Diminished 3rds

SouthPark · 2024-07-25T19:14:45+00:00

lilypad Here is a good one. I've taken 3 classes from him at out local community college. He explains things very well. Breaking Barlines Generally ver...

twocats

SouthPark That's why they shutted up and didn't say a word after realising they're wrong.

No, it's because there's no point in explaining it to you. I'm shutting up, too 🙄

Josephine

SouthPark

Maybe it's a good idea to leave a conversation for a while when you feel frustrated or angry. When you keep writing when you feel like that there is a chance you are starting to write things that are not very nice. And I think that just happened.

SouthPark

Josephine I wasn't frustrated. I didn't start it.

Make sure to notice how that started. It was someone else.

But good point made ... it's better that I don't get drawn into being set up. You can see what was happening.

twocats not sure why you're insisting on incorrectly explaining music theory if you don't know music theory?

SouthPark

Simonb Of course you call it whatever you like, but it is a diminished 3rd.

The main thing is ... a diminished third is not a third of any sort.

Simonb Diretonic is a very knowledgeable chap

He is indeed. But he's incorrect in this particular case.

iternabe

Simonb Another way to think of it (in my simplistic way) is it's equivalent to double sharps and double flats. Why do we call any note a double sharp/flat? F## is actually a G. Ebb is actually a D etc etc. But of course we do have double sharps and double flats to make sense when writing music sometimes.

I like this analogy. I know nothing about music theory, so I googled. One particular answer on Quora by Allen Bachelder makes a whole lot of sense to me.

The gist is "third" refers to all intervals that the two written note letters (e.g. C-E) has one more note letter (e.g. D) between them. So, any permutation of C-E, no matter how many sharps or flats are added, are all thirds. For example, Cb-E, Cb-E#, C-Eb, C#-Eb, Cb-Eb, and even to the extreme C##-Ebb!

Along the same logic, anything C-D is "second", like C#-D# (which is enharmonic to the diminished third C#-Eb).

I have no proof this is correct. But if Allen Bachelder is who as his signatures claims with a doctorate from Eastman School of Music, and says that the rule outlined above is how you pass the theory exam there, then I think it's pretty convincing.

Simonb

iternabe
Hi
Yes, I was going to post something similar.
I think this is correct, but I'm sure there are better qualified people than me who'll confirm it.

I've studied theory academically at a high level (equiv to honours degree), but it was quite a long time ago now, and unless you keep using it you tend to forget it. Especially as you get older!

Cheers

diretonic

SouthPark Diretonic and tc3 already know that they're wrong. That's why they shutted up and didn't say a word after realising they're wrong.

I hadn’t ‘shutted up’. I’d hoped you would do some research and understand your error.

Ultimately, as Simon has pointed out, it will make no difference to you or the kind of music you make if you name a diminished third incorrectly. You can happily develop a home-spun theory of your own, neither you nor your music will come to any harm. But a serious student participating in this forum could carry forward your mistake and fail a question in an important examination.

The pity is you’ve dug yourself so deep in your error you’ve persuaded yourself to dig deeper. So please, make an effort to stop. Understand the notion of ‘received opinion’ and refrain from corrupting accepted theory. (Perhaps at this point the thread could be locked to prevent your further confusion?)

SouthPark

diretonic You're the one that failed. Just to confirm .... you reckon that the interval formed by C# and E-flat belongs in the category of a 'third', right? And you think that this particular kind of 'third' is classified as a 'diminished third', right?

It is you that needs to do research and understand your mistake.

TC3

diretonic I just saw SouthPark's comment quoted in your post. I have them on ignore, so I haven't seen any of their responses, and don't intend to.

diretonic

TC3 I just saw SouthPark's comment quoted in your post. I have them on ignore, so I haven't seen any of their responses, and don't intend to.

TC3, what a good idea. By responding to his nonsense I realise I'm an accomplice to the crime....now where's that ignore button....

SouthPark

Yep ... that would be about right. If you were 100% confident that you are right, then you would have shown formal theory ... from text books, official music theory documents etc by now.

Basically ... you thought you understood what a diminished third (interval) is ... but you didn't realise that it is not a 'third' (interval) of any sort at all. It is a result of carrying out a semitone reduction operation on a minor third, resulting in a major second interval.

