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#1210597 - 06/02/09 08:29 PM Harmony Exercises - Post #1
Kreisler Offline


Registered: 11/27/02
Posts: 13759
Loc: Iowa City, IA
Hello all,

A recent discussion got people interested in doing and sharing their work on some harmony exercises. Looking for material, I stumbled upon the San Francisco Conservatory's website. They have a variety of additional exercises online for their theory and musicianship courses. (They use Aldwell-Schachter)

So I propose a bit of a homework share. Let's start with the first worksheet - common chords.

Go here:

http://www.sfcmtheory.com/figured_harmony/figured_harmony.htm

And download "1.c Exercises"

Eventually, I'd like to get through the whole set. So...who will be the first to post?

(Do any of the exercises you want - I'd urge everyone interested to participate regardless of skill level. Give it a try. I'll do my best to provide my solutions with some commentary.)

Happy Harmonizing!
_________________________
"If we continually try to force a child to do what he is afraid to do, he will become more timid, and will use his brains and energy, not to explore the unknown, but to find ways to avoid the pressures we put on him." (John Holt)

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#1210909 - 06/03/09 09:19 AM Re: Harmony Exercises - Post #1 [Re: Kreisler]
pianovirus Offline
500 Post Club Member

Registered: 04/24/07
Posts: 951
Loc: Basel, Switzerland
Good to have some common material, and I'm also interested to join you folks in going through the whole set over time.

Some stupid questions to begin with (I hope I don't get disqualified for them smile ):

1.) Is the task in ex. 1c to fill in two middle voices, obeying the rules of 4-part setting?

2.) Given that this is called 'common chords' does this mean we are allowed to use T, S, D and their parallels in ground form, but no inversions or other chords than these?

3.) What is the meaning of the '#' and 'natural' signs below the system? I'm just not familiar with the notation.
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#1210924 - 06/03/09 09:49 AM Re: Harmony Exercises - Post #1 [Re: pianovirus]
DragonPianoPlayer Offline
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Registered: 12/12/06
Posts: 2368
Loc: Denver, CO
I've also been interested in joining. (But I may not have enough time to do all the exercises I want to until late this month.)

Here are my questions:
Based on the notes provided, I would guess that inversions are permitted.

Kreisler, is there a reason you have jumped to exercise 1c and skipped 1a Common Chords: Cadences and 1b Common Chords: Sequences? It seems to me that understanding and working through these exercises would help with understanding 1c.

Rich
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#1210971 - 06/03/09 11:17 AM Re: Harmony Exercises - Post #1 [Re: DragonPianoPlayer]
Kreisler Offline


Registered: 11/27/02
Posts: 13759
Loc: Iowa City, IA
I thought people might be more interested in the longer examples that are in a more musical context. I'm happy to entertain questions and comments on the foundational exercises in 1a and 1b.

Perhaps we should devote this post to anything in 1...

And yes, I believe the 1c examples are given to fill in inner voices.
_________________________
"If we continually try to force a child to do what he is afraid to do, he will become more timid, and will use his brains and energy, not to explore the unknown, but to find ways to avoid the pressures we put on him." (John Holt)

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www.youtube.com/user/UIPianoPed

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#1210976 - 06/03/09 11:24 AM Re: Harmony Exercises - Post #1 [Re: Kreisler]
mkorman Offline
Full Member

Registered: 06/26/04
Posts: 180
Loc: Connecticut, USA
Also, since the symbols below the staff are figured bass, and subsequent exercises deal with inversions, I think all of these chords are to be done in root position.

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#1210987 - 06/03/09 11:38 AM Re: Harmony Exercises - Post #1 [Re: mkorman]
keystring Offline
Yikes! 10000 Post Club Member

Registered: 12/11/07
Posts: 11558
Loc: Canada
Kreisler, I'm interested in the one that has sequences, because my book has already touched on it and I think I can grow into that one. However, I am missing the approach that is used for sequences. Is there either a resource for that, or is it something that can be sketched out in a few words?

