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.

diretonic

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.

    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. 🙂

        keystring just a detail, Just Intonation is not a temperament at all. It’s a technique that players use while playing with others to raise or lower there pitch frequency to achieve a certain harmonic quality. It’s not one of the temperaments.

          Emeton keystring just a detail, Just Intonation is not a temperament at all. It’s a technique that players use while playing with others to raise or lower there pitch frequency to achieve a certain harmonic quality. It’s not one of the temperaments.

          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.

            keystring

            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.

            @keystring
            There was something else I wanted to mention about intervals. Obviously there are two competing systems. The traditional system goes back centuries. I think your idea of talking about trees is a good explanation of how it works.

            If you have three trees and you want to talk about how much space they take up, you can put a rope touching the tree on the left and stretching to the tree on the right plus the tree in the middle. That would be a very good description of the traditional concept. We can then talk about the whole thing with this in mind. And that describes what we have with a third when we talk about having three letters. Then we sort of refine it by talking about the absolute distance from one to two to three, again talking about those trees.

            When we talk about a diminished 3rd, it might be like keeping those three trees in mind but decreasing the distance between those trees so they become narrower together. This may be forcing the analogy, so I'll let other people decide whether any of this works for adults.

            Regardless, in my own teaching I call this system letter intervals. It doesn't describe what we hear, only what we see on a page. We can't quite say that a minor 3rd and an augmented second is exactly the same thing, although if they are not exactly the same thing they are very, very close in sound. And on the piano they are exactly the same.

            The more modern system and the one I always use could be called the sound interval system. And this system only cares about what we hear. So if we redefine a minor third as one and a half tones, and we redefine an augmented second as one and a half tones, we are free to either consider them as exactly the same thing, or slightly change the tuning if we are thinking about an older tuning system that is not equal temperament.

            Some of these intervals do not have universal sound names. For instance, we have a tone, and we have a tritone. Unfortunately the name "bitone" does not exist. But that interval would describe the distance of two tones. And it plugs a gap.

            In contrast, the term tritone not only exists but is used universally. And for that interval, when we are listening to it, we don't care if it is an augmented 4th or a diminished 5th. We simply hear that it is slightly bigger than a 4th or slightly smaller than a fifth. We then play what we hear or make a piece of music with that interval. Then if we notate it, we decide which look is more appropriate. For instance, if you are putting this interval into context and your tritone is opening up to a fifth, it is likely that you will play that tritone a bit sharper. If it is shrinking to a 4th you will play that tritone a bit flatter. You make the adjustment according to what you hear, either based on theory, or based on your preference.

              GaryD

              keystring

              The intervals are parts of chords which are parts of progressions. To understand the intervals you need to move on to how the chords they’re in function in actual progressions.

                Emeton The intervals are parts of chords which are parts of progressions. To understand the intervals you need to move on to how the chords they’re in function in actual progressions.

                Beyond recognising and naming intervals (as covered in various recent threads here) what is there to understand about intervals in particular?

                In an elementary presentation of intervals peculiarities such as augmented intervals can be mentioned. In this ex. note how the top voice in the ii 4/3 chord moves chromatically upward. The bVI+6 chord to an elementary student studying theory, as in this thread, might spend way too much effort convincing themselves that it just like a dominant 7th chord. It’s a waste of time doing that and if you don’t have an actual theory instructor that can tell you, ‘wait until 3rd semester and it will be explained’. The bVI+6 chord doesn’t function as a dominant 7 chord whatsoever but more as a convenient artifice brought about from the chromatic voice movement between all voices moving from the ii 6/4 through the bVI+6 to the I 6/4.

                  Emeton The intervals are parts of chords which are parts of progressions. To understand the intervals you need to move on to how the chords they’re in function in actual progressions.

                  A lot of things interrelate in music. The purpose (focus) of this thread is understanding the traditional interval names. These names link to written music and where notes themselves are given a name (C# vs. Db for example). It's in the learner forum so tries to stay basic.

                  We did expand to usage at the point that Ranjit brought in the harmonic minor scale to show where we have an aug2. This still relates to interval names in a basic way, in that it illustrates that these intervals are actually found in music - but still in a basic way.

                  Since it all interrelates I can see how you'd want to go further into other topics. For example, when we have an aug6 chord where the actual chord sounds like the "dominant 7" chord (function i.e. where it goes) but is spelled (for "C7") with A# instead of Bb, the reason the chord is spelled that way is due to the next chord it's going to in context of the music - so that in turn we'll find aug6, or in an inversion, we'll find a dim3. This is probably what you're thinking of. I suggest to make this a new topic in a new thread. (That new thread would probably be best planned in advance for some kind of order. It could get complicated otherwise.)

