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.

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'.

    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 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.

            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 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.

                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.

                My best explanation: Imagine there are always 7 notes in a scale. Those notes can be "altered" but you can't have more basic notes than that. The accidentals reflect the +1/-1 semitone distances that the notes in a given scale have.

                So, if you have a C# harmonic minor scale, it will be some variant of CDEFGABC.
                ... And how do you fit that in?

                C# D# E F# G# A Bx C#

                Pretty simple. 🙂

                  ranjit So, if you have a C# harmonic minor scale, it will be some variant of CDEFGABC.
                  ... And how do you fit that in?

                  C# D# E F# G# A Bx C#

                  Pretty simple.

                  Was that an explanation of intervals, or something else?

                  (Of course there aren't always 7 notes in a scale. 😉 ) - but first I'm not sure which question you're addressing.

                    @SouthPark. I read your response here. You seem to be seeing the name "diminished" as some kind of operation or action. That is not what is going on. You have a reference interval such as your M3. Then you want to give "size" names to the others - they're bigger or smaller than your reference interval. It's just what that interval "is", size-wise. When you have an m3, it is what it is. It's not that C Eb actually "is" a reduced CE. It's just a comparison and a name. C Ebb is even smaller; it is a "diminished size" - but that doesn't mean something was done to CE to make it become C Ebb. That C Ebb is just there.

                    It's like "big John", "gigantic John", "little "John", and "tiny John" - four guys in a group you and you call them that to tell them apart. But "tiny John" didn't come into existence by someone hammering "big John" down to a smaller size. He's that guy whose name is also John and he's tiny.

                    The important thing is that names are used for communication. We don't need to have any kind of names when we do music by ourselves. People share names and definitions and agree that that's what they are, sometimes even silly ones. It evolved as it evolved, and here we are.

                      keystring It's like "big John", "gigantic John", "little "John", and "tiny John" - four guys in a group you and you call them that to tell them apart. But "tiny John" didn't come into existence by someone hammering "big John" down to a smaller size. He's that guy whose name is also John and he's tiny.

                      This is a 'perfect' analogy!
                      It shows how a 'minor' change can make a 'Major' difference, and 'Augments' rather than 'diminishes' the answers posted in 'unison' by others.👏

                          keystring I read your response here. You seem to be seeing the name "diminished" as some kind of operation or action.

                          KS. I specifically indicated it. It can depend on perspective though. But you will find in sources a take on that ..... such as a definition of diminished third is a minor third reduced by one semitone.

                          I did mention that the words diminished third is not to be interpreted to be a type or kind of 'third'. And indeed ... a diminished third is certainly not a type of 'third' or third degree interval in our major/minor system.

                          If anyone reckons diminished third is a type of third, then they better demonstrate third degree based on 'our' major and minor scale/chord system.

                          Like some country's language system ... they pack in their rules or conditions ... where it's a case of being taught those conditions or rules, otherwise one can't communicate properly unless those rules are learned ... such as porpoise is not pronounced as porpoys (rhyming with bor boys). And turqoise is not pronounced like porpoise. Etc.

                          For intervals like major third ... and minor third, I explained various approaches for understanding those intervals, based on workable numbers and patterns. Based on the major and/or minor system.

                          Yes indeed ... the diminished third interval is defined. It's not a 'type' of third though.

                          I don't mind if there are multiple 'official' or 'authority' sources specifically showing how their diminished third is third degree in the major and/or minor scale system. But looks like nobody has done that or shown that. Third degree.

                          And ranjit was pretty much conjuring up a different scale system I think ... which is not our scale system that most people are focusing on. It's like saying a sixth is still a sixth if you reduce it by five semitones ..... which is analogous to anyone thinking that a diminished third is still a 'type' of third interval based on our major/minor system.

                          If we teach people based on our major/minor system ... then they better show clearly (explain) how their diminished third is truly third degree. Otherwise, they really will get a fail grade here.

                          Failing is fine though. They can always pass next time around if allowed to resit the test. And for this particular test ... yes ... they are allowed to resit it.

                          The test question here is ... do you think a diminished third is a type of 'third' (in the major/minor system only)? Yes .... or no. And if yes .... justify your answer by showing how it is third degree in major and/or minor scale system only. That is only to focus on this popular system only, without getting into pseudo-science space, or nested systems - as in getting away from the focus of attention.

