I was wondering if any of you could help me with an issue I'm having. I have been using pitch-class sums to represent how dark or light a scale feels. So for example, C major, when you add all of its values together from pitch-class space, would have a sum of 38. C Phrygian, on the other hand, would have a sum of 34. Now I thought this might be because the smaller intervallic distances, when related to the root of the scale, would be causing the sum to be lower in the case of C Phrygian, therefore the scale would be shown to be darker. But the whole process seems rather dubious to me.

So I tried other ways of representing a scale's darkness or lightness by mapping them onto the circle of fifths. C major had most of its intervals on the 'brighter' fifths side whereas C Phrygian had most of its intervals mapped on the 'darker' fourths side. But again it doesn't feel like a strong way to represent it academically.

I think I was going to try a third way of cross-referencing with the harmonic series. The method here was to take a 12-tet approximated harmonic series (sorry JI fans) and make the assumption that intervals that find themselves further away from a fundamental of C have a weaker pull to said fundamental thus making it more dissonant/ dark. For example, the interval b9 would be the 9th interval to appear in this 12-tet approximated harmonic series, whereas a natural 2 would be the 5th interval to appear making it more consonant than the aforementioned b9. This would also make C Phrygian darker than C major as many of its intervals would be further away from the C fundamental than the intervals in the C major scale. But again I'm unsure of this method, mainly because it uses an approximated harmonic series. 

So basically what I'm asking is, is there a way you can represent consonance and dissonance/ brightness and darkness in an objective and quantifiable way?

It is my pleasure to announce the publication of my new article “The Defects of A Reigning Theory”. It criticises Schenkerian theory. A list of suggested major defects of Schenkerian theory is exposed below. Each one of those headlines is examined separately in the article.

1. Repudiation of the subdominant function and the plagal cadence.

2. Imposition of an exaggerated notion of functional prolongation, which leads to elimination of stepwise cadences as well as implied cadences over a pedal point.

3. Repudiation of ascending melodic lines and the leading tone as structurally important factors in background analysis.

4. Interpretation of typical six-four chords as dissonant sonorities.

5. Neglect of rhythm and phrase structure as important factors in tonal analysis.

Of course, one cannot build a representative house on two beams (Tonic and Dominant), and it is there where the trouble begins.

The link from which you can read and download the article is:

http://casopisi.junis.ni.ac.rs/index.php/FUVisArtMus/index

I hope you have a good reading, and I welcome comments on this matter. 

Best regards,

Dimitar Ninov

Texas State University

Some fellow theorists and composers contacted me privately about my article "Interior Cadences in the Sentence of Schoenberg" (link provided in my previous discussion with the same tilte) implying that that "it couldn’t be on a more important topic". This stimulated me to emphasize a few important things about cadencs in general, as follows:

The presence or absence of a cadence is not determined by the bass position of the last two chords in a harmonic progression, but by the functional interaction between the chords at the end of a musical gesture. The bass may enhance or diminish the effect of a cadence.

Therefore, instead of staring anxiously at the last two bass notes of a given harmonic progression in an attempt to recognize or deny a cadence, the analyst had better listen to the interaction among harmonies and other elements of texture as they shape a musical idea into a state of relative or absolute conclusion.

The beauty of cadence lies in its nuances of strength. The elimination of these nuances practically kills the concept of cadence, leaving the analyst with no choice but to call “a cadence” only the root position authentic closure. This approach drains music analysis of color and diversity, and makes it gray, monotonous, highly predictable, and uniform. I feel sorry for all those students who are taught harmony and musical form in this manner. For them, all the variety of cadential nuances, all the colorful palette of cadential formulas will remain hidden if not forbidden, along with the opportunity to make music analysis more flexible and more open to real music.

Thank you. I welcome any kinds of comments on the above reflections.

With best wishes,

Dimitar Ninov

Texas State University

I am pleased to announce the publication of my new article “Interior Cadences in the Sentence of Schoenberg” in Musicological Annual, which is available in both hard copy and online issue. I am sure this will be an intriguing and provocative reading for those who specialize in tonal harmony and musical form. Therein I take an issue with my friend William Caplin’s notion of cadence, his allegation that all sentences lack interior cadences, and his assumption that functional prolongation inevitably negates cadence.

You could read and download this article here:

Dimitar Ninov – Interior Cadences in the Sentence of Schoenberg. Musicological Annual, Vol. 57 No. 1 (2021), pp. 131-148

https://revije.ff.uni-lj.si/MuzikoloskiZbornik/issue/view/735/566

The topic is pretty engaging and a subject of debate, but I have always had the feeling that the traditional notion of cadence is overwhelmingly supported across the musical world, while the so-called “new concept of cadence” which only recognizes two cadential types: PAC and a root position IAC – has only been supported by the Schenkerian community. With that being said, I welcome all kinds of expressed opinions on that matter.

