A team led by Andrea Halpern created 35 short tunes [...] Each tune was then modified to have a minor-key and major-key variant -- this involved changing just a few notes in each tune. Then three expert musicians rated each clip for musicality and how "major" or "minor" each clip sounded. The 24 best examples of tunes with readily-identifiable major and minor keys were selected for study. The researchers then played the clips for 18 musicians, with over 8 years of musical training, and 18 non-musicians, with less than 6 months of training. The listeners were first briefly trained either to recognize major/minor keys or "happy" and "sad" music. Several examples of each type were played, and then for seven clips, the listeners were asked to identify whether it was major or minor (or happy or sad), and given feedback on whether their answers were correct. Finally, they were tested on new clips, while wearing a cap which had 30 electrodes designed to measure electrical activity in the brain. The data was collected on an EEG device. Regardless of whether they were trained to recognize happy and sad music or major and minor keys, the musicians were extremely accurate, averaging about 90 percent correct. But non-musicians had a different result: When they were trained in the major-minor method, non-musicians averaged just 63 percent correct for tunes in a major key. What's more, after the experiment, participants were asked what strategy they used to respond, and many non-musicians said they just listened for whether the music sounded happy or sad. Those who used this strategy averaged 75 percent accuracy, while the remainder who used no strategy were just 53 percent accurate -- statistically no better than chance.
A team led by Andrea Halpern created 35 short tunes [...] Each tune was then modified to have a minor-key and major-key variant -- this involved changing just a few notes in each tune. Then three expert musicians rated each clip for musicality and how "major" or "minor" each clip sounded. The 24 best examples of tunes with readily-identifiable major and minor keys were selected for study.
The researchers then played the clips for 18 musicians, with over 8 years of musical training, and 18 non-musicians, with less than 6 months of training. The listeners were first briefly trained either to recognize major/minor keys or "happy" and "sad" music. Several examples of each type were played, and then for seven clips, the listeners were asked to identify whether it was major or minor (or happy or sad), and given feedback on whether their answers were correct.
Finally, they were tested on new clips, while wearing a cap which had 30 electrodes designed to measure electrical activity in the brain. The data was collected on an EEG device.
Regardless of whether they were trained to recognize happy and sad music or major and minor keys, the musicians were extremely accurate, averaging about 90 percent correct. But non-musicians had a different result:
When they were trained in the major-minor method, non-musicians averaged just 63 percent correct for tunes in a major key. What's more, after the experiment, participants were asked what strategy they used to respond, and many non-musicians said they just listened for whether the music sounded happy or sad. Those who used this strategy averaged 75 percent accuracy, while the remainder who used no strategy were just 53 percent accurate -- statistically no better than chance.
My understanding from your diaries is that major keys are more harmonic (their intervals represent "smaller" fractions), aren't they?
I still probably failed the test in the article.
Interval (music) - Wikipedia, the free encyclopedia
# semitones Interval class Generic interval Common diatonic name Comparable just interval Comparison of interval width in cents equal temperament just intonation quarter-comma meantone 0 0 0 perfect unison 1:1 0 0 0 1 1 1 minor second 16:15 100 112 117 2 2 1 major second 9:8 200 204 193 3 3 2 minor third 6:5 300 316 310 4 4 2 major third 5:4 400 386 386 5 5 3 perfect fourth 4:3 500 498 503 6 6 3 4 augmented fourth diminished fifth 45:32 64:45 600 590 610 579 621 7 5 4 perfect fifth 3:2 700 702 697 wolf fifth 737 8 4 5 minor sixth 8:5 800 814 814 9 3 5 major sixth 5:3 900 884 889 10 2 6 minor seventh 16:9 1000 996 1007 11 1 6 major seventh 15:8 1100 1088 1083 12 0 0 perfect octave 2:1 1200 1200 1200
So I think you're right--music is one of those langauages where I'm close to illiterate--I can read a bit, but not much--certainly not enough to confidently sight-read western notation. Don't fight forces, use them R. Buckminster Fuller.
I get a lot of information from your diaries. This is the case when you think, if only I would had known that back then... when I was given to try things without a clue.