                          Also keeping in mind that 'flatting' is merely a 'construct'. And in a minor scale .... the 'flatting' of the third degree (in minor scale) results in the 'second'. And that still gets people into the rules territory - like how to tweak the system to handle spanners in the works, like perfect fourth and perfect fifths ... (ie. to sort out terms like minor 4th, major 4th, minor 5th, major 5th).

                            This is a section for learners including those just starting out with theory. It should not be made complicated with philosophies and what-ifs. The naming of intervals is within a specific system which is based specifically on the standard Western 7-note major scale we all learn. I tried to set this out as clearly as possible in the other thread.

                            It is an antiquated and therefore awkward system, but it is the system that is used, so we have common terms and concepts within that system. It's the "common" system that is used, and it's set up the way it's set up. It is for written notation. The by-ear player doesn't have to care whether he just played G# or Ab.

                            The names we get from that system are artificial, but related to real things: the quality of sound of an interval, and a distance between notes measured in semitones. The latter are real. Whether we play C D# or C Eb, the shared sound and piano keys are what are real and count.

                            There are attempts aplenty to substitute a different system, because it is so awkward. Nonetheless this system is used almost universally, so it's good to have some understanding of the system as it's set up. We should not make it more complicated and scary. Those kinds of speculations might be interesting for some in another section, but not the learner group.

                            ranjit My best explanation: Imagine there are always 7 notes in a scale. Those notes can be "altered" but you can't have more basic notes than that. The accidentals reflect the +1/-1 semitone distances that the notes in a given scale have.

                            So, if you have a C# harmonic minor scale, it will be some variant of CDEFGABC.
                            ... And how do you fit that in?

                            C# D# E F# G# A Bx C#

                            I answered rather late last night. What I asked then still stands, namely I'm not sure what you are addressing. 🙂

                            There are not always 7 notes in a scale btw. Pentatonic, octatonic, whole tone, and chromatic spring to mind immediately.

                            You are correct about the common 7-note scales. There are exactly 7 letter names for notes: A, B, C, D, E, F, G - and in any 7-note scale, each letter can only be used once. I think that's what you're pointing out. (?)

                                Rob It shows how a 'minor' change can make a 'Major' difference, and 'Augments' rather than 'diminishes' the answers posted in 'unison' by others

                                I absolutely love puns! 🤩 (thx)

                                • Rob likes this.

                                  keystring I answered rather late last night. What I asked then still stands, namely I'm not sure what you are addressing. 🙂

                                  Right, I meant to address the reason why you sometimes use "augmented second" instead of "minor third". Typically it has to do with scale degree relationships.

                                  keystring There are not always 7 notes in a scale btw. Pentatonic, octatonic, whole tone, and chromatic spring to mind immediately.

                                  Of course. But I find this a much better way to explain things. Including every caveat at the start tends to make explanations confusing. Explain the simplest case clearly and as succinctly as possible. Then, go into other possibilities.

                                      One of the main things here is that - I think that with enough thinking for everybody here --- they will eventually come to understand that the interval associated with C# and E-flat is absolutely not a type of third in our major/minor scale system.

                                      It is not any sort of third in our major/minor scale system. That is what I'm saying all along.

                                      Hi Southpark

                                      No, everyone else has just given up trying to explain it to you.

                                      Regards

                                      Simon
                                      All round average Jazz, Blues & Rock player.
                                      Currently working towards ABRSM grade 8.

                                        Simonb That's the thing ... you must demonstrate with the popular major/minor system only - that a diminished third interval is third degree .... with either the major or minor system only.

                                        Go ahead and show how a dim 3 interval is third degree in our popular major/minor scale system.

                                        And no ... you're not allowed to go outside the boundaries ... such as to introduce another scale system that isn't our major/minor scale system ... such as a minor version of our minor scale system.

                                        If all of you cannot show it (third degree) ... then you will know that I'm right ... and you folks ... or the ones that are disagreeing ..... are wrong.

                                        And I did mention it ... it's ok to be wrong. You will just learn from this.

                                        I'm not going to give anyone the 'third degree' if they didn't understand or realise that a dim 3 interval is not a type of third in our major/minor system.

                                          I've never heard of a "major / minor system", popular or otherwise.
                                          There is no reason why a dim 3 interval should be any kind of degree. Apples and oranges. Something is being mixed up here.