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Thread: Increasing / Decreasing intervals

  1. #31
    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by millionrainbows View Post
    Well, why didn't you say that before?
    I did? I thought?

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by Minor Sixthist View Post

    So... this isn't a unison thing..? It's just a descending and diminished thing. Like, descending diminished intervals don't exist?

    I'm going to need a second to reflect on this.



    Just think of F to E as a "reverse augmented unison."

    ...But all this questioning is good, because it helps us to recognize the diatonic/scalar nature of much CP music theory, its accompanying lingo, and how sometimes this defies logic. This might come in handy on this forum.
    Last edited by millionrainbows; Jun-20-2019 at 12:57.

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  4. #33
    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by Minor Sixthist View Post
    Ok, now this is definitely where my previous thinking diverges. The way I saw it, if one of them were raised by an accidental, it would make an augmented unison, and if one of them were lowered, that would make a diminished unison. Is that faulty thinking? Bear with my stream of consciousness here...I might be slow right now because it's late, but I was thinking of a fifth as an easy example to apply here.. If I have C to G, perfect — C to G#, now it's augmented, and C to Gb, now it's diminished...
    Imagine this number line:

    -1, 0, 1

    Now imagine that Cb = -1, C = 0, and C# = 1. What we are measuring is the integer difference from C to Cb and C#. The difference in both cases is a semitone, which is bigger than a unison. Hence, two different augmented unisons:

    C-C — 0 semitones
    C-Cb — 1 semitone (bigger than 0, so augmented)
    C-C# — 1 semitone (bigger than 0, so augmented)

    By contrast, in your second example C-G, C-G#, C-Gb, all of the intervals are different:

    C-G — 7 semitones
    C-G# — 8 semitones (bigger than 7, so augmented)
    C-Gb — 6 semitones (smaller than 7, so diminished)

    Quote Originally Posted by millionrainbows View Post
    J
    ...But all this questioning is good, because it helps us to recognize the diatonic/scalar nature of much CP music theory, its accompanying lingo, and how sometimes this defies logic. This might come in handy on this forum.
    Maybe, but not in this case, where the logic is perfectly clear. ^ ^ ^
    Last edited by EdwardBast; Jun-20-2019 at 13:13.

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by EdwardBast View Post


    Maybe, but not in this case, where the logic is perfectly clear. ^ ^ ^
    Number lines are logical, that's why serialists and set theory composers use them.

    I think what's confusing about the "augmented unison" is that it does not recognize "directionality" of the movement, only the "size" of the interval.

    As you may recall, in the OP of this thread, Classicum asked "If I want to specifically indicate a minor second which is decreasing in frequency in a way that makes it unambigious (so it can't mean an increasing minor second), what is the correct musical terminology to indicate it?" This is a question of ascent or descent (directionality), not of interval size.

    On this point, the concept of the "augmented unison" defies logic (so to speak), as it addresses only the size of the interval, not its ascent or descent (directionality).

    Of course, to someone immersed in the lingo and the concepts of diatonic/scalar thinking, it does not defy logic.

    But this makes it clear why set-theory uses a number line, because serial music is not diatonic or scalar, and diatonic/scalar concepts only confuse the issue for that kind of musical thinking.
    Last edited by millionrainbows; Jun-20-2019 at 13:35.

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    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by millionrainbows View Post
    I think what's confusing about the "augmented unison" is that it does not recognize "directionality" of the movement, only the "size" of the interval.

    On this point, the concept of the "augmented unison" defies logic (so to speak), as it addresses only the size of the interval, not its [I]ascent or descent (directionality).
    There is no confusion because directionality is never an issue. It is always irrelevant.

    Consider a fifth from F up to C. Add a sharp to the F (upward directionality) and we have a diminished fifth. Flat the F (downward direction) and the interval is an augmented fifth.
    Last edited by EdwardBast; Jun-20-2019 at 14:04.

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by EdwardBast View Post
    There is no confusion because directionality is never an issue. It is always irrelevant.
    Well, that was the OP's question.

    Consider a fifth from F up to C. Add a sharp to the F (upward directionality) and we have a diminished fifth. Flat the F (downward direction) and the interval is an augmented fifth.
    I was specifically addressing the augmented unison; so was the OP's question about semitone movement from C-C# and C-B.

    But if you want to be completely logical, directionality does matter; it depend on which note gets the change.
    Consider a fifth from F up to C. Add a sharp to the C (upward directionality) and we have an augmented fifth. Directionality can either augment or diminish an interval.
    Last edited by millionrainbows; Jun-20-2019 at 14:20.

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  9. #37
    Senior Member BrahmsWasAGreatMelodist's Avatar
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    Quote Originally Posted by Woodduck View Post
    Hmmm... This feels like a linguistic briarpatch. Lets see (puts thinking cap on)...