A ridiculous question: how does "most unharmonious" piano music (with most or all intervals pretty ugly) sound? Maybe you came across something while making the dissonance diary...
http://en.wikipedia.org/wiki/Consonance_and_dissonance
(Debussy & Stravinsky are about as liberated as I get...)
So--the most naturally dissonant intervals--where the frequencies are all clashing (and this can be effected by pitch, too--so that two notes played far apart on the keyboard have different vibrational relationships, and if you swap notes over you get different effects (e.g. play a low A and a high C, then play a low C and a high A)--would not be called ugly--(but I might hear them as ugly because the lack of resolution would disturb my ears, say)--it would be called "sound"--and "organised sound" is one way of starting to think about defining music (etc!)
Schoenberg is famous for developing the twelve tone series, where each of the twelve semitones in a standard western octave are played in succession, no repetitions of notes until the series (all twelve notes) has been played.
Schoenberg is okay (I'm at work so I can't go searching); Webern is the name I would most associate with "most or all intervals pretty ugly".
I'll tell you my theory; but have a listen, it's certainly music that is attempting to do specific things--maybe post up what you found?
So: serialism, twelve tone, Schoenberg, Webern, Cage...
More narrowly still, the term is used to describe music that is neither tonal nor serial, especially the pre-twelve-tone music of the Second Viennese School, principally Alban Berg, Arnold Schoenberg, and Anton Webern.
Composers such as Alexander Scriabin, Béla Bartók, Paul Hindemith, Sergei Prokofiev, Igor Stravinsky, Edgard Varèse, however, have written music that has been described, in full or in part, as atonal.
http://en.wikipedia.org/wiki/Atonal_music
(As I wrote, for me Stravinsky and Debussy are both everything tonal and most things beyond, whereas some of the other names never did anything tonal--or very little.)
Right, my theory: you see, the a-tonal serialism was (let's say) developed before, during, and after WWI--so there was a technical element (developing Debussy et al's developments, natural movements in the western musical tradition); but I think there was also a moral element--
--well, my theory is that with serialism etc they (in their own words) wished to pare music back to its bare bones, lose all the superfluous sounds--
--but as you wrote above, the harmonics are already creating definite patterns within a single note--specific resonances, so (for me) music that refuses to enter tonality (there are rules about how many major intervals you can have together etc...so it's not just "choose, mix and match"--there's an element of "you must not be tuneful")--
Anyways, Webern--and Berg; I have a friend who enjoys Berg, can't tell you which pieces--a piano concerto? I'll find out this evening, let you know. Don't fight forces, use them R. Buckminster Fuller.
That's sloppy--I'll take it back. Really I'd like to find a few examples, but I can't until late tonight. It's a whole musical period and I don't want to prejudice ideas--of course, they all understood tonality, so in at least one way (by not being tonal) there is tonality (the lack of something--the shape its absence creates)--ach! I mean, I'm very happy to be corrected by those who know more about these composers and this period.
(btw, Pierre Boulez is the composer/conductor to search for--there are plenty of pieces on youtube--also interviews.) Don't fight forces, use them R. Buckminster Fuller.
So....religious ideas, light and dark, moral confusions...I see it growing out of that (the way I see Heidegger's philosophy caught in religious ideas put against world events--Heidegger was german, Schoenberg was austrian--there's a tortuousness I find in both--not party people; committed to ideals that were going strangely wrong--heh...that's my reading!)
Anyways, here's the film (5:23):
Don't fight forces, use them R. Buckminster Fuller.
But instead of having a key note there's an equally rigid tone row, which gives the notes very little freedom of movement. The row is fixed and although you can do all of things to it - play it backwards, forwards, upside down, and so on - it's the one element that you're not allowed to change directly.
So it's not really free at all, and it doesn't sound democratic. Hardly anyone enjoys listening to it, because it usually sounds angular, ugly and sterile. It's more of a mechanised collectivisation of music - shifting blocks around for the sake of a process which most people can't hear directly.
I don't understand why composers didn't just cut loose and compose completely in freeform, where the notes could go wherever they wanted to go without that kind of arbitrary structure. But apparently composing without a predefined structure and method was too frightening, too much of a challenge and not nearly serious enough.
