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It does, but sort of indirectly. I actually don't use it much any more, but it was very helpful in the beginning. It's a quick and accurate way to get from letters on a lead sheet to fingers on the keys. It gets you playing the chords a little quicker, and then the playing is what leads to understanding how the chords work.

Yes, I can see now that it works.

Like keystring, and probably most of us, my spatial sense of the keyboard is marked out by black keys interrupting the evident symmetry of the white keys which are all equally spaced. The fact of this failing to tally with the musical spacing - B to C is a semitone while C to D is a tone - is an anomaly I've just come to accept.

But if you go to the back of the keys at the fallboard, where you need to place your diagram, it's an entirely different story. All intervals are proportionally spaced. By lining-up the notches with the key centres, black or white, the paradox is resolved!

Here's a link:

http://www.youtube.com/watch?v=cK4REjqGc9w

He left the colors the same,
but did raise some of the whites and lowered some blacks,
so all notes in a row are a whole tone apart:
C D E Gb Ab Bb
Db Eb F G A B

I can see how that works for you. Essentially you have a pictorial representation of how the intervals relate. For example, a major chord consists of this:
C(major 3rd = 4 semitones)E(minor 3rd = 3 semitones)G
where we're seeing the distance from C to E, and E to G.
Simplified that is
C(bigger)E(smaller)G

I have an image like that in my head, and I imagine that if you don't, then you are just memorizing things like "4 semitones" or "major 3rd" --- a pile of facts. So I see its usefulness. And then you are also automating some reflexes relating to the instrument that's between your hand and the keys. Eventually the rest of the associations kick in. Cool idea.

OK. So what I want to know is, why do we like ii - V - I?
Or why do we like ii7 - V7- I even better?

Actually, "like" is not really the issue;
what we really need to know:
what are the progressions that are most likely to occur
and therefore the ones we need to learn first?

Maybe we should start a list:
I V7 I
I IV V I
I ii7 V7 I
I I#o ii
etc.

But where does the list come from?
The Circle of Keys is a start.
But that doesn't explain when to use 7th,
or when to use minor vs major,
or dim or aug or 6 9 11 13.
Admittedly, some of those are probably more advanced topics,
but beginners don't even know what's "advanced" vs. what's "fundamental".

So as we build the list above,
we should sort it,
with the "basics" first and "advanced" progressions later.

Then part of our analysis should be:
* here are the "basic" progressions I've found
* here are some others I don't recognize or understand yet.

America or God Save the Queen
Have we started this one yet?
I took a quick look and it has an unusual form, 3x2 measures + 4x2 measures.
Most songs are even multiples of two or four.

Happy Birthday: 4 lines of 2 measures, but lines split after 2nd beat.

Lili Marlene: 3 lines of 4 measures,
but the 4 measures split into two groups of two.
Also, beginning with the second line, most groups start with a pick-up from the previous measure.

tinman, yes we have started it. It's on a new thread Begining Analysis 01: America / God Save The Queen.

Sorry I've been missing for several days -- I have several thoughts, but no time to put them in order!

It comes from what has worked thus far in music.

When you move from the tonic (I) chord to ii, IV or vi you maintain a concord. As soon as you use a chord with the leading note in it (ii, V, or vii dim) you create discord. The dissonance creates tension and consonance releases it. The ear wants to return to consonance.

The climax of most songs occurs on the dominant. The use of the dominant seventh increases the tension by introducing the tritone, three whole tones and the most dissonant interval in Western music, between the 3rd and flat 7th degrees of the chord.

The V7-I move works because of the leading note effect (Western music is essentially shaped on and defined by the 7-8 resolution at the end of a major scale), the tritone resolution and the move of a perfect fifth in the bass, the most fundamental move in all of music.

ii is the dominant of V so the move ii-V-I is moving from the dominant of the dominant to the dominant and then on to the tonic. The ii in this instance is frequently heard in second inversion so that the root movement of a fifth is avoided that would have created a premature resolution on the dominant.

