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A_SN wrote:whatever reason there may be for saying that E in a Ab minor scale isn't a sixth must be pointless. Then what is a sixth in a Ab minor scale?
Ok, here is the Ab natural minor scale with the notes numbered:

Code: Select all

Ab, Bb, Cb, Db, Eb, Fb, Gb, Ab 
1   2   3   4   5   6   7   8
As you can see, the sixth note is Fb.
E is not a note in the scale of Ab natural minor.
That would be just as wrong as the aforementioned F-natural in E minor.
A_SN wrote:I get that it tells you something different, but it's like the same notes either way.
They may sound the same in equal temperament, but there is an important theoretical difference.
A_SN wrote:Why is a F in A minor a sixth but a E in Ab minor an augmented fifth? It's the exact same thing transposed.
No, it's not.
F is a minor sixth above A.
E is an augmented fifth above Ab.

If you wanted a minor sixth above Ab, you would need Fb.
A_SN wrote:You have to wonder at that point if the distinction is real or if it's a construct that has little to do with what you hear.
The two things aren't necessarily mutually exclusive.

Example:
Their, There, They're
All three words sound the same in English, but yet each has a different meaning. They are not interchangeable. Depending on context, one will be correct and the other two will be wrong. And there are times when a sentence can have its meaning completely changed by using the wrong spelling. So using the right spelling is important.
Unfamiliar words can be looked up in my Glossary of musical terms.
Also check out my Introduction to Music Theory.

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JumpingJackFlash wrote:
A_SN wrote:whatever reason there may be for saying that E in a Ab minor scale isn't a sixth must be pointless. Then what is a sixth in a Ab minor scale?
Ok, here is the Ab natural minor scale with the notes numbered:

Code: Select all

Ab, Bb, Cb, Db, Eb, Fb, Gb, Ab 
1   2   3   4   5   6   7   8
As you can see, the sixth note is Fb.
E is not a note in the scale of Ab natural minor.
That would be just as wrong as the aforementioned F-natural in E minor.
A_SN wrote:I get that it tells you something different, but it's like the same notes either way.
They may sound the same in equal temperament, but there is an important theoretical difference.
A_SN wrote:Why is a F in A minor a sixth but a E in Ab minor an augmented fifth? It's the exact same thing transposed.
No, it's not.
F is a minor sixth above A.
E is an augmented fifth above Ab.

If you wanted a minor sixth above Ab, you would need Fb.
A_SN wrote:You have to wonder at that point if the distinction is real or if it's a construct that has little to do with what you hear.
The two things aren't necessarily mutually exclusive.

Example:
Their, There, They're
All three words sound the same in English, but yet each has a different meaning. They are not interchangeable. Depending on context, one will be correct and the other two will be wrong. And there are times when a sentence can have its meaning completely changed by using the wrong spelling. So using the right spelling is important.
Ah okay thanks, that's a pretty great explanation, so I see what you mean. :tu:

Basically my problem is that I insist on using scientific pitch notation because I want each note of 12-TET to have its own unambiguous non-contextual name (only to throw it all away and use numbers instead), whereas with non-scientific notation you have to be careful where the name you give a note puts it in terms of intervals (which is what you said when you said I don't understand intervals).

I like your analogy, and I know it's gonna sound like a weird thing to argue, but I like to think that if like many people you don't know the difference (but those people still know unambiguously what they mean in all cases) and you don't communicate in writing (an analogy to me only using a notation that would be analogous to using phonetic writing), then no one will know you can't tell the difference between the three words, and it won't matter. So as an outsider who only has an interest in learning how to speak but no interest in becoming literate (imagine he's blind, so he couldn't read or write anyway) the distinction in spelling borders on the irrelevant. So if you know that you should throw a '6' in there, you don't need to figure out whether that's an augmented fourth or a diminished fifth as the necessity for the distinction might be lost on you and by not using proper notation I'd think there would be no way to really know that the distinction is lost on you.

