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Thread: Increasing / Decreasing intervals

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    Senior Member mikeh375's Avatar
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    It's an interesting question MR. Why not a c natural and a c flat unison? For one, it's a more awkward spelling as opposed to c and b natural, as would be d and d flat or even E flat and E double flat. My guess is that in CP the diminished unison spelling is hard to fit harmonically and stylistically speaking in easier less complex language. Simplicity, clarity and directness is always the most effective. Consider how an e natural and e double flat sounds, let alone looks. Technically a diminished unison on paper but having no aural relationship and certainly not practical.
    These days, I could easily justify a c and a c flat unison or similar to my own satisfaction, depending on their resolution and practicality for players.
    But it really isn't a unison anyway is it...
    Last edited by mikeh375; Jun-12-2019 at 15:38.

  2. #17
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by EdwardBast View Post
    Yes, ST is correct. "A descending minor second" would be the way to say it if the notes were C and B. Note, however, that 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.
    So the word "second" in 'minor second' refers to the next scale degree; if it doesn't fit a scale, it's a semitone or half-step.

    "Tone" and "semitone" are thus called, because all diatonic scales consist of half-steps and whole steps; "tone" is the larger possible distance in a scale; "semitone" is the smaller possible half-step of a scale.

    All this terminology is biased towards thinking in diatonic scales. So, one must not only learn the lingo, but also should learn to "think" diatonically. All contexts are "scale" contexts.
    Last edited by millionrainbows; Jun-19-2019 at 14:21.
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    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by millionrainbows View Post
    So the word "second" in 'minor second' refers to the next scale degree; if it doesn't fit a scale, it's a semitone or half-step.

    "Tone" and "semitone" are thus called, because all diatonic scales consist of half-steps and whole steps; "tone" is the larger possible distance in a scale; "semitone" is the smaller possible half-step of a scale.

    All this terminology is biased towards thinking in diatonic scales. So, one must not only learn the lingo, but also should learn to "think" diatonically. All contexts are "scale" contexts.
    The terms simply mean different things. Semitone and half step mean a certain acoustic difference in pitch. Minor seconds and augmented unisons are defined by nomenclature and are required by diatonic scale systems and other phenomena. So half of this terminology is biased towards diatonic scales and half isn't.
    Last edited by EdwardBast; Jun-19-2019 at 20:21.

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by EdwardBast View Post
    The terms simply mean different things. Semitone and half step mean a certain acoustic difference in pitch. Minor seconds and augmented unisons are defined by nomenclature and are required by diatonic scale systems and other phenomena. So half of this terminology is biased towards diatonic scales and half isn't.
    I would have thought that 'semitone' is also based on scale nomenclature, since scales consist of "tones" and "semitones."

    WIK says, under the "Semitone" heading (which includes "Half step"): In music theory, a distinction is made between a diatonic semitone, or minor second (an interval encompassing two different staff positions, e.g. from C to D♭)...
    ...and a chromatic semitone or augmented unison (an interval between two notes at the same staff position, e.g. from C to C♯).

    I would think that "step" refers to scale steps.

    Also under the heading "Semitone" WIK says: "A semitone is also called a half step or a half tone," I assume 'half tone' is not dependent on scale or staff nomenclature;

    "Step" is not defined.

    So, one needs to be careful to distinguish "what kind of semitone" one is talking about.
    ================================================== =====

    Under the heading "Major second", Wik says: "Intervals composed of two semitones, such as the major second and the diminished third, are also called tones, whole tones, or whole steps."

    "A second is a musical intervalencompassing two adjacent staff positions (see Interval number for more details). For example, the interval from C to D is a major second, as the note D lies two semitones above C, and the two notes are notated on adjacent staff positions. Diminished, minor and augmented seconds are notated on adjacent staff positions as well, but consist of a different number of semitones (zero, one, and three).

    WIK, under the heading "Interval:"
    "In music theory, an interval is the difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.

    In Western music, intervals are most commonly differences between notes of a diatonic scale. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C♯ and D♭. Intervals can be arbitrarily small, and even imperceptible to the human ear.

