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A Journey into Sound Part VII -- Consonance & Dissonance (with videos)

by rg Sat May 3rd, 2008 at 05:56:17 AM EST

Saturday bump up for our sound journey - In Wales

Note: If you click to play a video, hear no sound, and the video stops at exactly 00:02 you have come across the firefox/ET video bug.  At present the solutions are: close the window, re-open and try again (not always effective); wait for another time (which sometimes works but involves waiting); view the diary in a different browser; or click the link below the image to view the clip directly in youtube


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


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."

The theme is Ah, vous dirai-je, Maman.

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


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


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


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


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


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


Okay--!  Time for an interval.


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


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


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


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?


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


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


Previous diaries:

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

Two more for you:

First, The Hunt with the pictures added.

And then there's this (3:48):

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Tue Apr 29th, 2008 at 07:45:43 PM EST
Once again very comprehensive. I see you even dragged in a bit on temperament...

There is some evidence that Bach's "Well Tempered Clavier" wasn't written to prove the virtues of equal temperament. Even Bach wasn't ready for such a break with traditional musical theory. Rather he used a tempered scale where all the keys were at least acceptable, but where there were still noticeable differences in the intervals when going from one to another.

I think there are a few recordings around which use such tuning systems to play this work.

Perhaps you will get to it in a future installment, but the next logical step is to discuss timbre. Certain instruments have widely different sound qualities depending upon which note is being played. For example both the clarinet and oboe have very weak tones for those notes which are played with just one finger covering the tone holes (the "break").

The string family produces different tone quality when one plays on an open string or one that is stopped at a shorter length. The French Horn (before keys) had muffled tones for the accidentals and clear tones for the natural harmonics.

There are examples of pieces written to make use of these tonal differences explicitly, while there are others where the composer tried his best to ignore them.

When electronic music first started there was a great deal of interest in exploring the new types of sounds that could be created, but the shift to keyboard-based synthesizers has stifled some of this creativity since the the interface limits the types of expression one can create.

Policies not Politics
---- Daily Landscape

by rdf (robert.feinman@gmail.com) on Wed Apr 30th, 2008 at 08:33:16 AM EST
Heh, I felt I had to write something about temperament after your previous comments on the subject--you know, one of the things about writing these diaries is that I'm learning a lot while searching for pieces, all the info about ratios and temperaments came from that--

Timbre was covered in Part V (a co-production with Greg Whitman.)  You're right about all the things that could be said--these diaries are long but there's a lot I leave out; my idea is that I'll take one track and in the comments others can follow others--widen the range, head in different directions, that kind of thing.

With videos if possible, so that there are sounds to match words (or just sounds!)

I'm planning to do twelve diaries--next up I'm not sure, maybe Ornament, or Form & Function; there's also Major/Minor--

But yeah, I don't want it to all become too technical--more music, less words about music, but I'm also interested in the mechanics of sound production--and have become more so through writing the diaries.  Here's a find I enjoyed but didn't put in the diary--I'm sure you know all this already, so this is just an excuse to post it!

The mythical story of how Pythagoras worked out that sounds came in ratios:

According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when one day he passed blacksmiths at work, and thought that the sounds emanating from their anvils being hit were beautiful and harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. He went to the blacksmiths to learn how this had happened by looking at their tools, he discovered that it was because the anvils were "simple ratios of each other, one was half the size of the first, another was 2/3 the size, and so on."


If you find any videos of pieces played on well-tempered instruments, esp. two different keys on the same instrument--please post them; it would be great to hear the difference (answering the question: "Why do composers talk of the 'mood' of a key?"  My very limited experience with a harpsichord says that E Major is the brightest--)...it would be great to have some video examples to listen to.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Wed Apr 30th, 2008 at 10:34:23 AM EST
[ Parent ]
I've just started reading Oliver Sacks' new book "Musicophilia" which is full of stories about people with brain disorders and their relation to music.

In some cases hearing certain music triggers epileptic attacks, in other people hear music during such attacks, etc.

Then there is the whole subject of synesthesia where people see colors in response to music or other cross sensory effects. Scriabin seems to have had this condition and used color with some of his works.

Policies not Politics
---- Daily Landscape

by rdf (robert.feinman@gmail.com) on Wed Apr 30th, 2008 at 11:57:21 AM EST
[ Parent ]
The mood issue is problematic. I always think of F major as the happiest of the happy keys. Trevor Horn said that D minor was the best key for pop because D on the bass provided the best foundation. D sharp minor - all the black notes - is slightly spooky.

But all of this would have to depend on A=440 being a standard, and given that A used to wander all over the place, and A=450 or 460 isn't totally unheard of even today - it sounds sharper and more exciting - it's hard to imagine there's any genuine consistency.

According to the perfect pitch courses I've seen, each key has a different subjective experience. From my limited experiments, there seems to be some truth to this. The F sharp in B always honks a little, and you don't seem to get that honk in other keys.

