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#1906147 - 05/31/12 06:00 PM Alternate names for intervals
Gary D. Online   content
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I am going to start with something that may seem very obvious, but I don't think it is.

First, a statement: it is very clear that a simple tritone will show up with equal frequency as an aug4 or a dim5.

But how many other intervals have two spellings that are approximately as common?

I have my own ideas about this but would be interested, first, in what other people assume. The question may be more complicated than it first seems to be.
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#1906149 - 05/31/12 06:05 PM Re: Alternate names for intervals [Re: Gary D.]
Morodiene Offline
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Originally Posted By: Gary D.

I am going to start with something that may seem very obvious, but I don't think it is.

First, a statement: it is very clear that a simple tritone will show up with equal frequency as an aug4 or a dim5.


Technically, wouldn't the aug4 br written as a 4th with a sharp on the top note (except for the B-F one), and a dim5 be written as a 5th with a flat on the top note? Or are you not concerned with how it's spelled but rather how it's defined?


Edited by Morodiene (05/31/12 06:06 PM)
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#1906155 - 05/31/12 06:12 PM Re: Alternate names for intervals [Re: Gary D.]
Legal Beagle Offline
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What gets a little dicy is the parameters of what you're asking. For example, what springs to my mind is Maj2 and min7. Same interval, two very common (but different) spellings and applications.

But maybe you'd say no, that's not the same interval, that's just an inversion... but so is your example of aug4/dim5, so maybe that is what your asking?
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#1906158 - 05/31/12 06:20 PM Re: Alternate names for intervals [Re: Morodiene]
Gary D. Online   content
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Originally Posted By: Gary D.

I am going to start with something that may seem very obvious, but I don't think it is.

First, a statement: it is very clear that a simple tritone will show up with equal frequency as an aug4 or a dim5.

Originally Posted By: Morodiene

Technically, wouldn't the aug4 br written as a 4th with a sharp on the top note (except for the B-F one),

No. Bb-E is an aug 4th. No sharp. C#-Fx has a double sharp on top. But perhaps you mean simply to raise the 4th? I may misunderstand what you are saying! smile
Quote:

and a dim5 be written as a 5th with a flat on the top note? Or are you not concerned with how it's spelled but rather how it's defined?

OK. I think we are trapped in terminology. In a chord, #4 means to raise a P4 1/2 step. b5 means to lower a P5 by 1/2 step. Is that what you mean?

Let me clarify that first...


Edited by Gary D. (05/31/12 07:06 PM)
Edit Reason: quotes screwed up
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#1906162 - 05/31/12 06:22 PM Re: Alternate names for intervals [Re: Gary D.]
Morodiene Offline
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Originally Posted By: Gary D.

OK. I think we are trapped in terminology. In a chord, #4 means to raise a P4 1/2 step. b5 means to lower a P5 by 1/2 step. Is that what you mean?

Let me clarify that first...


Yes, that is what I mean. A aug4 will always be written as a 4th altered somehow, and a dim5 will always be an altered 5th. smile
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#1906163 - 05/31/12 06:23 PM Re: Alternate names for intervals [Re: Legal Beagle]
Gary D. Online   content
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Originally Posted By: Legal Beagle
What gets a little dicy is the parameters of what you're asking. For example, what springs to my mind is Maj2 and min7. Same interval, two very common (but different) spellings and applications.

But maybe you'd say no, that's not the same interval, that's just an inversion... but so is your example of aug4/dim5, so maybe that is what your asking?

Not exactly.

C-F# is an aug4
C-Gb is a dim5

They are not inversions of each other.

C-F# and F#-C are inversions. But it is true that the tritone is the only interval that inverts yet retains the same sound.

What I had in mind was this:

Aug2, m3. Which is more common? At first glance it seem obvious. But in scales, the aug2 is very common - the harmonic minor scale is the most obvious example, but it can happen anywhere, since scales generally are formed alphabetically, when possible.


Edited by Gary D. (05/31/12 06:24 PM)
Edit Reason: typo
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#1906170 - 05/31/12 06:32 PM Re: Alternate names for intervals [Re: Gary D.]
PianoStudent88 Online   content
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[cross-posted with the world...]

Morodiene, couldn't an augmented 4th be written with a flat on the bottom note, and a diminished 5th with a sharp on the bottom note? For example, Ab-D, or G#-D. But I think Gary is disintinguishing between interval meaning sound, as determined by two physical keys on the keyboard, or two notes played on an instrument, or sung one after another; and comparing/contrasting that with interval meaning the name we give it.

For example, C-F#, C-Gb, B#-Gb, Dbb-E## all press the same two notes on the piano and sound exactly the same. But they all have different names: augmented fourth, diminished fifth, doubly-diminished sixth, quadrupally augmented second laugh . OK, some of these might practically never appear in music (although Gary is a walking encyclopedia of astonishing notation examples, so I will wait with eagerness for an example with my exotic Dbb-E##). But it shows that intervals as sound is a different thing from intervals as names.

Legal Beagle, is it fair to consider inversions as the same interval? They have neither the same sound nor the same name under any naming convention. They do contain the same two pitch classes, but surely there must be a name for "two pitch classes, considered as pitch classes rather than pitches" that doesn't overload the already overloaded word "interval"? Aug4/dim5 isn't just an inversion: both names can be played by the exact same two physical notes: middle-C and F# above, or middle-C and Gb above. Same sound, regardless of what you call the notes.


Edited by PianoStudent88 (05/31/12 06:33 PM)
Edit Reason: cross-post
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#1906182 - 05/31/12 06:52 PM Re: Alternate names for intervals [Re: PianoStudent88]
Legal Beagle Offline
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Originally Posted By: PianoStudent88
[cross-posted with the world...]
Legal Beagle, is it fair to consider inversions as the same interval? They have neither the same sound nor the same name under any naming convention. They do contain the same two pitch classes, but surely there must be a name for "two pitch classes, considered as pitch classes rather than pitches" that doesn't overload the already overloaded word "interval"? Aug4/dim5 isn't just an inversion: both names can be played by the exact same two physical notes: middle-C and F# above, or middle-C and Gb above. Same sound, regardless of what you call the notes.

Yes, of course. Didn't mean to confuse the issue, just playing a little Devil's advocate with the boundaries. Sorry, carry on and don't mind me.
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#1906183 - 05/31/12 06:55 PM Re: Alternate names for intervals [Re: Gary D.]
keystring Offline
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I've been hung up on the idea of how intervals are taught for quite a while. Intervals have two sides to them: what they are (what we hear - the distance between notes), and how they are named. If we distinguish between the two from the beginning, I suspect that things will be a lot clearer.

The "IS" --- An interval is a distance between two notes. When played together a given interval will have a particular quality of sound such as a "minor second" setting your teeth on edge, the "minor third" being smooth and sad, while the "major third" is smooth and happy (this is subjective of course). If we want to measure that distance, like when using inches on a measuring tape, we might think of semitones or tones.

The "NAMING" --- Involves the actual written notes that appear on the page. For this we count how many notes are involved (CE and CEb are some kind of 3rd because they involve three notes C,D,E). The qualities for each interval are called "major", "minor", "diminished", or "augmented" and these come from what got invented via a major scale and the diatonic notes of that scale - everyone here knows that part.

So we get CD# and CEb, one being called an augmented 2nd, the other a minor 3rd, but on the piano they both create the same quality, use the same piano keys, and the distance we measure between the two keys or pitches is the same. The thing that's the same is the "is" part. It's what we hear.

The Tritone is the only interval name that actually refers purely to the "is" --- refers to what we hear whether it is called an aug4 or a dim5. Of course somebody can turn this around and say "The tritone can have two spellings".

I don't know if this is useful to anyone else, but to me it seems important.

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#1906188 - 05/31/12 07:00 PM Re: Alternate names for intervals [Re: Legal Beagle]
keystring Offline
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Legal Beagle, I'm familiar with what you wrote. We learned a handy rule of 9: CA is a maj6, AC is a min3, 6 + 3 = 9, and each interval type when inverted because the opposite of the other (major becomes minor etc.) They fit together, but they are not the same interval. A maj6 does not sound like a min3, while an aug2 does sound like a min3.

