keystring That puts us on the same page. Good enough.

We're on the same page now K.S. The centimetre (distance) units is equivalent to the integer multiple of semitone units.

When we use the definitions of major and minor intervals in the form of unison, major second, minor second, major third, minor third etc --- there is a direct but non-linear mapping. Eg. unison maps to zero semitone. Minor second maps to 1 semitone. Major second maps to 2 semitones. Minor third maps to three semitones. Major third maps to four semitones. Perfect fourth maps to FIVE semitones. Perfect fifth maps to SEVEN semitones etc.

Some people do take advantage of the above mapping.

I don't have a problem with you or teachers teaching what you want to teach.

And earlier, I was only pointing out that when you wrote 'A' is sixth one over from 'C', it should be 'A' is the sixth one in the set of notes 'C to A' in C major scale, which is the application of the SPAN-of-notes method.

Another example of that is E4-sharp and C5. Since E4-sharp is the lower note, we go for E4-sharp major scale, which has this sequence E♯, F, G, A♯, B♯, C, D -- and then finally back to E# of course. And the E4-sharp and C5 spans six notes. Major sixth interval. Here, we can say that from E4-sharp to C5, we have a span of notes equal to six. We have a major sixth interval.

I think it was great that we had this conversation, and also the discussion in this thread and the other thread about the diminished third interval. It looks like everyone has learned something - which benefits all of us.

keystring You and I seem to be on the same page, where you've decided to use the word "span" to describe what I call "1st house, 2nd house, 3rd house..." which is less abstract than the word "span" which frankly I'd have to look up and might still get wrong.

Once you have been taught what span-of-notes means --- which probably takes 10 seconds or less to convey (ie. span of notes being the number of notes covered/contained in a set/sequence of notes) --- then you will never forget it for the rest of your life.

        We have some common ground but I'm afraid you slipped up on the "E# major scale" 😏

        SouthPark E♯, F, G, A♯, B♯, C, D -- and then finally back to E#

        We don't usually have a scale written out as "E# major scale", which doesn't make it impossible. Did you try playing what you wrote out at the piano, before posting? (I always double check) Try it - it doesn't sound like a major scale. A quick indication is that E#, F .... are the same piano keys, and B#, C are also the same piano keys.

        I've written out an E# major scale, and juxtaposed F major. If you play these on the piano you should hear the same thing.

        E# to C is dim6 (what you were after)
        F to C is P5
        That's a quick check, because you'll be playing the same piano keys. We know that dim6 = P5, and we also see and hear it.
        However, in the E# major scale there is no C. There is a B# ---- and E# to B# is a P5. It also fits neatly.

        This was kinda fun. 🙂

        The problem happened in trying to write out this interesting scale. It happens. That's why I try to play what I write out before sending, to make double sure. 🙂

            keystring We don't usually have a scale written out as "E# major scale"

            K.S. There indeed is an E sharp major scale. As long as we follow that pattern ... tone, tone, semitone etc .... the major scale will sound like .... a major scale. It's all relative.

                SouthPark K.S. There indeed is an E sharp major scale. As long as we follow that pattern ... tone, tone, semitone etc .... the major scale will sound like .... a major scale. It's all relative.

                Are you taking the time to carefully and fully read what others write? I take care in my posts, double checking before sending. I literally wrote out an E# major scale. Did you not see it?

                The notes you wrote out do not give us a major scale because you made some mistakes: If you play what you wrote out at the piano you'll hear it. I also did a sound file letting you hear that.

                Please do go back and take your time reading everything. Otherwise we're not communicating. thx.

                  keystring We have some common ground but I'm afraid you slipped up on the "E# major scale"

                  Earlier .... I was meaning to write e-flat major scale.
                  E♭, F, G, A♭, B♭, C, and D.

                  The two notes I was meaning to set the example for is ... E-flat and C.

                  So now we see the value of myself laying out the foundations ... and explaining my procedure comes in handy.

                  The interval E5-flat and C5 in the E-flat major scale is a major sixth. Spanning 6 notes.

                      SouthPark Earlier .... I was meaning to write e-flat major scale.

                      It is important when writing in a forum to double check before posting. Otherwise time is wasted, including the reader's, and you can be taken less seriously when you end up making gross mistakes. Before I posted my notation, I played it to make double sure.

                      The rest is the same as what I presented which is unsurprising since it's basic. The answer of M6 is correct.

                          keystring It's fine K.S. In my post .... I did mention the pattern .... tone, tone, semitone etc. So you will know that the sequence I had earlier doesn't follow that pattern. And you know full well my example intention is to demonstrate a major 6 interval. And as I told you .... it should have been E-flat and C as the example pair. I was thinking of E-flat ...... not E-sharp, since E sharp is an F in absolute terms.

                          Hence the importance of me writing the process ... so it's easy to see that cross checking indicates that my example really was to meant to be what I wrote. E4-flat and C5.

                          Likewise .... when you make mistakes like writing A is 6 notes over from C ..... same deal.

                            I think all has been written that can be written on this tangent. I'm done.

                            Almost done. E# major scale will be F major scale. F, G, A, B♭, C, D, E

                            If considering F4 and C5, then the procedure is to take the lower note. It is F. So use F major scale. If the lower note had been F# instead, then would use F# major scale. But we're dealing with the lower note being F. So F major scale.

                            In this case .... F4 and C5 interval spans 5 notes in F major scale. Perfect fifth interval.

                            Better cover F4-sharp and C5 as well. Lower note is F#, so choose F# major scale.