Which is odd, because it would have been much more 'democratic' than the tone row idea.
Especially, I think Stravinsky's use of horns is very free--I think of brass and woodwind as being less needy of exact tonal relationships (I don't know--because in themselves their sound worlds are fairly variegated--)
Then (in my theory) came WWI and tonality was frivolity was not understanding the depth of resonance--tonality was a pretending that there could be consonance in a world where--etc....
The next move was to use synthesised sounds (Messiaen's use of the Martenot)--and then...well...but yeah! I think there is a wide space for compositions that experiment with the full range of tibral expressions available through whatever instruments can be brought together:
To get people to repeat the music at other moments and in other locations, it has to be created in a medium where re-production is possible--so there's a technical apsect--but anyways, I think the freedom to work without predefined structure and method arrived with (or just before) Beethoven. For my ears, the serialist exercises sound much better played on a classical guitar--so timbre has a lot to do with it-- Don't fight forces, use them R. Buckminster Fuller.
Well, I would say there's only so much freeform you can do with a piano--fixed notes--and Debussy, Prokofiev, and Stravinsky did what you describe--cutting loose and composing freeform--but composing rather than a live improvisation (a la Keith Jarret)--so I suggest they were completely free (or became free) to use sounds as they preferred.
Debussy was famously fond of non-harmonic scales like the whole-tone, and his music is often constrained by that. Prokofiev and Stravinsky are closer to what I had in mind, and I think they were more successful because they're both listened to more than Webern is now.
But I think the problem with serialism was that it wasn't about structure, it was about structure which only existed on paper and had no acoustic justification. All of the other development until then had been about the sound, and about using tonality as a language for metaphors.
Serialism was about an idea which was divorced from the sound. It was a single method which didn't allow any freedom to include metaphor, but it was a metaphor, and if you used it there was only one thing you were allowed to say - which was mostly a tortured and angtsy squeak-bang-thud.
So music went elsewhere, to jazz, which was much more free harmonically while still having enough structure to be non-trivial.
heh....I suppose each piece is constrained in some way if it has structure (even 4'33--which is time constrained)...I don't think of Debussy as constrained simply because he acted completely freely within the possibilities of (mainly that I've heard) the piano, but yeah, with his own constraint that he loved certain timbres, certain elegant effects--which I like too! And I'm sure there are pieces of his that demonstrate the opposite of whatever another piece demonstrates.
it was about structure which only existed on paper and had no acoustic justification
That describes my feeling exactly, and yeah about the jazz break-off, in classical it's there with Ravel (and others of course, but I remember it specifically with Ravel's piano concerto)--
later on I'll post a piece of serialism written for the classical guitar, I do think timbre comes into it, and I suppose a composer could write dynamic markings onto their twelve tone series inversions etc. such that the notes are random (at least in the originating order) but the attack, forte piano, slurs etc. are set by the composer--
Still, it's not a natural sound world for my ears--I can maybe admire a piece and maybe find interesting dynamics, but my ears need some tonality--or maybe the one atonal piece, just to show it can be done, but not a series of them....
...I have friends, though (musicians) who very much appreciate, for example, Webern and Berg--so there's also a playability aspect--for some musicians there's an enjoyment in playing musical inversions, pallindromes etc. Don't fight forces, use them R. Buckminster Fuller.
5:27
i think it was more the desire to encode a protocol that all could centre around and then elaborate, like the difference between tossing a ball around and playing cricket.
an agreement that all use a point of reference to jam off of.
self-organising?
before we made these agreements, we probably did a much more random kind of thing, not serious maybe, and as for frightening...lol!
i guess you had to be there...
i get that you're probably referring to the illusion of safety one opts for by 'following the rules', rather than some kind of rawer anarchic approach.
but one is free to do that, the benefit of having rules is that they create some form to the culture, which then bathes children as they grow, and can draw its power to be so very evocative, resonating with ancient memories, maybe back to the dna level.
this helps explain why foreign music takes much longer to get the average head around.
i love the dalai lama's dictum ' learn the rules, so that you learn how to break them correctly', and i think music shows it to be true, tho' it goes even further.