What I have in Horwood is a brief bit where the pattern in the soprano either ends up zigzagging its way down i.e E,F,D,E,C,D,B,C or descending in seconds like a scale. The pattern or approach he uses is "using a series of chords with roots raising a fourth and falling a fifth alternatively. This is sometimes known as the dominant sequence." [diagramatic examples follow]

Is that generally "it"? Is there more? Something I/we should know? [assessing whether to try it when I get the time]

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#1211043 - 06/03/09 12:59 PM Re: Harmony Exercises - Post #1 [Re: keystring]
Kreisler Offline


Registered: 11/27/02
Posts: 13759
Loc: Iowa City, IA
Okay, here's the 2nd sequence from worksheet 1b.

The idea behind a sequence is that you have a pattern that is repeated at a higher or lower pitch level. Thus, whatever we use for the 1st measure we simply move down a step for the 2nd measure, and so on until the final cadence requires a break in the pattern.

My inner monologue went something like this:

"Okay, so we have roots in the bass and begin with a 3rd in the soprano. Usually, we like to double the root, so let's double the root in the alto and add the 5th in the tenor. The second measure has the 5th in the soprano, so the tenor and alto get the doubled root and the 3rd. Tenor can't go down to the third because it's a huge awkward jump. Tenor can't really go down to the fifth because it creates direct fifths with the bass (approaching a perfect consonant by similar motion is ethically questionable in counterpoint land.) So tenor has to go up to the 3rd, and the alto part gets to sit on the C:



I was unhappy with this for two reasons. First, I used to sing tenor (long ago), and that high A, while common in virtuoso operatic arias, is just a bit too high for my tastes.

So I thought I'd try the other option - begin by doubling the root in the tenor and put the 5th in the alto. This actually works out pretty well, the only problem being the direct fifths from beat 3 to beat 1, but that's not too bad because it's between the inner voices and one of them is stepwise.

Here's the finished result with the cadence added at the end:

_________________________
"If we continually try to force a child to do what he is afraid to do, he will become more timid, and will use his brains and energy, not to explore the unknown, but to find ways to avoid the pressures we put on him." (John Holt)

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#1211048 - 06/03/09 01:05 PM Re: Harmony Exercises - Post #1 [Re: Kreisler]
Kreisler Offline


Registered: 11/27/02
Posts: 13759
Loc: Iowa City, IA
Oh, and somebody proofread me. I actually make a lot of mistakes, and while I'll do my best to edit this stuff before I post it, I can guarantee some mistakes will creep in.

Also, I tend to write based on experience, my ear, and my own version of "the rules." In my annotations, I'm giving you the way I think about things, and they may or may not line up with how the material is presented in textbooks or by real theorists. (For example, I'm pretty sure there's something fishy about what I said about direct fifths earlier, but it seems to work for me.)

YMMV! laugh
_________________________
"If we continually try to force a child to do what he is afraid to do, he will become more timid, and will use his brains and energy, not to explore the unknown, but to find ways to avoid the pressures we put on him." (John Holt)

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www.youtube.com/user/UIPianoPed

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#1211051 - 06/03/09 01:09 PM Re: Harmony Exercises - Post #1 [Re: Kreisler]
Kreisler Offline


Registered: 11/27/02
Posts: 13759
Loc: Iowa City, IA
HAHAHA! Found my first error already. The B in the tenor on m. 1 beat 3 and the A on m. 2 beat 3 in the first example should be down a step. The tenor should stay on the same note for beats 2 and 3 in both measures.

Ugh..this is why theory teachers always tell you to play your examples. Unfortunately, I'm sitting in the coffee shop and too lazy to get the headphones out. :P
_________________________
"If we continually try to force a child to do what he is afraid to do, he will become more timid, and will use his brains and energy, not to explore the unknown, but to find ways to avoid the pressures we put on him." (John Holt)

www.pianoped.com
www.youtube.com/user/UIPianoPed

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#1211198 - 06/03/09 04:36 PM Re: Harmony Exercises - Post #1 [Re: Kreisler]
nlogn Offline
Full Member

Registered: 05/02/09
Posts: 108
Originally Posted By: Kreisler
HAHAHA! Found my first error already. The B in the tenor on m. 1 beat 3 and the A on m. 2 beat 3 in the first example should be down a step. The tenor should stay on the same note for beats 2 and 3 in both measures.

