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#1908450 - 06/04/12 08:39 PM Re: Alternate names for intervals [Re: Gary D.]
keystring Online   content
Yikes! 10000 Post Club Member

Registered: 12/11/07
Posts: 11803
Loc: Canada
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
500 Post Club Member

Registered: 01/25/12
Posts: 521
Loc: Canada
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
500 Post Club Member

Registered: 01/25/12
Posts: 521
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: 5551
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 Online   content
5000 Post Club Member

Registered: 11/26/07
Posts: 5363
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 Online   content
5000 Post Club Member

Registered: 11/26/07
Posts: 5363
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. Offline
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 Online   content
5000 Post Club Member

Registered: 11/26/07
Posts: 5363
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. Offline
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. Offline
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 viiĀ°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 Online   content
5000 Post Club Member

Registered: 11/26/07
Posts: 5363
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. Offline
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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