of course the notion of what's correct sets off a whole other relativism, lol.. where do these agreements come from? how long do they last historically?
my guess is music and its rules are a self-emerging process, embedded within us, but dependent on synergy between local materials and regional sounds of flora and fauna to imitate, to flower.
i also think that western music is attracting more new listeners in asia than vice versa, but i could be wrong. same with s. america, or russia.
same with wine and sake or tequila or vodka...
it would be droll if aliens arrived and played music that was actually earthier than what most people have on their ipods here.
cause a lot of what people enjoy on earth sounds pretty alien to me!
except jimi, natch...
the blues and jazz habit of smudging notes, messing with the microtones, makes music come full circle for me, it knows the rules, there is a tonal 'homepage', but you can sally off where it gets lawless.
how far you go, and how long you stay, is the challenge presented by minds and hearts and nervous systems who haven't heard the rules broken so intelligently (or charmingly, another Great Indefinite!) before, and can only stand so much of what tilts over into chaos for them, and the fruit starts to fly, or beer bottles if you're in tornado country.
took me a long time to get coltrane for that reason...
fascinating series, rg!
when i get broadband, i'm gonna take a whole weekend and play all those youtubes, man what a treat, like waiting for xmas! The person who says it cannot be done should not interrupt the person doing it. Chinese Proverb.
Back in the day, composers would write "Cadenza", which means "Make the next bit up as you like"--an improvisation section, found in a piano concerto, say. So the beginning of Beethoven's 5th Piano concerto starts with cadenzas--that Beethoven wrote out! "Hey, that's the solo--now play it."
I was told that Bach was in the habit of writing out ornaments (trills and such) in full, whereas most composers left it to the musicians how to embellish--the sign was an idea not a list of specific notes.
So, piano concertos as rock gigs, with built in solo moments--and then the solo parts slowly get filled in (the composer might write in a few bars with the idea that the player can improvise around that structure etc.)
And--hey--listening to the whole series--! I think most diaries take about an hour (or so) to listen to. I really do think they make a lot less sense without the music--a lot of the comments following videos are coming out of the various sound worlds presented by the preceding video (well, that's my idea, whether it works...heh!)--in this diary, I felt the Sor piece played by Segovia said everything--once the context had been set for minor-major with the intro and the Radiohead piece--
So--let's hope you get broadband soon! Don't fight forces, use them R. Buckminster Fuller.
That was allegedly Glenn Gould's excuse for improvising when playing Mozart. If that's true, then it explains why I find Mozart's piano concerto solos rather bland :-) When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes
Most musicians now would play pre-written notes, so no improvisation. I found this with a quick google, though:
Why do these listeners get impatient? Perhaps because the cadenza rarely lives up to what it's supposed to be - a fantasy that sounds improvised, with enough of the unexpected to keep you on the edge of your seat. Nowadays, in a Mozart concerto, most pianists play a cadenza that was composed well ahead of time (sometimes by Mozart for a student, sometimes by someone more recent). Too often, it's obvious that everything was planned in advance.
But not when the pianist is Robert Levin. Like Mozart himself in concerts, Levin makes up his own cadenzas on the spot. Hearing him plunge in after the orchestra stops is like watching someone walk a tightrope without a net. In a Levin cadenza, anything can happen.
http://www.bsherman.org/levinstagebill.htm
The tour was a double act with his sister who was only a few years older - rated a much better performer, but not such a creative improviser.
He'd have been horrified by the modern idea of 'Here's the piece, these are the notes, play it exactly as it's written or we shoot you.'
I try to think of famous women composers - aren't they more rare than women mathematicians? What are the most famous names in this list?
The Deutsche Bahn does better than Wikipedia. They have (had? Anyone know where you can find a list of named trains?) a train named after Fanny Hensel.
One of the most famous names in the list is probably Annette von Droste-Hülshoff, but not as a composer. A few years ago (probably 1998), Münster had a festival dedicated to her, which included some compositions by her father, who taught her music. A rare instance of a male composer being remembered only because of his relation to a female one.