                  Emeton In an elementary presentation of intervals peculiarities such as augmented intervals can be mentioned. In this ex. note how the top voice in the ii 4/3 chord moves chromatically upward. ......

                  Emeton, we cross-posted. Would you like to start a new thread on the topic of progressions and movement on chords? For the reason in my post where we cross-posted.

                  The topic of intervals for learners which goes all the way to dims and augs is already a vast and complex one.

                  The purpose is to help to understand the aug and dim intervals. I hope that someone will play through my example; it’s a pretty basic progression.

                    Keystring's knowledge of theory is impressive and exhaustively explained in this post, and may be helpful to those who want to dig into the intricacies of this aspect of music theory, and I applaud his efforts and his willingness to share.

                    I'm a practical guy and I have a rather practical approach to playing music. If someone is going to primarily play piano (as an example, since this is mostly a piano oriented forum) by reading notes on a page, little to no knowledge of music theory is required; you just play what's written.

                    If a player wants to improvise, a knowledge of chords, scales and/or modes, is helpful, but certainly not necessary. Knowing how scales and chords fit the key of the song offers a framework of what's available in terms of tonal choices, and whether the player wants to play "inside" or "outside" of the changes. But again, players with good ears may be able to improvise without knowing much theory.

                    If a player wants to venture into composing, theory is certainly helpful in being able to construct a piece that makes sense, technically, and tonally, speaking. But let's face it, there are plenty of song writers who have composed, or constructed, songs that have been accepted by the public; some who couldn't even read music, let alone understand the theory.

                    For those scholarly folks who want to want to discuss the intricate workings of music theory, things like intervals, diminished 3rds, and how they're called, and when to call them, can probably fill countless hours of discourse, much like what famous writers did at their local pub with regard to storytelling, syntax, grammar, or plot. But for the majority of people who want to play the piano, or any other instrument, none of it matters.

                      GaryD The traditional system goes back centuries. I think your idea of talking about trees is a good explanation of how it works.

                      I was grasping, but I have used trees, or houses, or any row of "things" multiple times in the past to sort out what this naming system is actually about. In discussions among adults and teens, this has worked. It also solves a problem created by how interval names are created, when we're told that these names describe a "distance" between intervals. That's a glitch, because when we describe actual distance, we measure using standard unchanging units like inches, centimeters, ounces, and the starting point is always zero. People see on the piano that CE involves two whole tones, or four semitones, and "3" doesn't add up (literally). The word "distance" is misleading. (That's what SP had been trying to get at, and why he invented the word "span" for this).

                      Ok, so we have "distance" and this peculiar way of naming it. A student trying to understand rather than just memorizing stuff can be confused by what they actually perceive. So I wondered whether in real life we have something similar, and yes, we do:

                      My parents farmed, and when you're out in the field you make do with what's around you, and you're also repeatedly working with familiar landmarks. You may gauge the "distance" for this many trees without ever measuring anything. I may indeed need to stretch a rope or wire and for whatever reason I'm counting out trees, or rocks, or whatever. There are plenty of times in real life that we "measure out" things without every using a unit of measure.

                      The old naming system we inherited is sort of like the old farmers and their fields and familiar landmarks. Instead of unevenly spaced trees and "1st tree, 2nd tree, 3rd tree" we have unevenly spaced notes, always in the same sequence of spacing regardless of where you start. It is not really "distance" in how we "measure" distance.

                      An important step may be simply realizing that the interval names are not measured distances in how we understand measurement, but this other thing. And then linking that to actual measurement, whether semitones. Some people do this instinctively. There are two things. This "1st 2nd 3rd" naming thing; the actual distance of intervals.

                      GaryD ..... The more modern system and the one I always use could be called the sound interval system. And this system only cares about what we hear.

                      Yes. This touches on "actual distance" (as in standard measurement) and in this, C D# and C Eb are in actuality the same distance apart (because they are) and "on the piano" have the same sound quality. I have seen a few ways of expressing intervals in alternate ways - the one I saw first was by semitones. All of them touch on the reality of our "1st tree, 2nd tree" system with unevenly spaced trees is quite awkward, esp. as music gets less diatonic.

                      I'm only going as far as the idea of two views: one being how the interval naming system is set up .... so as to be able to use it, and know what it's not - and the "realness" where C D# and C Eb are the same piano keys emitting the same sound quality played on the piano.

                      And then ... in this thread ....... how to learn to use that system. (My first three posts)