Thank you. I hope you enjoy the reading.

Dimitar Ninov

Texas State University

It is my pleasure to announce that my theoretical article "Functional Nature of The Cadential Six-Four" from 2016 is now available on-line in Musicological Annual. Two new articles of mine will be published by the end of this month, one in this journal, and one in another journal. I hope you will enjoy this essay which argues that the Cad. 6/4 is not a mere V chord with two non-chord tones, but much more than that, including the possibility of fusing with a passing tonic six-four on a strong beat. Here is the link:

Dimitar Ninov, "Finctional Nature of The Cadential Six-Four". Musicological Annual Vol. 52 No. 1 (2016), pp. 73-96

https://revije.ff.uni-lj.si/MuzikoloskiZbornik/issue/view/551/338

I should like to alert you to the publication of a new two-part study on my website, entitled "Mozart's Delayed Dominants" at http://www.channanwillner.com/online.htm. Part I demonstrates that in Mozart's (and in other late 18th-century) sonata form, the arrival of the structural dominant is often delayed almost to the end of the exposition by long-range bass unfoldings and voice exchanges. Part II observes how the dominant is similarly delayed by temporarily incomplete treatment of the composition's structural register.

With thanks, and apologies for cross-posting,

Channan

1.  drag and drop notes into the staff - written part of exam

2.  record themselves playing scales, clapping rhythms, playing sight-reading pieces for keyboard part of exam

Thanks for your suggestions!

I recently rekindled my interest in computer programming, and I have been working on coding a music theory program. It has two parts: a tool for visualizing set theoretical relations, and one for visualizing triadic and seventh-chord transformations on a Tonnetz.

In teaching these topics, I have found it helpful for many students to be able to see such relations/transformations presented in a visual format. I hope that some of you will find the program useful or fun.

This is in an early stage, so I would very much appreciate people testing it out, trying to find bugs, or making suggestions for changes/additions. Here is a link for the current Windows executable:

https://www.dropbox.com/s/w72zkidmjndnt96/arkhe.zip?dl=0

You will need to unzip the folder and then run the exe file. Documentation can be read in the program, or you can just open the doc.txt file in the folder. I used Python for this (and only two third-party modules), so if anyone has an interpreter installed and would prefer the script, I could provide that as well.

Thanks!

Best,

Jim Bennett

james.n.bennett@gmail.com

To what extent are the following two examples conventional/schematic in classical/romantic repertories/pedagogies?

1. Bass line do-te-LA-sol-do at a cadence supporting Cm - Cm/Bb - D7/A - G7 - Cm

2. Connection of I6/3 to ii7 via a dim7 chord such that the highest voice descends 5-b5-4 and the lowest voice descends 3-b3-2

Thanks for the help!

Stephen

By setting 1 to a unit of time, either series can be realized as a rhythm in which the rhythm's ordered series of inter-onset intervals is an expanding or contracting triangular series, measured according to this unit.

I can think of isolated examples of such a rhythmic series. But I'm wondering if there is a composer or type of music for whom/which this sort of thing is a distinctive aspect, assuming n of sufficient size (and variety) to be distinctive.

Thanks,

-Scott Murphy

I am working with an advanced undergraduate who stumbled into Lewin and transformation theory.  He would like to gain enough fluency to understand the application to his own research, but that's about all we have time for right now.  Can anyone recommend a good primer that would get us started?  I've found several articles claiming to be "introductions" but would love a recommendation from someone who knows this field well.  Thank you for any help.  (richard.hoffman@belmont.edu) 

Best,

Rick Hoffman

Belmont University

The claim reminds me of the bias inherent in the well-known Texas Sharpshooter fallacy, where a Texan "fires his gun at the side of a barn, paints a bullseye around the bullet hole, and claims to be a sharpshooter." Within that context, then, I offer the following narrative: 

1. We assume a dyadic model should be maximally parsimonious because that’s the traditional way modern theorists have modeled musical objects—from the conformist Tonnetz and the Power Towers to the Chicken-Wire Torus, Weitzmann regions, and Cube Dance. 
2. We manipulate a sketch of the space based on the assumption of (1) until we achieve maximal P_{1,0} parsimony along most axes.
3. We realize this structure could be modeled (only) by a Möbius strip.
4. We proclaim to have discovered the “fundamental shape of two chords.”