                            F♯, G♯, A♯, B, C♯, D♯, E♯

                            F# and C# spans five notes ... perfect fifth, while we want F# and C, which is 1 semitone less than the perfect fifth interval. So F# and C is associated with a diminished fifth interval.

                              SouthPark Almost done. E# major scale will be F major scale. F, G, A, B♭, C, D, E

                              In other words, this, which I posted a day ago.

                              keystring If you play these on the piano you should hear the same thing.

                              (acknowledgment would have been nice 🙂 )

                              Your conclusions are all correct, and the way you approached it was valid.

                                  Hi

                                  This is a very simple way of thinking about the diminished 3rd that Keystring and I discussed privately whilst this thread was locked.

                                  If you take the C major scale that we all know and love...
                                  C D E F G A B C

                                  And if we zoom in on the first 3 notes of the scale C D E
                                  These are the root, 2nd and 3rd of the scale.

                                  Any combination of notes that involve C and D will always be called a 2nd.
                                  So C and D# is an augmented 2nd, even though it sounds the same as a minor 3rd; but it cannot be called a minor 3rd because it does not contain any form of E - the 3rd note of the scale.

                                  Any combination of notes that involve C and E will always be called a 3rd.
                                  So C# and Eb is a diminished 3rd, even though it sounds the same as a major 2nd; but it cannot be called a major 2nd because it does not contain any form of D - the 2nd note of the scale.

                                  That is how I think about the theory behind these intervals when looking at written music. You have to consider the key signature, the accidentals and how they relate to the root, 2nd and 3rd. That is the music theory we have! It isn't perfect, but it's very unlikely to change.

                                  Of course if you only hear the intervals and you have good musical ears you would name the intervals the other way around. You will hear a major 2nd when it's actually written as a diminished 3rd on paper. Though maybe if someone had perfect pitch and they heard the interval in context, I suppose it's just possible they might work out that it's not a major 2nd??

                                  All that said I'm not an expert 🙂, and it's 16 years since I last studied theory seriously.

                                  Cheers

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

                                    A diminished third in chorale music, string quartet or other ensembles that can employ ‘just’ intonation is not enharmonic to a major second.

                                      Emeton A diminished third in chorale music, string quartet or other ensembles that can employ ‘just’ intonation is not enharmonic to a major second.

                                      This is a good point.

                                        Emeton A diminished third in chorale music, string quartet or other ensembles that can employ ‘just’ intonation is not enharmonic to a major second.

                                        You are correct. That is why in discussing this I try to say "when played on the piano" - i.e. an instrument where pitches are fixed and can't be created by the player. It's probably a good idea to keep it at that simple level.

                                            Simonb You have to consider the key signature, the accidentals and how they relate to the root, 2nd and 3rd

                                            I would be careful about key signature. You can have a scale not belonging to the key, either because the we've modulated, or because the composer felt like doing who knows what. Also, for example if you're considering DF for music in the key of C .......

                                            Rather than writing tons here and making a mess, there is the other thread I started.

                                              keystring on the piano in the key of ‘C’ there is a special dominant 7th chord called the Augmented 6th chord which is built from the Ab in root position, spelt Ab C Eb F#. The Eb and F# here are an Augmented 2nd. The two outer voices - Ab + F# resolve outwards, the Ab down to G and the F# up to G, the C stays where it is and the Eb moves up to E spelling G C E G which is the I 6/4 chord. It’s good to have an example shown when presented with a ‘factoid’ like augmented 2nd.

                                                  Emeton keystring on the piano in the key of ‘C’ there is a special dominant 7th chord called the Augmented 6th chord which is built from the Ab in root position, spelt Ab C Eb F#. The Eb and F# here are an Augmented 2nd. The two outer voices - Ab + F# resolve outwards, the Ab down to G and the F# up to G, the C stays where it is and the Eb moves up to E spelling G C E G which is the I 6/4 chord. As a beginner it’s good to have an example shown when presented with an advanced ‘factoid’ like augmented 2nd even if you don’t have to completely understand it.

                                                  Good example. Yes, we started having examples of usage in the thread I started which is devoted only to intervals. Ranjit gave the example of harmonic minor, which has an aug2 in it. I put in a fully diminished chord where if you extend it, or have an inversion, you also have aug2.

                                                  It's kind of awkward having two threads now. This one is for theory resources in general: that one was for intervals specifically and was born of the fact that this thread had been shut down. Dunno if we can make the move over to the interval thread.

                                                  -- added: I hope you don't mind that I also responded to your post in the other thread. I'm of two minds about keeping that one up.

                                                    @Emeton - I hope you don't mind me bringing your post over here as well, since you made an important point.

                                                    Emeton on the piano in the key of ‘C’ there is a special dominant 7th chord called the Augmented 6th chord which is built from the Ab in root position, spelt Ab C Eb F#. The Eb and F# here are an Augmented 2nd. The two outer voices - Ab + F# resolve outwards, the Ab down to G and the F# up to G, the C stays where it is and the Eb moves up to E spelling G C E G which is the I 6/4 chord. As a beginner it’s good to have an example shown when presented with an advanced ‘factoid’ like augmented 2nd even if you don’t have to completely understand it.

                                                    You are right about the aug2, which adds to examples that Ranjit started. The Ab F# is our aug6 interval ofc.

                                                    Playing this chord at the piano, it sounds like Ab7 (Ab C Eb Gb) but has this other spelling because of where it's going. The The Ab Gb is an m7. Ab F# is aug6. They are enharmonic equivalents, and also the notes F# and Gb are enh. equivalents. That's why the chord sounds the same, though they go to different places. So that's "music grammar". (like its and it's)

                                                      Hi Keystring, I can help! Just tell me which posts you would like moved to which thread.