For tritones, I understand that they are written either as 5ths or 4ths - the 5th is lowered a half step, and the 4th is raised a half step. I can't imagine a funky tritone with a double sharped third (CEx) - so is it safe to say that in the real world tritones are ONLY written as 4ths or 5ths?

Btw, as I understand it, the aug4 and dim5 are the only intervals that DO stay the same interval when reversed --- they both remain tritones, whereas for example a major chord, inverted, becomes a minor chord etc.

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#1906190 - 05/31/12 07:01 PM Re: Alternate names for intervals [Re: PianoStudent88]
Gary D. Online   content
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Originally Posted By: PianoStudent88
[cross-posted with the world...]
Morodiene, couldn't an augmented 4th be written with a flat on the bottom note, and a diminished 5th with a sharp on the bottom note? For example, Ab-D, or G#-D. But I think Gary is disintinguishing between interval meaning sound, as determined by two physical keys on the keyboard, or two notes played on an instrument, or sung one after another; and comparing/contrasting that with interval meaning the name we give it.

That is exactly correct.

For those who have not stumbled over these notation problems, I think we have a good analogy in English:

Thair could be a phonetic spelling for three words, including a contraction. In internation phonetics there is a symbol for "th", for the vowel sound in air, stare, pear, and so on. There is also a symbols for the final "r" sound, and that might be omitted for the British pronunciation.

There are obvious advantages in have precise, phonetic symbols. We avoid the problem of there, their, and they're. However, we also lose grammar, and we lose the ability to trace back in time where these spellings came from.

Music notation is not nearly so bizarre as English spelling, but its rules are complex. Notation provides us with additional information, so the various choices we have about how to spell a chord (or other things) have many potential advantages.

The disadvantage is that we lose the pure sound. When we are in equal temperament, a tritone is what it is. It is a sound. Spelling does not even enter our minds when an interval is isolated.

In contrast, a M7 written any other way than the standard way (C-B, F#-E#, Bb-A) is very unusual. I do have an example of when it is written in this manner: E-Eb, which becomes a diminished octave. That happens in a variant spelling of a sharp 11 chord, which I would be interested in discussing in another thread, at another time. smile
Quote:

For example, C-F#, C-Gb, B#-Gb, Dbb-E## all press the same two notes on the piano and sound exactly the same. But they all have different names: augmented fourth, diminished fifth, doubly-diminished sixth, quadrupally augmented second laugh . OK, some of these might practically never appear in music (although Gary is a walking encyclopedia of astonishing notation examples, so I will wait with eagerness for an example with my exotic Dbb-E##). But it shows that intervals as sound is a different thing from intervals as names.

At the moment I can't imagine a tritone being written other than in the two standard ways. Now, having said that, I may run into an exception in the next 24 hours. Usually intervals go no farther than diminished or augmented, and that is generally true for 3rds, 6ths and 7ths. So, for instance, finding an alternate spelling for a P5 will be very hard, or an example of this happening will be hard to find. Generally you can simply rule out doubly diminshed or augmented intervals as so bizarre that you simply don't ever have to worry about them unless you run into one - at which point you will probably do what I do, curse the composer! laugh
Quote:

Legal Beagle, is it fair to consider inversions as the same interval? They have neither the same sound nor the same name under any naming convention. They do contain the same two pitch classes, but surely there must be a name for "two pitch classes, considered as pitch classes rather than pitches" that doesn't overload the already overloaded word "interval"? Aug4/dim5 isn't just an inversion: both names can be played by the exact same two physical notes: middle-C and F# above, or middle-C and Gb above. Same sound, regardless of what you call the notes.

It is useful to mentally link inverted intervals, but to use the same name for them will usually result in great confusion. We could, for instance, say that a M2 is an inversion of a m7, or vice versa, but we don't want to give them the same name. Now, having said that, what happens when we invert a G7 chord? Well, the G-F, m7, becomes a M2, if we do not consider open voicings. So the concept of inverting intervals is useful.
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#1906196 - 05/31/12 07:08 PM Re: Alternate names for intervals [Re: Morodiene]
Gary D. Online   content
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Originally Posted By: Morodiene
Originally Posted By: Gary D.

OK. I think we are trapped in terminology. In a chord, #4 means to raise a P4 1/2 step. b5 means to lower a P5 by 1/2 step. Is that what you mean?

Let me clarify that first...


Yes, that is what I mean. A aug4 will always be written as a 4th altered somehow, and a dim5 will always be an altered 5th. smile

Exactly!!!

Sorry for my mix-up. That's why I checked! wink
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#1906214 - 05/31/12 07:37 PM Re: Alternate names for intervals [Re: keystring]
Gary D. Online   content
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Originally Posted By: keystring
I've been hung up on the idea of how intervals are taught for quite a while. Intervals have two sides to them: what they are (what we hear - the distance between notes), and how they are named. If we distinguish between the two from the beginning, I suspect that things will be a lot clearer.

I agree.
Quote:

The "IS" --- An interval is a distance between two notes. When played together a given interval will have a particular quality of sound such as a "minor second" setting your teeth on edge, the "minor third" being smooth and sad, while the "major third" is smooth and happy (this is subjective of course). If we want to measure that distance, like when using inches on a measuring tape, we might think of semitones or tones.

Yes, but what I would like to get away from, for sound only, are the names you just used. I would prefer half step, step or whole step, etc.

m3 could be called a quarter octave, just as a tritone is a half octave.

M3 could be called a double-step. I would prefer to teach intervals by number only, 2 3 4 5 6 7, as an intro and use the other descriptions I just used to fine tune the exact distance. I need this for my very young students, but it also helps my older students.

I will GET the standard names later. I am not really doing anything new, but the order in which I present things is reversed.
Quote:

The "NAMING" --- Involves the actual written notes that appear on the page. For this we count how many notes are involved (CE and CEb are some kind of 3rd because they involve three notes C,D,E). The qualities for each interval are called "major", "minor", "diminished", or "augmented" and these come from what got invented via a major scale and the diatonic notes of that scale - everyone here knows that part.

And perfect - p4 and p5, for example.
Quote:

So we get CD# and CEb, one being called an augmented 2nd, the other a minor 3rd, but on the piano they both create the same quality, use the same piano keys, and the distance we measure between the two keys or pitches is the same. The thing that's the same is the "is" part. It's what we hear.

Which is why I am suggesting "quarter octave". For those who already know the conventional system, this may be annoying, but I know for a fact that it helps beginners.
Quote:

The Tritone is the only interval name that actually refers purely to the "is" --- refers to what we hear whether it is called an aug4 or a dim5. Of course somebody can turn this around and say "The tritone can have two spellings".

But your point is correct. I would add that the octave is almost 100% standard in its spelling, and both the P4 and P5 are very close to 100% standard. And we can take care of m2 and M2 with 1/2 step and (whole) step. The problem intervals for using just one name are the 3rds, the 6ths and the 7ths. smile
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#1906231 - 05/31/12 08:27 PM Re: Alternate names for intervals [Re: Gary D.]
LadyChen Offline
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Originally Posted By: Gary D.
So, for instance, finding an alternate spelling for a P5 will be very hard, or an example of this happening will be hard to find. Generally you can simply rule out doubly diminshed or augmented intervals as so bizarre that you simply don't ever have to worry about them unless you run into one - at which point you will probably do what I do, curse the composer! laugh


You may see a double aug fourth (AA4th) -- here is my example pulled from the aug6 chord thread:

"Due to some of the awkward voice leading (and confusing accidentals), you'll sometimes see the perfect 5th in a Ger6 chord spelled as a double augmented 4th .. and yes, it is ironic that doing so makes things simpler lol. So.. a ger6 chord built on Eb .. you get Eb, G, C# and A# (instead of Bb). We do this because, in voice leading, there is a general rule that raised notes should resolve upwards and lowered notes should resolve downwards.

In the example of the Ger7 chord spelled Eb G C# A#, it resolves to a V6/4 - V5/3 (in this example - D). When you spell the Bb enharmonically as A#, the A# resolves upwards to B. This is preferred to a Bb resolving upwards to B."