Ugh..this is why theory teachers always tell you to play your examples. Unfortunately, I'm sitting in the coffee shop and too lazy to get the headphones out. :P

And there I was thinking those were some interesting-sounding chords.
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#1211235 - 06/03/09 05:44 PM Re: Harmony Exercises - Post #1 [Re: pianovirus]
keystring Offline
Yikes! 10000 Post Club Member

Registered: 12/11/07
Posts: 11558
Loc: Canada
Quote:
What is the meaning of the '#' and 'natural' signs below the system? I'm just not familiar with the notation

It means that that particular chord will have that kind of accidental in it.
Quote:
Given that this is called 'common chords' does this mean we are allowed to use T, S, D and their parallels in ground form, but no inversions or other chords than these?

I had to look that one up. A "common chord" simply means one of the chords that in root position has three notes a third apart, i.e. occupying 3 adjacent lines or space in closed position: major, minor, aug or dim.


Edited by keystring (06/03/09 05:50 PM)

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#1211257 - 06/03/09 06:12 PM Re: Harmony Exercises - Post #1 [Re: keystring]
Kreisler Offline


Registered: 11/27/02
Posts: 13759
Loc: Iowa City, IA
Yes, the # is figured bass shorthand for #3 and means a sharp third above the bass. You'll see things like b6, natural-3, etc...

They all relate to an interval above the bass NOTE. (Not necessarily the root of the chord.)
_________________________
"If we continually try to force a child to do what he is afraid to do, he will become more timid, and will use his brains and energy, not to explore the unknown, but to find ways to avoid the pressures we put on him." (John Holt)

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www.youtube.com/user/UIPianoPed

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#1211260 - 06/03/09 06:20 PM Re: Harmony Exercises - Post #1 [Re: Kreisler]
pianovirus Offline
500 Post Club Member

Registered: 04/24/07
Posts: 951
Loc: Basel, Switzerland
Here's my take on the 1st sequence in exercise 1b. Is this correct or are there any mistakes?



In that website, every topic seems to have some sequences associated with it. I have never seen sequences used so prominently. In my (German) books on harmony, sequences are just mentioned on one or two pages. In particular, one of them mentions "The functional analysis of sequences..." (like indicated by me below the notes) "...is usually not very helpful." This makes sense to me since after one atomic part the entire sequence is essentially predetermined, isn't it? The book recommends just to label the first atomic part (in this case bar 1: T D) and for the repetitions just mention their anchor points (here: bar 2=Tp, bar 3=S, bar 4=Sp).

So in a nutshell I'm currently a bit confused what is the learning goal from filling out the sequences? Oddly I also did not find anything on it in the Aldwell/Schachter book (3rd ed) which seems to be the basis for these exercises.

In any case, this is going to be fun. I hope we will have enough motivation to do this for some time!

PS. In my post, the image appears downscaled as compared to the original and therefore the lines look a bit strange. Does anyone know how I can adjust the scaling?
PPS. Thanks keystring & Kreisler for the notation explanation.


Edited by pianovirus (06/03/09 07:29 PM)
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#1211289 - 06/03/09 07:22 PM Re: Harmony Exercises - Post #1 [Re: nlogn]
keystring Offline
Yikes! 10000 Post Club Member

Registered: 12/11/07
Posts: 11558
Loc: Canada
Is this the right idea? It's another exercise in 1b

(Sorry about the smudgy appearance)

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#1211296 - 06/03/09 07:32 PM Re: Harmony Exercises - Post #1 [Re: Kreisler]
keystring Offline
Yikes! 10000 Post Club Member

Registered: 12/11/07
Posts: 11558
Loc: Canada
Quote:
Yes, the # is figured bass shorthand for #3

Do accidental always refer to the 3 (middle note of chord in root position)?

