Aug. and dim.chords

[violinist4ever]

Hey, everyone, how are you guys? I have a question, but it might seem silly to you... Can someone explain diminished and augmented chords in a way that I can understand? I can't believe that I've gotten this far and I still don't understand it. Somehow, I've been able to kind of "get by" in classes without really knowing it. I've asked my teachers in previous semesters, but I just don't seem to get it. Does anyone have a trick to this or something? Thanks!

[OperaTenor]

Try this:

Augmented: Major thirds stacked on each other

Diminished: Minor thirds stacked on each other

If you look at major or minor chords, they are a combination of major and minor thirds.

Generally speaking, of course.

[bignaf]

Originally posted by OperaTenor:


Generally speaking, of course.

why?

[bignaf]

oh you mean inversions, I guess.
that's the cool thing about aug chords and diminished 7th chords (3 minor 5rds stacked), they are the same stacking in their inversion, and you can continue stacking those thirds without changing the chord.

[OperaTenor]

Yes, didn't want to get into inversions, just trying to KISS.

[Selma in Sandy Eggo]

In the KISS spirit, I don't suppose any of you music majors could explain all those chords and progressions and stacked whatchamacallits in terms of how-many-half-steps? So that a confused amateur could push buttons on a keyboard and go "OH! Aha!"

And, while we're at it, how come sometimes a half-step moves you to an adjacent white key, and sometimes it moves you to an adjacent black key? What's that all about?

[OperaTenor]

As far as intervals are concerned, it's all strictly mathematical.

Interval / # of notes seperating

2nd / next adjacent note(eg. C-D, F-G, Ab - Bb, etc.)
3rd / one note seperating(eg. C - E, Bb - D, F - A, etc.)
4th / three notes seperating(eg. C - F, Bb - Eb, F - Bb, etc.)
...and so on....

The terms "major" and "minor", as they apply to intervals, refer to all intervals except 4ths and 5ths. Simply put, for 2nds and 3rds, a minor interval is composed of an odd number of half steps, and a major interval is composed of an even number(eg. a minor 3rd has 3 half steps, a major 3rd has 4). The opposite is true for 6ths and 7ths(a minor 6th has 8 half steps and a major 6th has 9). Once again, this does not apply to 4ths and 5ths. These intervals(2nds, 3rds, 6ths & 7ths) can be further "augmented" or "diminished" by a half step, and the terms are self-explanatory as to which direction the change goes. These terms are rarely used beyond a compositional context, because they can be better described by a simpler term(eg. a diminished 3rd is actually a major 2nd, an augmented 6th is actually a minor 7th).

As for 4ths and 5ths, they can be "perfect", "diminished" or "augmented". "Perfect" refers to the root interval; in the case of a 4th, it is 5 half steps above the bottom note, and a "perfect" 5th(aside from being full - - and another thread goes alky) is 7 half steps above the bottom note. As in the case with all other intervals, "augment" and "diminish" move the distance one half step accordingly. Interval of note(pun intended ): An augmented 4th and diminished 5th are the same interval(enharmonic is the term), and is known as a "tritone". It is the most strident interval in western music, and you hear one every time you hear a two-pitch car horn honk. It is also the interval used in emergency vehicle sirens, but alternating in pitch instead of simultaneous.

An additional note(pun once again intended): The signs "b"(flat) and "#"(sharp) move the note they are written with one half step down or up, respectively.

As for the second question, it is because the keys on a piano keyboard are not evenly distributed; there are alternating groupings of 4 white keys divided by 3 black keys, and 3 white keys divided by 2 black keys. If you look at a piano keyboard as simply successive notes instead of thinking in terms of white vs. black keys, it is simply a succession of half steps. The keys are organized the way they are mainly to assist the pianist in knowing where he/she is on the keyboard by feel, so they don't have to look down while reading music.

I fully expect *ig to correct me if I got anything wrong. My Theory 101 class was 27 years ago, and I'm just going on memory(and experience).

Clear as mud?

<small>[ 01-31-2006, 05:35 PM: Message edited by: OperaTenor ]</small>

[OperaTenor]

After all that, I realize I left out an important interval: The octave. It is the interval of an 8th, and is rarely referred to in terms other than "perfect"(I believe it falls under the same rules as 4ths and 5ths), once again because it can be described in much simpler terms of neighboring intervals(major 7th instead of diminished octave/8th, or minor 9th instead of augmented octave/8th).

And another thing: as intervals progress above the octave distance(i.e., 9ths, 13ths, 10ths, etc.), the above rules apply, the correlation being what the interval would be if you subtracted 7. For instance, An interval of a 9th is equivalent to, for purposes of rules, an interval of a 2nd, and so on.

[BigJon@Work]

I'm bored, mommy, make it stop.

[OperaTenor]

Originally posted by BigJon@Work:
I'm bored, mommy, make it stop.