But out of curiosity (and while we're at it I might as well not stay that ignorant), let's say I play in a blues scale, 0 3 5 6 7 10, what determines whether '6' is an augmented fourth or a diminished fifth (assuming there's no notation to refer to, just a musically illiterate guy playing a guitar)? Would the way it's used (mostly the adjacent notes) indicate that? For instance if I play 7-6-7 would it make 6 be an augmented fourth by virtue of being used with the perfect fifth? What if you go 5-6-7 and the 6 sounds like it's introducing the 7 by sort of gliding into it, would it make the 6 be a diminished fifth? Thanks.
Developer of Photosounder (a spectral editor/synth), SplineEQ and Spiral

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If we have pitch classes based on semitones, 0 through 12, and we were to make a system of notation for reading full scores with it, we would have something similar to a piano roll. We could make it more compact than piano roll by using all of the trapping of a traditional score, except with one line or space for each semitone. I suspect that most people who cannot sightread music would say, this sounds better than using sharps or flats. Most people who can sightread music would probably say, no, this is less efficient because intervals are spaced out more and harder to recognize instantly. There are practical implications here, and it does revolve around how real music tends to behave. If most music had melody like Flight of the Bumblebee, then your scientific notation would be superior. But since a lot of our melodies are revolving around 7 note scales are closely related scales, the traditional notation is very practical *even* when many of those notes are sharp or flat (remembering the key signature is more efficient than having to put up with more spread out information).
A_SN wrote: But out of curiosity (and while we're at it I might as well not stay that ignorant), let's say I play in a blues scale, 0 3 5 6 7 10, what determines whether '6' is an augmented fourth or a diminished fifth (assuming there's no notation to refer to, just a musically illiterate guy playing a guitar)? Would the way it's used (mostly the adjacent notes) indicate that? For instance if I play 7-6-7 would it make 6 be an augmented fourth by virtue of being used with the perfect fifth? What if you go 5-6-7 and the 6 sounds like it's introducing the 7 by sort of gliding into it, would it make the 6 be a diminished fifth? Thanks.
I don't really believe it's so important to distinguish in a case like this, and there may even be some disagreements on the "right" answers. To me an augmented fourth or diminished fifth almost has to resolve to something. Your 7-6-7 and 5-6-7 examples both have 6 leading to 7. On a piano sheet that 6 is likely to be the raised fourth because it is leading to the fifth. Blues guitarist can actually bend the string (which the blues pianist is basically trying to mimic with these slides) and so maybe he won't think of it as two discrete notes at all.

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Nystul wrote:If we have pitch classes based on semitones, 0 through 12, and we were to make a system of notation for reading full scores with it, we would have something similar to a piano roll. We could make it more compact than piano roll by using all of the trapping of a traditional score, except with one line or space for each semitone. I suspect that most people who cannot sightread music would say, this sounds better than using sharps or flats. Most people who can sightread music would probably say, no, this is less efficient because intervals are spaced out more and harder to recognize instantly.
You mean like the DAWs typically do? That sucks big time, it's like you have a bunch of rectangles floating around, and it's not easy telling what note they are. It might work better if those rectangle are overlaid with the number they represent, but then it kind of defeats the point of the piano roll. Just writing a bunch of numbers on a piece of paper works better if you ask me.
There are practical implications here, and it does revolve around how real music tends to behave. If most music had melody like Flight of the Bumblebee, then your scientific notation would be superior. But since a lot of our melodies are revolving around 7 note scales are closely related scales, the traditional notation is very practical *even* when many of those notes are sharp or flat (remembering the key signature is more efficient than having to put up with more spread out information).
I agree with the Flight of the Bumblebee thing, but even for regular heptatonic music it works great. Compare:
7 2 3 5
3 2 0
0 3 7 5 3 2
2 3 5 7 3 0 0

and
G D Eb F
Eb D C
C Eb G F Eb D
D Eb F G Eb C C

The numbers one doesn't fare unfavourably I think, I think it looks pretty clear, and you don't have to worry about the scale (well this one's easy it's in C minor) so if that tune was played in a different key it'd be just the same numbers. And you know, when you're used to it it's always the same numbers you see, so it just makes sense. And remember, if things start getting a bit chromatic (I listen to a lot of jazz so a lot of things may start off pentatonic and progressively go all over the place) then it stays simple (well, you get more different numbers so you lose the comfort of always seeing the same few numbers, but still).
I don't really believe it's so important to distinguish in a case like this, and there may even be some disagreements on the "right" answers. To me an augmented fourth or diminished fifth almost has to resolve to something. Your 7-6-7 and 5-6-7 examples both have 6 leading to 7. On a piano sheet that 6 is likely to be the raised fourth because it is leading to the fifth. Blues guitarist can actually bend the string (which the blues pianist is basically trying to mimic with these slides) and so maybe he won't think of it as two discrete notes at all.
Mmmh yeah so maybe not the best example. But kind of in the same vein I was thinking of when you play a 5 and bend it back and forth to a 6, I think in that case the 6 would be a diminished fifth, as it kind of stands in for the 7, like not bending far enough to produce a 7 in a way.
Developer of Photosounder (a spectral editor/synth), SplineEQ and Spiral

