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Consonance and dissonance

In music, a consonance (Latin consonare, "sounding together") is a harmony, chord, or interval considered stable, as opposed to a dissonance, which is considered unstable (or temporary, transitional).

Here's what I think most people these days would think of as a piece of music full of consonance.

Ritchie Valens- Oh Donna (2:18)

Link: http://www.youtube.com/watch?v=CHPBObnlmuk

And here's a piece that most people would agree is full of dissonance.  Song starts at 00:26.

World Domination Enterprises - Hotsy Girl (2:09)

Link: http://www.youtube.com/watch?v=kdstKEfqtrk

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Technically, consonance is where the various sounds have simple relationships one with the other, so starting with a root note (the tonic) the octave above it has a ratio of 2:1 (with a string, it's length has been halved), and the other notes have ratios as follows:

Major 2nd - 9:8
Minor 3rd - 6:5
Major 3rd - 5:4
Perfect 4th - 4:3
Perfect 5th - 3:2
Minor 6th - 8:5
Major 6th - 5:3
Minor 7th - 16:9
Major 7th - 15:8

There's a simple way to work out which note is which: Twinkle Twinkle Little Star (or the french, Ah! vous dirai-je, Maman) goes as follows:

Twinkle (tonic)
Twinkle (fifth)
Little (major sixth)
Star (fifth)
How I (major fourth)
Wonder (major third)
What you (major second)
Are (tonic)

Mozart did some variations on this; I'd like you to listen to the next clip for two reasons:

1. To hear the notes rather than read words about them
   
2. I was once told, "One way to get into Mozart is to listen to his theme, then think about how you would go about varying it.  Once you've thought about that, have a listen to how Mozart goes about it."

Points to note:

The first variation (right hand virtuosity) starts at 00:41
The second variation (left hand virtuosity) starts at 1:06
The third variation starts at 1:30
The fourth variation (2:06) starts getting dissonant  Why is it dissonant?  Because he's playing two notes right next to each other, that's a minor second and the ratio of the minor second is 16:15--the bigger the numbers the more the vibrations conflict with each other
The fifth variation (2:46)--he turns the piece from major to minor--it's the same numbers but now we get the minor versions--

& etc. Here's the piece.

Mozart - 12 Variation "Ah, vous dirai je, maman" K.265 (5:18)

Link: http://www.youtube.com/watch?v=71f2fahFhDE

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The tonic, the fourth, and the fifth have the simplest ratios--so you find them in a lot of music.  The next piece has a guitar melody over the top of chords that move 4,5,1,1.

Ali Farka Toure & Ry Cooder, Soukora (5:59)

Link: http://www.youtube.com/watch?v=FwMr3foanNk

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The next piece uses lots of other chords and goes at quite a speed--it still sounds consonant (Mr Bach!)--except, hold on, what's that sound at 00:34?

Wanda Landowska: Bach, Prelude & Fugue no. 21 (3:23)

Link: http://www.youtube.com/watch?v=C7iDVBohp-E

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You can have the one underlying tone (the key of the piece) and melodies and harmonies on top;  you can change the tone (modulate from one key to another)--from the first to the fourth to the fifth sounds good--but what about if you want to move everything up nine semitones?  Trouble is, an instrument that is perfectly tuned for the first fourth and fifth will sound more and more out of tune if you start changing which note is the first (and therefore which notes are the fourth and the fifth i.e. changing key.)  Various things were done through the centuries to deal with this problem--that instruments were limited to which keys they could play in (and sound tuneful)--with a western-tradition compromise arriving thus:

Equal temperament

Equal temperament is a musical temperament, or a system of tuning in which every pair of adjacent notes has an identical frequency ratio. In equal temperament tunings an interval -- usually the octave -- is divided into a series of equal steps (equal frequency ratios). For modern Western music, the most common tuning system is twelve-tone equal temperament, sometimes abbreviated as 12-TET, which divides the octave into 12 (logarithmically) equal parts. It is usually tuned relative to a standard pitch of 440 Hz.

Now all the notes could be moved to, and all the various relationships developed from any note--

and in the meantime, as the centuries had passed, more and more tones were being brought into the acoustic fold, or maybe the ears of the listeners were accepting a wider and wider range of tones as acceptable.  Also, the church had lost power; music was no longer from the western god and to be given back to the western god as explained in musical theory.  Now music was about tension and resolution--those dissonances were useful because the listener's ear ached to be brought to--ah!  Orgasm--the perfect consonances--and so a clever composer would move the listener through twists and turns, here's the consonance, no, it's something else!  Formalism (it does this, then that, then the other) gave way to expressionism--found in Mozart (who was also a formalist, a crossover composer from one period to another)--expressionism--ah!  Express your romantic self--the romantics, Beethoven.  The beginning of the fifth symphony:

He also wrote the wonderfully consonant 6th--here it is, all thirty plus minutes in case you've never heard it before.

