The tritone comes from NOT tuning the 3rd purely, but usinf equal temperament.
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Had to try it out -- there is indeed a dissonant resultant, not from a major third, but from a TRIAD -- probably from the major third/fifth conflct of overtones.
BUT!!! compare the sine waves with an equal tempered third: it is much, much, much worse.
Listen to http://mysite.verizon.net/guglielmo/sine_torment.mp3
the first, sine waves at 250, 500, 750, 1000 (C) , 1250 (E), 1500 (G)
the second, sine waves at 250, 500, 750, 1000 (C) , 1260.2 (E'), 1500 (G)
!!!
([edit] John A -- I believe DG was saying the PURE major third causes the dissonance. S/He used the word 'tuned', anyway.
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I´m not sure how much microtonal work Ligeti actually has done. Lontano and stuff is chromatic if I´m not wrong. I´m not sure it he actually ever has done microtonal work.
The German Frank Zender has done a lot of microtonal work, exploring differential tones. Recently I was very fascinated by pieces by the Austrian Georg Haas: 1. string quartett and "Einklang freier Wesen". I really liked that.
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@gugliel said:
the first, sine waves at 250, 500, 750, 1000 (C) , 1250 (E), 1500 (G)
the second, sine waves at 250, 500, 750, 1000 (C) , 1260.2 (E'), 1500 (G)
I don't hear the first ones as dissonances at all - it sounds like maybe there's an overloaded signal level, but there's no beating of "out-of-tune" intervals like there is in the second example.
You can work this stuff out mathematically - sum and (especially) difference tones.
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gugliel,
sorry about that... you're right, and I actually was a little concerned about the association of Lutoslawski with Penderecki when I wrote that.
I guess I was going with the general conversation, and thinking of the fact that _some_ of the techniques Lutoslaski used in the later pieces had a sound somewhat similar to certain moments in Penderecki, at least to somone not familiar with the former's work. Anyway, point well taken!
I actually came to Penderecki through Lutoslawski, as well, which has probably always effected my comparison of the two. Also, I heard Lutoslawski's later works before hearing the earlier ones. I never seem to "discover" anyone or anything in chronologic order!
J.
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William,
Chromatic refers to the lack of modal harmony. The free use of non-tonality whilst staying true to the basic tones and semitones of ALL music (eastern music is also based on this despite what so many people tend to perport).
Evan Evans
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Actually what Mathis was probably trying to say, is better translated as Chromaticism. it doesn't mean even that a minor second melodic interval even be present in the score. it simply means the free use of non-tonality and without roots in modal harmony.
Evan Evans
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Bill, I only have the Lontano score at home and just had a look again and I really don´t find any accidentals other than naturals, flats and sharps.
I agree with Evan about the chromatism of eastern music. I don´t hear microtonality in there. It´s different tuning and maybe different tunings to choose from, but the thinking is still in halfsteps. When talking about microtonility, I think of quartertones and smaller, or specified deviations to generate differential or sum tones.
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Lux Aeterna, Atmospheres -- both chromatic, not microtonal, unless my memory deceives me. I've looked at both scores, but don't own them or have access to them presently. Penderecki specifies quartertones, specifically, in various works including the famous St Luke Passion. I sang that (in the chorus) last year, and there is nothing other than chromaticism in the choral parts, but the strings have a few quartertones. Not sure about the solo vocal parts.
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Chromatic does not refer to "lack of modal harmony" - plenty of chromatic music is modal also.
All right Mathis and Gugliel you can both slug me because I was in error about calling these microtonal. I looked up Ligetti's statement and he described his work on these pieces - Lontano, Apparitions and Lux Aeterna - as "micropolyphonic" not microtonal, though the sound is utterly different from chromatic atonalism. On Lux Aeterna he said "I broke with my preceding style of chromatic tone clusters (as in Atmospheres or Requiem). It is a 16-voice micropolyphonic piece with diatonic voice leading of complex canons."
The sound of this actually performed is so far from the clear distinctions of chromaticism in for example Berg or Webern that it something basically different and has clearly audible warping of the 12 written tones, but it is something that happens in the mind of the listener. It would be interesting to compare this to a similarly scored but definitively microtonal piece. I know this will enrage some people but exactly the same thing happens in the 4th movement of the Tchaikovsky 6th: there is a line in the strings which does not exist anywhere on the page, but only in the mind of the listener.