First, Selma asked.
Second, if you're bored with a music post, you can always go hang out in the Barracks.
Third, you could always post something original yourself.

[Selma in Sandy Eggo]

Originally posted by BigJon@Work:
I'm bored, mommy, make it stop.

That was actually reasonably clear (of course, I'm used to engineers.) It could use a little rephrasing and cleaning up before it would be KISS qualified.

[OperaTenor]

Originally posted by Selma in Sandy Eggo:
That was actually reasonably clear (of course, I'm used to engineers.) It could use a little rephrasing and cleaning up before it would be KISS qualified.

Thanks.

Could be simpler? Can you pretend I'm from Missouri?

[BigJon@Work]

Originally posted by OperaTenor:
Second, if you're bored with a music post, you can always go hang out in the Barracks.
Third, you could always post something original yourself.

Vroom, roof job! OT, your joke antenna need a 6 myriameter service and repair

Check who's started the most musical threads in the last few months.

<small>[ 01-31-2006, 07:13 PM: Message edited by: BigJon@Work ]</small>

[Selma in Sandy Eggo]

Sweetie, we know you're from Misery. On the days you're not busy being a professional Zonie, that is.

You'd start like:

Music is calculated in octaves. For each octave starting with a note of a frequency N, there is a note with a frequency of 2N. The notes of frequency N and 2N will be named with the same letter name, and will be the base note for the scale.

The octave is divided into regular portions called half-steps. Relative to each base note, a major scale is composed of notes at intervals such that the:
2nd note is <x1> half-steps above the base;
3rd note is <x2> half-steps above the second note;
4th note is <x3> half-steps above the third note;
5th note is <x4> half-steps above the fourth note;
6th note is <x5> half steps above the fifth note;
7th note is <x6> half-steps above the sixth note;
8th note (which is also the octave, and is twice the frequency of the base note) is <x7> half-steps above the 7th note.

The minor scale is similarly constructed, with the exception that the spacing of the notes relative to the base note will be:
2nd note is <y1> half-steps above the base;
3rd note is <y2> half-steps above the second note;
4th note is <y3> half-steps above the third note;
5th note is <y4> half-steps above the fourth note;
6th note is <y5> half steps above the fifth note;
7th note is <y6> half-steps above the sixth note;
8th note (which is also the octave, and is twice the frequency of the base note) is <y7> half-steps above the 7th note.


This tutorial pattern would be repeated for all the variations of the term "scale", going into the intricacies of augmented, diminished, and so forth. Then chords defined as note patterns, with the number of half-steps named so that the uninitiated can count them off on the keyboard.

See what tech writers are good for?

<small>[ 01-31-2006, 09:44 PM: Message edited by: Selma in Sandy Eggo ]</small>

[OperaTenor]

Actually, that explanation, however logical, doesn't address intervals and their characteristics. The relationships between intervals, scale and modality are pertinent to the discussion of "those chords and progressions and stacked whatchamacallits in terms of how-many-half-steps", and simply saying note X is N half steps above the "base" note doesn't tell you anything about what defines that interval.

With reference to augmented and diminished chords, for instance, from my explanation you should now know that the stacked major thirds in the augmented chord are 4 half steps apart, and the stacked minor thirds in the diminished chord are 3 half steps apart.

As an added bonus, next time you hear a car horn or a siren, you can impress your friends by telling them the reason the horn/siren is so obnoxious is because it's a tritone.

*igJon, musta forgot my , just like you did.

<small>[ 02-01-2006, 01:49 AM: Message edited by: OperaTenor ]</small>

[Selma in Sandy Eggo]

Oh, yes. Explanation would end up being a full chapter by the time it was done, would need illustrations and a glossary and a frequency chart and stuff. With charts, and illustrations, and 8x10 glossy photos with a paragraph on the back - wait, that's a different story!

[1st_oboe]

4+5=8
And I can prove it.
-----------------


C to F= p4th
F to C= p5th

Since C to C= p8th
then 4+5=8

[Selma in Sandy Eggo]

Originally posted by 1st_oboe:
4+5=8

Only for very small values of 5.

Works best in a base-twelve notation

[Nicole Marie]

Originally posted by Selma in Sandy Eggo:

Music is calculated in octaves. For each octave starting with a note of a frequency N, there is a note with a frequency of 2N. The notes of frequency N and 2N will be named with the same letter name, and will be the base note for the scale.

This is a pretty basic example but composition is deeper then this. Follow OT, he is showing the best examples of how western music is structured.

<small>[ 02-03-2006, 10:57 AM: Message edited by: Nicole Marie ]</small>

[Selma in Sandy Eggo]

OTs explanations are certainly more complete than my example of instructional/explanatory layout. Music majors invariably assume more background knowledge than the audience possesses; they share this problem with all other types of subject matter experts.

It also triggered my conditioned response. There are a fair number of us here who only qualify as "audience". To the non-musically trained, your explanations or OTs can be a bit baffling even though they are complete and accurate.