Page 2 of 3 FirstFirst 123 LastLast
Results 16 to 30 of 42

Thread: Did Wagner's music lead to atonality?

  1. #16
    Senior Member Woodduck's Avatar
    Join Date
    Mar 2014
    Location
    Ashland, OR
    Posts
    16,016
    Post Thanks / Like

    Default

    Quote Originally Posted by millionrainbows View Post
    It's not my problem if you feel 'misrepresented,' which I don't think you really do. You're just trying to invalidate me as a person.

    It's hard to back-up anything on this subject with real substance. If we have an idea what Wagner was doing from a theoretical standpoint, it can be justified with "It was because he was a dramatist" or "he was the supreme tonalist; he rejected younger composers."

    If Wagner was an advanced tonal thinker, which I think he was, what was he thinking from a theoretical standpoint? Explain it. It's far easier to justify it all with "Wagner the man," because of "father-figure complexes" in many males, arising from the suppression of the libido into a sublimated 'hero' complex.
    This is all fantasy. I've said none of what you're claiming.

  2. #17
    Senior Member millionrainbows's Avatar
    Join Date
    Jun 2012
    Location
    USA
    Posts
    14,691
    Post Thanks / Like
    Blog Entries
    137

    Default

    Quote Originally Posted by Woodduck View Post
    This is all fantasy. I've said none of what you're claiming.
    Even if I pasted the post you said it in, you'd disagree. Or have I already posted it? Oh, ha ha, yes, I did!

    Here it is:

    Originally Posted by Woodduck
    Your explanation for the theories of the "Wagner leads to atonality people" is very conciliatory! Actually, I don't think all those people have the same theory about how an expanded tonality "evolves" into atonality. There was Schoenberg's concept of "the emancipation of the dissonance,"which postulated that, over time, people learn to regard harmonies previously considered dissonant as consonant, and that logic therefore dictates that we go all the way and remove the tonal functions that provide the criteria for what's consonant and what isn't. Then there's the notion that because Romantic composers were making harmony more and more chromatic and using more chords that couldn't be "explained" by reference to theoretical systems then current, the obscuring of tonal centers which resulted would inevitably lead to a "breakdown of tonality" and its total abandonment as a constructive principle in music.

    Wagner would have spat out his coffee at such notions. No composer in history was more attentive to tonal relationships than he was, or exercised more far-reaching and iron-handed control over them. He was, however, well aware of what a Pandora's box of potential abuses his enriched tonal vocabulary would open up for aspiring composers tempted by what he described as "effects without causes." Young composers, he said, would come to him with compositions filled with novel and complicated harmonies, hoping to be praised for their expressiveness and creativity, and he would be quick to set them straight.

    Wagner's music does indeed force us to think of musical form - and this includes harmony - in ways that Bach's or Mozart's does not. But it no more implies, or suggests as desirable, the negation of the very principle of tonality than theirs does. I would dispute your suggestion that in his music "other phenomena (the linear movement of highly chromatic lines and the sheer sound of the harmonies that result), start to become as important to listeners' actual experience of the music as the underlying tonal grammar." Wagner's radical movement away from a "top-down" approach to harmonic structuring - in which the stations of tonal movement, the "functional" pillars of tonal harmony, are explicitly stated as the audible scaffolding of a basically abstract form - to a "bottom-up" approach - in which tonal structuring is guided by a sense of dramatic/expressive narrative inherent in the tonal language - is not a movement away from tonality but an extrapolation of a potential which had been present in it from the start and was in fact adumbrated many times in the work of earlier composers. What Wagner saw was the extent of that potential to create large-scale dramatic works in which the expressive language of tonal harmony could guide the creation of coherent musical statements without signaling its "mechanics" to the conscious mind of the listener.

    A real comprehension of what Wagner was doing in his music depends first and foremost on an intuitive sense of its organicity, its underlying logic, and that depends on our ability to abandon the Classical expectation that musical form, particularly form based on tonal structures, is created and perceived "from the top down." The musical conservatives of his day were opposed to his conception of musical form; I've known people, even musicians, who are not comfortable with it even today, and can't listen to a Wagner opera without feeling disoriented and irritated by the refusal of the music to congeal into neat structures. Wagner's mature works are an uncompromising expression of the Romantic conception of music as the language of the soul, a language which comes "from the bottom up," and Wagner uses drama as the scaffolding on which our conscious mind can fixate while the music goes to work on our unconscious.