I just looked this up in my book, and one of the examples is Beethoven's Piano Sonata op. 57, second movement, mm 6. The last eighth note of the bar spells a ger6 chord as Bbb-E (there's your AA4th) -G-Db. Yikes. I don't think it's terribly common though.

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#1906252 - 05/31/12 09:36 PM Re: Alternate names for intervals [Re: PianoStudent88]
Morodiene Offline
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Originally Posted By: PianoStudent88
[cross-posted with the world...]

Morodiene, couldn't an augmented 4th be written with a flat on the bottom note, and a diminished 5th with a sharp on the bottom note? For example, Ab-D, or G#-D. But I think Gary is disintinguishing between interval meaning sound, as determined by two physical keys on the keyboard, or two notes played on an instrument, or sung one after another; and comparing/contrasting that with interval meaning the name we give it.

For example, C-F#, C-Gb, B#-Gb, Dbb-E## all press the same two notes on the piano and sound exactly the same. But they all have different names: augmented fourth, diminished fifth, doubly-diminished sixth, quadrupally augmented second laugh . OK, some of these might practically never appear in music (although Gary is a walking encyclopedia of astonishing notation examples, so I will wait with eagerness for an example with my exotic Dbb-E##). But it shows that intervals as sound is a different thing from intervals as names.



Please see my clarification with Gary's post afterwards. I was just saying that anything called an aug4 would have to be some form of 4th, and I had given the sharped top note as an example of such, but not the ONLY way something could be aug4.
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#1906257 - 05/31/12 09:47 PM Re: Alternate names for intervals [Re: Gary D.]
PianoStudent88 Online   content
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Now I understand. Thank you, Morodiene.
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#1906275 - 05/31/12 10:59 PM Re: Alternate names for intervals [Re: Gary D.]
keystring Offline
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Originally Posted By: Gary D.
And we can take care of m2 and M2 with 1/2 step and (whole) step. The problem intervals for using just one name are the 3rds, the 6ths and the 7ths. smile

I see what you are saying. I am thinking, however, of calling these things: whole step & half step; semitone & tone (Cdn, British); tritone; quarter octave & octave --- as descriptions and/or measurements. I am thinking of reserving the word "name" for the "grammar" part. We WILL run into terms like "minor 3rd, augmented 2nd" etc., and they do have their place because of the grammar in music. I think it is important to be aware of these two aspects so that we don't mix them up (or get mixed up by them). What do you think?

The on the "what it is / what it sounds like / pure measurement" side, the idea of half octave and quarter octave has tickled my imagination. I suppose that the "major third" could be seen as a 1/3 octave if it had any use which it probably does not. It is, however, another division of the octave which we can see when we think of the augmented chord.

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#1906339 - 06/01/12 02:42 AM Re: Alternate names for intervals [Re: Gary D.]
Nikolas Offline
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I'm not sure I'm following this thread and the recent threads fully. Though I'm enjoying them as heck, so keep them up! (And thanks Gary and Keystring mainly (and morodiene) for offering so much already).

Now...

I'm not sure this came up, but even if the aug4th and dim5th are the same pitches, in effect they are used differently and for different reasons. This applies to most tonal music. (eg. C-F# would be resolved to B(b)-G, while C-Gb would be resolved to Db-F(b)). The spelling is there to help with the grammar. An exception to that is always voice and melody leading... As mentioned in the example by LadyChen!

I will agree that it tends to be confusing for beginners, and I will also confess that in my own writings, drafts and scores I very rarely will use this system. I have my own numbering (1-12... duh!) and it serves me fine for my purposes!

Finally, I should note that in other instruments (strings, for example and winds... everything else anyhow) things are NOT equal. An aug4 will tend to sound a bit different than a dim5th! We pianists are so content to have our very specific and set keyboard and forget what's going on outside this! I know for a very fact that if I write a melody as such: C - F# - E the F# will be a bit off for most violinists and it will be my will to do so (especially in a very complicated music). If, on the other hand, I go C - Gb - E the Gb will come closed to the F and thus to the E eventually...
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#1906341 - 06/01/12 02:45 AM Re: Alternate names for intervals [Re: Gary D.]
Nikolas Offline
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Gary, something I missed in my previous post (dang this forum software!!!)

Quote:
In contrast, a M7 written any other way than the standard way (C-B, F#-E#, Bb-A) is very unusual. I do have an example of when it is written in this manner: E-Eb, which becomes a diminished octave. That happens in a variant spelling of a sharp 11 chord, which I would be interested in discussing in another thread, at another time.
Actually in contemporary music it's far from uncommon! Apart from the reasons I mentioned above in other instruments, I frequently run into trouble with my bizarre chords. E-Eb might be uncommon, but... E-Eb-Bb-D is another issue altogether. Because if you go for D# instead of Eb, then you have to go to A# instead of Bb and then there's this bizarre A#-D coming your way which is not fine. In which case you put a natural on the bottom note (the natural E) to make sure nobody's confusing it as an octave and you're done!

(And this is why my proof readers do NOT like me! grin)
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#1906346 - 06/01/12 03:15 AM Re: Alternate names for intervals [Re: Nikolas]
Gary D. Online   content
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Originally Posted By: Nikolas

I'm not sure this came up, but even if the aug4th and dim5th are the same pitches, in effect they are used differently and for different reasons. This applies to most tonal music. (eg. C-F# would be resolved to B(b)-G, while C-Gb would be resolved to Db-F(b)). The spelling is there to help with the grammar. An exception to that is always voice and melody leading... As mentioned in the example by LadyChen!

Yes, but there is extreme chromaticism right in the middle of tonality. There is a mixture. I posted a reference to a famous Chopin Etude where tritones are used chromatically, and I assure you there is no connection between the choice of aug4 or dim5 and pitch, and there would not be on any instrument.

Then there is another factor: even if we consider a temperament that is extremely different from equal temperament - for example mean tone - the unevenness of intervals has nothing to do with their spelling but rather their position on the keyboard. The dreaded "Wolf Tone", Ab - Eb, is equally horrendous no matter how you spell it. Minor thirds change in each key. Everything changes in every key. So if you play a harmonic minor scale in all keys, the aumented 2nd will be flat or sharp according to the blasted tuning, not according to our preference.

In contrast, stringed instruments have no fixed pitch. There you can "tweak" your intervals as you wish. However, I would argue that adjusting intervals is an intuitive thing, and when it is taught through a system, it won't work well. C F# G will make an intuitive musician want to do something to F#, not because it is written as an F#, but because it tends to sound better a bit sharp.

C Gb F, because of the half step down and the nature of the perfect 5th, is very likely to cause the player (or singer) to shade the tritone a bit lower.

More: what if these intervals are not notated? Then we listen, we play. We shape pitch intuitively, and the possible spelling when notated has nothing to do with it.

Now, what if we learn to blindly use notation to shape our pitches? My argument is that puts the cart before the horse.

One other thing: the amount that pitch is shaded or adjusted in a full orchestra is greatly ruduced by the time you get to very chromatic Romantic music. There you have many instruments, and each wind instrument has certain notes that are sharp or flat to the tempered scale - built in idiosyncracies. The same pitch can be and is flat on one instrument, sharp on another. Trying to make all these different instruments conform to any theoretical non-tempered tuning system when modulation is going on continually would produce chaos.

On the other hand, if something is in a fixed key and very diatonic, no modulations, THEN different tuning tweaks can be used, and some conductors insist on them.
Quote:

I will agree that it tends to be confusing for beginners, and I will also confess that in my own writings, drafts and scores I very rarely will use this system. I have my own numbering (1-12... duh!) and it serves me fine for my purposes!

On piano I want my young students to absolutely nail major and minor triads, root position, in all keys. I want them to have dom7 chords in all keys, root position. For me major and minor serves as "home base" for three note chords, not counting doublings, and the dom7 is home base for all sorts of seven chords. For something like a dom7 chord, the moment we start talking about how to write them, I stress four lines or four spaces. That seems logical to me. The trick is to add flats or sharps, never both, until what is notated produces the sound we already know.

This sounds easy, but of course it is not for most students - as you know!

I teach two things at the same time: playing chords by feel/ear, independent of musical notation, and playing notation, following it exactly. To me these are two extremes. One is creative, intuitive, free, exploratory, and when exploring no sound is wrong.