Since this is a beginner theory section, can you explain what concord and discord are, and what maintaining one might mean? Also, do you think that there is no difference on which of the chords you would use at any time (which I think is part of the question)?

Thanks keystring, Richard, johnsprung and Pianostudent88 for helping me to understand how we know whether it is a sharp or flat. I understand it now! (well at least I think/hope I do; whether it bears out in practice is to be seen). John and Richard, the charts and guides are great and will hopefully help me to improve my recognition of the intervals and chords because if I don’t recognize the chord just from looking at it, it seems I have to count halfsteps! That’s the only way I can seem to do it when I don’t recognize it just by looking, which isn’t so bad when I have pencil and paper in front of me and time to figure it out, but hopefully one day I’ll be better at recognizing them more easily just by looking at the score or at the piano.

Pianostudent88, I appreciate your detailed explanation which was really helpful and clear. I’ve had a go at the interval exercises you posted a link to. They are good practice! So far I’m only through up to the fourths (page 4). It’s still a brain strain to do these exercises. Here are the ones that keystring posted—I had a go at these too:

E G__ B___

E, G#, B

A C__ E___

A C# E

Db F__ A___

Db, F, Ab

Can you get this one:
B D__ F__

B D# F#

The tonic ma7 and a more sophisticated ear refute that.



- and yet, to me, this is a warm, bluesy interval. If we're talking about bare intervals I believe most would find the natural 7 (e.g. C-B) or b9 (C-Db) far more unsettling.



In so far as we can define a dog, and divine its shape, by referring only to the tip of its tail.

Excellent. The reason I gave you this exercise was to start answering your question about chord types (kinds) and accidentals.

A "kind" of chord means whether it is major, minor, and other qualities such as diminished etc., but we will stay with major and minor for now. Each "kind" of chord has a particular quality, and this is something you can hear. All of the chords that you formed were major chords. People often hear major chords as having a "happy" sound and might even attach a colour like yellow or orange. In contrast, a minor chord is often associated with a "sad" sound, and maybe blue or green.

So you formed four chords built on the roots E, A, Db, and B respectively. Our chords are triads, which means in root position they are stacked like snowmen on adjacent lines or spaces. This also means that the letter names will skip one. That is why we had E G_ B___ which you filled out as E G# B. You could look at the black key in the middle and say "wait a minute, couldn't I call that note Ab instead of G#?", and you would be correct. If you wrote E Ab B and somebody played it, you would hear the same thing. But it would no longer be a triad with notes on adjacent lines like a snowman because the Ab would bump against the B, and you would no longer be skipping letter names. Therefore we chose E G_ B_ specifically.

This should give you the relationship between chords and accidentals. You start with a chord kind --- say major --- You have the notes of the triad which is:
E + some kind of G + some kind of B.
We need that "G" to be a semitone (half step) higher in order to have the 4 half steps from E, and to get it a semitone higher, we add a sharp. That is what sharps do. They move the note a half step higher in pitch, which we get on the piano by moving one piano key to the right. We use accidentals to make that happen.
--------------
Conversely, we also had Db F__ A___
The A is too high for it to be a P5 from Db or a minor 3 (3 half steps) from F. So you correctly lowered the A by a half step by making it Ab. The Ab lowers a note by a semitone, which on the piano means moving to the next piano key to the left.

So this is one way of looking at how chords and accidentals relate. Is anything unclear or are there any questions from this?

Continuing ... Your next question, Valencia, was about key signatures and chords.

Let's take our E G# B, which is an E (major) chord. We know why we need G#. This chord is in the key of E major, where the notes are:

E, F#, G#, A, B, C#, D#, E. We already have G# in the scale which we started from the tonic. One question you will ask yourself is "What is the I chord of E major?" You find it by skipping every second note, looking for the snowman, and you get that same EG#B. The key signature of E major has 4 sharps: F# C# G# D#, so we don't have to use an accidental, because the G# is already in the signature.