And the name 'diminished third' does not mean that it is in the category of a 'third'.

The word 'diminished' only signifies the operation carried out on a minor third interval to form a different interval. The result (outcome) being a 'major second' interval, but is equivalent to the defined 'diminished third' interval.

Keeping in mind that the name 'diminished third' is an interval equivalent to a 'major second' (interval). But the word 'third' in 'diminished third' absolutely does not mean that the diminished third interval is a 'third' (of any kind). It is absolutely not a 'third' (of any variety).

twocats

SouthPark I was not trying to be mean and I apologize if it came off that way. But please think about the likelihood of you being correct when everyone else is disagreeing with you, including people who have studied theory at a high level.

I'm going to put you on Ignore for my own peace of mind. Your attitude reminds me of my dad, who was a brilliant man who thought that his opinion was worth more than everyone else's, even if he knew nothing about the subject. There's just no point in having a discussion.

SouthPark

twocats But please think about the likelihood of you being correct when everyone else is disagreeing with you, including people who have studied theory at a high level.

For other aspects of music theory, there can be uncertainty. But the probability of me being wrong in this particular aspect (topic) of 'diminished third' is zero.

With the major and minor scale ... once you 'diminish' a minor third, the resulting interval will be no longer a 'third' (of any kind), even though they/we/you call it a diminished third.

That name (diminished third) is only due to the operation that was/is carried out/applied. It does not mean that a 'diminished third' interval is another 'class' (or incarnation or realisation or type or kind etc) of a 'third interval'.

The rest of your post ... due to the particular 'veil' (ie. V.I.) tactics you're using ... well ...... I'm not going to 'go there'.

For records - the origins of the 'not a third of any sort' (theory discussion) is from this - LINK related to POST.

MandM

I generally have precious little knowledge about music theory, but I found the article at the below link to be an interesting read:

https://music.stackexchange.com/questions/105433/whats-the-reason-for-naming-major-second-a-diminished-third

One of the authors appears to suggest that it depends on the context of sheet music whether an interval is shown as a diminished third or as a major second. Please note here that the emphasis is not on whether it IS a major second or it IS a diminished third (I think the author recognizes the enharmonic equivalency), but instead how either of them is SHOWN in sheet music notation.

I think in case of Aron Bernstein's "Intervals Part 2" video at 53 seconds, Aron explains the convention how to show a third in music notation, and that one can modify the third from major to minor to diminished by adding music notation (sharp/flat). And I understand from Wiki (Diminished Third) that in 12-tone equal temperament, a diminished third is enharmonic with the major second. But since the video at 53 seconds does not specifically focus on music context, the question does not arise which enharmonic notation representation (diminished third or major second) Aron should/could have shown. The presentation at that point focuses on third intervals, and consistent with that he shows the notation representation of a third with added sharp/flat to arrive at diminished third, major third, and minor third. I think Aron did not intent to talk about a second interval at that moment, so he opted not to mention at that time that a diminished third is enharmonic to a major second, and consequently did not use the notation representation for a major second.

That's just my 2 cents. All the best.

SouthPark

Thanks for posting MandM. I don't have a problem with the names 'diminished third' and 'major second' (intervals) being equivalent/enharmonic etc.

I'm just pointing out to diretonic, twocats and tc3 that a 'diminished third' isn't actually a 'third' (or is no longer a 'third') once we lop off a semitone from a minor third interval. (or equivalently lopping off two semitones from a major third interval).

Major and minor intervals are based on note spans and/or counting degree (relative to a reference note). Once a diminishing is carried out on a 'third' (eg. on a minor third) - the result is no longer going to be a 'third' of any kind.

The name 'diminished third' is actually meaning we cut down a minor third interval to create another interval, which somebody had to give a name for -- and that name turned out be 'diminished third'. It is not actually a type of 'third' (interval). It pertains to an operation applied to a particular kind of 'third' (eg. the minor third). After the operation, we end up with a chosen name that tells us what operation was done on something (or equivalently - the result of the operation with the operation name) - ie. the diminishing of cutting down of something - leading to the name 'diminished third' (interval). And that interval is not a type of 'third'.