The other involves paying attention to as many composers as possible, subconsciously absorbing their styles and their notational preferences.

In a perfect world those two extremes would merge, and we would have complete musicians. If only that happened more often. frown
Quote:

Finally, I should note that in other instruments (strings, for example and winds... everything else anyhow) things are NOT equal. An aug4 will tend to sound a bit different than a dim5th! We pianists are so content to have our very specific and set keyboard and forget what's going on outside this! I know for a very fact that if I write a melody as such: C - F# - E the F# will be a bit off for most violinists and it will be my will to do so (especially in a very complicated music). If, on the other hand, I go C - Gb - E the Gb will come closed to the F and thus to the E eventually...

This idea is very different for winds. Wind instruments are in tune with themselves, and adjusting is called "lipping". There are weird problems, and I will give you just one:

On trumpet an E is played 12, second line in the treble. A very good player will be able to lower the pitch, because 1 and 1 together are sharp, but there is a limit to how fast the first valve slide can be moved. In faster passages, the note is sharp. End of story. The octave above is played open, and it is flat, about 13 cents. Yes, you can lip it up, but in faster passages you will always hear that it is flat. Without perfect pitch you can tell what key a trumpet player is in by these idiosyncracies. A medium speed scale sounds radically different in each key, and that quality is fixed, as in non-tempered piano tunings.

Woodwinds have similar problems. If you listen carefully, you will hear that the greatest clarinet players in the world play a little flat in their low register. High notes inevitably go sharp. Ask a trumpet player hitting high G to shade the pitch down, and he will laugh at you. That note is so high, just hitting it every time is a major accomplishment. Even on trombone, where most positions can be shaded, if a first position note is flat (because of the nature of harmonics) there is nothing to be done except to lip it up unless the player is using an unusual system in which he plays ALL positions a bit further out and compensates by pushing in the main tuning slide.

That just skims to surface. smile

I would say that stringed instruments and the human voice have the greatest pitch flexibility. There a soloist can and often does bend everything, in much the way you described!
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#1906352 - 06/01/12 03:31 AM Re: Alternate names for intervals [Re: LadyChen]
Gary D. Online   content
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Originally Posted By: LadyChen

"Due to some of the awkward voice leading (and confusing accidentals), you'll sometimes see the perfect 5th in a Ger6 chord spelled as a double augmented 4th .. and yes, it is ironic that doing so makes things simpler lol. So.. a ger6 chord built on Eb .. you get Eb, G, C# and A# (instead of Bb). We do this because, in voice leading, there is a general rule that raised notes should resolve upwards and lowered notes should resolve downwards.

In the example of the Ger7 chord spelled Eb G C# A#, it resolves to a V6/4 - V5/3 (in this example - D). When you spell the Bb enharmonically as A#, the A# resolves upwards to B. This is preferred to a Bb resolving upwards to B."

You are exactly right! The Beethoven example could have been written several ways, and his spelling there is illogical vertically but very logical horizontally. That's where the weird intervals occur, when two or more voices are moving chromatically, often in opposite directions.

In a strange way this is consistent. We know, for instance, that a M3 and a dim4 are both common. You don't have to go any farther than C E Ab to see that, Caug, which is correct spelling if the next chord is C F Ab - Caug to Fm/C.

In the same manner, you can have this:

D-G moving outward to Db-G# to C-A. I can't think of a practical place to do that, but I'm sure sooner or later I will find it.

I think in general that the moment we think something is too weird to be used, someone uses it, and effectively. That said, I can't think of any standard interval, by number that is TRIPLY shrunk of expanded.

Cb E# would be a doubly augmented 3rd. Would anyone use that. Hmm...

I can't think of a place where I have seen that.

I THINK we can content ourselves with sticky to intervals that have two common ways of being written, with roughtly equal frequency, and others that have two ways where one is far more common that that other but where the uncommon one is still used a LOT and is very useful.

For the latter idea, m7/aug6 is probably a good example. C-Bb is going to be much more common than C-A#, but C-A# is important for augmented 6th chords, and those appear quite frequently. smile
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#1906354 - 06/01/12 03:37 AM Re: Alternate names for intervals [Re: keystring]
Gary D. Online   content
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Originally Posted By: keystring
Legal Beagle, I'm familiar with what you wrote. We learned a handy rule of 9: CA is a maj6, AC is a min3, 6 + 3 = 9, and each interval type when inverted because the opposite of the other (major becomes minor etc.) They fit together, but they are not the same interval. A maj6 does not sound like a min3, while an aug2 does sound like a min3.

Musical math:

3+3=5
3+3+3=7
3+3+3+3=9

The reason is that our weird tradional system double counts notes. It is like saying, "Take three steps," then counting your starting place as the first step. It is counter-intuitive, but we are stuck with it.
Quote:

For tritones, I understand that they are written either as 5ths or 4ths - the 5th is lowered a half step, and the 4th is raised a half step. I can't imagine a funky tritone with a double sharped third (CEx) - so is it safe to say that in the real world tritones are ONLY written as 4ths or 5ths?

It is safe to say that anything else is going to be highly unusual, but don't rule it out! Just be ready to curse. laugh
Quote:

Btw, as I understand it, the aug4 and dim5 are the only intervals that DO stay the same interval when reversed --- they both remain tritones, whereas for example a major chord, inverted, becomes a minor chord etc.

That is correct.
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#1906434 - 06/01/12 09:12 AM Re: Alternate names for intervals [Re: Gary D.]
apple* Offline


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this is all above my head. I never learned any of this stuff. I can easily recognize 4ths, 6ths, 5ths.. that's about it. I don't know why that is even important unless one is a singer.
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#1906451 - 06/01/12 10:05 AM Re: Alternate names for intervals [Re: Gary D.]
keystring Offline
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Originally Posted By: Gary D.
Originally Posted By: keystring
Legal Beagle, I'm familiar with what you wrote. We learned a handy rule of 9: CA is a maj6, AC is a min3, 6 + 3 = 9, and each interval type when inverted because the opposite of the other (major becomes minor etc.) They fit together, but they are not the same interval. A maj6 does not sound like a min3, while an aug2 does sound like a min3.

Musical math:

3+3=5
3+3+3=7
3+3+3+3=9

The reason is that our weird tradional system double counts notes. It is like saying, "Take three steps," then counting your starting place as the first step. It is counter-intuitive, but we are stuck with it.


For the "naming" system, which is the one that is usually taught first traditionally, I count how many notes are involved in terms of note names. It is not complicated. CE involves 3 notes C,D,E. EC involves 6 notes. We don't have to worry about sharps or flats for counting how many notes are involved: E,F,G,A,B,C = 6. It is as simple as counting a row of toys. This little trick of 6 + 3 = 9 is handy for checking yourself since it is faster to count to 3 than to count to 6, but really, it isn't necessary.

I've had this idea of 3 + 3 = 5 presented to me before. Here is what I see: A family comes to visit: John, Mary, and Dot. John and Mary are husband and wife: 2 people. Mary and Dot are mother and daughter: 2 people. There are 3 people all together: 2 + 2 = 3. Same thing, no? But I would never think of it this way, because it would be confusing, and it doesn't help me. Yes, in CEG you have a major 3rd from C to E, and a minor 3rd from E to G, and P5 from C to G, but to me that is like John, Mary, and Dot. We've already counted the E; and to find the interval of C to G I don't have to add the two thirds, I can just see how far G is from C.

I can see, however, how a student might look at our CEG and say "Wait a minute. I know CE is a major 3rd, EG is a minor 3rd, CG is a P5 - so a third and another third makes a 5th? That doesn't add up."

For anyone mystified by the math:
Quote:
3+3=5
3+3+3=7
3+3+3+3=9

3+3=5 is referring to something like this: CEG: CE = major 3, EG = minor 3, CG = P5. We have a major 3rd plus a minor 3rd in the chord but altogether the chord spans a P5.

3+3+3=7. CEGB. same as above, plus GB = a major 3rd. From the lowest note to the top note we have a major7, since CB is maj7.

I've never added up intervals. To me it's like they are lined up in a row and if I want to see the distance between any two notes, I look at that distance. I don't think about it a lot, I just do it. The beauty about music is that even though it can look complicated, it usually has some simple principals sitting underneath.