Who knows why?

Meanwhile - the weird chord in the Bach piece is a diminished 7th, which was about as dissonant as things got in those days, and includes the infamous flattened fifth.

It's a nice general purpose chord which can go in any direction, and it adds a bit of drama, so Bach used it quite a bit.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Sat May 3rd, 2008 at 09:48:23 AM EST
[ Parent ]
The way I understand it is that the difference between the keys is related to the root.  If you tune perfect fifths and accurate major thirds to C, it'll have an effect on pieces in F# minor.  If you tune them to F, then whatever note relates to F the way F# relates to C (C?--the raised fourth!) will have (if I've understood correctly) the same feel in relation to the root.  So when the composers talked about the feel of a key, it would always be in relation to C as the root and then the various tuning mechanisms brought out different flavours as the key varied.

With the advent of synthesisers, any relationships can be created and then re-created in realtime as preferred, so the idea of G having a particular feel makes no sense--all the relationships sound the same and as you say, C has moved around so it can't be a strict pitch thing.

With instruments, though (again, if I've understood it right), there do exist notes that are better for the structure--trumpets and trombones are built around specific tones; strings sound different if you tune them more than a tone above or below--the tensions are noticeably different--

If I say I like Es on electrics and Ds on an acoustic, I think that means the way the strings resonate when held down in those patterns with those instruments--

What intrigued me when I played on the harpsichord is that different keys did seem to have a different feel; what Robert has pointed me to and said about temperament made me think that tuning harpsichords a certain way around C does give keys specific flavours--

I came to Bach via the sound of the piano, so the Well-Tempered Clavier had a different meaning to me; the various keys didn't matter much, they just mean playing from different starting points; but I think there are probably lots of enjoyable things Bach was doing for the player and listener that can only be heard when played on correctly tempered instruments.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Sat May 3rd, 2008 at 07:40:37 PM EST
[ Parent ]
The way I understand it is that the difference between the keys is related to the root.  If you tune perfect fifths and accurate major thirds to C, it'll have an effect on pieces in F# minor.

No, there should be no difference at all between harmonic ratios for each key in equal temperament. In effect you get exactly the same scale with exactly the same relationships, only it can start on any frequency. Conventionally its tuned to A440, but there's no reason why you couldn't tune it half a semitone above that - around A450 - and in theory the scale should still have the same mood.

Of course if people really have a kind of rudimentary perfect pitch that won't be true. It would be an interesting thing to experiment with.

Synthesizers are usually tuned with equal temperament because even when you get access to the tuning tables, hardly anyone knows how to calculate the ratios needed to use them. Apparently non-Western scales are popular in Arab countries, and synths are regularly tuned to non-Western scales there. But in Europe and the US, equal temperament is usually the default aznd it's rarely changed.

Harpsichords, I don't know - I suspect not. It probably depends how early-music the player is trying to be. There are various tunings with names like Kirnberger and Valloti which are all variations on not-quite-equal temperament, and I'd expect those to sound different away from the home key.

Perfectly tuned keys sound very strange to Western ears. Terry Riley did an album called Shri Camel in perfect intonation and it's not easy to listen to, because all the intervals sound out of tune - at least until you get used to them.

The other thing about equal is that introduces movement. There's a theory that because the intervals all beat slightly, there's a subconscious tendency to want to move on, which means that music speeded up and became busier as temperament moved away from perfect intervals.

I'm not sure how true that is, but it's an interesting idea.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Sat May 3rd, 2008 at 08:54:48 PM EST
[ Parent ]
I found this on YouTube it illustrates one of the most recent ideas on how Bach tuned his harpsichord.


Policies not Politics
---- Daily Landscape

by rdf (robert.feinman@gmail.com) on Wed Apr 30th, 2008 at 12:03:34 PM EST
I seem to have stumbled on someone even more obsessive about this than me. He has a whole web site devoted to this with lots of musical examples:


Policies not Politics
---- Daily Landscape

by rdf (robert.feinman@gmail.com) on Wed Apr 30th, 2008 at 12:15:02 PM EST
Bradley Lehman's website is a recent discovery of mine, too. I found this application of his Bach temperament especially fascinating, by the Hungarian jazz musician Szolt Kaltenecker:

On his Myspace page, Paradox Perspective, from the CD Impossible.

On his trio's website, Nocturne and Home Alone, from the same album.

You're clearly a dangerous pinko commie pragmatist.

by Vagulus on Sat May 3rd, 2008 at 03:35:34 PM EST
[ Parent ]
Zsolt, not Szolt. ("Zs" is spoken like "j" in the French "jour".)

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Sun May 4th, 2008 at 05:11:54 PM EST
[ Parent ]
My mistake indeed. I noticed on re-reading my post but it was too late. Thank you for the phonetic equivalent.

