From: larryh@cabezon.uucp (Larry Huntley)
Subject: Re: Triads well?
Organization: Logic Modeling Inc of Beaverton Oregon
Date: Wed, 18 Nov 1992 19:25:11 GMT

In article <1992Nov17.185250.13975@EE.Surrey.Ac.UK> css1rs@valar.ee.surrey.ac.uk (Russell Smithers) writes:
>Look are we all dead? I have just asked a question, would some kind soul
>at least respond to it so I know we are all alive? Please.

    Huh?  What?  Oh, a TRIAD!  We thought you said NAIAD and were all out
    beating the bushes looking for water-nymphs.

    Well...a triad is a chord.  Specifically, a chord built with three tones
    of the scale.  The major triad is built of the first, third, and fifth
    degrees of the scale.  For C-Major, this works like this:


	Degree     1  2  3  4  5  6  7  8(Octave)
	Note Name  C  D  E  F  G  A  B  C

    So, the C-Major triad is C-E-G.

    The minor triad is the same except the third degree is flattened by
    a half-tone.

    Brian E (egras@ohstpy.mps.ohio-state.edu) just recently posted a good
    short course on intervals, triads, and chord construction, part of which
    I will now include - 

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From: egras@ohstpy.mps.ohio-state.edu
Subject: Re: Weird Theory Question...(intervals)

	In a Major key, the notes diatonic to that key are given in scale 
degrees :
		1 = tonic
		2 = supertonic
		3 = mediant
		4 = subdominant
		5 = dominant
		6 = submediant
		7 = leading tone (or subtonic)

Note:  These names are all the same in minor keys with the exception of
the subtonic.  The subtonic is not the same as the leading tone in minor keys.
The leading tone is always a half step down from the tonic (or a major 7th
interval up from the tonic, as we shall soon see) regardless of the quality of 
the key (i.e. major or minor).  For major keys, the leading tone and the
subtonic are coincident.  For minor keys, you must sharpen the the 7th scale
degree to produce a leading tone (e.g. in e minor, d# is the leading tone, but
d natural is the subtonic).  The leading tone is much more important than the
subtonic since the leading tone really helps to establish the key more than
the subtonic does.  The reason is that the leading tone is unstable and wants
to resolve up to the tonic.

	Now for intervals:  If you want to know an interval above a certain 
note, go to the MAJOR key where that is the tonic.
		tonic to tonic is a Perfect 1st (unison) or Perfect 8ve(octave)
		tonic to supertonic is a Major 2nd
		tonic to mediant is a Major 3rd
		tonic to subdominant is a Perfect 4th
		tonic to dominant is a Perfect 5th
		tonic to submediant is a Major 6th
		tonic to leading tone (subtonic) is a Major 7th   
		
	Compound intervals (i.e. those greater than an octave) are usually
just given by what by what it would be if the pitch is transposed to fit into 
the octave.

	To include any possible arrangement, we define the following:
		If you flatten a major interval, it is a minor interval.
		If you flatten a minor interval, it is a diminished interval.
		If you flatten a Perfect interval, it is a diminished interval.
		If you sharpen a Perfect interval, it is an augmented interval.
				
This is now complete.  
Note:   A sharpened major interval is an augmented interval, but this is the 
	same pitch as a Perfect interval.(e.g. C to E is a Major 3rd, C to E# is
	an augmented 3rd which sounds the same as the Perfect 4th, C to F.)
	The same sort of statements could be made for doubly diminished or
	doubly augmented intervals.

	
   	Now for chord spellings.  First, triads:

    Major triad:  Root, Major 3rd above root, Perfect 5th above root	
    minor triad:  Root, minor 3rd above root, Perfect 5th above root
    diminished triad: Root, minor 3rd above root, dim. 5th above root
    augmented  triad: Root, major 3rd above root, aug. 5th above root


>   Name                Formula         
> ----------------    ------------
> Major seventh        1, 3, 5, 7
        Major triad with a Major 7th above the root (Major-Major 7th)
 
> Minor seventh        1, b3, 5, b7
	minor triad with a minor 7th above the root (minor-minor 7th)
 
> Dominant seventh     1, 3, 5, b7
	Major triad with a minor 7th above the root (Major-minor 7th)
 
> Half-diminished 
>   seventh            1, b3, b5, b7  ** -- I've heard this one called a "minor
>                                           7th flat 5".
	diminished triad with a minor 7th above the root (dim-minor 7th)

> Diminished seventh   1, b3, b5, bb7
	diminished triad with a diminished 7th above the root (dim-dim 7th)
 	(also called a full diminished 7th chord)

> Minor/Major seventh  1, b3, 5, 7
	minor triad with a Major 7th above the root (minor-Major 7th)
	(This chord isn't very common)

> Dominant seventh  
> Augmented fifth      1, 3, #5, b7   ** -- I've heard this one called a "minor
>                                           "dominant 7th sharp 5".
	Augmented triad with a minor 7th above the root (aug-minor 7th)
	(In general, augmented chords are uncommon.  Augmented 7th chords
	 are even less common.)
 

	You can name plenty more types of chords and give them whatever name
you want.  The above are the most common of the triads and 7th chords.  I 
haven't even spoke of 9th or 13th chords, but it is easy to see how the above
format is generalized to include any type of chord.

BrianE

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	Thank you, Brian.  I hope this has helped, Russell, and we'll try
	to be more lively next time.

	- Larry Huntley


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