Here is the current list. But DB, and others, are reducing the number of named trains (why, I don't get it - how is it a problem to regular interval timeplan?...). However, I don't find any trace of an EC/IC/ICE Fanny Hensel in the past, either. *Traitor*, n. A benighted individual who perceives an illusory distinction between serving his nation and abetting the criminals who govern it.
I wonder whether they could be reducing the number of named trains to prepare the ground for Austrian-style sponsorship of trains? They have awful things like "Hollywood Filmkomplex" and the like. The most annoying is the "WIFI-express". With a name like that you expect to have WiFi on board, only to discover that WIFI is Austrian for Wirtschaftsförderungsinstitut - and that they don't regard installing WiFi as an appropriate form of Wirtschaftsförderung...
Could you narrow it down to train type (e.g. EC/IC/ICE/etc.), and roughly which year?
Austrian-style sponsorship of trains
Heh... last week in Vienna, I too saw that "Hollywood Megaplex" train, and also "EZA Fairer Handel" and some expresses named for web addresses...
But, seriously, ÖBB still kept nice names like "Mozart" and "Allegro Don Giovanni" and has room for sillyness like "Willkommen im Parlament", so I don't get what rides DB. (And DB has effects beyond borders - say, why drop the decades-old "Hungária" name for EC 170/171 Budapest-Hamburg and "Ján Jesenius"->"Alois Negrelli" for EC 170/171 Budapest-Berlin?) *Traitor*, n. A benighted individual who perceives an illusory distinction between serving his nation and abetting the criminals who govern it.
its exactly this tension and release that makes art art, i reckon.
the tension as someone pushes at the rules, and the release when they fold back into the groove, whether rhythmic, melodic or harmonic.
coming home! the further and riskier the journey, the sweeter the return...
but if you try to lead people too far from what they recognise, they'll fall away, so if you want the support of your listeners you have to gauge how far out they can handle it. or you could die, as that always raises the 'appreciability', a la nick drake.
if you don't invite them to savour some new 'way round the block', you're muzak!
elevator music, where if you shut your eyes you can see the musicians sneaking looks at their watches to see how long before they can knock off and go get drunk....to wash off the memories of the pallid melodies, charmless arrangements, flaccid orchestration, trite piled on shite...
sure makes you appreciate 'silence', (if there is such a thing!) The person who says it cannot be done should not interrupt the person doing it. Chinese Proverb.
Anyways, that's the end of my theory! Don't fight forces, use them R. Buckminster Fuller.
But I like your name better.
It's interesting that you can split the scale into equal steps without breaking anything too badly, so it could just be that there's a tendency to pick the first X ratios which can be distinguished by a typical listener and can be made practically distinct on an instrument.
If you try to work with a finer split you get more notes than people can hear, can play, can write, and can be bothered to remember.
So scales will tend to have a small number of notes - 5, 7, 12 - modified by local rules about ordering, ornaments and intonation, which will give each scale its flavour. Scales based on harmonics seem to be the most natural, but others are possible, and the exact ratios will always be a little fuzzy, and not quite perfect physics.
Why do we not use a ten-tone or twenty-tone equal-tempered scale? Is there something special about twelve? The answer is: Yes, the twelve-tone equal-tempered scale is remarkable. The nearly perfect intervals seen in the table above are not typical of other equal-tempered scales. Consider the six basic consonant intervals less than an octave (described above): 3/2, 4/3, 5/4, 6/5, 5/3, 8/5. The twelve-tone equal-tempered scale is the smallest equal-tempered scale that contains all six of these pure intervals to a good approximation - within one percent. Let's compare the twelve-tone equal-tempered scale to some other scales. * All equal-tempered scales with 14 notes or fewer (except the twelve-tone equal-tempered scale) contain at most only two of the six basic intervals within one percent. * Several equal-tempered scales with between 15 and 30 notes (notably the 19-tone and 24-tone scales) contain all six basic intervals, but in none of these scales are the intervals more nearly pure than in the twelve-tone equal-tempered scale. * The 31-tone equal-tempered scale has all six basic intervals to a good approximation, some with better accuracy than the twelve-tone scale, but the most important fifth (3/2) interval is less accurate than in the twelve-tone scale (218/31=1.495). Some Indonesian music actually uses a 31-tone equal-tempered scale. * The 41-tone equal-tempered scale is the first with a better fifth (3/2) interval than the twelve-tone scale (224/41=1.5004). * The 53-tone equal-tempered scale has all six basic intervals with a better accuracy than the twelve-tone scale (231/53=1.49994).
