A diminished third in chorale music, string quartet or other ensembles that can employ ‘just’ intonation is not enharmonic to a major second.
Intervals - explanation (let's see how it goes)
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.
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I started a separate thread while this one was locked that attempted to sort of teach traditional interval names and how to get at theme, in three separate posts for clarity. It's here. It explains what Simonb has put out, but maybe in more stages.
https://forum.pianotell.com/d/1014-intervals-explanation-lets-see-how-it-goes/36
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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.
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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.
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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.
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@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.
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rsl12 Hi Keystring, I can help! Just tell me which posts you would like moved to which thread.
If everyone is ok with it, that might be good. I'd say the posts that came after the freeze was lifted that are on the topic of intervals. Is that enough info?
This might also free up this thread for its original purpose, which was about resources for theory in general.
Done!
rsl12
Thank you.
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Any interval with a span of three letters is a third. We can distort this third to any degree that we wish on the page, to the point where it becomes either stupid or impractical. This third is still a third, and that is simply a fact, and that's why to be precise in traditional theory we have to qualify what kind of third we are talking about.
Major and minor thirds are obviously the most common in music. But diminished thirds such as C# and Eb are not uncommon. Cutting to the chase, both a diminished third and a major second will have exactly the same sound in an equal temperament system. I call them both tones for simplicity.
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GaryD Any interval with a span of three letters is a third. We can distort this third to any degree that we wish on the page, to the point where it becomes either stupid or impractical. This third is still a third, and that is simply a fact, and that's why to be precise in traditional theory we have to qualify what kind of third we are talking about.
Exaaaactly! I think we ran out of patience to press this home but keystring took up the cudgel...I don't know if it worked...
GaryD Any interval with a span of three letters is a third. We can distort this third to any degree that we wish on the page, to the point where it becomes either stupid or impractical. This third is still a third, and that is simply a fact, and that's why to be precise in traditional theory we have to qualify what kind of third we are talking about.
Major and minor thirds are obviously the most common in music. But diminished thirds such as C# and Eb are not uncommon. Cutting to the chase, both a diminished third and a major second will have exactly the same sound in an equal temperament system. I call them both tones for simplicity.
Fantastic to see you here. Responding in the intervals thread seems the best place, because so much was set out here.
I like that you mentioned the "equal temperament system" because this addresses the part that Emeton brought up about string quartets etc. for different temperaments. I think we often simplify this to "as you hear it when playing the piano".
diretonic Exaaaactly! I think we ran out of patience to press this home but keystring took up the cudgel...I don't know if it worked...
That cudgel got a tad heavy and a wish to rest weary arms. I think possibly we did get somewhere. I think I came in just as you dropped yours. 
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I had to check back. I did not use the term "just intonation" at all, but when responding to GaryD I did state that his reference to equal temperament went to something that you had written - and in your post you did indeed refer to just intonation. My own exposure was two decades ago before I ever studied theory. There was the idea of tunings on violin, and one of them was "like the piano" / referred to as equal temperament, and the other wasn't.
For learners trying to get a basic idea of the naming system of intervals, I don't think we need go to tunings - esp. for piano students since we have pre-tuned systems. On piano if we play C Eb and then C D#, we have exactly the same quality. It's simplistic but it's a start.
For the other tunings, it starts getting sticky when other instruments are involved - for example, do you want to clash with a piano if you want your D# to be slightly flatter that Eb but the piano will still have that same tuning since it's a piano? But that is way past the scope of the question of naming intervals for piano students and might want its own thread for those interested.
GaryD But diminished thirds such as C# and Eb are not uncommon.
I was trying to think where C# Eb might come up in music but didn't want to mess it up amateurishly.
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keystring I was trying to think where C# Eb might come up in music but didn't want to mess it up amateurishly.
We are probably talking about an Eb7 chord. As you know, in that chord when we rewrite the top note to a C sharp we have what is called an augmented 6th chord. I always think in equal temperament because it's simplifies things. So in this tuning system the spelling of that chord makes no difference in what we hear. But in traditional teaching we have to respell it, if it is going to go up to the next chord because we want to see a minor second as that top note moves up.
When we use this augmented 6th chord spelling but move the top note to the bottom, that's when we get to this C sharp to E flat thing. I simply hear it as a tone. But the traditional name is going to be augmented second. And that's where it happens.