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#1211315 - 06/03/09 08:15 PM Re: Harmony Exercises - Post #1 [Re: keystring]
pianovirus Offline
500 Post Club Member

Registered: 04/24/07
Posts: 951
Loc: Basel, Switzerland
Originally Posted By: keystring
Quote:
Yes, the # is figured bass shorthand for #3

Do accidental always refer to the 3 (middle note of chord in root position)?


AFAIK, in basso continuo notation, an accidental without a number always refers to the third of a chord. In contrast, e.g. an augmented 4th would be denoted as 4#.

Edit: As often, Wiki seems to have some good summary:
http://en.wikipedia.org/wiki/Figured_bass
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#1211317 - 06/03/09 08:16 PM Re: Harmony Exercises - Post #1 [Re: pianovirus]
keystring Offline
Yikes! 10000 Post Club Member

Registered: 12/11/07
Posts: 11558
Loc: Canada
Thank you. smile

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#1211324 - 06/03/09 08:25 PM Re: Harmony Exercises - Post #1 [Re: keystring]
pianovirus Offline
500 Post Club Member

Registered: 04/24/07
Posts: 951
Loc: Basel, Switzerland
Ex. 1c, part 1 -- any comments/hints would be welcome (tomorrow, I plan also to look at others' "homework", e.g. keystring, Kreisler). I just played it and it sounds quite strange!! (something wrong?)



I have tried to consider the following rules for harmonization (but I'm tired and have little experience so I guess there are quite some errors):

Doubling of notes:
--Never double the leading tone when it is part of V or VII
--Double more stable parts, often the root. The final chord almost always contains the root doubled.
--Never double the 7; in 7th chords sometimes the root is doubled and the 5th omitted

Forbidden parallel motions:
--Parallel unisons, octaves, and fifths WITHIN THE SAME PAIR OF VOICES
--Consecutive octaves or 5ths resulting from contrary motion
--Hidden 5ths or octaves (i.e. a 5th or octave is approached by similar motion): far less dramatic than real parallels, but at least avoid hidden octaves in the outer voices unless soprano moves by step

Btw, a more comprehensive summary of the "rules" is given on p. 78 of Aldwell/Schachter.

Good night from Switzerland for now smile
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#1211379 - 06/03/09 09:52 PM Re: Harmony Exercises - Post #1 [Re: pianovirus]
agent3x Offline
Full Member

Registered: 05/24/08
Posts: 147
Loc: United States
I'd love to participate. Can someone tell me how to post images of the exercises as everyone has been doing?

Also, I've always wondered, what's the big deal with all these parallels? I just don't hear anything strange. I'm studying theory on my own, and came across "implied parallels." This is frustrating! If I don't hear normal parallels, how can I catch implied ones?

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#1211380 - 06/03/09 09:54 PM Re: Harmony Exercises - Post #1 [Re: pianovirus]
agent3x Offline
Full Member

Registered: 05/24/08
Posts: 147
Loc: United States
Originally Posted By: pianovirus
Here's my take on the 1st sequence in exercise 1b. Is this correct or are there any mistakes?



In that website, every topic seems to have some sequences associated with it. I have never seen sequences used so prominently. In my (German) books on harmony, sequences are just mentioned on one or two pages. In particular, one of them mentions "The functional analysis of sequences..." (like indicated by me below the notes) "...is usually not very helpful." This makes sense to me since after one atomic part the entire sequence is essentially predetermined, isn't it? The book recommends just to label the first atomic part (in this case bar 1: T D) and for the repetitions just mention their anchor points (here: bar 2=Tp, bar 3=S, bar 4=Sp).

So in a nutshell I'm currently a bit confused what is the learning goal from filling out the sequences? Oddly I also did not find anything on it in the Aldwell/Schachter book (3rd ed) which seems to be the basis for these exercises.

In any case, this is going to be fun. I hope we will have enough motivation to do this for some time!

PS. In my post, the image appears downscaled as compared to the original and therefore the lines look a bit strange. Does anyone know how I can adjust the scaling?
PPS. Thanks keystring & Kreisler for the notation explanation.



What do the symbols "T, D, Tp, etc." mean?