    I've managed to get my hands on a copy of the book from which the excerpt you've quoted comes: "The manipulation of unstated tonics in motivic sequence then becomes a direct manipulation of an unconscious psychological process of projecting order. It is not an invention or deviation from the theoretical structure of tonal practice, but a realization of possibilities inherent within the system. As such it represents a profound stylistic advance, and the possibilities which it opened may remain largely unexplored by later composers." The book, "Musical Structures in Wagnerian Opera" by Marshall Tuttle, is a work of thorough scholarship and meticulous analysis, and it isn't an easy read (I'm skimming parts of it first time around). But it's definitely confirming and filling out my long-standing intuitions about Wagner's music and how it works. Among other things, it helps me understand why his scores are full of changes of key signature when it's often impossible to find more than a bar or two that actually seems to be in the specified key - and why, despite surface appearances, Wagner stated that one should never leave a key until one has said everything necessary within it.

    I understand Tuttle's suggestion that "the possibilities which [Wagner's techniques] opened may remain largely unexplored by later composers" to indicate, not that composers declined to push his techniques further lest they inevitably confound the listener's tonal expectations or be forced to leave tonality behind, but that they simply could not manipulate the surface vocabulary of his style with the intuitive control of the layers of tonal organization, mediated through motivic sequence and metamorphosis, which enabled him to generate a sense of narrative inevitability and expressive specificity on a grand scale. There's a great deal of post-Wagnerian music that sounds "Wagnerian" but, in any profound sense, isn't. Tuttle's observation also points out the fundamental fact that Wagner's music took the form it did under the impetus of the need for dramatic expression - "dramatic" in the specific sense. Tuttle's book shows in (sometimes ponderous) detail how dramatic ideas and musical structures are inseparable in the operas, to the extent that, more than with any other composer, understanding the latter is essential to understanding the former, and how the precise manipulation of tonal relationships provides a key to that understanding. Wagner was so convinced that music could be an articulate language, and so relentless and thorough in the use of hamony's tools to achieve that end, that he would eventually call his operas "deeds of music made visible."

    I would say that anyone who thinks that Wagner's music "leads to" atonality doesn't understand very much about it. Scholarly scuffles over how to name the Tristan chord are apt to be missing the forest for the trees.

    What sort of "tonal expansion past chromaticism" are you thinking of? What do you mean by "tonal logic," much less of a "higher" sort? Different tonalities already exist in various world musics. Is there something they have in common that might inform a "higher" tonality featuring "new tonal relations"? Why would it be "higher"?


    Since you should already have explained this, if you are going to make such claims, I might ask the same question of you: what is meant by "the expressive language of tonal harmony could guide the creation of coherent musical statements without signaling its "mechanics" to the conscious mind of the listener"? That sound vague to me.

    What do you mean, in real musical terms, by "A real comprehension of what Wagner was doing in his music depends first and foremost on an intuitive sense of its organicity, its underlying logic, and that depends on our ability to abandon the Classical expectation that musical form, particularly form based on tonal structures, is created and perceived "from the top down."?

    This sounds like so much hot air, unless it's too much trouble to explain in real musical terms. But I quoted it from your reply to someone else, when you had your guard down. It reveals you as a Wagner fanboy with CP training which stops there, not much more.

    So, once again, I ask:

    If Wagner was an advanced tonal thinker, which I think he was, what was he thinking from a theoretical standpoint? Explain it.
    Last edited by millionrainbows; Apr-07-2020 at 17:33.

  3. #18
    Senior Member NLAdriaan's Avatar
    Join Date
    Feb 2019
    Location
    The Netherlands
    Posts
    1,062
    Post Thanks / Like

    Default

    I think Liszt should actually be the object of this thread.

    Liszt, father-in-law of Wagner, made steps ahead deep into the 20th century in his last creative period. The music that Liszt composed since the 1870's comes from a different planet compared to his earlier music. You can hear directions towards impressionism of Ravel and Debussy (a misrepresented modernist himself) and atonal music (Bagatelle sans tonalité). Liszt kept these works largely to himself. Still, this music is not well known as his mainstream virtuoso work. And Liszt obviously knew his fanbase wouldn't understand this music

    It is well-known that Wagner, who also was the neighbor of Liszt in Bayreuth, largely ignored this late music by Liszt and had very strong negative opinions about it. This leads to the logical conclusion that Wagner was not, at least not consciously, a modernist avant la lettre. Liszt however was leading the way as an avantgardist, be it in obscurity, where his late works unfortunately still are. These works deserve our attention as they represent the true inner spirit of the composer. I can't think of any composer whose 'late creative period' is so much in contrast to his earlier works.
    Last edited by NLAdriaan; Apr-07-2020 at 17:35.