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A_SN wrote: But out of curiosity (and while we're at it I might as well not stay that ignorant), let's say I play in a blues scale, 0 3 5 6 7 10, what determines whether '6' is an augmented fourth or a diminished fifth (assuming there's no notation to refer to, just a musically illiterate guy playing a guitar)? Would the way it's used (mostly the adjacent notes) indicate that? For instance if I play 7-6-7 would it make 6 be an augmented fourth by virtue of being used with the perfect fifth? What if you go 5-6-7 and the 6 sounds like it's introducing the 7 by sort of gliding into it, would it make the 6 be a diminished fifth? Thanks.
IMHO there is no difference between the augmented 4th and the diminished 5th from the point of view of the human ear. I don't think a tritone will really sound more like a #4 or a b5 depending on the context, it's still the same interval from the point of view of the human ear. Of course it will have different resolutions (#4 typically a step upwards, b5 typically a step downwards) and the traditional division between #4 and b5 is partly based on this, but I think this is much more a result of the whole musical context where the interval happens, rather than a property of the interval itself. Because of this, I don't think any of the following are "real" intervals from the point of view of the human ear: augmented 2nds, diminished and augmented 3rds, diminished 4ths, augmented 5ths, diminished and augmented 6ths, diminished 7th. This is also why I don't analyze the bVI7 chord as an augmented 6th (other than being more jazz than classical influenced): sure, the top note resolves upwards (which is the basis for notating it as a #6 in classical music), but it's still totally a minor seventh, it just happens to resolve upwards.

For me, the difference between #4 and b5 is first and foremost an orthographic one. Both can be used, but usually one will be way easier to read. Kindof like how "leukaemia" and "leukemia" are both correct, but "leukemia" is way easier to read (sorry British readers!). The traditional rules on when to use #4 or b5 are simply there to make you pick the one that is easiest to read. Writing the Eb major scale as D# F G G# A# C D is not incorrect at all - all the notes have their proper value! But it's also totally heinous to read and you'd never want to hand out a part written like that. That's also why double sharps and flats exist - not to satisfy some theoretical principle (such as writing the "correct" b5 as Bbb in the key of Eb) but rather because in some rare cases, there's no good way to write down something and they're the least worst options.

There are some tuning systems that have more than 12 notes per octave, in which case #4 becomes different from b5 and so on, but they are very rarely used and usually very experimental (and rarely have good songs written for them!). The exception is when notating classical Turkish music, but that never modulates very far from simple keys like D or G, which makes accidentals pretty easy to figure out.

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MadBrain wrote:Writing the Eb major scale as D# F G G# A# C D is not incorrect at all
It is actually, and I would have thought obviously so!
Unfamiliar words can be looked up in my Glossary of musical terms.
Also check out my Introduction to Music Theory.

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MadBrain wrote:IMHO there is no difference between the augmented 4th and the diminished 5th from the point of view of the human ear. I don't think a tritone will really sound more like a #4 or a b5 depending on the context, it's still the same interval from the point of view of the human ear. Of course it will have different resolutions (#4 typically a step upwards, b5 typically a step downwards) and the traditional division between #4 and b5 is partly based on this, but I think this is much more a result of the whole musical context where the interval happens, rather than a property of the interval itself. Because of this, I don't think any of the following are "real" intervals from the point of view of the human ear: augmented 2nds, diminished and augmented 3rds, diminished 4ths, augmented 5ths, diminished and augmented 6ths, diminished 7th. This is also why I don't analyze the bVI7 chord as an augmented 6th (other than being more jazz than classical influenced): sure, the top note resolves upwards (which is the basis for notating it as a #6 in classical music), but it's still totally a minor seventh, it just happens to resolve upwards.