    In physical terms, an interval is the ratio between two sonic frequencies. For example, any two notes an octave apart have a frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For this reason, intervals are often measured in cents, a unit derived from the logarithm of the frequency ratio."
    Last edited by millionrainbows; Jun-19-2019 at 23:34.
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  5. #20
    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by millionrainbows View Post
    I would have thought that 'semitone' is also based on scale nomenclature, since scales consist of "tones" and "semitones."

    WIK says, under the "Semitone" heading (which includes "Half step"): In music theory, a distinction is made between a diatonic semitone, or minor second (an interval encompassing two different staff positions, e.g. from C to D♭)...
    ...and a chromatic semitone or augmented unison (an interval between two notes at the same staff position, e.g. from C to C♯).

    I would think that "step" refers to scale steps.

    Also under the heading "Semitone" WIK says: "A semitone is also called a half step or a half tone," I assume 'half tone' is not dependent on scale or staff nomenclature;

    "Step" is not defined.

    So, one needs to be careful to distinguish "what kind of semitone" one is talking about.
    ================================================== =====

    Under the heading "Major second", Wik says: "Intervals composed of two semitones, such as the major second and the diminished third, are also called tones, whole tones, or whole steps."

    "A second is a musical intervalencompassing two adjacent staff positions (see Interval number for more details). For example, the interval from C to D is a major second, as the note D lies two semitones above C, and the two notes are notated on adjacent staff positions. Diminished, minor and augmented seconds are notated on adjacent staff positions as well, but consist of a different number of semitones (zero, one, and three).

    WIK, under the heading "Interval:"
    "In music theory, an interval is the difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.

    In Western music, intervals are most commonly differences between notes of a diatonic scale. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C♯ and D♭. Intervals can be arbitrarily small, and even imperceptible to the human ear.

    In physical terms, an interval is the ratio between two sonic frequencies. For example, any two notes an octave apart have a frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For this reason, intervals are often measured in cents, a unit derived from the logarithm of the frequency ratio."
    Sigh. It's pretty simple:

    Seconds, thirds, fourths, etc. are nomenclature with diatonic implications.

    Tones and semitones are acoustic phenomena harking back to Ancient Greek theory.

    Whole and half steps are sloppily used in either category. They are rooted in diatonic theory, but are used as synonyms for tones and semitones — just to confuse people.
    Last edited by EdwardBast; Jun-20-2019 at 00:30.

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  6. #21
    Senior Member Minor Sixthist's Avatar
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    Quote Originally Posted by millionrainbows View Post
    That logic fails when considering the "augmented unison."

    There is no such thing as a "diminished unison," because, even when diminishing it, the unison interval increases in size.

    Music Theory for Dummies, p.113: "There is no such thing as a diminished unison, because no matter how you change the unisons with accidentals, you are adding half steps to the total interval."

    Alfred's Essentials of Music Theory: A Complete Self-Study Course for All Musicians, p. 153: "Since lowering either note of a perfect unison would actually increase its size, the perfect unison cannot be diminished, only augmented."

    For me, I can't help but question the standard terminology, since a "unison" is not an interval; it is "zero" in terms of distance.

    But apparently to the CP mind, traveling "backwards" from a unison, thus "diminishing" it, is verboten, unless, by the existing logic, we are considering only the distance of an interval (increase or decrease) rather than its ascent or descent. Does anyone follow this logic?

    If so, then what is the CP reason that "diminished unisons" cannot exist, in terms of nomenclature and staff, accidentals, scale context, etc.?

    Already confused. Why can we have an augmented unison but not a diminished unison? Regardless of any terminology in question, whether mine or yours or OP's — why aren't these two congruent in terms of naming their movement?
    Last edited by Minor Sixthist; Jun-20-2019 at 01:22.

  7. #22
    Senior Member Minor Sixthist's Avatar
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    Quote Originally Posted by millionrainbows View Post
    For me, I can't help but question the standard terminology, since a "unison" is not an interval; it is "zero" in terms of distance.
    This alone I understand. You could go up 9 half steps from C and have A - you've ascended a major sixth.

    But if you go up a half step from C, you are at C# just fine - but what have you ascended? The interval of some kind of a unison? As you proposed, is it really ascent or descent if the intervallic distance is 0?