  4. Likes millionrainbows, Woodduck liked this post
  5. #19
    Senior Member millionrainbows's Avatar
    Join Date
    Jun 2012
    Location
    USA
    Posts
    14,691
    Post Thanks / Like
    Blog Entries
    137

    Default

    Quote Originally Posted by NLAdriaan View Post
    I think Liszt should actually be the object in this thread. Liszt, father-in-law of Wagner, made steps ahead deep into the 20th century in his last creative period. The music that Liszt composed since the 1870's comes from a different planet as his earlier music. You can hear directions towards impressionism of Ravel and Debussy (a misrepresented modernist himself) and atonal music (Bagatelle sans tonalité). Liszt kept these works largely to himself. Still, this music is not well known as his mainstream virtuoso work. And Liszt obviously knew his fanbase wouldn't understand this music

    It is well-known that Wagner, who also was the neighbor of Liszt in Bayreuth, largely ignored this late music by Liszt and had very strong negative opinions about it. This leads to the logical conclusion that Wagner was not, at least not consciously, a modernist avant la lettre. Liszt however was leading the way as an avantgardist, be it in obscurity, where his late works unfortunately still are. These works deserve our attention as they represent the true inner spirit of the composer. I can't think of any composer whose 'late creative period' is so much in contrast to his earlier works.
    You mean to say that Wagner wouldn't have spat out his coffee at such notions? Or did he? But this elevation of Liszt contradict's Woodduck's assertion that Wagner was the apotheosis of advanced tonality (modernism).
    Last edited by millionrainbows; Apr-07-2020 at 17:39.

  6. #20
    Senior Member Woodduck's Avatar
    Join Date
    Mar 2014
    Location
    Ashland, OR
    Posts
    16,016
    Post Thanks / Like

    Default

    Quote Originally Posted by NLAdriaan View Post
    I think Liszt should actually be the object of this thread.

    Liszt, father-in-law of Wagner, made steps ahead deep into the 20th century in his last creative period. The music that Liszt composed since the 1870's comes from a different planet compared to his earlier music. You can hear directions towards impressionism of Ravel and Debussy (a misrepresented modernist himself) and atonal music (Bagatelle sans tonalité). Liszt kept these works largely to himself. Still, this music is not well known as his mainstream virtuoso work. And Liszt obviously knew his fanbase wouldn't understand this music

    It is well-known that Wagner, who also was the neighbor of Liszt in Bayreuth, largely ignored this late music by Liszt and had very strong negative opinions about it. This leads to the logical conclusion that Wagner was not, at least not consciously, a modernist avant la lettre. Liszt however was leading the way as an avantgardist, be it in obscurity, where his late works unfortunately still are. These works deserve our attention as they represent the true inner spirit of the composer. I can't think of any composer whose 'late creative period' is so much in contrast to his earlier works.
    Yes, Liszt experimented with harmonic discontinuities beyond what Wagner did. I wouldn't say that they took him "deep into the 20th century," but your basic point is certainly right. Wagner had the problem of giving coherence to lengthy dramatic structures, and was always intensely aware of the role of tonality in achieving that. Liszt was sitting at his piano playing around with harmony. Wagner reached for striking harmonic effects when he needed them. Liszt did so just because he liked them.

  7. #21
    Senior Member Woodduck's Avatar
    Join Date
    Mar 2014
    Location
    Ashland, OR
    Posts
    16,016
    Post Thanks / Like

    Default

    Quote Originally Posted by millionrainbows View Post
    You mean to say that Wagner wouldn't have spat out his coffee at such notions? Or did he? But this elevation of Liszt contradict's Woodduck's assertion that Wagner was the apotheosis of advanced tonality (modernism).
    Woodduck never said that Wagner was the apotheosis of "modernism." I don't consider Wagner a "modernist," though he was reasonably considered, and was, avant-garde in his time.

    I don't like to use the term "modernism" in this generalized and careless way. It's confusing rather than specific and useful.

