# Increasing / Decreasing intervals



## Classicum

Assume each tone is played individually. As far as I know the names of intervals (minor second, major third, octave etc.) can mean both a tone increasing or decreasing in frequency. So for example a minor second can mean both C C# (played in that order) but also C B (in that order).

This is a question of terminology. 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?

I could simply say "decreasing minor second" 
and it will probably be understood but I'm wondering if that is that the official terminology or something else?


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## SuperTonic

I think the proper terminology for going down in pitch by a half step would be a descending minor second.


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## EdwardBast

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.


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## Woodduck

You don't want the term "frequency" here. That's a concept in acoustics, not in music theory. "Increasing frequency" - meaning faster vibration of a vibrating body - gives us a higher pitch, but there's no reason to mention that physical phenomenon in referring to the construction of music. Ascending or descending intervals are simply named by the number of scale steps involved.


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## millionrainbows

"Think diatonically" and all will be well. 
What's the distinction between a 'diatonic semitone' and a 'chromatic semitone'?
Is a 'chromatic semitone' the same as an 'augmented unison'?
Would C#-C be a 'diminished unison'?


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## Minor Sixthist

As SuperTonic said, the best answer to your question regarding the correct terminology would be “ascending / descending (given interval,)” rather than “increasing / decreasing.”

Regarding frequencies: you’re not technically wrong, but intervals are better understood as ratios of frequencies rather than, say, a number line on which notes can be graphed by increasing frequency. You wouldn’t be wrong that a higher note has a greater frequency but the way intervals are best conceptualized is by their ratios. E.g, any given octave represents a frequency ratio of 2:1 from the higher to the lower. Each interval we think of in the diatonic scale has an integer (whole number) ratio.

I would disagree that a discussion of frequency has “no reason” to intersect with the discussion of intervals. Indeed frequencies can be key in the discussion of acoustics, which is a branch of physics dealing with all matters of sound, but in a question asking if there’s a key definitional difference between ascending/descending intervals - the answer would be no, because the ratios that define each interval remain static, it’s just each end of the ratio would of course have to correspond with the correct half of the interval. From the higher to the lower C would represent a ratio of 2:1 Hz, and from the lower to the higher I guess you could imagine the ratio being 1:2, though typically an octave is simply represented as 2:1 with the implication being that the higher note has a greater frequency. 

Definitionally - and I feel like your question involves aiming to use terms correctly with definitions - intervals might be best understood by the frequency ratios. In fact the measurement of ‘cent’ is actually a logarithm derived from the frequencies of given notes in Hz... in tuning the exacting of the ratio has everything to do with frequency.

Again, though, the only question you did explicitly ask was best addressed by Super.


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## Woodduck

Minor Sixthist said:


> As SuperTonic said, the best answer to your question regarding the correct terminology would be "ascending / descending (given interval,)" rather than "increasing / decreasing."
> 
> Regarding frequencies: you're not technically wrong, but intervals are better understood as ratios of frequencies rather than, say, a number line on which notes can be graphed by increasing frequency. You wouldn't be wrong that a higher note is a greater frequency but the way intervals are best conceptualized is by their ratios. E.g, any given octave is represents a frequency ratio of 2:1 from the higher to the lower. Each interval we think of in the diatonic scale has an integer ratio like this, IIRC.
> 
> I would disagree that a discussion of frequency has "no reason" to intersect with the discussion of intervals. Definitionally - and I feel like your question involves aiming to use terms correctly with definitions - intervals are best understood by their ratios, as each basic interval we could think of has a different one. In fact the measurement of 'cent' is actually a logarithm derived from the frequencies of given notes in Hs... in tuning the exacting of the ratio has everything to do with frequency.
> *
> Again, though, the only question you actually did ask was best addressed by Super.*


Did you win or lose that debate with yourself?


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## Minor Sixthist

Woodduck said:


> Did you win or lose that debate with yourself?


Evidence for lost: wrote a bunch on what was not explicitly asked; for won: it was all worth it to correct you?


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## Woodduck

Minor Sixthist said:


> Evidence for lost: wrote a bunch on what was not explicitly asked; for won: it was all worth it to correct you?


It would have been, if only.


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## Minor Sixthist

Woodduck said:


> You don't want the term "frequency" here
> ...
> there's no reason to mention that physical phenomenon in referring to the construction of music.


Hmm...so you wouldn't agree that my point on frequency ratios suggests that there could, indeed, be a reason to mention frequencies in a question about intervals and their terminology?

Just purely playing Duck's advocate, though with due deference, as always. Most of all a question for potential self-improvement.


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## Woodduck

Minor Sixthist said:


> Hmm...so you wouldn't agree that my point on frequency ratios suggests that there could, indeed, be a reason to mention frequencies in a question about intervals and their terminology?
> 
> Just purely playing Duck's advocate, though with due deference, as always.


There could be a reason for anything one wants to do. But do we want to do that particular thing - i.e. bring in the physics of acoustics - here? The OP just wants "unambiguous terminology" to describe movement by a half step. What terms could be less ambiguous than "movement by a half step"?


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## Minor Sixthist

Woodduck said:


> There could be a reason for anything one wants to do. But do we want to do that particular thing - i.e. bring in the physics of acoustics - here? The OP just wants "unambiguous terminology" to describe movement by a half step. What terms could be less ambiguous than "movement by a half step"?


Understood.
Sometimes I worry I 'miss the point' more than I should... am I becoming a big TC bloviator? 

I only meant to earn that title in 30 or so more years.


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## Woodduck

Minor Sixthist said:


> Understood.
> Sometimes I worry I 'miss the point' more than I should... am I becoming a big TC bloviator?
> 
> I only meant to earn that title in 30 or so more years.


