major scale is C D E F G A B C so the C key signature has no sharps or flats.

Moving clockwise we go up to the fifth note of the C major scale - G.

The G major scale is G A B C D E F# G so the G key signature uses one sharp, F#

Moving clockwise we go up to the fifth note of the G major scale - D.

The D major scale is D E F# G A B C# D so the D key signature uses two sharps, F# and C#

You continue moving up a fifth until you get to C# which requires seven sharps in the key signature to construct a C# major scale.

That's the sharps taken care of, so for the flats we go back to C.

Moving anti-clockwwise we go up to the fourth note of the C major scale - F

The F major scale is F G A Bb C D E F so the F key signature uses one flat, Bb

You continue anti-clockwise, moving up to the fourth note until you get to Cb which requires seven flats to contruct a Cb major scale.

Notice that the major scale pairs of B and Cb; F# and Gb; C# and Db actually sound the same. They are enharmonic. You play the same combination of white and black keys on a piano or frets and strings on the guitar. They are distinctively named however and while you'll rarely see a piece written in C# or Cb, it is useful to be aware of their existence and the reason for it.

Going back to your E#/F question again...

If we didn't use E# instead of F, every F and F# note would need to be written on the same line on the stave and have to be proceeded by the use of a sharp or natural symbol which would make for a messy and confusing piece of notation.

[Mikey D]

Don't forget we've only had equal temperment from about mid 1830's, and it wasn't widely spread until early 1900's for tuning purposes.

I'll let wikipedia do the explaing:

"Intervals in different systems of tuning

In equal temperament, there is no difference in tuning (and therefore in sound) between intervals that are enharmonically equivalent. For example, the notes F and E♯ represent exactly the same pitch, so the diatonic interval C–F (a perfect fourth) sounds exactly the same as its enharmonic equivalent – the chromatic interval C–E♯ (an augmented third). In systems other than equal temperament, however, there is often a difference in tuning between intervals that are enharmonically equivalent. In tuning systems that are based on a cycle of fifths, such as Pythagorean tuning and meantone temperament, these alternatives are labelled as diatonic or chromatic intervals.

Under these systems the cycle of fifths is not circular in the sense that a pitch at one end of the cycle (e.g. G♯) is not tuned the same as the enharmonic equivalent at its other end (A♭); they are different by an amount known as a comma. This broken cycle causes intervals that cross the break to be written as augmented or diminished chromatic intervals. In meantone temperament, for instance, chromatic semitones (C–C♯) are smaller than diatonic semitones (C–D♭),[31] and with consonant intervals such as the major third the chromatic equivalent is generally less consonant.

The exception to this classification is the tritone, of which both enharmonic forms (e.g. C-F♯ and C-G♭) are equally distant along the cycle of fifths, making them inversions of each other at the octave. Because of this the ambiguity cannot be resolved where octave equivalence is assumed, and the label diatonic or chromatic for either form of tritone is not useful in the context of tuning (the choice is arbitrary, and therefore unspecific).

If the tritone is assumed diatonic, the classification of written intervals by this definition is not significantly different from the "drawn from the same diatonic scale" definition given above as long as the harmonic minor and ascending melodic minor scale variants are not included. Aside from tritones, all intervals that are either augmented or diminished are chromatic, and the rest are diatonic."

So in the older days, E# and F weren't the same.

[queenofthedepths]

That's fascinating, but I'm not quite sure I understand... are you saying that if Bach (for example; could be any pre-equal temperament musician) wrote an Ab, it would sound different to a G#? If so, how would one go about playing these different notes on a harpsichord? Or a flute or whatever... or even a fretted bass guitar? If I've understood that article correctly, the 1st fret on a standard tuned G string is half a comma sharper than a G# and half a comma flatter than an Ab?
But I always thought we had equal temperament as standard ever since Pythagoras anyway

[jakenewmanbass]

[quote name='Mikey D' post='156041' date='Mar 12 2008, 02:58 PM']So in the older days, E# and F weren't the same.[/quote]

Absolutely, and if you talk to string players they (and I) can tell the difference between flats and sharps in relation to the key. Eg the C# in A major has a different brighter quality to the more dark and sombre Db of B flat minor tiny differences and more about tonal qualities of keys than anything else.
Thats why Ellington/Strayhorn tunes have their own qualities, lots of Db, rich, thick and luscious sounds for ballads.

Edited March 12, 2008 by jakesbass

[Mikey D]

[quote name='queenofthedepths' post='156050' date='Mar 12 2008, 03:10 PM']That's fascinating, but I'm not quite sure I understand... are you saying that if Bach (for example; could be any pre-equal temperament musician) wrote an Ab, it would sound different to a G#? If so, how would one go about playing these different notes on a harpsichord? Or a flute or whatever... or even a fretted bass guitar? If I've understood that article correctly, the 1st fret on a standard tuned G string is half a comma sharper than a G# and half a comma flatter than an Ab?
But I always thought we had equal temperament as standard ever since Pythagoras anyway [/quote]

He wrote the "Well tempered" clavier, not the equal temperment clavier. This is why historians think that composers wrote in certain keys to get a certain mood etc.

Harpsichord tuning is another kettle of fish. There are many ways to tune it. WHen you play in some keys, it sounds very pleasing, but in others it would sound intolerable due to the tuning of the instrument as a fixed pitch instrument won't be in tune with it self, unlike a violin where you can 'fret' where you want.

Nope, thats why you get the Phythagorean comma when you go completely around the just tempered cycle of fifths, you don't end up on exactly the same note.

Regarding the guitar etc, due to the nature of a standard fretted instrument, it is never dead on exactly in tune everywhere, its as near to it though. That's why people like buss feiten and others have other ways of tuning the guitar.

[Mikey D]

[quote name='jakesbass' post='156058' date='Mar 12 2008, 03:17 PM']Absolutely, and if you talk to string players they (and I) can tell the difference between flats and sharps in relation to the key. Eg the C# in A major has a different brighter quality to the more dark and sombre Db of B flat minor tiny differences and more about tonal qualities of keys than anything else.
Thats why Ellington/Strayhorn tunes have their own qualities, lots of Db, rich, thick and luscious sounds for ballads.[/quote]

Right on...

[jakenewmanbass]

[quote name='queenofthedepths' post='156050' date='Mar 12 2008, 03:10 PM']That's fascinating, but I'm not quite sure I understand... are you saying that if Bach (for example; could be any pre-equal temperament musician) wrote an Ab, it would sound different to a G#? If so, how would one go about playing these different notes on a harpsichord? Or a flute or whatever... or even a fretted bass guitar? If I've understood that article correctly, the 1st fret on a standard tuned G string is half a comma sharper than a G# and half a comma flatter than an Ab?
But I always thought we had equal temperament as standard ever since Pythagoras anyway [/quote]
quite simply put, on a fretless (just an example it does apply to others) or a double bass there's a bigger gap between semitones than it first appears, and the longer you are dealing with that, the more acutely aware of the differences you become. Thats in my experience. There are of course people who can't even tell when their fretted instrument is out of tune

[Mikey D]

[quote name='queenofthedepths' post='156050' date='Mar 12 2008, 03:10 PM']If I've understood that article correctly, the 1st fret on a standard tuned G string is half a comma sharper than a G# and half a comma flatter than an Ab?[/quote]


Just to clarify this bit:

If you sat at a just tempered piano and played a low g#, then the next D, then the next highest A all the way through to the Ab up the keyboard, then you are a comma out.

This is why we have equal temperment, to even out the differences over the octaves.

Edited March 12, 2008 by Mikey D

[queenofthedepths]

Ah, still more fascinating... must explain why fretless is so wonderful!

[Mikey D]

[quote name='queenofthedepths' post='156068' date='Mar 12 2008, 03:23 PM']Ah, still more fascinating... must explain why fretless is so wonderful![/quote]


Personally I find find all this side of music very interesting. There's a great pdf available on the net called the maths in music or something, extremely heavy reading and very long, but some good content.

The difference between a good fretless and a great fretless player is someone who really does adjust their tones when playing in a certain key to make the intervals truer.

[Mikey D]

[quote name='Paul_C' post='155799' date='Mar 12 2008, 10:05 AM']another oddity for you..

a diminished 7th chord is written R b3 b5 bb7 (which is also a 6th)[/quote]
But it comes from the diminished scale where the 6th is flattened and you can't have two sixths in a scale now can you!

[The Funk]

Have I missed someone use the word "enharmonic"?

[bnt]

I find all this fascinating too, and sometimes I'm amazed that the equal-tempered scale works as well as it does. It's based on a particular mathematical formula (exponential) that is a very close - but not exact - match to basic harmony principles. Using that Cycle of Fifths as an example: we call 7 semitones or frets a fifth, but it's not really:
- harmonic fifth: tones on the pure ratio of 3:2, or [b]1.5[/b]
- 7 semitones: 2^(7/12) = [b]1.4983071[/b]

If you follow both of those ratios round the cycle of fifths, you apply the frequency ratio 12 times, which in maths terms means raising it to the power of 12:
- 7 semitones: 1.4983071 ^ 12 = [b]128[/b] = [i]exactly[/i] 7 octaves higher (because 2^7 = 128) = still in tune
- harmonic fifth: 1.5 ^ 12 = [b]129.74634[/b] = 7 octaves and a bit sharp.

Apologies for the maths - but one interesting side-effect of this process is the possibility of using octaves with a different number of semitones. There are folks out there with 19-tone guitars, and Steve Vai has a 16-tone guitar somewhere in his collection.

Edited March 12, 2008 by bnt

[jakenewmanbass]

[quote name='The Funk' post='156089' date='Mar 12 2008, 03:38 PM']Have I missed someone use the word "enharmonic"?[/quote]
you haven't, it was on the tip of my tongue and is the correct way to describe the difference between the two/one notes/note.

[P-T-P]

[quote name='jakesbass' post='156169' date='Mar 12 2008, 04:32 PM']you haven't, it was on the tip of my tongue and is the correct way to describe the difference between the two/one notes/note.[/quote]

Actually, you both missed it!

I'll claim first use, think Mikey D mentioned it too.