  8. #22
    Senior Member Woodduck's Avatar
    Join Date
    Mar 2014
    Location
    Ashland, OR
    Posts
    16,016
    Post Thanks / Like

    Default

    Quote Originally Posted by millionrainbows View Post
    what is meant by "the expressive language of tonal harmony could guide the creation of coherent musical statements without signaling its "mechanics" to the conscious mind of the listener"? That sound vague to me.
    Harmonic progressions, long passages, and whole pieces of music can feel purposeful and cohesive without the explicit or conspicuous stating of tonal centers, tonics, dominants, etc. to grab the listener's attention and orient him, as is the typical practice in Baroque, Classical and much Romantic music. Generating a sense of coherence on an unconscious level was an art that Wagner mastered. This is not to say that he couldn't or didn't create music that wore its tonal heart on its sleeve; set the preludes to Tristan and Meistersinger side by side to see the principle. Both hang together beautifully, but with the former piece the listener neither knows nor cares how he does it. Passages from within the operas are even less obvious, and we're not supposed to think about it. Tonal (and motivic, and rhythmic) organization become a dramatic, more than a formal, language.

    What do you mean, in real musical terms, by "A real comprehension of what Wagner was doing in his music depends first and foremost on an intuitive sense of its organicity, its underlying logic, and that depends on our ability to abandon the Classical expectation that musical form, particularly form based on tonal structures, is created and perceived "from the top down."?
    That's another way of making the same point. "From the top down" could mean "from the conscious mind down." As listeners to Wagner's musical/dramatic narrative, we are not conscious, intellectually, of his methods in the way that we're conscious of Beethoven's. We're not supposed to be. His job was to make this work musically, and he did so on a level not seen before and rarely equaled since. The third act of Tristan is in my opinion a dramatically and musically integrated structure with which nothing else in music can be reasonably compared.

    This sounds like so much hot air, unless it's too much trouble to explain in real musical terms. But I quoted it from your reply to someone else, when you had your guard down. It reveals you as a Wagner fanboy with CP training which stops there, not much more.
    Blah blah blah...

    So, once again, I ask:

    If Wagner was an advanced tonal thinker, which I think he was, what was he thinking from a theoretical standpoint? Explain it.
    What exactly do you want me to do? Read Wagner's mind as he sits composing? Take you through a score and point out secondary dominants? I'm making a general statement about his methods.

    You're so demanding.
    Last edited by Woodduck; Apr-07-2020 at 21:19.

  9. #23
    Senior Member NLAdriaan's Avatar
    Join Date
    Feb 2019
    Location
    The Netherlands
    Posts
    1,062
    Post Thanks / Like

    Default

    I looked for some comprehensive evidence, which I found in an interview with Nike Wagner (great-granddaughter) by the German magazine 'der Spiegel' in 2011, the full article can be found here: https://www.spiegel.de/international...-a-775814.html. If you look into anything on the Wagner family, controversy and deep conflicts are around any corner, still to this day. A NYT article calls the Wagners 'the most dysfunctional musical family in Europe'. The quote below is clear enough, where of course Nike Wagner represents a faction of this family herself.


    SPIEGEL: What did people say about Liszt in your home, the Villa Wahnfried?

    Wagner: He never counted for anything in the Wagner household. In fact, people would poke fun at him now and again, calling him 'the abbot' or dismissing him as a mere drawing-room performer. Richard Wagner despised that kind of musician and considered them to be nothing more than a showman. He also despised Liszt because he composed symphonies and religious works [which he did not consider to be serious enough]. Wagner thought Liszt was crazy in his later years. And yet his late works and their emerging atonality were far more modern than Wagner's. But it's true that Richard loved and always respected Franz. Liszt's music wasn't buried until after his death.

    SPIEGEL: In July 1886, Cosima refused to halt the festival even though her father was dying in Bayreuth. His death was kept secret.

    Wagner: He died in the house next door, poorly looked after, and in great pain. Suddenly, the loneliness that the restless Liszt had presumably always carried around became visible. Maybe the somewhat formal way he addressed people, which was seen as coldness on his part, was simply a form of escape. Indeed Liszt appears far more mysterious today than the ever-exuberant Wagner, who externalized everything. Liszt was discreet. His ego was delicate, and he never forced himself center stage, an interesting contrast to his skillfully executed public performances.

    SPIEGEL: He supported his son-in-law unreservedly.

    Wagner: Wagner felt guilty about Liszt all his life. He knew he was indebted to him. He also said so in public time and again, especially after he had made the breakthrough in Bayreuth.