That progression offers quite the non sequitur, though it does seem representative of the bias that plagues many efforts in music theory (and mathematical music theory, in particular) to provide objective models of musical passages. But I'll leave that criticism for another post.  

| B - - - | Fm7 - - - | Ema7 - - - | C#m7 - F#11 - | B - - - | ...

I'd be very interested in any thoughts on that "Fm7".  The rest of the progression is conventional.

Recording here: https://youtu.be/s6fPN5aQVDI (first chorus is at 0:45).

I have been wondering recently about the tradition of playing/performing Schenkerian graphs at the piano. It's an idea I've heard about several times, and one I associate with the direct students or 'grand-students' of Schenker. However, I can't recall ever having seen it discussed explicitly in print. Can anyone recall references to playing Schenker graphs in published articles or books?

[Incidentally, what brought this most recently to mind is the fact that Lewin insists repeatedly throughout his Morgengruß essay that his readers should be sure to play through his reductions. He's not speaking from a Schenkerian perspective -- and in fact distances himself from it -- but it got me wondering about what the state of Schenker pedagogy looked like in 1970s and 80s, and if it's documented in print anywhere.]

Thanks in advance,

Bill O'Hara

https://www.academia.edu/36495364/What_is_a_Leading_Tone

 Bernd Willimek

Some musicians have written long articles or even books about the Tristan chord, they plunge into a jungle of linear connections and interpret it in a very abstract way, making a big deal of this sonority. However, apart from the multidirectional potential of the half-dim. 7 per se –something that Wagner explores to a certain extent throughout the prelude, the opening chord may have a simple interpretation. I am offering you two interpretations of it, beginning with the simpler one.

1. If we consider the tone G# an appoggiatura, then the chord is not half-dim.7, even enharmonically. Its structure only crystallizes in the next moment, when the appoggiatura resolves into the tone A. Then we can hear the chord B7-5 in second inversion as a double dominant with a lowered fifth (V7-5 of V) in the key A minor. This interpretation is confirmed by the resolution into the E7 chord (elliptical resolution). Thus the progression B7-5 – E7 will be heard as DD 4/3 alt.- D7 in the key A minor. Yes, the altered dominant contains an augmented sixth, but the geographic nickname "French" is irrelevant to harmonic function anyway.

Jazz people will hear the chord as F7-5 instead of B7-5 and will call it "a tritone substitute for V of V" but this is just another way of labeling an inverted and altered dominant of the dominant. Whenever they write bII7-5 of....they shall be aware that the true meaning of this chord is V4/3 (b5) of...because these chords are enharmonic.

2. If we do not consider the gone G# as an appoggiatura, then the sonority F-B-D#-G# coincides enharmonically with F half-dim7, and may be interpreted as an altered and inverted DVII7 in the key of A minor: VII2 (with a raised fifth). Here the half-diminished seventh chord is reinterpreted as a chord of the augmented sixth. When this chord is placed in root position, it reveals G#-B-D#-F, stemming from the VII dim7 chord, whose fifth then is raised. This interpretation is not so natural, because it ignores the appoggiatura, but the sequence DVII2 alt – DD 4/3 alt – D7 makes sense (two dominants of Am surrounding a double dominant).

Not a big deal. As for other resolutions of the half-dim. sonority that reveal other interpretations as a true altered chord, yes, one could write a whole chapter about them.

Thank you,

Dimitar Ninov

Texas State University

I just uploaded a short youtube video presenting a harmonization devised in my theory III class at Texas State. We harmonized a melody with modal mixture in D minor. Interestingly, the "raised" mediant triads borrowed from D major worked very smoothly and did not change the style drastically - simply moved it a little towards the boundaries of Late Romanticism and the beginning 20th century; it still sounds romantic.

Of course, the false claim that still circulates in some books, "The only common element borrowed from major into minor is the Picardy third" has always been irrelevant. Those who repeat this cliché are unaware of the fact that the harmonic and melodic scales of minor and major illustrate the influence of the opposite mode, that is - they are a conspicuous result of Modal interaction. Yes. Modal mixture is older than tonality. It begins with Musica ficta.

Please do not forget that saying "major V in a  minor key is obtained in harmonic or melodic major" is the same as saying "major V in a minor key is borrowed from the opposite mode" It would be nonsensical to claim that, for example, "major IV in a minor key is not borrowed" but "minor IV in major key is borrowed." I hope not many colleagues teach students that way...

I hope you will enjoy the video. Here is the link:

Dr. Ninov-Theory III-Modal Mixture-minor key-27 Feb 2018

Your video will be live at:

https://youtu.be/rk5xdh4Ex7I

Best regards,

Dimitar Ninov

Texas State University