    I understand the paradox there. But I still have trouble with the fundamental (ugh no pun intended) difference between an augmented and diminished unison, as you elaborated in your post.
    Last edited by Minor Sixthist; Jun-20-2019 at 01:23.

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  9. #23
    Senior Member Bwv 1080's Avatar
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    In modern terminology it’s not a minor second, just 1. a whole step is 2 minor third is 3 etc

    With ‘a’ and ‘b’ commonly used for minor and major sevenths, respectively

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    Senior Member Woodduck's Avatar
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    Quote Originally Posted by Minor Sixthist View Post
    Why can we have an augmented unison but not a diminished unison? Regardless of any terminology in question, whether mine or yours or OP's — why aren't these two congruent in terms of naming their movement?
    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.

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    Senior Member Minor Sixthist'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.
    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...

    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?
    Ok. I think I see what you're saying: by definition augmenting is making the intervallic distance greater, and diminishing is making it lesser. So it's because diminishing wouldn't make the space between two unison notes lesser, it would make it greater — so it would have to be augmented. I got it.

    But then... wait. Doesn't that just mean no descending diminished interval at all could exist?

    C to G, descending P4. C to Gb — NOT descending diminished 4th! Because the space is greater...

    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.

    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.
    Funny, because in my ~6 years of theory/ET, I am almost positive we used both "augmented unison" and "diminished unison." Granted, these funky outliers are not the intervals we focused on for training very often, but then again if I had learned that only augmented unisons were acceptable, I don't think that knowledge would've completely slipped my mind and allowed me to get confused over this tonight.

    So basically is what you're saying that everything I know is a lie? Come on, I'm not due for another weekly crisis until next week.
    Last edited by Minor Sixthist; Jun-20-2019 at 07:25.

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    Senior Member Woodduck'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...



    Ok. I think I see what you're saying: by definition augmenting is making the intervallic distance greater, and diminishing is making it lesser. So it's because diminishing wouldn't make the space between two unison notes lesser, it would make it greater — so it would have to be augmented. I got it.

    But then... wait. Doesn't that just mean no descending diminished interval at all could exist?

    C to G, descending P4. C to Gb — NOT descending diminished 4th! Because the space is greater...

    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.



    Funny, because in my ~6 years of theory/ET, I am almost positive we used both "augmented unison" and diminished unison." Granted, these funky outliers are not the intervals we focused on for training very often, but then again if I had learned that only augmented unisons were acceptable, I don't think that knowledge would've completely slipped my mind and allowed me to get confused over this tonight.

    So basically is what you're saying that everything I know is a lie? Come on, I'm not due for another weekly crisis until next week.
    Sad to say, it's too late in the day for me to move one more brain cell over this.

    Nighty night...

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    Senior Member Minor Sixthist's Avatar
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    Quote Originally Posted by Woodduck View Post
    Sad to say, it's too late in the day for me to move one more brain cell over this.

    Nighty night...
    Don't be pressured to move any more. One of three is a lot to lose!
    Last edited by Minor Sixthist; Jun-20-2019 at 07:44.

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    Quote Originally Posted by Minor Sixthist View Post
    Don't be pressured to move any more. One of three is a lot to lose!
    No problem. Your last question only required one.

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    Senior Member Minor Sixthist's Avatar
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    Quote Originally Posted by Woodduck View Post
    No problem. Your last question only required one.
    .....................

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  21. #30
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by EdwardBast View Post
    Sigh. It's pretty simple:

    Seconds, thirds, fourths, etc. are nomenclature with diatonic implications.

    Tones and semitones are acoustic phenomena harking back to Ancient Greek theory.

    Whole and half steps are sloppily used in either category. They are rooted in diatonic theory, but are used as synonyms for tones and semitones — just to confuse people.
    Well, why didn't you say that before?
    "The way out is through the door. Why is it that no one will use this method?"
    -Confucious

    "In Spring! In the creation of art it must be as it is in Spring!" -Arnold Schoenberg

    "We only become what we are by the radical and deep-seated refusal of that which others have made us." -Jean-Paul Sartre

    "I don't mind dying, as long as I can still breathe." ---Me

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