    SPIEGEL: Although it's the 200th anniversary of Liszt's birth in October, the festival isn't marking the occasion.

    Wagner: That's incomprehensible, embarrassing and scandalous. The city of Bayreuth does this and that, but it doesn't owe Franz Liszt anything. That's the exclusive responsibility of the Wagner family. The Wagners are deeply indebted to Liszt. It would be historically irresponsible to deny that. I was deeply hurt that my cousins were deaf to my appeals to open up the concert hall for a major festival and birthday concert on October 22. It would have been a wonderful event, as well as a way to start repaying that debt.

    SPIEGEL: Liszt was Catholic and had received his minor orders in Rome. Wagner was Protestant. What was your childhood like from a religious point of view?

    Wagner: Traditionally Protestant. But probably only because of Johann Sebastian Bach.
    Last edited by NLAdriaan; Apr-08-2020 at 10:26.

  10. #24
    Senior Member millionrainbows's Avatar
    Join Date
    Jun 2012
    Location
    USA
    Posts
    14,691
    Post Thanks / Like
    Blog Entries
    137

    Default

    Wager took tonality to its limits by exploiting its most "glitchy" feature, the viiº chord. Diminished sevenths can have 4 possible roots. That's why it's ambiguous, it's as simple as that.

  11. Likes Woodduck, mikeh375 liked this post
  12. #25
    Senior Member Woodduck's Avatar
    Join Date
    Mar 2014
    Location
    Ashland, OR
    Posts
    16,016
    Post Thanks / Like

    Default

    Quote Originally Posted by millionrainbows View Post
    Wager took tonality to its limits by exploiting its most "glitchy" feature, the viiº chord. Diminished sevenths can have 4 possible roots. That's why it's ambiguous, it's as simple as that.
    The diminished seventh is an obvious device for modulating and achieving a feeling of instability or uncertainty. Weber used it dramatically in his operas, and Wagner followed suit. But Wagner's fullest expansion of tonality didn't occur until he realized the possibilities of the half-diminished seventh. In his later works - from the first chord of Tristan on - it becomes his personal "signature," used in all its inversions and its potential for chromatic sliding as his primary harmonic pivot and source of instability, ambiguity and tension. In his earlier works it's heard mostly "in embryo" as a component of a V9 or as a vii or a ii with an added sixth. Later on it would shed such obvious functions and could dominate long sequences in which tonal centers and roots make only fleeting appearances, the harmony slipping from one half-diminished chord to another, often remote one, on its way to some clearer tonal marker.

  13. Likes mikeh375, Torkelburger, Bwv 1080 liked this post
  14. #26
    Senior Member
    Join Date
    Feb 2017
    Posts
    361
    Post Thanks / Like

    Default

    Quote Originally Posted by Woodduck View Post
    The diminished seventh is an obvious device for modulating and achieving a feeling of instability or uncertainty. Weber used it dramatically in his operas, and Wagner followed suit. But Wagner's fullest expansion of tonality didn't occur until he realized the possibilities of the half-diminished seventh. In his later works - from the first chord of Tristan on - it becomes his personal "signature," used in all its inversions and its potential for chromatic sliding as his primary harmonic pivot and source of instability, ambiguity and tension. In his earlier works it's heard mostly "in embryo" as a component of a V9 or as a vii or a ii with an added sixth. Later on it would shed such obvious functions and could dominate long sequences in which tonal centers and roots make only fleeting appearances, the harmony slipping from one half-diminished chord to another, often remote one, on its way to some clearer tonal marker.
    He was ahead of his time. If we split the tritone in 12 equal, we can get in some sense 13 equal where 4th inversion of half-diminished chord is the basic chord with similar structural properties to the triad in 7 equal (in a way diatonic scale is 7 equal, embedded in 12 equal). Wyshnegradsky used regularly a 13 note scale in his 1/4 tone works, but I think the best division of octave for such ultrachromatic, half-diminished seventh works is 36 or 37 equal ( if we are after two chromas in the scale; if we are after only one, 22 is probably better than 24). Still, I doubt it is easy to hear a 13 note scale or complex chords (like 5:6:7:8 - fourth inversion of half-diminished) as tonal, because of many well knons facts from psychoacoustics. (Numbers like 3, 7, 13, 21, 31 are very good for harmonic systems, because of their mathematical properties - check any book on projective geometry and translation planes for more information).