Don't worry. The prize for Big TC Bloviator is coveted by many and the competition is fierce. Why, I've racked up over 13,000 posts in little more than 5 years, but I dare not take even a brief vacation lest I return and find the title stolen from me. My money is on paulbest (836 posts since April, 837 by the time i finish writing this...OOPS! 838!)

EDIT: 839!... OOPS...


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## Minor Sixthist

Woodduck said:


> Don't worry. The prize for Big TC Bloviator is coveted by many and the competition is fierce. Why, I've racked up over 13,000 posts in little more than 5 years, but I dare not take even a brief vacation lest I return and find the title stolen from me. My money is on paulbest (836 posts since April, 837 by the time i finish writing this...OOPS! 838!)
> 
> EDIT: 839!... OOPS...


Well, at the evident rate you'd better hope there's not an upper limit on that 'edit' feature...


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## millionrainbows

Minor Sixthist said:


> As SuperTonic said, the best answer to your question regarding the correct terminology would be "ascending / descending (given interval,)" rather than "increasing / decreasing."


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.?


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## mikeh375

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...


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## millionrainbows

EdwardBast said:


> 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.


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## EdwardBast

millionrainbows said:


> 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.


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## millionrainbows

EdwardBast said:


> 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."


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## EdwardBast

millionrainbows said:


> 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.


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## Minor Sixthist

millionrainbows said:


> 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?


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## Minor Sixthist

millionrainbows said:


> 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.


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## Bwv 1080

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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## Woodduck

Minor Sixthist said:


> 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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## Minor Sixthist

Woodduck said:


> 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.


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## Woodduck

Minor Sixthist said:


> 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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## Minor Sixthist

Woodduck said:


> 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!


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## Woodduck

Minor Sixthist said:


> 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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## Minor Sixthist

Woodduck said:


> No problem. Your last question only required one.


:scold: .....................


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## millionrainbows

EdwardBast said:


> 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? :lol:


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## EdwardBast

millionrainbows said:


> Well, why didn't you say that before? :lol:


I did? I thought?


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## millionrainbows

Minor Sixthist said:


> 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." :lol:

...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.


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## EdwardBast

Minor Sixthist said:


> 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)



millionrainbows said:


> 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. ^ ^ ^


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## millionrainbows

EdwardBast said:


> 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.


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## EdwardBast

millionrainbows said:


> 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 _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._


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## millionrainbows

EdwardBast said:


> 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.


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## BrahmsWasAGreatMelodist

Woodduck said:


> 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.


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## EdwardBast

millionrainbows said:


> 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!



millionrainbows said:


> 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!


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## Minor Sixthist

millionrainbows said:


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


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## Minor Sixthist

EdwardBast said:


> 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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## mikeh375

BrahmsWasAGreatMelodist said:


> 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)


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## EdwardBast

mikeh375 said:


> 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.


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## millionrainbows

EdwardBast said:


> 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.


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## Woodduck

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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## mikeh375

EdwardBast said:


> 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.


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.


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## mikeh375

Woodduck said:


> .............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?


Imagine how composers feel Wooduck, are our brains totally addled? - no (well, ok, maybe a little). In the day to day of CP composing, the aug. unison is not an issue and I doubt it is theoretically too. One can understand its application in bitonal spelling and dodecaphony however, I'd like to see a non ambiguous aug.unison (simultaneously too) in a CP academic context.
Would anyone consider a blue note (say a c natural over a c sharp in an A7 harmony) as an example?...that's as close as I can get so far to such a thing in common use.


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## millionrainbows

Woodduck said:


> 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?


Yes, just make damn sure you call it by the right name. :lol:


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## EdwardBast

Woodduck said:


> 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?


No, there is nothing more to say about the issue raised in the OP. You've summarized it succinctly. I summarized it with similar clarity pages ago.

Mikeh and I are now on whether augmented unisons have an aural reality distinguishing them from minor 2nds. I gave an example where I think the difference can readily be heard, if one listens from 8:15 to 8:45 in this video. The Gb at 8:31, I suggested, is an augmented unison above the F that precedes and follows it, even though it is notated as a minor 2nd.








millionrainbows said:


> Yes, just make damn sure you call it by the right name.


As the OP stated:



Classicum said:


> This is a question of terminology.


So, yes, the whole point of the thread, which everyone but you seems to understand, is about finding the right names.


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## mikeh375

EdwardBast said:


> Mikeh and I are now on whether augmented unisons have an aural reality distinguishing them from minor 2nds. I gave an example where I think the difference can readily be heard, if one listens from 8:15 to 8:45 in this video. The Gb at 8:31, I suggested, is an augmented unison above the F that precedes and follows it, even though it is notated as a minor 2nd.


I found it especially interesting from b28 cf. Compound aug. unisons or just accented (appoggiatura!) enharmonic maj7ths resolving to the flattened 7ths? Some chords have the feel of that bluesy A7 chord I mentioned above with the major and flattened 3rd and most notable (for me at least) is that they all have simultaneity, which may not absolutely essential, but is a surely a plus for an interval in the dock..


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## BabyGiraffe

See Zarlino's writing for augmented and diminished unisons and similar . But this was way before 12 equal temperament. Honestly, most of these questions and terminology make no sense without learning the deeper meantone theory (and are almost useless in general, if we just stick to 12 equal where atonal integer notation is way superior musical system).
Btw, Vicentino used such modulations - I guess for the untrained ears some of the chords change colour slightly, not really modulate (there are some youtube recordings, I think they recorded the singers separately, then retuned to 31 equal, then mixed them together)


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## millionrainbows

EdwardBast said:


> So, yes, the whole point of the thread, which everyone but you seems to understand, is about finding the right names.


I love and respect you, too, Edward.


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