MandM

SouthPark I hear you, or at least I know where you are coming from. You are pointing out that the below (a diminished third) has only 2 steps, so why would it be referred to as a type of third interval.

I think the others know that the diminished third has only 2 steps, but I think they want to point out that there is value/reason why a 2-step interval is sometimes shown in sheet music in diminished third notation, and then referred to as a "third" (diminished).

Some of my background is in programming, so here is a (not quite fitting, but the best that I can do for now) example:

The mathematical term (3-1) = ? You say why would it not be 2 ? It's clearly a 2, no ? Let's not call it 3, or anything else.

However, there may be benefits in calling the result still a "3" but with a modifier added. Maybe call the modifier "minus" where it is understood that minus refers to "-1". What could be the benefit ? Maybe keeping the term a "3" simplifies programming, variable labeling, relative offset, or something to that effect.

So, that is why I do not mind so much that a 2-step interval, in certain situations, is being referred to and shown as diminished third. I trust that there are benefits in music why this methodology was kept. Wish you a good weekend.

SouthPark

MandM Know what you mean there in your above post. Thanks for adding to the discussion - which is regarding definition and also the particular system(s) being considered.

You are seeing it well. Very well. The modifier in the discussion --- is the 'diminishing' modifier. Once that modifier is applied to the operand or argument (ok ... we'll just leave it at either an operator or a function) -- the result is going to be in the system programming - the rules.

Here, the operation done on a minor third leads to a result - which they define a 'diminished third'. Certainly - we can choose to define the result with that name. And this is where system rules, definition, communications is important (if we choose to make it important that is). If someone chooses to believe that the result is a type of class etc of a 'third' - then they need to explain it based on the rules of the system(s) - in this case, the major and minor scale system(s).

In those systems - the 'thirds' are based on either note spans or based on integer multiples of semitone units between the notes. For most theory that everybody learns - going with the note spans approach is often convenient for discussions, as the number 3 will conveniently pop-up, and easy for many people to understand. Once the term 'diminished third' comes up - that's when people become confused. They just didn't ever realise that the definition 'diminished third' relates to the modifier - or the modification carried out. The words 'diminished third' doesn't at all mean a type of 'third'.

Your last comment is excellent - regarding benefits in having the term 'diminished third'. Fully respecting the music theory - and the incredible work done and accumulated from the past up to now.

You too MandM! --- have a good weekend too. Best regards.

keystring

SouthPark here was one thing I detected in the Intervals Part 2 lessons after going to that link -- is a mistake/error in the lesson. At 53 seconds, the interval C# and E-flat is a 'second' (major second). The teacher told people that it is still a third. Also noticed that the Part 1 intervals lessons doesn't cover black coloured notes

I don't have time atm to watch the video. However, C# to Eb is indeed a 3rd, not a 2nd. Several ways to get there:

CE = M3
C Eb = m3

C# Eb = dim3

or ....
C# E# = M3
C# E = m3
C# Eb = dim3

check: dim3 is enharmonic equivalent of M2 (the part you discovered)

Edit: I have no idea why that one line comes out bold and huge. I'm not shouting - it's the software.

Edit 2: I now see there's a whole discussion about this. For anyone who is starting to learn, trust me: the teacher is correct, that that is a dim3.

SouthPark

keystring I don't have time atm to watch the video. However, C# to Eb is indeed a 3rd, not a 2nd. Several ways to get there:

KS -- thanks for your post. This exactly relates to the discussion or point etc ----- as in -- people or most people think the words 'diminished THIRD' is a class/type/kind of 'third'. It is not a class/type/kind of third. It is a name, where the operation name and what was 'operated' on -- are included in the name.

That is 'diminished third' is defined as - carried out a semitone removal operation on a minor third interval. Or equivalently carried out a tone reduction operation on a major third. That's in the name.

The name 'diminished third' doesn't mean that the result of the diminishing operation gives you a 'type' of 'third'. That is - a 'diminished third' interval is not a type or class of 'third' interval at all.

keystring

I've created a separate thread teaching the main premises of interval naming conventions in the traditional system. Hopefully it will be helpful to whoever might need it.

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