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#1906475 - 06/01/12 10:45 AM Re: Alternate names for intervals [Re: apple*]
keystring Offline
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Originally Posted By: apple*
this is all above my head. I never learned any of this stuff. I can easily recognize 4ths, 6ths, 5ths.. that's about it. I don't know why that is even important unless one is a singer.

A lot of the things in this thread look complicated. Stuff in theory books can look complicated too. When working with harmony theory we work with chords, and chords have intervals; voice leading rules involve intervals. We can't get away from them. But I believe that if we can get to a basic understanding first, then we can always go back to some very simple things. However it seems that theory often seems to spend next to no time on the rudiments, glossing over them, so we don't get that first solid thing to rely on.

I'd go for two fundamental things, and this is how I taught it for getting at those fundations:

First fundamental: The most basic and fundamental thing is what intervals actually are. They are a distance between two notes. If we use an actual measuring device such as semitones / half steps (two names for the same thing), then we can see this distance. We can hear this: BC, F#G, AbA or G#A - strike two adjacent piano keys and we hear a common quality to this tiny interval. We hear what is the same about it regardless of where we play it.

For the "what it is" we can also explore the intervals before learning to name them anything. CD, CE, CF, CG.... how does each of them "feel" to you? Do they all feel the same? Is one more or less pleasant? This is very fundamental, but maybe if someone plays CF# and then feels relief with CG, later things in music make sense. What about encouraging exploration from a very early time. Then later when music gets complicated, go back to this same simple exploration to get one's bearings. Essentially that's the tack I tried when we went to complicated theory, and it seemed to work.

I believe it is absolutely essential to distinguish between what an interval is, getting in touch with the reality of it, and on the other hand, how intervals get named. I know the subject is "alternate names for intervals", but before we can even go there we have to look at intervals in the raw. Otherwise it is easy to get lost. On the other hand, if we have a firm foothold on the "what it is" side, we have something to fall back on.

Second fundamental: Naming: The fact that there are naming conventions which have to do with the grammar of written notation. Otherwise we can be stuck with learning early on that the sound we hear "is" a major 3rd, and later when we hear that same sound it "is" an augmented 2nd, with a hasty note that, well, we call these "enharmonic equivalents". If on some level we have a grasp that this quality of sound is what it is as per above, and that it is clothed in different names, then it's not a big deal. But if we think that the name defines it 100%, it can muddy up everything.

There is a different fundamental principal going on with the naming of intervals. It is very simple. We count how many note names are involved - nothing more than that at its simplest level. If there are 3, then it's a 3rd. If there are 5, then it's a 5th. The biggest problem is in overthinking it, and trying to see meaning in it. There isn't any. That's it.

Then we go about memorizing or in some way learning what major and perfect intervals are, which is easiest done via a C major scale, always counting up from the tonic. Anything a half step below a major is a minor. The perfects are I, IV, V & octave. Getting at diminished and augmented is a next stage, simply a matter of one more half step.
------------------
If we have these two sides of it, then we can wend our way through all the complicated grammar rules that come up. The "obvious and simple things" sitting at the bottom are what helps make sense of everything else.

When we got to the more complicated theory, the temptation was to get cerebral. But that was the time to go right back to the beginning, and get at it from these two points of view.

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#1906622 - 06/01/12 03:43 PM Re: Alternate names for intervals [Re: keystring]
LadyChen Offline
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Originally Posted By: keystring
I've never added up intervals. To me it's like they are lined up in a row and if I want to see the distance between any two notes, I look at that distance. I don't think about it a lot, I just do it. The beauty about music is that even though it can look complicated, it usually has some simple principals sitting underneath.


I only have one student right now who can glance at a solid interval, and name it immediately just by how it is shaped visually on the staff. My others either count the lines and spaces between the notes, or name the two notes and then figure out how far apart they are. I don't know how to get them to that next stage of instant recognition. Maybe just through repetition?

(As background info, none of my students have been studying for more than 2 years)

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#1906784 - 06/01/12 08:51 PM Re: Alternate names for intervals [Re: LadyChen]
Gary D. Online   content
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Originally Posted By: LadyChen
Originally Posted By: keystring
I've never added up intervals. To me it's like they are lined up in a row and if I want to see the distance between any two notes, I look at that distance. I don't think about it a lot, I just do it. The beauty about music is that even though it can look complicated, it usually has some simple principals sitting underneath.


I only have one student right now who can glance at a solid interval, and name it immediately just by how it is shaped visually on the staff. My others either count the lines and spaces between the notes, or name the two notes and then figure out how far apart they are. I don't know how to get them to that next stage of instant recognition. Maybe just through repetition?

(As background info, none of my students have been studying for more than 2 years)

My situation is not different at all, really, with those who have only played two years or less.

I THINK that people learn to play things, and that makes a link between what they feel and what they hear.

For instance, if you can get your young students to play major and minor chords, triads, in all keys, just by feel, two things may happen:

1) They may start to associate the sound of major/minor with the feel of these chords.

2) They may develop a primitive understand of intervals through the chords themselves, separate from notation.

I find that most people will pick up the idea that the "outside" of these root positoin triads are perfect 5ths. They can "extract" the 5th from the chords. From that they can easily learn that all P5s are the same color except for Bb-F and B-F# - two white keys or two black keys.

From there we can count black keys and reason out why F-B and B-F are actually the same "size", and why they need to be "adjusted" to make the 5ths we need for major/minor chords.

Once the P5 is in place, major and minor triads allow us to point out that we have two different sized 3rds, a big one and a small one. Again, we can count keys. I teach major/minor as a 3rd finger toggle, all keys, both hands.

From there it seems easy. I don't give a hoot about interval names, the traditional ones - in the beginning. I think they are horrendously confusing if taught FIRST. Later they become necessary.

Instead, we say as my students are reading music: "Oh, what do we have here? Can you see how that is an Eb major chord, but SCRAMBLED? Look, I'll play the chord, the simple way. Now, you compare your chord with mine. Can you find an Eb? And a G? And a Bb? We can spread them all over the place. We can clone them. We can put any of those three notes on the bottom, any on the top. We can space them out wide. We can both play them at the same time. We can run them up and down the whole keyboard."

That approach seems to get the essence of what major and minor chords are, and how to begin recognizing that they can be scrambled in a near infinity of ways.

When THAT knowledge is in place, then I worry about naming the intervals.

Does that make any sense? smile


Edited by Gary D. (06/01/12 08:55 PM)
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#1906808 - 06/01/12 09:45 PM Re: Alternate names for intervals [Re: Gary D.]
LadyChen Offline
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Originally Posted By: Gary D.
Does that make any sense? smile



That makes lots of sense. It's completely backwards from how we traditionally teach, but that makes it even more appealing to me! lol

I have one student, okay maybe my *favorite* student, who is exactly how I was as a beginner. You can't teach him any 'rules' unless he knows why he's doing it. He constantly asks "why?" and I LOVE it. It's an especially awesome lesson if he manages to stump me and I have to tell him I'll find out and get back to him at his next lesson. We learn the theory stuff in his little method book, but he asks so many questions that we're actually getting into fairly advanced concepts considering he's in book 1 of his method series. He would latch on to major and minor triads in under five minutes, and I think he would have a lot of fun with them. I can already predict that he will dislike major triads but enjoy playing minor triads fortissimo at the low end of the piano wink.

My others are just starting to learn about whole steps and half steps in their method book. It would probably be a perfect time to introduce major and minor triads for them. I'll give it a try next week and report back smile.

Originally Posted By: Gary D.
Cb E# would be a doubly augmented 3rd. Would anyone use that. Hmm...


I've been forcing myself to play in key signatures with lots of sharps because I'm scared of them, and have been playing more 20th c music lately, so I'm going to keep a look out for the AA3rd. I wouldn't be surprised to find one .. composers do some crazy stuff.

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#1907157 - 06/02/12 02:05 PM Re: Alternate names for intervals [Re: LadyChen]
Gary D. Online   content
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Originally Posted By: LadyChen
Originally Posted By: Gary D.
Does that make any sense? smile

That makes lots of sense. It's completely backwards from how we traditionally teach, but that makes it even more appealing to me! lol

I don't believe great teachers, teaching little children, EVER taught in the way we are told is traditional. I doubt there was much tradional about how Mozart's father taught young Mozart.