For me, the difference between #4 and b5 is first and foremost an orthographic one. Both can be used, but usually one will be way easier to read. Kindof like how "leukaemia" and "leukemia" are both correct, but "leukemia" is way easier to read (sorry British readers!). The traditional rules on when to use #4 or b5 are simply there to make you pick the one that is easiest to read. Writing the Eb major scale as D# F G G# A# C D is not incorrect at all - all the notes have their proper value! But it's also totally heinous to read and you'd never want to hand out a part written like that. That's also why double sharps and flats exist - not to satisfy some theoretical principle (such as writing the "correct" b5 as Bbb in the key of Eb) but rather because in some rare cases, there's no good way to write down something and they're the least worst options.

There are some tuning systems that have more than 12 notes per octave, in which case #4 becomes different from b5 and so on, but they are very rarely used and usually very experimental (and rarely have good songs written for them!). The exception is when notating classical Turkish music, but that never modulates very far from simple keys like D or G, which makes accidentals pretty easy to figure out.
Yeah I would tend to see things the same way, notes/intervals with different names sounding the same, because I want to see things on a pretty low level (hence the integer notation, that's pretty low-level, no fancy concept there), but I realise that this has to do with my equal temperament-centric point of view and my dismissiveness towards classical music theory constructs. But even then I can see plainly how writing a major scale has "D# F G G# A# C D" is quite wrong, sure, the scientific pitch notation in 12-TET is correct, but practically speaking that's awful, you've got two Gs and no E or B, you wouldn't want to use that for notation, it just makes everything worse to the max. Just imagine sheet music written that way (ah so that must be why there has to be a different letter for each note in the scale, otherwise it just craps up the sheet notation with notes that share the same line. I know, that's a pretty basic epiphany, but better sooner than later).
Developer of Photosounder (a spectral editor/synth), SplineEQ and Spiral

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JumpingJackFlash wrote:
MadBrain wrote:Writing the Eb major scale as D# F G G# A# C D is not incorrect at all
It is actually, and I would have thought obviously so!
Not in 12-tet (which is the normal context for this, ofc)

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MadBrain wrote:
JumpingJackFlash wrote:
MadBrain wrote:Writing the Eb major scale as D# F G G# A# C D is not incorrect at all
It is actually, and I would have thought obviously so!
Not in 12-tet (which is the normal context for this, ofc)
On the basis of this logic I present you with the following alternative notation:

D# D### D##### D###### D######## D########## D###########

I wonder why this never caught on as a way of notating Eb?

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sjm wrote:
MadBrain wrote:
JumpingJackFlash wrote:
MadBrain wrote:Writing the Eb major scale as D# F G G# A# C D is not incorrect at all
It is actually, and I would have thought obviously so!
Not in 12-tet (which is the normal context for this, ofc)
On the basis of this logic I present you with the following alternative notation:

D# D### D##### D###### D######## D########## D###########

I wonder why this never caught on as a way of notating Eb?
:clap:

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MadBrain wrote:
A_SN wrote: There are some tuning systems that have more than 12 notes per octave, in which case #4 becomes different from b5 and so on, but they are very rarely used and usually very experimental (and rarely have good songs written for them!). .
The tuning systems of Western orchestras and choirs have far more than 12 notes. If you take, say, E# and Db, not only are they different pitches, but they're different in different historical styles and interpretive schools, and, depending on the styles, each may have different intonations according to context.

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MadBrain wrote:
JumpingJackFlash wrote:
MadBrain wrote:Writing the Eb major scale as D# F G G# A# C D is not incorrect at all
It is actually, and I would have thought obviously so!
Not in 12-tet (which is the normal context for this, ofc)
No, it's got nothing to do with temperament.
There are many things wrong with the above, but perhaps the most obvious one is that you don't start Eb major with a D#. By definition, it (obviously) must start with Eb. To do otherwise would be like spelling Ceiling with an S, or Xylophone with a Z!

Sounding alike doesn't necessarily follow that two things are the same.

Writing the Eb major scale using any notes (or any spelling of notes) other than Eb F G Ab Bb C and D is objectively wrong.
Unfamiliar words can be looked up in my Glossary of musical terms.
Also check out my Introduction to Music Theory.