The answer is: Yes, the twelve-tone equal-tempered scale is remarkable. The nearly perfect intervals seen in the table above are not typical of other equal-tempered scales. Consider the six basic consonant intervals less than an octave (described above): 3/2, 4/3, 5/4, 6/5, 5/3, 8/5. The twelve-tone equal-tempered scale is the smallest equal-tempered scale that contains all six of these pure intervals to a good approximation - within one percent.
Let's compare the twelve-tone equal-tempered scale to some other scales.
* All equal-tempered scales with 14 notes or fewer (except the twelve-tone equal-tempered scale) contain at most only two of the six basic intervals within one percent. * Several equal-tempered scales with between 15 and 30 notes (notably the 19-tone and 24-tone scales) contain all six basic intervals, but in none of these scales are the intervals more nearly pure than in the twelve-tone equal-tempered scale. * The 31-tone equal-tempered scale has all six basic intervals to a good approximation, some with better accuracy than the twelve-tone scale, but the most important fifth (3/2) interval is less accurate than in the twelve-tone scale (218/31=1.495). Some Indonesian music actually uses a 31-tone equal-tempered scale. * The 41-tone equal-tempered scale is the first with a better fifth (3/2) interval than the twelve-tone scale (224/41=1.5004). * The 53-tone equal-tempered scale has all six basic intervals with a better accuracy than the twelve-tone scale (231/53=1.49994).
[0, 1, 1, 2, 2, 3, 1, 5, 2, 23, 2, 2, 1, 1, 55, 1, ... ]
the first few approximants are
0, 1, 1/2, 3/5, 7/12, 24/41, 31/53, 179/306, 389/665, 9126/15601, ...
so the 5, 12, 41, 53, 306, 665 tone scales as good for the 3:2, 4:3, 8:3... harmonics as you can cope for. Especially 12, 53 and 665 tone scales are good, because the next partial quotients 3, 5 or 23 are large. (The devil must be using the 666-scale.)
What about other important ratios?
The continuous fraction for 5:4 is [0, 3, 9, 2, 2, 4, 6, 2, 1, 1, 3, 1, 18, 1, ...] with the first two approximants 0, 1/3, 9/28, 19/59, 47/146, 207/643, 1289/4004... Here we have 1/3=4/12 (and there is nothing better until the denominator 28). This luck is a bit of coincidence.
The continuous fraction for 5:3 is [0, 1, 2, 1, 4, 22, 4, 1, 1, 13, 137, 1, 1, ...] with the first two approximants 0, 1, 2/3, 3/4, 14/19, 311/422, 1258/1707.... Here again, 2/3=8/12 and 3/4=9/12 (and there is nothing better until the denominator 19), which must be very convenient for the major and minor subtonalities...
So the 12 is helped by the fact that it is richly divisible.
Pity the pythagoreans didn't know about logarithms. When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes
amazing, thanks.
12 is a number that has such mythic resonance. The person who says it cannot be done should not interrupt the person doing it. Chinese Proverb.
Dice have been used throughout Asia since before recorded history.
The oldest known dice were excavated as part of a 5000-year-old backgammon set, at the Burnt City archeological site in south-eastern Iran. Excavations from ancient tombs in the Harappan civilization,[4] seem to further indicate a South Asian origin. Dicing is mentioned as an Indian game in the Rig Veda, Atharva Veda[5] and Buddha games list. It is also mentioned in the great Hindu epic, the Mahabharata, where Yudhisthira plays a game of dice against the Kauravas for the northern kingdom of Hastinapura.
http://en.wikipedia.org/wiki/Dice#History
There is a comment somewhere else in this thread quoting an article with the question of why we don't use 10 regular intervals. The Babylonians knew that 12, 24, 30, 60 and 360 were richly divisible, that's where their number system comes from and note the only place it survives is in astronomy and timekeeping.
There is nothing new under the Sun, etc. When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes