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#1211434 - 06/03/09 11:46 PM Re: Harmony Exercises - Post #1 [Re: agent3x]
Kreisler Offline


Registered: 11/27/02
Posts: 13759
Loc: Iowa City, IA
Originally Posted By: agent3x
I'd love to participate. Can someone tell me how to post images of the exercises as everyone has been doing?


I've been using the in-house one:

http://www.pianoworld.com/Uploads/fileuploader2.html

Oh, and as best I can tell:

T = Tonic
D = Dominant
S = Subdominant

..and the little p means down a third from those, but I can't figure out what it stands for. laugh
_________________________
"If we continually try to force a child to do what he is afraid to do, he will become more timid, and will use his brains and energy, not to explore the unknown, but to find ways to avoid the pressures we put on him." (John Holt)

www.pianoped.com
www.youtube.com/user/UIPianoPed

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#1211482 - 06/04/09 02:02 AM Re: Harmony Exercises - Post #1 [Re: Kreisler]
agent3x Offline
Full Member

Registered: 05/24/08
Posts: 147
Loc: United States
Thanks, Kreisler.

I had a try at 1C 6. I tried to maintain closed voicing, which resulted in the tenor getting a bit high. I also always doubled the root; I don't think I ever needed to stray away from that.



And 1C 4 with more open voicing, also always doubling the root. I'm not sure about the F in measure 5. I thought the 7th step is always raised in a minor key to create a leading tone, but the exercise didn't indicate to do so with bass symbols in this case, so...




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#1211489 - 06/04/09 02:52 AM Re: Harmony Exercises - Post #1 [Re: Kreisler]
pianovirus Offline
500 Post Club Member

Registered: 04/24/07
Posts: 951
Loc: Basel, Switzerland
Originally Posted By: Kreisler
[quote=agent3x]I
Oh, and as best I can tell:

T = Tonic
D = Dominant
S = Subdominant

..and the little p means down a third from those, but I can't figure out what it stands for. laugh


I'm sorry, there seem to be some international differences smile
I think what we are calling a parallel key http://de.wikipedia.org/wiki/Paralleltonart
(and as you can see on Wiki we denote by the letter p or P, depending on whether the chord is minor or major) seems to be called a relative key in English (the key with the same key signature)
http://en.wikipedia.org/wiki/Relative_key

Hope this clarifies things. As I said I'll try to learn the international conventions but it may take a while smile
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#1211519 - 06/04/09 06:41 AM Re: Harmony Exercises - Post #1 [Re: pianovirus]
keystring Offline
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Registered: 12/11/07
Posts: 11558
Loc: Canada
That's interesting, Pianovirus. Yes, A minor / C major are known as relative major and minor because they are related to each other in the same key. the expression "parallel" that you have shared with us seems to reflect the fact that the pitches with their intervals follow exactly the same path like railway tracks.

You should know that in the case of C major vs. C minor, in the US (and maybe further) the expression "parallel" is used. In Canada and I think Britain (and ??) we say "tonic major/minor" to reflect that the tonic is the same. I was actually bothered when I first learned that our "tonic" was called "parallel" for that railway track reason - the notes don't move parallel to each other. wink But in any case, you might run into the word "parallel" and if your Paralleltonart means relative key, then it could cause confusion if you suddenly saw people talking about "parallel" but meaning "same tonic".

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#1211547 - 06/04/09 08:04 AM Re: Harmony Exercises - Post #1 [Re: keystring]
pianovirus Offline
500 Post Club Member

Registered: 04/24/07
Posts: 951
Loc: Basel, Switzerland
Thanks keystring, it's good to know the pitfalls in translating! I definitely meant what you refer to as relative (or in Canada tonic) major/minor. I'll make sure to search the correct translation in the future instead of guessing smile

As an aside, there seem to be some more terms with slightly different meanings in different languages. For example I noticed a while ago that the term 'serial music/serialism' seems to be used with a much broader meaning in English than the corresponding 'serielle Musik' in German. The German term refers strictly and exclusively to the developments in the music of Anton Webern, Messiaen and others who extended Schoenberg's idea of a series to other properties of sounds than pitch (loudness, color, duration, etc.). Schoenberg's own music would not be described as 'seriell' in German, but merely as 'dodecaphonic'. In contrast, it seems to me that 'serial music' in English is not limited to this specific context but would also comprise Schoenberg's 12-tone music etc.