Where teachers go wrong, in my opinion, is that they find things that are logical to young children, then assume they will not be logical to older kids and adults.
Quote:

I have one student, okay maybe my *favorite* student, who is exactly how I was as a beginner. You can't teach him any 'rules' unless he knows why he's doing it. He constantly asks "why?" and I LOVE it. It's an especially awesome lesson if he manages to stump me and I have to tell him I'll find out and get back to him at his next lesson. We learn the theory stuff in his little method book, but he asks so.

I LOVE being stumped. It means I get to learn something new!
Quote:

[...] many questions that we're actually getting into fairly advanced concepts considering he's in book 1 of his method series. He would latch on to major and minor triads in under five minutes, and I think he would have a lot of fun with them. I can already predict that he will dislike major triads but enjoy playing minor triads fortissimo at the low end of the piano wink

If you can teach anyone all the majors and minor at once, that is highly unusual. I have to teach them by groups, color and feel, then work towards chromatic playing. And for minors, I have to teach them first as a "morph" from major - this includes the really smart students of all ages.

But people definitely have feelings about chords. Many of my students like experimenting with minors played randomly, because ANY combination sounds like some freaky TV show or movie they have seen. smile
Quote:

My others are just starting to learn about whole steps and half steps in their method book. It would probably be a perfect time to introduce major and minor triads for them. I'll give it a try next week and report back smile.

I would do it this way: the moment they are able to play a simply C major chord, give them G and F. They all feel the same, so there is no coordination problem. And that is I IV and V.

Next teach A, D and E. It is easy for people to extend their longest finger to a black key, and this gives I IV and V in the key of A - which you don't even have to mention.
Originally Posted By: Gary D.
Cb E# would be a doubly augmented 3rd. Would anyone use that. Hmm...

Originally Posted By: LadyChen

I've been forcing myself to play in key signatures with lots of sharps because I'm scared of them, and have been playing more 20th c music lately, so I'm going to keep a look out for the AA3rd. I wouldn't be surprised to find one .. composers do some crazy stuff.

I've heard other people say that sharps are harder. I THINK that may be because the V7 of sharp keys are less common. That said, there are SO many famous pieces in C# minor, and there are many more than four sharps that actually show up in such pieces.


Edited by Gary D. (06/02/12 02:07 PM)
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#1907291 - 06/02/12 06:27 PM Re: Alternate names for intervals [Re: Gary D.]
LadyChen Offline
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Originally Posted By: Gary D.

I would do it this way: the moment they are able to play a simply C major chord, give them G and F. They all feel the same, so there is no coordination problem. And that is I IV and V.



Yeah, they are already playing pentascales in C and G, so I don't think picking out 1-3-5 will be too tough. And I like the idea of adding the "major-minor toggle".

Originally Posted By: Gary D.

I've heard other people say that sharps are harder. I THINK that may be because the V7 of sharp keys are less common. That said, there are SO many famous pieces in C# minor, and there are many more than four sharps that actually show up in such pieces.


I always thought it was because I played in wind ensembles for so many years -- winds tend to play in keys with flats. It was a challenge when I played with a full orchestra -- playing sharp keys on the trombone felt really weird. I love flats -- I would take 6 or 7 flats over 5 sharps any day. I need to find someone to transpose Bach's P&Fs in C# major into Db for me.... I could do it myself, but it seems like a lot of work.

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#1908450 - 06/04/12 08:39 PM Re: Alternate names for intervals [Re: Gary D.]
keystring Offline
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I just got the significance of this and went back to find the quote:
Originally Posted By: Gary D.
m3 could be called a quarter octave, just as a tritone is a half octave.

First off, a couple of years ago I ran into a new idea - getting a sense of theory via the instrument which fuses what we hear, feel in our hands, and theory from that angle as one thing.

Well, I know intellectually that an m3 (or aug2 etc.) is 1 1/2 whole tones, 3 semitones, the middle of C minor, and has a particular sound. I also know that 4 in a row give me a diminished 7 chord.

But here is another way of "perceiving it". First we have our "half octave" which cuts our octave directly in half, right at the tritone. Then when I have that tritone, I cut it in half again and I get a minor third. Instead of building a dim7 from a row of minor thirds, or some other way, I start with my octave, and slice it twice from big to little.

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#1908463 - 06/04/12 09:13 PM Re: Alternate names for intervals [Re: keystring]
LadyChen Offline
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Originally Posted By: keystring


But here is another way of "perceiving it". First we have our "half octave" which cuts our octave directly in half, right at the tritone. Then when I have that tritone, I cut it in half again and I get a minor third. Instead of building a dim7 from a row of minor thirds, or some other way, I start with my octave, and slice it twice from big to little.


It's nice to think of this mathematically. We have an octave made of 12 semi-tones. So how many ways can we divide it evenly?

- 6 whole tones (whole tone scale)
- 4 minor thirds (dim7 plus octave)
- 3 major thirds (augmented major triad plus octave)
- 2 tritones
- 1 octave

very nifty smile

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#1908468 - 06/04/12 09:21 PM Re: Alternate names for intervals [Re: Gary D.]
LadyChen Offline
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Loc: Canada

update -- I had two students today -- both have been with me for two years now. We had talked about half steps last week, and we did whole steps this week. They both already know their C and G pentascales by rote, but we analyzed them using whole steps and half steps and then built the F pentascale using the pattern. Then we built triads from the pentascales and I demonstrated happy triads and sad triads and how you could make the happy chord sad by lowering the 3 -- and wow, that was a hit lol. I had them show me their "happy" triads in C, F and G and then make them "sad".

One funny thing is that I'd already introduced flats and sharps to one of these girls but not the other. It was actually easier building the F pentascale with the one who *didn't* know about flats or sharps yet. She was completely focused on half steps and whole steps and not what the notes were 'called'. Maybe all these labels just get in the way of understanding patterns. Of course, we need something to call them eventually, but I'm starting to think I'll teach the concepts first and add the labels afterwards.

Another thing I have issues with is calling major and minor triads happy and sad... it's how I was taught when i was their age (7 or 8), and my students like it, but if the minor chord sounds sad, does the dim chord sound *really* sad? LOL! Anyway.. I think I will replace the happy and sad labels with major and minor next week to avoid all that confusion.


Edited by LadyChen (06/04/12 09:23 PM)

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#1908540 - 06/05/12 12:33 AM Re: Alternate names for intervals [Re: LadyChen]
AZNpiano Offline
5000 Post Club Member

Registered: 08/07/07
Posts: 5590
Loc: Orange County, CA
Originally Posted By: LadyChen
Another thing I have issues with is calling major and minor triads happy and sad... it's how I was taught when i was their age (7 or 8), and my students like it, but if the minor chord sounds sad, does the dim chord sound *really* sad? LOL!

Diminished chords sound "scary" and "evil."

Whatever works. Some kids are so tone deaf, nothing will get them to hear major/minor/diminished/augmented. Try getting them to hear the different 7th chords.
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#1908561 - 06/05/12 01:47 AM Re: Alternate names for intervals [Re: AZNpiano]
Nikolas Offline
5000 Post Club Member

Registered: 11/26/07
Posts: 5429
Loc: Europe
Originally Posted By: AZNpiano
Originally Posted By: LadyChen
Another thing I have issues with is calling major and minor triads happy and sad... it's how I was taught when i was their age (7 or 8), and my students like it, but if the minor chord sounds sad, does the dim chord sound *really* sad? LOL!

Diminished chords sound "scary" and "evil."
for my students the diminished chords sound 'magical' and there's a reference to the D minor Fantasy (Mozart... the first 'run' which ends up in CEbF#A... :D).
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#1908563 - 06/05/12 01:51 AM Re: Alternate names for intervals [Re: LadyChen]
Nikolas Offline
5000 Post Club Member

Registered: 11/26/07
Posts: 5429
Loc: Europe
Originally Posted By: LadyChen
very nifty smile
Same reason we have 12 months and 12 (24) hours in the day. Not to mention the 'dozen' and the fact that 13 is considered an extremely unlucky number in most societies!