You're clearly a dangerous pinko commie pragmatist.
by Vagulus on Sun May 4th, 2008 at 06:47:22 PM EST
[ Parent ]
Started watching this last night, have to watch the rest tonight so I can comment properly.

This series is pleasently time consuming.

Any idiot can face a crisis - it's day to day living that wears you out.

by ceebs (ceebs (at) eurotrib (dot) com) on Wed Apr 30th, 2008 at 12:55:18 PM EST
rg, this entire series is so brilliant, concise, well-formed, AND illuminating.  Vielen Dank.

"Life shrinks or expands in proportion to one's courage." - Anaïs Nin
by Crazy Horse on Wed Apr 30th, 2008 at 02:32:37 PM EST
Hey, what happened to classical music?  My theory is that it simply moved into films.

How true! I present Ennio Morricone: Extasy of Gold - first the concert version (03:29):

...then as clip from The Good, The Bad And The Ugly (03:51):

*Lunatic*, n.
One whose delusions are out of fashion.

by DoDo on Thu May 1st, 2008 at 02:50:59 PM EST
I'm going to suggest that whereas the Planet of the Apes soundtrack was very much subdued by the dialogue (it was the trailer, though), in your two clips--waking up in a huge graveyard! -- the music (wonderful mix of soundtrack and film effects [the bark of the dog]) gives a very particular feel to the images...

which the music does in Planet of the Apes--though I think in Planet of the Apes more was lost by the concentration on the...not the visuals, it was the narrative-over-the-top....


Ignore the images in the next piece, just the music--

the theme, the sax, the crescendo....

It says at wikipedia that "The cartoon character created for the opening credits of the movie by Friz Freleng was animated in time to the tune."  Whereas my ears say (maybe erroneously!) that Morricone's theme was written while watching the scene....backwards forwards...

I could be wrong!  It's a way of looking at it....that some put the music to the pictures, while others put the pictures to the music--

an intriguing mix.  In each case to produce a new thing--the pictures with music--where each element is complementary to the other.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Thu May 1st, 2008 at 07:49:50 PM EST
[ Parent ]
Whereas my ears say (maybe erroneously!) that Morricone's theme was written while watching the scene....

Nope, just the opposite. From what I know, director Sergio Leone often used to play the music for the actors while filming! But there was a back-and-forth included: Leone's films are like compositions themselves, he knew what angles, takes, timings and cuts he wants, and wrote detailed and technical scripts. So, already at the start of a project, Leone and Morricone would sit down with Leone's script and get an idea of what kind of music is needed in which scene.

*Lunatic*, n.
One whose delusions are out of fashion.

by DoDo on Fri May 2nd, 2008 at 08:01:57 AM EST
[ Parent ]
As an example of how much Leone could bring acting in synch with Morricone's music, here is a scene from Leone's final masterpiece, the nearly four-hour-long mafia epic Once Upon A Time In America -- this is one scen where I know for certain that the music was played for the actors (it's 09:59 long, with music in the first half and the last fourth):

Also watch this BBC documentary clip, where they talk about and demonstrate the synchronisation from 04:30 in. (But the speaker is wrong to claim Once Upon a Time In The West was the first they filmed this way.)

*Lunatic*, n.
One whose delusions are out of fashion.

by DoDo on Fri May 2nd, 2008 at 08:40:03 AM EST
[ Parent ]
Superb series! Thank you very much!
by PerCLupi on Sat May 3rd, 2008 at 06:17:08 AM EST
I've created a diary listing this series in the indices - if there are other sounds and music related diaries then let me know and I will add them to the list.  

Also, were all of these diaries originally posted on a wednesday? I'll add the dates in if so.

by In Wales (inwales aaat eurotrib.com) on Sat May 3rd, 2008 at 06:18:40 AM EST
Hey, thanks for that!  Much appreciated.    And thanks for the front-paging on Saturdays--

The Timbre diary was posted on a Friday; I think the others were all Wednesday postings.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Sat May 3rd, 2008 at 07:23:15 PM EST
[ Parent ]
No problem, it's a great series.  I'll stick the dates into the list now.
by In Wales (inwales aaat eurotrib.com) on Sun May 4th, 2008 at 03:54:32 AM EST
[ Parent ]
You can see the dates in the URL of the diaries. I believe the very first one was on a Saturday or Friday, too.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Sun May 4th, 2008 at 05:14:07 PM EST
[ Parent ]
Oh yes, I never realised that. Thanks.
by In Wales (inwales aaat eurotrib.com) on Sun May 4th, 2008 at 05:51:26 PM EST
[ Parent ]
Thank you for this really remarkable post, which made my morning. A fascinating review (and I loved the examples you linked to.)  Thanks again.
by Edouard (edouard@salebetedeletethis.net) on Sat May 3rd, 2008 at 12:12:13 PM EST

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