TC3 Yes, that link gives a neat explanation.
Diminished 3rds
SouthPark I admit that I've only scratched the surface of my former teacher's website. We covered the lessons on chords for our recent class. The intervals would have been for an earlier class.
One of my favorite examples that he's used in class for identifying triads and their inversions as they appear in sheet music is to imagine a snowman. Root position is the basic snowman. First inversion is the snowman with his head popping off. Second inversion is the snowman with his feet coming off. I don't remember if his website uses this example or not.
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diretonic The source that lilypad referenced is correct about the interval C# to Eb. It's called a diminished 3rd.
It is not a third though.
That is - it is not a third -- unless for example (which is actually not going to happen) we define and actually somehow use another scale (eg. a different scale) - such as a 'semitone scale' ....... based on all twelve notes in full sequence.
eg. C, C#, D, D#, E, F, F#, G, G#, A, A#, B
But that sort of semitone 'scale' is not what I or maybe a bulk of people actually use for their piano music - that sort of scale. Although - we or some people often will run that semitone sequence up and down the piano for finger and thumb exercises etc.
We generally just deal with the minor scale and/or major scale.
And for those scales (major or minor) - thirds of any sort are based on (depending on perspective) span of three notes, or can be based on relative degree of a higher note in relation to a lower note - where the lower note can temporarily be used as a tonic/root of the major or minor scale of its own letter name (in this case, third degree will be where the higher note is located - relative to the temporary tonic).
It pretty much means that a 'diminished third' is not a 'third' in our popular scale system.
In other words, a 'diminished third' does not mean that the result of diminishing a third is another 'third'. It means that we end up with an interval that is no longer a 'third' after we carry out that operation on a minor third.
Or in other words - in our system, a 'diminished third' is actually a major second interval in our major/minor scale system. And a diminished third is not a type of 'third'.
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twocats I'm not sure what your intention is here.
But I'm not going to be typing every permutation in my posts. Eg. C# and D#, and D-flat and E-flat, and C# and E-flat, and D-flat and D#. When the first note is the lower note ..... regardless of its symbolism, and the second note is the higher note, also regardless of its symbolism, the interval span is a major second (equivalent to a 'diminished third' interval) ... for those combinations mentioned above. I'm telling to you and diretonic etc that the 'diminished third' interval is not another classification/category of a 'third' interval.
If you reckon a diminished third is truly a 'third' .... then go ahead, and make my day. 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.
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SouthPark the "diminished" part of "diminished third" has a meaning. Someone posted a link with a very good explanation.
I find it hard to understand why you keep arguing your (incorrect) point if you don't have any music theory background. It's like my dad arguing with my sister about a chemistry thing because "my intuition says blah blah blah". She has a Ph.D. in chemistry. If you don't understand, then it's best to just let it lie, or even better, study the subject until you understand it! But don't keep arguing with everyone with totally wrong information and expect that someone will be won over.
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twocats Nope ... the point is ... I pointed out that the guy in the vid incorrectly wrote and said that the interval is a third. It is not a third obviously. And diretonic wrote that the source is correct. And the source and diretonic and tc3 are all incorrect.
On the contrary. It's you that didn't understand the situation, and then decided to conjure up something about me not knowing theory.
I see what's happening now. You failed to understand that the discussion was actually about the mistake the guy made ... where he mistakenly told people that the interval is still a third. And indeed it is not a third.
It's actually possible that you don't understand that a diminished third is not a third of any kind in the scale system we're using ... the major/minor scale. That is ... you're the one that doesn't understand something here. And yet, you're firing disrespectful shots when it's you that hasn't even understood the situation ... not a good habit.
I will write this ... if you diminish a third ... then the result of that operation requires a name ... such as 'diminished third'. It's no longer a third at all. The name 'diminished third' does not mean it is still a third of 'some' or any kind.
I will also write ... those geniuses that make up the theory reckon that the diminished third is an operation on a minor third. Specifically the operation reduces a minor third interval by one semitone. Equivalently .... it probably could also be considered as reducing a major third interval by two semitones.
Hi Southpark
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.
It's a similar logic with diminished 3rds.
Diretonic is a very knowledgeable chap, and you only have to look it up on-line to find out that he's right.
Of course you call it whatever you like, but it is a diminished 3rd.
The joy of music theory 
Cheers
Simon
All round average Jazz, Blues & Rock player.
Currently working towards ABRSM grade 8.
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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?
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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.
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?)
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
Simon
All round average Jazz, Blues & Rock player.
Currently working towards ABRSM grade 8.
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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.
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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....
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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).
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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.