________________

But...

Thing is that the one thing that I find fundamentally wrong in how we deal with intervals, and their definitions, is the fact that the first and the last note are included. I mean C - E is a third, because it's C, D, E... Then E - G is another third (E, F, G) and this is why if you turn it into math it screws up our brains (3+3=5, etc...). It's like those old twisted questions my father used to say, to prove that we had 11 fingers, instead of 10! (Count from 10 down to 6, including 10, and you have 1 hand left. Then ad the other 5 fingers bingo: You're up to 11! :D).
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#1908571 - 06/05/12 02:29 AM Re: Alternate names for intervals [Re: Nikolas]
LadyChen Offline
500 Post Club Member

Registered: 01/25/12
Posts: 521
Loc: Canada
Originally Posted By: Nikolas


But...

Thing is that the one thing that I find fundamentally wrong in how we deal with intervals, and their definitions, is the fact that the first and the last note are included. I mean C - E is a third, because it's C, D, E... Then E - G is another third (E, F, G) and this is why if you turn it into math it screws up our brains (3+3=5, etc...). It's like those old twisted questions my father used to say, to prove that we had 11 fingers, instead of 10! (Count from 10 down to 6, including 10, and you have 1 hand left. Then ad the other 5 fingers bingo: You're up to 11! :D).


Yeah, that messes up my students too. I always have to remind them to count the first and last note.

I only had one student (this year) ask why two thirds, C-E and E-G, didn't equal a sixth. He's very mathematical, so when I pointed out that his calculations were counting the E twice, he understood why 3+3=5. phew!

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#1908572 - 06/05/12 02:33 AM Re: Alternate names for intervals [Re: LadyChen]
Gary D. Online   content
4000 Post Club Member

Registered: 08/30/08
Posts: 4814
Loc: South Florida

Originally Posted By: LadyChen

update -- I had two students today -- both have been with me for two years now. We had talked about half steps last week, and we did whole steps this week. They both already know their C and G pentascales by rote, but we analyzed them using whole steps and half steps and then built the F pentascale using the pattern. Then we built triads from the pentascales and I demonstrated happy triads and sad triads and how you could make the happy chord sad by lowering the 3 -- and wow, that was a hit lol. I had them show me their "happy" triads in C, F and G and then make them "sad".

I lost a job when I first moved into this area, working as "an assistant" to someone who probably was running a business like the typical music-school-sweat-shop. I'm glad I didn't get it, since soon afterwards I built up my own student base and worked for myself, but what got me rejected?

I didn't know the term "tetrachord". Well, DUH!!! Of COURSE the first four notes of any major scale are also the last of another, and vica versa. But it never occurred to me to name the concept. I absolutely tortured my brass students with major scales, because they are always on exams. How students play those scales makes or breaks an audition for "chairs" from middle school on, and knowing them for the greatest range possible also has a huge impact on power, tone, flexibility and so on.

But to this day I have never taught tetrachords except in passing.

Now I see "pentachord" is very popular. Was it always so? It seems to be used for what I think of as five-finger positions, the first five notes of major scales, and could also be the first five notes of minor scales, with just the 3rd lowered. But I honestly don't know. So I'm getting that out of the way first. smile
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#1908574 - 06/05/12 02:39 AM Re: Alternate names for intervals [Re: Gary D.]
LadyChen Offline
500 Post Club Member

Registered: 01/25/12
Posts: 521
Loc: Canada
Originally Posted By: Gary D.



I didn't know the term "tetrachord". Well, DUH!!! Of COURSE the first four notes of any major scale are also the last of another, and vica versa. But it never occurred to me to name the concept. I absolutely tortured my brass students with major scales, because they are always on exams. How students play those scales makes or breaks an audition for "chairs" from middle school on, and knowing them for the greatest range possible also has a huge impact on power, tone, flexibility and so on.

But to this day I have never taught tetrachords except in passing.

Now I see "pentachord" is very popular. Was it always so? It seems to be used for what I think of as five-finger positions, the first five notes of major scales, and could also be the first five notes of minor scales, with just the 3rd lowered. But I honestly don't know. So I'm getting that out of the way first. smile


haha thanks for clearing that up. My pedagogy teacher talks about tetrachords sometimes but I had no idea what she was talking about until now.

And yes, I think the pentascale is a relatively new thing. I mean, it always existed, but seems to be more commonly taught in early piano now. I certainly was never taught any pentascales when I first started out. They are now part of the technical requirements for the preparatory RCM (Royal Conservatory of Music in Canada) exams, which may explain why they have been more commonplace.

Edit -- and yes, there are minor and major pentascales. Since they only use the first 5 notes of the scale, we don't have to worry about harmonic, melodic and natural minors.


Edited by LadyChen (06/05/12 02:50 AM)

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#1908575 - 06/05/12 02:43 AM Re: Alternate names for intervals [Re: Gary D.]
Nikolas Offline
5000 Post Club Member

Registered: 11/26/07
Posts: 5429
Loc: Europe
heh... I will admit that I wasn't fully aware of what a tetrachord was either... :$ ... I have used it in my compositions thought! ha

Gary: About the pentachord: I would assume that it's the last five notes that provide an issue here... The melodic minor scale (upwards) has the same five notes as the major scale with the same name!... Perhaps this has something to do with it?


Edited by Nikolas (06/05/12 02:45 AM)
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#1908576 - 06/05/12 02:45 AM Re: Alternate names for intervals [Re: LadyChen]
Gary D. Online   content
4000 Post Club Member

Registered: 08/30/08
Posts: 4814
Loc: South Florida
Originally Posted By: LadyChen

update -- I had two students today -- both have been with me for two years now. We had talked about half steps last week, and we did whole steps this week. They both already know their C and G pentascales by rote, but we analyzed them using whole steps and half steps and then built the F pentascale using the pattern. Then we built triads from the pentascales and I demonstrated happy triads and sad triads and how you could make the happy chord sad by lowering the 3 -- and wow, that was a hit lol. I had them show me their "happy" triads in C, F and G and then make them "sad".

I lost a job when I first moved into this area, working as "an assistant" to someone who probably was running a business like the typical music-school-sweat-shop. I'm glad I didn't get it, since soon afterwards I built up my own student base and worked for myself, but what got me rejected?

I didn't know the term "tetrachord". Well, DUH!!! Of COURSE the first four notes of any major scale are also the last of another, and vica versa. But it never occurred to me to name the concept. I absolutely tortured my brass students with major scales, because they are always on exams. How students play those scales makes or breaks an audition for "chairs" from middle school on, and knowing them for the greatest range possible also has a huge impact on power, tone, flexibility and so on.

But to this day I have never taught tetrachords except in passing.

Now I see "pentachord" is very popular. Was it always so? It seems to be used for what I think of as five-finger positions, the first five notes of major scales, and could also be the first five notes of minor scales, with just the 3rd lowered. But I honestly don't know. So I'm getting that out of the way first. smile
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#1908581 - 06/05/12 02:57 AM Re: Alternate names for intervals [Re: Nikolas]
Gary D. Online   content
4000 Post Club Member

Registered: 08/30/08
Posts: 4814
Loc: South Florida
Originally Posted By: Nikolas
Originally Posted By: AZNpiano
Originally Posted By: LadyChen
Another thing I have issues with is calling major and minor triads happy and sad... it's how I was taught when i was their age (7 or 8), and my students like it, but if the minor chord sounds sad, does the dim chord sound *really* sad? LOL!

Diminished chords sound "scary" and "evil."
for my students the diminished chords sound 'magical' and there's a reference to the D minor Fantasy (Mozart... the first 'run' which ends up in CEbF#A... :D).

I teach diminished chords as "grease", and I cover them VERY early, in the four note version. My reasoning is that the tritone is really important, the the most consonant intervals in music, other than the unison and octave, are on either side. So having that tritone, by feel, by key counting, OUTSIDE of notation, is really useful. Later we can explain how it occurs in dominant 7 chords.

Meanwhile we have this "neat thing" that is just SCREAMING to go somewhere. I don't ask students to give me a sound, or a feeling. I ask them: "Does this sound like a good chord to end a piece with?"