Post

A_SN wrote: I agree with the Flight of the Bumblebee thing, but even for regular heptatonic music it works great. Compare:
7 2 3 5
3 2 0
0 3 7 5 3 2
2 3 5 7 3 0 0

and
G D Eb F
Eb D C
C Eb G F Eb D
D Eb F G Eb C C

The numbers one doesn't fare unfavourably I think, I think it looks pretty clear, and you don't have to worry about the scale (well this one's easy it's in C minor) so if that tune was played in a different key it'd be just the same numbers. And you know, when you're used to it it's always the same numbers you see, so it just makes sense. And remember, if things start getting a bit chromatic (I listen to a lot of jazz so a lot of things may start off pentatonic and progressively go all over the place) then it stays simple (well, you get more different numbers so you lose the comfort of always seeing the same few numbers, but still).
A string of letters or numbers won't work for trying to present a developed musical idea, because they present such limited information. We might resort to this sort of communication on a forum where embedding proper notation will require a lot of extra effort and use of other websites. For limited purposes it can be good enough. But here the rhythmic information is not clearly presented, and it's even a guess whether each note is up or down from the one before it. And at least for us who play keyboard instruments, reading one note at a time won't be good enough to get very far. There can be a lot of dense chords (or worse, dense polyphony). On sheet you are basically looking at a chord shape and trying to avoid writing in individual note names which would take too long to read. OK, first chord from bottom to top: 10, 2, 7, 10, 7, 10, 2, 7. An eighth note later: 0, 3, 9, 0, 9, 0, 3, 9. Etc. Hmm. Still needing to show the rhythm and octave information as well. A conductor's condensed score will have similar challenges, although the conductor only has to wave his arms so...

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Nystul wrote:A string of letters or numbers won't work for trying to present a developed musical idea
Sure, mostly about the rhythmic notation, but my personal use of this notation is to learn and remember tunes (not read them as I play them, but it's my belief that you should know by heart what you play, even if I realise it's not possible with certain classical pieces in particular). It turns out that the way you learn a tune is what sticks with you (which is a problem when you learn a tune from the wrong key, but that's another problem), so by learning by a combinations of numbers and geometry on my major thirds guitar fingerboard (the geometry of it is surprisingly clear) I can remember lots of things quite easily. And again for my personal use concerning the rhythm I don't feel a need to notate it as I believe that you need to 'hear' the music you want to play to get it right (but again I play things I've heard before, rhythmic notation would remain a problem were I to notate a composition of mine, although since I do it on paper I can always find ways to do that).

And yeah chords are a problem to notate in a concise way with that approach, I haven't dived into that problem yet but I'm sure one could think of a clever way to notate it (like mmmh I don't know, using chord names! Sometimes I wonder where do I find all the inspiration..). Otherwise on paper when two notes play concurrently I write the notes in parallel on two parallel horizontal lines, that works well enough on paper, even though it's still all the numbers and if you've got a lot of the same chords it's probably better to just indicate just the chord name. Ideally besides chord names I'd find a way that says "play these numbers transposed by that number" in a terse way. Maybe something like putting the numbers to play transposed between parentheses (it can be a vertical one, as used for matrices in maths) and right before them the number by which to transpose (which wouldn't be as concise as using chord names though... unless... you used a fixed way to represent the current chord like "()" and you only put numbers in the brackets when the chord changes).

But in your example in the middle of each thing a note is omitted. So there would hardly be a concise way to represent that no matter what, would there?
Developer of Photosounder (a spectral editor/synth), SplineEQ and Spiral

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JumpingJackFlash wrote:[...]
No, it's got nothing to do with temperament.
There are many things wrong with the above, but perhaps the most obvious one is that you don't start Eb major with a D#. By definition, it (obviously) must start with Eb. To do otherwise would be like spelling Ceiling with an S, or Xylophone with a Z!

Sounding alike doesn't necessarily follow that two things are the same.

Writing the Eb major scale using any notes (or any spelling of notes) other than Eb F G Ab Bb C and D is objectively wrong.
You're missing my point. The difference between Eb and D# only exists on paper, and it exists only for one reason: making parts easier to read. Following the English spelling metaphor, "X" isn't a real sound in English - it's just a fancy way of spelling "ks" or "gz". "X" exists only from when you write the word down, until when you read it. It doesn't exist before or after that, unlike other consonants such as "p" or "b" which are real sounds. You only use "X" in "xylophone" because it's easier to read than "zylophone", due to the fact that it's been spelled with an "x" millions of times before (and also because it makes you look smarter).

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