Likewise on Atmospheres - it is scored chromatically but you don't hear it because of the extreme emphasis on color, as well as the creation of perceived overtones and shifts in harmony due to these colors. It is an almost supernatural piece of music.
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No problem, William -- the sounds are unique for sure, and don't know if they would be richer with microtones. Currently, I'm most interested in microtones in connection with 'purer' sounds, tuning and playing with overtones, rather than in pushing past clusters like Ligeti toward pink noise.
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Wow, I did not realize Atmospheres was not microtonal. What an accomplishment then.
Evan Evans
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@William said:
The sound of this actually performed is so far from the clear distinctions of chromaticism in for example Berg or Webern that it something basically different and has clearly audible warping of the 12 written tones, but it is something that happens in the mind of the listener. It would be interesting to compare this to a similarly scored but definitively microtonal piece. I know this will enrage some people but exactly the same thing happens in the 4th movement of the Tchaikovsky 6th: there is a line in the strings which does not exist anywhere on the page, but only in the mind of the listener.
Likewise on Atmospheres - it is scored chromatically but you don't hear it because of the extreme emphasis on color, as well as the creation of perceived overtones and shifts in harmony due to these colors. It is an almost supernatural piece of music.
I definitely agree.
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Wow, I did not realize Atmospheres was not microtonal. What an accomplishment then.
Evan Evans
Atmosperes starts with every chromatic note from the lowest double bass over I think five or perhaps seven octaves played PP or PPP. The tone cluster to beat all tone clusters and one of the most extraordinary sounds in orchestral music.
Ligeti lost it from the Horn Trio onwards sadly. There's an interesting article on Ligeti here:
http://journals.cambridge.org/bin/bladerunner?REQUNIQ=1092827382&REQSESS=560253&117000REQEVENT=&REQINT1=229080
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Dave
Sorry if I rant but my chin hit the floor when I read your Ligeti comment. I have to say that Ligeti’s most recent works (the piano Etudes) are widely accepted as being the most important new works for piano since Boulez sonata no2, and in my opinion they have advanced musical thought (as well as technical possibilities) by a greater extent than any of his previous works, including his earlier "micropolyphonic" pieces.
To clarify, as I understand it, micropolyphony is a term Ligeti used to describe a block of very closely spaced chromatic, polyphonic writing, usually played very quickly. This technique is what gives works like Lontano their hazy, shimmering type effect. What sounds like a static chromatic line is actually many lines, very close together, played very quickly.
Strange to say but you can hear the idea most clearly executed in one of his more "jokey" pieces for two harpsichords "Hungarian Rock". As the repeated figures speed-up the attacks from each instrument suddenly become "almost" unperceivable (once you get beyond more than one every 5 ms or so) and you have a single chromatic block of sound, kind of shimmering. It's very odd to play, in some ways very similar to Piano Phase.
If people are interested in these pyschoacoustical tricks then first set of Piano Etudes is definitely worth listening to.
Good discussion as ever.
Nick
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I think "continuum" is probably the clearest example of where extremely fast-moving sound turns into a haze.
(BTW I'm really enjoying Fennesz's "Venice" album at the moment. I love his way of using granular synthesis to create a hidden rapid movement inside otherwise slow-moving sounds - he's definitely a cut (!) above the other glitch musicians. He's not the first person ever to do granular stuff, but he's more musical, less geeky about it than most of them.)
Isn't the point about micro-polyphony that the cloud-like density of the writing means you can't make out the individual lines any more. Tallis's "Spem In Alium" - written half a millenium ago - also gives me that feeling. It's written for forty polyphonic lines (eight 5-part choirs), and by the time all forty are singing, you really can't make out the individual lines. It's a fantastic piece of music.
Laters
Guy
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Nick,
Not ranting at all - impassioned. Glad to see it.
I don't know enough post Horn Trio Ligeti to justify my huge overgeneralisation but it was interesting to see your response which is what I was hoping to encourage. Hopefully others will be enthused to explore some of the later Ligeti you've mentioned.
I did feel let down by Ligeti with his Brahmsian Trio - and even as a piece of post-romantic music I personally don't think it works so well. It was like Ligeti was my avante garde hero and then he turns his back on us. I never really understood why he did that. Still I was young and headstrong.
My favourite Ligeti is still the pre trio Orchestral and chamber music. The Aventures and Nouvelle Aventures are a complete riot - what imagination - what daring and importantly what fun. I saw them sung by three naked singers at the Queen Elizabeth Hall 20 odd years ago [:O]ops: . Quite an experience for a college student.