Now, in your world, Nikolas, the answer would be: "Why not?" wink

But for those who are used to more conventional sounds, it is quite a leap to accept a diminished chord as final.

And to me it can sound really REALLY cool, but it has an emotion linked to it. Debussy's "Mists" ends on C moving to Bdim, and there is an Ab thrown in, way up in the treble, so he ends with what traditionalists first seem to explain as a vii°7 chord. (I don't teach it that way.)

At any rate, the idea of dividing up an octave into "quarters" or "thirds" seem incredibly important to me. One leads to the fully diminished chord, and that is EVERYWHERE. The other leads to the augmented chord, and that is an immediate gateway to the world of whole-tone scales and chords. smile
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#1908583 - 06/05/12 03:07 AM Re: Alternate names for intervals [Re: LadyChen]
Ben Crosland Offline
Full Member

Registered: 03/11/10
Posts: 421
Loc: Worcester, UK
Originally Posted By: LadyChen

I only had one student (this year) ask why two thirds, C-E and E-G, didn't equal a sixth. He's very mathematical, so when I pointed out that his calculations were counting the E twice, he understood why 3+3=5. phew!


Whenever I explain the 8va symbol, I always ask the student to tell me what the symbol for "2 octaves higher than written" would be. The look of confusion I get when I have to inform them that their answer of "16va" should, in fact, be "15va" is as priceless as it is inevitable smile
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#1908584 - 06/05/12 03:16 AM Re: Alternate names for intervals [Re: Gary D.]
Nikolas Offline
5000 Post Club Member

Registered: 11/26/07
Posts: 5429
Loc: Europe
Originally Posted By: Gary D.
Meanwhile we have this "neat thing" that is just SCREAMING to go somewhere. I don't ask students to give me a sound, or a feeling. I ask them: "Does this sound like a good chord to end a piece with?"

Now, in your world, Nikolas, the answer would be: "Why not?" wink

But for those who are used to more conventional sounds, it is quite a leap to accept a diminished chord as final.
Actually... The answer 'Why not?' comes really really late, unfortunately in the life of my students, and it's not because of me. Most of my students are transfers (since I've been living in Greece for 3-4 years now), and thus they all have remains from their previous teachers... frown

I'm so eager to offer to my students alternatives that I end up composing on the minute to provide some ideas... No piano student of mine has been caught up in composing something. Perhaps it's because they don't like it, perhaps it's because they're intimidated by me and my strong personality... Not sure why. (But this comes to reply to the other thread about 'teaching composition as part of your piano teaching').

________________

The idea of dividing the octave to equal intervals is a fun aspect and hugely important (and the tritone is also the core of tonal music in either way, so it goes right in there in my teachings...).

________________

Ben: I had a serious student asking me what the 15va is... I had to explain and it took quite a bit to get her to understand the 'why' part! Not to mention that this person also had issues with transposed instruments! A pianist at heart, she had trouble understanding the fundamentals of transposing instruments (Clarinet in Bb, etc). Had a fun 3 hours teaching her these things, as she's extra cute actually! ^_^ ha
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#1908585 - 06/05/12 03:20 AM Re: Alternate names for intervals [Re: LadyChen]
Gary D. Online   content
4000 Post Club Member

Registered: 08/30/08
Posts: 4814
Loc: South Florida

Originally Posted By: LadyChen

update -- I had two students today -- both have been with me for two years now. We had talked about half steps last week, and we did whole steps this week. They both already know their C and G pentascales by rote, but we analyzed them using whole steps and half steps and then built the F pentascale using the pattern. Then we built triads from the pentascales and I demonstrated happy triads and sad triads and how you could make the happy chord sad by lowering the 3 -- and wow, that was a hit lol. I had them show me their "happy" triads in C, F and G and then make them "sad".

I approach it all from the opposite angle. My students play all sorts of scale patterns without fully understanding what is going on, because I push reading as one of two "Most Important Things". (The other is the opposite, learning to trust the ear, explore, and in the beginning I approach this without notation)

I can go to any key fairly early by using accidentals instead of key signatures, then I can leap from that TO key signatures. You will see some method books using that logic. I think that allows us to push students ahead sooner to more advanced reading concepts, that do not necessarily ask for more advanced coordination.

But for presenting the actual notes in major scales, I use CHORDS to get me to the same place.

There are just a few basic chords that absolutely nail down "pentachords" without teaching them that way.

1) Learn major chords in every key. (I now cover that with my smart six and seven year-olds.)
2) Play those majors chromatically, both ways, and in random patterns (for exploration).
3) Make the students name all those majors as flat names when descending but with sharp names when ascending:

Example, they say: C C# D D# E F etc., but C B Bb A Ab G etc.

My reasoning behind this is to show, IMMEDIATELY, weird chords like A# major and Db major are not only possible, they are used. But saying the names that way really nails down the black key names, since they really have no names, taking their names from the white keys on each side with a direction symbol, # or b to show move left/right.

Once they have the majors, it is easy to have them explore minor. It is just a half step morph.

But for 2 and 4, the degrees, I push these chords, using C as an example key:

Csus, Csus2, Csus4(add2), the latter being a double suspension chord. That double-suspension nails down those added degrees, and then you can mention the 4 being a whole step down from 5 and 2 being a whole step up from 1.

From that you can go right to rather sophisticated progressions. Then throw in a dim triad and an aug triad, and you get things like this:

Cm Csus Csus2 Cm Cdim Cm Csus4(add2) to either Cm OR C, and then you have the Picardy 3rd. smile

I have been shocked but also greatly pleased to find out that little kids can not only do this, but they seem to love playing with these chords. Play by feel means that ultimately a Gb double suspension is no harder than one in C.

And the freedom of moving without fear to all 12 keys, within the first six to nine months, makes everything easy.

Throw in a C6 and Cmaj7, allowing two hands to work it out, covers the whole scale AND introduces the concept of adding another note a whole step over the fifth OR 1/2 step under the octave.

The dom7 chord can be shown at any time: add an octave to a major triad, then drop the top note down a whole step. And when you start with C7, then you get to explain to a child why the C7 does not "belong" to C, and why it just screams to go to F.
Quote:

One funny thing is that I'd already introduced flats and sharps to one of these girls but not the other. It was actually easier building the F pentascale with the one who *didn't* know about flats or sharps yet. She was completely focused on half steps and whole steps and not what the notes were 'called'. Maybe all these labels just get in the way of understanding patterns. Of course, we need something to call them eventually, but I'm starting to think I'll teach the concepts first and add the labels afterwards.

That is exactly what happens. But I don't have the same problem with chords, since it is a matter of rote, repetition, memorization, feel and sound all coming together. If I can develop a sophisticaed feel for chords in all keys, THEN saying, "Lets take the C scale in the RH and add chords in the LH," is really easy.

But another tack is to allow students to play with chords, progressions, both hands, then start to pull notes OUT of the chords. It sounds backwards, but then what you play in the RH, at first, can come right out of the chords, and added tone can be shown as "in between notes", which we normally call passing tones - and so on.
Quote:

Another thing I have issues with is calling major and minor triads happy and sad... it's how I was taught when i was their age (7 or 8), and my students like it, but if the minor chord sounds sad, does the dim chord sound *really* sad? LOL! Anyway.. I think I will replace the happy and sad labels with major and minor next week to avoid all that confusion.

You can avoid this by allowing your students to express how THEY feel about the chords. Most of my students agree that parallel minor chords feel more serious, more heavy, or maybe darker. But they also agree that parallel minor chords can end something, and it sounds final. Just use the Darth Vader March for illustration. It has only three chords: Gm, Ebm/D#m, C#m. When you get to the final Gm chord, no one is going to say: "Wow, that really sounds HAPPY." But the feeling may be of excitement, of drama, etc.

Parallel majors seem to have a more exotic sound, without the darkness. smile


Edited by Gary D. (06/05/12 03:26 AM)
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#1908920 - 06/05/12 04:38 PM Re: Alternate names for intervals [Re: Gary D.]
LadyChen Offline
500 Post Club Member

Registered: 01/25/12
Posts: 521
Loc: Canada
Wow. I think...

I need to teach longer lessons.

grin

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