Karajan - Beethoven Symphony No. 6 In F Major 'Pastoral' (35:50)

Link: http://www.youtube.com/watch?v=HZGb-Kjy0S0

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The composers kept pushing at the dissonance boundaries--various innovations were made, audiences revulsed--repulsed by the dissonances--and then other composers took the innovations, played about with them, and soon enough they were commonplace and what had sounded terribly dissonant (and decadent etc.) was now perfectly acceptable.  By the early twentieth century the tonal palate had been fully opened.  It was no longer necessary to hang around the same tonal root--or any tonal root--melodies and harmonies would move according to the structures conceived by the composer.  We're used to hearing this music--we've heard so much it sounds far from dissonant--yet if you listen to the next piece and think for a moment in terms of Twinkle Twinkle Little Star--then wonder what the root note is, what's the fourth, the fifth etc...

I think what gives it consonance (for me) is the sense of it having an internal structure and its playing with romantic forms, including romantic passages--it's just very very wide (check out the piano solo, starting with the orchestra's introduction of the theme at 3.18 and the piano starting at 3:25!)

Yundi Li - Prokofiev Piano Concerto no.2 1st movement (11:00)

Link: http://www.youtube.com/watch?v=4GmXgjNWL8g

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That piece was premiered in 1913.  Another piece premiered in 1913 was Stravinsky's Rite of Spring.  Famously the audience booed and hissed (well, half of them did; the others applauded wildly)--how can this be!  Terrible!  What Stravinsky did (but note that Prokofiev was doing the same thing at the same time, just--to my ears--from a more romantic mindset) was declare: Here is tonality and here is everything else we call music and I put them together and voila!

The Rite Of Spring - The Adoration of the Earth (3:58)

Fantastic!  A really great recording, not too long and you get to see what all the instruments are up to--and what a beginning!

Link: http://www.youtube.com/watch?v=phIRRINOF-M

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Okay--!  Time for an interval.

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The Devil's Interval

has a ratio of 45:32!  Help!

Bill Bailey - The Devil's Door Bell (2:28)

Link: http://www.youtube.com/watch?v=rmoUxjVo-nw

The augmented fourth--the devil's interval!  Yet in non-western traditions the augmented fourth is common and sounds great (I really like the augmented fourth.)  To get a sense of it try Twinkle Twinkle Little Star and when you get to How--try going up a semitone and then going back to the twinkly fifth--that semitone difference between the now-augmented (=raised) fourth and the fifth--that's the sound you can hear in the next piece, it comes and goes (the sound) among all the other wonderful sounds...great piece.  Here it is.

Bafoulabe - Toumani Diabaté with Ballake Sissoko (6:27)

Link: http://www.youtube.com/watch?v=05BLnB66yNc

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One more piece relating to intervals: the major second.  In the indian scale this is RE and is seen as the wonderful note.  While SA (the root note) is...the root of everything, RE is the starting point for all kinds of wondefulnesses.  Here's a tuareg group using the major second, played on the electric guitar, it's the note that you hear at 00:02--ach--it's the last note of the riff, sounds great!

Touareg music (7:55)

Link: http://www.youtube.com/watch?v=Mvt55yopjAU

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My word, all that music, all those videos!  Only a few to go--and they're great too!

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The Twentieth Century in the U.S.

The ears have been opened, everything is up for grabs, and--african musicians have picked up western instruments and made their music with them, music which has a whole sideways view of consonance and dissonance.  The blues met classical instruments in New Orleans and out came jazz, which fed back and around and sideways until everyone was happy with sounds that, on the Twinkle Twinkle Little Star scale are way out in the far reaches of wild expression.  But as I said, we're used to the sounds--well, I find them all wonderful.

Benny Goodman and Peggy Lee - Why Don't You Do Right (2:30)

Link: http://www.youtube.com/watch?v=H6XF4Yf6qNI

Move forward a decade or two, cars are everywhere--the modern city is here!

Charles Mingus - Boogie Stop Shuffle (5:03)

Link: http://www.youtube.com/watch?v=ePMvgRGm73U

And, I ask you, how long did it take for that sound to work its way into the collective unconscious such that the following sounded just about...the same?

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And Finally

Hey, what happened to classical music?  My theory is that it simply moved into films.  Because films keep the music low and the voices high, it's easy to miss how open soundtracks are to all sorts of strange sonorities, but don't tell me the following piece doesn't fit perfectly into the traditon running through Prokofiev and Stravinsky et al.

the hunt (5:10)

A cornucopia of sounds and check out that horn at 1:03, it put THE FEAR into me when I watched the film way back when.

Link: http://www.youtube.com/watch?v=IbEF9Se2Fm0

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I hope you enjoyed the music, please add your own, the more collectivities the better!

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Previous diaries:

Part I
Part II
Part III
Part IV
Part V
Part VI