We have the original relationship of the chord as a pure chord, being major, with E in the root, and the middle note is G#. We have a second relationship, namely that if we want to find the tonic chord (I) we start with E and we again get E G# B.

Supposing we are in the key of A major (3 sharps: F#, C#, G#).

A, B, C#, D, E, F#, G#, A

E is the 5th note over. What is the V chord of A major? Again we can see it is E G# B. Again we don't need accidentals because that E is in the signature.

Key of B major (5 sharps: F#, C#, G#, D#, A#).

B, C#, D#, E, F#, G#, A#, B.

E is the 4th note over, and is the IV chord of B major. Again we have the notes for forming E G# B

How about D major (2 sharps: F#, C#)?
D, E, F#, G, A, B, C#, D

No, because we get EGB (no G#) which is Em.
We can also predict that because there is no G# in the signature, and we know the ii chord is always minor in a major key.

I don't know if this answers your second question, or if it confuses things.

I covered consonance and dissonance earlier in the thread when I first introduced the terms, post #2017754, 20 Jan 2013, 10:17am, PW time.

According to Pythagoras' Theory of Proportions, the simpler the vibration ratio is between two tones, the more consonant is their interval.

The ratio of an octave is 2:1, a perfect fifth is 3:2 and a major third is 4:5. The tritone, the most dissonant interval in the octave, is 32:45.

The degree of dissonance depends, therefore, on how easy it is to recognise the repeating pattern created by the different frequecy ratios.

The difference between using one chord over another is a question of personal choice but since the development of Western harmony there has been a preponderance of moves from tonic to subdominant major, dominant major and submediant minor compared to moves going to the supertonic and moves to the mediant minor are even more rare.

You could list the effect of each change from tonic to every other possibility, they are finite, but you can't describe the effect in universally accepted terms.

Leonard Bernstein's The Unanswered Question: Six Harvard Lectures argues that humans are 'programmed', not just conditioned, to appreciate tonality and register tension and resolution, which we can do almost from birth. He argues that tonal relations are built into nature and are understood instinctively.

Pardon my poor proofreading, that should be iii, V and vii dim.

The tonic major seventh is an unresolved chord. It is a softer sound than the flattened seventh and is more likely to be heard in Burt Bacharach's music than rock and blues. But so few western tunes end on it.

I have likened dissonance in an earlier post to enjoying chillis. You can acquire a taste for capsaicin and enjoy eating it but it is still an irritant and people who eat it in large amounts are typically unable to appreciate the subtleties of salad vegetables. People who enjoy dissonant intervals certainly have a wider palette but if it numbs their ear to the dissonance of Mozart I'm not sure I'd describe that as sophisticated.


History shows otherwise. The minor second interval, B-C, is 16:15 in just temperaments.

The tritone, I believe, was banned from church music at one time.

This is a quotation from wikipedia's entry on the tritone:

"Although this ratio [45/32] is composed of numbers which are multiples of 5 or under, they are excessively large for a 5-limit scale, and are sufficient justification, either in this form or as the tempered "tritone," for the epithet "diabolic," which has been used to characterize the interval. This is a case where, because of the largeness of the numbers, none but a temperament-perverted ear could possibly prefer 45/32 to a small-number interval of about the same width."

I'm not a jazz afficionado. Give me some examples of Jazz tunes that end on a seventh and I'll give them an honest listen and check out their popularity.


I am making posts on a public forum. These aren't intended to be lapidary inscriptions. Let me soften that from 'defined by' into 'characterised by'.
_________________________

The governments in the US and the UK in the early eighties declared that fat makes us fat and that two and a half million years of evolution was essentially wrong. Look at the state of the nations now after forty years of low fat, high carbohydrate diets!

We can't deny history. Nearly all Western music moves from tonic to dominant and back again. The ebb and flow of tension and release is what drives it and gives it movement; we talk about harmonic progression. Most Western music closes with a perfect cadence. The tritone doesn't have to sound bad, how delightful it is that you enjoy the sound as many do, it serves to mount excitement as in the climax of "Twist and Shout" (The Beatles and The Isley Brothers) but it's the release of the tension on the return to the tonic that gives us rest.

In playing the standard popular songs of the 30s/40s (Porter, Berlin, Gershwin etc) a pianist is as likely to finish on the 6th or the ma7 as the major. These are everyday subsitutions.



I can’t speak for the public palate, I suspect evidence is mixed. Both scotch bonnets and spinach leaves have space on my table so I don’t accept your assertion nor is the analogy sound.



As far as I know history says nothing about my suspicions regarding the relative tolerance to the intervals b5, ma7, b9 but by all means link me to something relevant.



It's still a gross oversimplification.



I think you’ve probably spent enough time marvelling at how most western music closes. Ditto your preoccupation with tonic and dominant. Of course such movements are peppered throughout but there’s so much more going on that your 7/8 resolution plays no part in. A beginners’ thread needs basic concepts but it serves nothing to make simplistic generalisations regarding the essence of music.

Tension and release? I prefer to travel and arrive. Better to travel…and this, the greater part of the journey, is where your 7/8 resolution gets second billing.

But frequency ratios of intervals – for whatever insight they might convey (none at all as far as I’m concerned) – have no bearing on the chaos of sonic interference that occurs when we play a chord. A four note chord has six simultaneous intervals banging against each other. A two handed ten-note chord has 45.

Dissonance and consonance are aesthetic issues. As far as I know there’s no useful science on this which will explain why our tastes and tolerances can be so radically different but links are always useful.

Hi PianoStudent88,

Nice idea for a thread! I'm still relatively new to posting on here and didn't really realize there was such an extensive conversation on analysis.

I like how you describe what analysis is for you. I'm definitely more pragmatic in my interest in analysis. I think I do it with a mind, ultimately, to be more informed in my own creativity.

Thanks for posting.

Richard, thank you for your answer on consonance and dissonance. I've taken the liberty of putting it all under one roof. Response or further thoughts in next post.


I found. It's part of the long post outlining a number of things, so I've taken the liberty of isolating this subject.



to which you have given us now

CONSONANCE and DISSONANCE as topic

I put together Richard's two sets of explanation in one place above.

Ok, mathematics (ratios) gives us one kind of understanding which is a scientific intellectual one. If we explore this side, I would like it to be real. Otherwise 3:2 etc. are just facts. So I looked for something stretchy but taut that will vibrate ergo a rubber band. If you stretch a rubber band over something and pluck it, you get a sound. That's how guitars work. If you push on your rubber band at some point, pushing that section right into the body holding it, and then pluck. You'll get a different note. Only the plucked side will vibrate because you have effectively shortened it. If you pushed it down at the half way mark of its length, then that's a ratio. What sound do you get at that ratio relative to the original sound?

So to translate this one sentence:

it means that if you get this ratio right with your stretchy whatever (rubber band) you should hear a tone that is a P5 of the original. The Greeks did a lot with this, and it tied in with philosophical ideals of the time.

But maybe we can get much more mundane and simpler for understanding this. Simply put:

Consonance involves note combinations that we generally hear as nice, smooth, easy on the ear, settled. What people perceived as consonant has varied over the centuries, and it will also vary between cultures, and genres of music. So this is a generalization.

If you play CG, CE, CEG, you will get that sense of smoothness, niceness etc.

Dissonance involves note combinations that we generally hear as unsettled, not smooth, vibrationy (my invention), and the theory is that we want that to resolve into consonance. Again there is a huge variation on perceptions.

If you put the flat of your hand on the piano hitting all the white and black keys at the same time, you have a dissonance. If you play CDb at the same time it probably "rubs" more than CD. The tritone (FB or BF = augmented 4th or diminished 5th) has an unsettled feeling, which is why it plays an important role in a V7 (GBDF) making the movement of V7-I so strong because of the contrast.

Meanwhile there is a lot of music where these tones are standard and considered pleasant, so what is considered consonant and dissonant is not written in stone.