    To the ear, a unison is a unison and can't be either augmented or diminished without ceasing to be a unison. On paper, though, we can have an augmented unison if two notes sounded simultaneously are written on the same line or space of the staff but one of them is raised or lowered by an accidental. But it seems clear from this that there can be no such interval as a diminished unison. Diminishing an interval reduces the number of semitones spanned by that interval, but a unison can't be reduced. Taking C up or down, to C# or Cb, gives us the same interval, spanning one semitone in either case, just as an augmented sixth would span the same number of semitones in either an ascending or descending direction.

    Does that sound right?

    I've never heard of the term "augmented unison" before now. I guess I should look for ways to use it in a sentence before it slips my mind.
    First, thanks for answering. I was going to say pretty much exactly this last night, but decided to let someone else do the dirty work (as I usually do on the theory forum haha). Thanks!

    However, I'm not sure about the highlighted part. I think, in certain contexts, you CAN hear an augmented unison without it ceasing to be a unison (it simply ceases to be a PERFECT unison). The interval would have to be established functionally (just like, say, an augmented 6th), but I think it's, in the right context, it's possible to hear a C and C# as a type of "unison" rather than a "second". I'll try to think of an example (Scelsi might have something, haha). Without context, I'm not sure hearing just those 2 notes (without seeing them on paper) firmly establishes the interval as either an augmented unison or a minor second (although you'd probably call it a minor second mostly because of previous encounters with that interval in tonal music).

    Kind of a pedantic point I guess (you might have just been using an everyday definition of unison and not a technical one), but it certainly brings up an interesting discussion about how we hear (or don't hear?) intervals in a functional context. We can certainly hear chords functionally (a minor 7th chord sounds different from a German augmented 6th chord), but do we hear intervals within a suggested chord functionally or just the chord itself? I'm not really sure this is a meaningful question, but it's food for thought.
    Last edited by BrahmsWasAGreatMelodist; Jun-20-2019 at 14:45.
    Casual composer, pianist, music enthusiast

  10. #38
    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by millionrainbows View Post

    I was specifically addressing the augmented unison; so was the OP's question about semitone movement from C-C# and C-B.
    Doesn't matter. The logic is exactly the same for all intervals: To put it bluntly: (only) Size matters!

    Quote Originally Posted by millionrainbows View Post
    But if you want to be completely logical, directionality does matter; it depend on which note gets the change.
    Consider a fifth from F up to C. Add a sharp to the C (upward directionality) and we have an augmented fifth. Directionality can either augment or diminish an interval.
    Yes, that's why direction is irrelevant: because only size is determinative!

    This is like a comedy routine where "completely logical" means dismantling logic. When you write "it depends on which note gets changed" that's because the choice determines whether the interval gets bigger or smaller. Which just proves once again that:

    Only size matters! Direction is never determinative. It couldn't be simpler. Three words cover every situation!
    Last edited by EdwardBast; Jun-20-2019 at 16:17.

    What greater comfort does time afford than the objects of terror re-encountered and their fraudulence exposed in the flash of reason?
    — William Gaddis, The Recognitions

    Originality is a device untalented people use to impress other untalented people and to protect themselves from talented people.
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  12. #39
    Senior Member Minor Sixthist's Avatar
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    Quote Originally Posted by millionrainbows View Post
    Just think of F to E as a "reverse augmented unison."

    ...But all this questioning is good, because it helps us to recognize the diatonic/scalar nature of much CP music theory, its accompanying lingo, and how sometimes this defies logic. This might come in handy on this forum.
    Interesting thoughts. I had never considered that diminished-descending anomaly. Then again, the teachers never seem to get through as much as they'd like to in music theory..

  13. #40
    Senior Member Minor Sixthist's Avatar
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    Quote Originally Posted by EdwardBast View Post
    Imagine this number line:

    -1, 0, 1

    Now imagine that Cb = -1, C = 0, and C# = 1. What we are measuring is the integer difference from C to Cb and C#. The difference in both cases is a semitone, which is bigger than a unison. Hence, two different augmented unisons:

    C-C — 0 semitones
    C-Cb — 1 semitone (bigger than 0, so augmented)
    C-C# — 1 semitone (bigger than 0, so augmented)

    By contrast, in your second example C-G, C-G#, C-Gb, all of the intervals are different:

    C-G — 7 semitones
    C-G# — 8 semitones (bigger than 7, so augmented)
    C-Gb — 6 semitones (smaller than 7, so diminished)
    Sensible explanation, thank you. You might say mathematics generally freak me out, so I might not have jumped right to the 'mathy' conclusion myself, though you elucidate just great. It really is a lot about 'absolute values.'

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    Senior Member mikeh375's Avatar
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    Quote Originally Posted by BrahmsWasAGreatMelodist View Post
    First, thanks for answering. I was going to say pretty much exactly this last night, but decided to let someone else do the dirty work (as I usually do on the theory forum haha). Thanks!