  15. Likes Woodduck liked this post
  16. #27
    Senior Member Woodduck's Avatar
    Join Date
    Mar 2014
    Location
    Ashland, OR
    Posts
    16,016
    Post Thanks / Like

    Default

    Quote Originally Posted by BabyGiraffe View Post
    He was ahead of his time. If we split the tritone in 12 equal, we can get in some sense 13 equal where 4th inversion of half-diminished chord is the basic chord with similar structural properties to the triad in 7 equal (in a way diatonic scale is 7 equal, embedded in 12 equal). Wyshnegradsky used regularly a 13 note scale in his 1/4 tone works, but I think the best division of octave for such ultrachromatic, half-diminished seventh works is 36 or 37 equal ( if we are after two chromas in the scale; if we are after only one, 22 is probably better than 24). Still, I doubt it is easy to hear a 13 note scale or complex chords (like 5:6:7:8 - fourth inversion of half-diminished) as tonal, because of many well knons facts from psychoacoustics. (Numbers like 3, 7, 13, 21, 31 are very good for harmonic systems, because of their mathematical properties - check any book on projective geometry and translation planes for more information).
    Sounds impressive. I wish it weren't way over my head!

  17. #28
    Senior Member millionrainbows's Avatar
    Join Date
    Jun 2012
    Location
    USA
    Posts
    14,691
    Post Thanks / Like
    Blog Entries
    137

    Default

    A "half-diminished" chord is known in jazz as a "min 7 b5" chord.
    In A minor:
    This also happens to be the ii function in a minor key (B-D-F-A).
    It could also be interpreted as a minor sixth: D-F-A with B as the sixth or thirteenth.

  18. #29
    Senior Member Barbebleu's Avatar
    Join Date
    May 2015
    Location
    Great Britain
    Posts
    3,844
    Post Thanks / Like

    Default

    In answer to the thread question - no, it didn’t,,

    Those who think it did are wrong. Those who, like all right thinking people, e.g. me, think it didn’t, are absolutely right.

    I will not be backing this up with outlandish pseudo-intellectual theorising.

    I bid you all a good night!
    Last edited by Barbebleu; Apr-09-2020 at 22:54.
    "...it is said that first your heart sings, then you play. I think if it is not like that, then it is only just combination of notes, isn't it? " - Pandit Nikhil Banerjee, Master of the Sitar.

  19. Likes NLAdriaan liked this post
  20. #30
    Senior Member
    Join Date
    Feb 2017
    Posts
    361
    Post Thanks / Like

    Default

    Quote Originally Posted by Woodduck View Post
    Sounds impressive. I wish it weren't way over my head!
    Well, there is the microtonal (xenharmonic) wikipedia online and there was some microtonal encyclopedia, if you are interested in such stuff. There are also many academic articles online and google books has previews (search for"Microtones and projective planes").

    Music of Wagner, other modernists and jazz idioms cannot be easily explained by standard theories, but microtonality deals easily with them - it looks all seventh and 9th chords and chromatic harmonies used in Western art music act as 7-limit harmony.

    https://en.wikipedia.org/wiki/7-limit_tuning

    There are several ways to retune 12 equal as 7-limit scale (which would be just a subset of a bigger system, just like 7-note diatonic is a subset of a bigger system).

    We can use Hasse diagrams to generate all possible chords in a given tuning system - in 5-limit the main intervals are 4/3, 5/4 and 6/5 - fourth, major and minor thirds, with chromas - 16/15 - diatonic semitone and 25/24 - chromatic semitone, so 19 equal is actually better than 12, because the difference between these small intervals is not tempered (the first chroma easily leads to pentatonic, the second one - to heptatonic scales); and chords are major/mnor triads and all their inversions.

    In 7-limit (a system that would support better barbershop chords and bluesy/jazzy intervals, btw, I am pretty sure that I have recordings of Debussy and Wagner that sound quite microtonally at some point) - the main intervals are 5/4, 6/5, 7/6 and 8/7 and chromas - 25/24, 36/35 and 49/48, so the generated JI systems (https://en.wikipedia.org/wiki/Fokker_periodicity_block) should be 3-dimensional (having two chromas and you cannot get it from single interval stacking modulo octave), unless one of these is tempered. (Here is another good article on generated tone systems, but it's behind a paywall - https://link.springer.com/chapter/10...642-39357-0_18)
    Last edited by BabyGiraffe; Apr-09-2020 at 21:21.

Page 2 of 3 FirstFirst 123 LastLast

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •