I'm a bit confused about the modes. I'm learning them by ear through this app, where the app explains what to listen for. For instance: dorian has 2b (flats), and lydian has 1# (sharp).
The thing I'm confused about: does lydian always have 1# in it? or dorian 2b? Doesn't this depend upon which major scale and mode? Or is the fixed amount of flats and sharps only applying if all modes are starting from C?
It's common to describe modes (or any seven-note scales) by how they compare to the major scale- major is sort of the "default" scale in western music and music theory.
Lydian has one sharp added to the parallel major scale. It could be described as 1-2-3-#4-5-6-7.
Dorian has two flats added to the parallel major scale. It could be described as 1-2-b3-4-5-6-b7.
You're right to think that if you start with a major scale with 3 flats (Eb major) and add the two flats to make Eb dorian, you end up with 5 flats. Or, if you added a sharp to make it lydian, you're returning the Ab to A natural- so the scale has 2 flats.
I find it helpful to think of the pitches as "raised" and "lowered" to avoid confusion. So Lydian, for example, has one raised pitch compared to major. The actual note name could be natural or sharp (or even double sharp), but it will still be "raised" in comparison to major.
Some concrete examples for Major and Lydian:
C Major / C Lydian C D E F G A B C C D E F# G A B C C# Major / C# Lydian C# D# E# F# G# A# B# C# C# D# E# Fx G# A# B# C# Db Major / Db Lydian Db Eb F Gb Ab Bb C Db Db Eb F G Ab Bb C Db
In the three Lydian scales shown, the changed pitch can be sharp (C Lydian), double-sharp (C# Lydian), or natural (Db Lydian), but it's still raised from its position in the corresponding major scale.
Being told by the app that a mode 'has one sharp', or 'has two flats' in itself is pretty useless. Unless it also highlights which number notes are affected.
It's not like 'there's a major key with one sharp', - which we all recognise as key G. And that sharp is the sharpened leading note, compared with the natural (F).
It's of paramount importance, therefore, to designate which note/s gets the sharp/flat - in comparison with the basic major scale.
So Lydian (with one sharp - that is vague) is the same as the major scale, BUT its 4th is sharpened. Mixolydian has one flat, BUT that is its 7th note, flattened when compared with its parallel major scale. G A B C D E F, compared with G A B C D E F♯. But even that's confusing - we just read that Mixolydian has one flat - there's not a flat in sight. It's the 7th note that's been flattened, producing F♮!
I'd hesitate to use the site or app that describes modes that way - I think it's quite confusing. There are far better ways in which to get to understand modes.
Here's what the other answers miss:
Think of modes as essentially rotations of a major scale. The formula for each mode is derived from its relationship to its parent scale. Understanding the mode names and how they relate to the parent scale helps us understand why the formulas are built the way they are. Let's see it in action:
Ionian (Major): C D E F G A B (1 2 3 4 5 6 7)
Now if we rotate this scale and go from "D" to "D", we get:
D E F G A B C
Cool, "D" is our tonal center now, but it's not "D major", in fact, we don't want it to be "D major" because we want to use the language of "C major" but with "D" as our tonal center.
So if we look at what's different between "D major" and this scale, we see that we're missing the "F#" and "C#".
This gives us "D Dorian" with a formula of 1 2 b3 4 5 6 b7, with the "b3" & "b7" representing "lowered" notes, in this case, "F", which would be "F#", and "C", which would be "C#" in D major. These are scale degrees that we altered from "D major" to fit our language of "C major".
Now let's rotate the same scale but starting on "F":
F G A B C D E
So, "F" is our tonal center but we're continuing to use the language of "C Major". Well, relative to "F Major", there is one note different, "B", which should be "Bb". So, we represent the formula as:
1 2 3 #4 5 6 7
to indicate that the 4th degree has been raised. Again, "F" is our tonal center, but keeping the language of "C major".
In order of scale degree the modes are:
Because all major scales in 12-EDO equal-temperament are all built using tetrachords, these formulas work for all rotations of all keys.
Hope that helps!
All modes contain the same repeating sequence of 7 pitch classes. The only difference is where in the sequence you start.
Personally, I think that the traditional names of the modes are a needless complication imposed by academic types who still buy into the silly idea that speaking in Greek makes one sound “smarter”. I prefer to just call them do-mode, re-mode, etc. Nevertheless, since that terminology seems to be “confusing” to some people, I will use the Greek names in this answer.
Now, let's assign each note a number from 0 to 11 based on the usual convention of twelve equal semitones in an octave: do=0, re=2, mi=4, fa=5, sol=7, la=9, ti=11. (That's one semitone for the mi-fa and ti-do intervals, and two semitones for the others.)
By subtracting the number assigned to the starting note or “tonic”, and adding 12 (one octave) to any number that goes negative, we can derive the notes of each scale as a sequence of semitones from the tonic.
You may prefer to refer to notes by letters instead of numbers, though. So let's assign the number “0” to the ever-popular tonic of C. Recall that 0=C, 2=D, 4=E, 5=F, 7=G, 9=A, and 11=B. The five “black key” notes (1, 3, 6, 8, 10) will need to use sharps or flats as appropriate.
The mapping of numbers to letters is context-sensitive: Note 6 is “F♯” in the Lydian scale, but “G♭” in the Locrian scale. This is needed in order to satisfy the requirement that each note in a scale use a unique letter.
For instance: dorian [re-mode] has 2b (flats), and lydian [fa-mode] has 1# (sharp).
This is indeed the case for scales starting on C. As you can see from my lists of notes above: C Dorian has two flats (E♭ and B♭) and C Lydian has one sharp (F♯).
But as you suspected, this only applies if you're starting from C. Let's try starting from E instead. Then 0=E, 1=F, 3=G, 5=A, 7=B, 8=C, and 10=D, so:
E Dorian now has two sharps, and E Lydian has five sharps. If you compare the E scales to the corresponding C scales, you see that they all have exactly four more sharps or four fewer flats than the C-based counterpart.