    However, I'm not sure about the highlighted part. I think, in certain contexts, you CAN hear an augmented unison without it ceasing to be a unison (it simply ceases to be a PERFECT unison). The interval would have to be established functionally (just like, say, an augmented 6th), but I think it's, in the right context, it's possible to hear a C and C# as a type of "unison" rather than a "second". I'll try to think of an example (Scelsi might have something, haha). Without context, I'm not sure hearing just those 2 notes (without seeing them on paper) firmly establishes the interval as either an augmented unison or a minor second (although you'd probably call it a minor second mostly because of previous encounters with that interval in tonal music).
    as you suggest, it wil be a minor second in the most important aspect of its existence (its sound) unless the frequencies of the two notes are also magically transformed by a kind of musical legerdemain.....I await your example for which the spelling, harmonic context and resolution will have to be impeccable if it's to be convincing to my ears as an aug. unison.

    There is one way to make an aug unison more convincing aurally of course and that would be with timbre...now I'm more open to that approach as being a more viable and practical manifestation of something that should be left in a dusty textbook...... I should say I am referring to CP here and not serialism - even a quick glance through a textbook came up with a potential aug unis. in Webern's op23 (the series written out in trope form)
    Last edited by mikeh375; Jun-20-2019 at 21:40.

  15. #42
    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by mikeh375 View Post
    as you suggest, it wil be a minor second in the most important aspect of its existence (its sound) unless the frequencies of the two notes are also magically transformed by a kind of musical legerdemain.....I await your example for which the spelling, harmonic context and resolution will have to be impeccable if it's to be convincing to my ears as an aug. unison.

    There is one way to make an aug unison more convincing aurally of course and that would be with timbre...now I'm more open to that approach as being a more viable and practical manifestation of something that should be left in a dusty textbook.....

    I think the Gb in the cello part at 8:31 (passacaglia theme from the third movement of Shostakovich's Tenth Quartet) might qualify as an augmented unison neighbor tone, albeit enharmonically spelled.

    https://www.youtube.com/watch?v=yQuIEjA4NNA

    What greater comfort does time afford than the objects of terror re-encountered and their fraudulence exposed in the flash of reason?
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  16. #43
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by EdwardBast View Post
    When you write "it depends on which note gets changed" that's because the choice determines whether the interval gets bigger or smaller. Which just proves once again that: Only size matters! Direction is never determinative. It couldn't be simpler. Three words cover every situation!
    In the isolated case of intervals, this is easier to say; but in a diatonic context one must be careful about using directionality in an 'absolute' manner, especially when dealing with chord inversion, which is a better example of how directionality is subject to diatonic considerations, and deviates from the 'absolute' logic of a number line, and interval size, to accommodate a diatonic context.

    C to C# is not an ascending minor 2nd, it is an augmented unison or, if one is referring only to its aural effect, a semitone or half step. C to Db would be an ascending minor 2nd.
    Unfortunately, as the augmented unison demonstrates, diatonic nomenclature is focussed on an interval's function and placement in a diatonic/scalar hierarchy, which to the uninitiated might seem to be to the detriment of considering the absolute value of an interval (its aural effect) outside of a diatonic context.

    In this way, diatonic thinking favors 'diatonic logic' over a more 'absolute logic' of interval size. Hence, we should be aware that applying a number line and absolute values (size) to diatonic intervals is counter-intuitive to diatonic thinking.
    Last edited by millionrainbows; Jun-21-2019 at 04:16.

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    Senior Member Woodduck's Avatar
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    This discussion seems to have surpassed the "dancing angels on pinheads" level of superfluousness.

    There is nothing problematic about having two alternative ways of describing the interval in question. One way refers to its sound - a movement by a semitone - and the other to its functional notation - an augmented unison. Whether we like the terms or not, their use would seem to have been clarified. Is there anything more to say about this?

    I'm all ears - or all eyes, depending on whether we're listening to the music or looking at it. If we do both at once, will our brains explode?

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  19. #45
    Senior Member mikeh375's Avatar
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    Quote Originally Posted by EdwardBast View Post
    I think the Gb in the cello part at 8:31 (passacaglia theme from the third movement of Shostakovich's Tenth Quartet) might qualify as an augmented unison neighbor tone, albeit enharmonically spelled.

    https://www.youtube.com/watch?v=yQuIEjA4NNA
    Possibly Edward, but to my mindset it is just motivic work that exploits major and minor harmony at an unsettling closeness, the spelling being practical for the player.
    I don't know the 10th 4tet but am a great Shostakovich fan and will have to listen to it, I have the box set by the Fitzwilliam 4tet and still haven't gone through them all yet.

    Here is the Webern example I edited in above. I haven't listened to the piece but these tropes show the utility of an aug.unison between D and D sharp and C and C sharp in serialism.

    webern.jpg
    Last edited by mikeh375; Jun-21-2019 at 08:41.

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