Ok, but enough for now with the babylonic confusions and sorry again. Back to our exercises!! smile

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#1212125 - 06/05/09 08:56 AM Re: Harmony Exercises - Post #1 [Re: pianovirus]
DragonPianoPlayer Offline
2000 Post Club Member

Registered: 12/12/06
Posts: 2368
Loc: Denver, CO
OK,

So here is my first set of tries on the first line in 1a, the Perfect Cadences.

I have two different versions of the first cadence and one of each of the other two.



This is the first time I've actually tried to do any harmonization since I took music theory for non-majors in college almost 30 years ago.

Rich
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#1212147 - 06/05/09 09:36 AM Re: Harmony Exercises - Post #1 [Re: DragonPianoPlayer]
pianovirus Offline
500 Post Club Member

Registered: 04/24/07
Posts: 951
Loc: Basel, Switzerland
The gurus here may be able to give more advice, but I see glaring octave parallels in bar 1 already!! laugh
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#1212149 - 06/05/09 09:40 AM Re: Harmony Exercises - Post #1 [Re: pianovirus]
DragonPianoPlayer Offline
2000 Post Club Member

Registered: 12/12/06
Posts: 2368
Loc: Denver, CO
Thanks Pianovirus, I see them - between Alto and Bass.

Here's an updated version with out those octaves.



Rich


Edited by DragonPianoPlayer (06/05/09 09:44 AM)
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#1212165 - 06/05/09 10:19 AM Re: Harmony Exercises - Post #1 [Re: DragonPianoPlayer]
pianovirus Offline
500 Post Club Member

Registered: 04/24/07
Posts: 951
Loc: Basel, Switzerland
Hi Rich,
there are still octave parallels in bar 1: A-F in alto and A-F in bass. Moreover, I think meeting of two voices on the same tone should not be so frequent as in your examples. But as I said, I'm not an expert, but a learner as you!
See you, virus.
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#1212279 - 06/05/09 01:46 PM Re: Harmony Exercises - Post #1 [Re: pianovirus]
Harmosis Offline
Full Member

Registered: 02/15/07
Posts: 308
Loc: California
It seems to me that a review of some rules might be helpful:

Voice Leading:

1] No parallel 5ths or octaves.
2] No voice crossing.
3] Keep voices in their respective ranges.*
4] Do not keep voices in the extremities of their ranges for extended periods of time.
5] Avoid leaps larger than a 5th (the octave is OK). An upwards leap of a minor 6th is OK if it is immediately followed by a minor 2nd in the opposite direction.
6] Avoid awkward leaps like tritones and augmented 2nds.
7] Direct 5ths/octaves - some professors don't make a big deal out of this; some do. I would say to at least avoid them in the soprano when leaping. If you can, avoid them in the bass voice as well.


Spacing:

Do not allow more than an octave between any two adjacent voices (i.e., alto-soprano, tenor-alto). However, you may allow more than an octave between the bass and tenor.

Doubling:

1] For triads in root position, double the root.
2] For triads in 1st inversion, double the root unless you cannot for voice leading reasons (i.e., to avoid parallel 5ths, etc).
3] For triads in 2nd inversion, double the 5th.
4] For 7th chords, if you omit the 5th, then double the root.
5] Do not double dissonant tones (i.e., tritones, 7ths, etc).
6] Do not double tendency tones (i.e., the leading tone or the 7th).


General guidelines:

- Melodic interest should be primarily in the soprano and bass.
- Keep common tones in the tenor and alto.
- Each voice should have a more-or-less sing-able line.
- Move each voice the shortest distance possible, preferring stepwise motion to leaps.


*Ranges - I've never seen any two theory books precisely agree on this, but here are the ranges that I was given in college.

Bass: E2 to D4 (E to d)
Tenor: C3 to G4 (c to g')
Alto: G3 to C5 (g to c")
Soprano: C4 to G5 (c' to g")

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Youtube! :)
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How struts define pitch variation between tunings
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