100 posts on this topic! I hope, that this will not delay the arrival of Dorico 4! Perhaps we all should sit back now and wait, what the Team is coming up with, when they had the time to work on this feature.
1 Like
In all of that, no one wanted to touch my comment that the term “voice” (singular) should not be applied to chords, which are the conjunction of “voices” (plural). To me, it a much worse sin against music than the diminished unison.
But so be it.
1 Like
Well, it’ my hope that the team checked out of this thread a long time back. Daniel weighed in, and the rest of us have had a fun time kicking the ball around. It’s been fun, and civil - thanks all for that. But I certainly hope Daniel and crew have steered clear of our antics…
2 Likes
Sorry, John. It reminds me of programmers calling the ` character “back tick” and typesetters railing against them, insisting it is a “grave accent”. We can debate the merits and meanings of terms till we’re blue in the face, but people with different concerns will continue to use words differently.
3 Likes
I’m sure it will have zero impact on the arrival of Dorico 4. The new features of Dorico 4 are all decided and I imagine that all the team is doing at the moment is ironing out bugs.
But I’m happy to keep on niggling about this sort of issue. Using concise, consistent and widely-accepted rules is essential to good music notation. I think a serious notation software needs to get these details right: that’s why I bought Dorico.
The terms Voices has been used in notation software since the 1970s, at least, to describe separate ‘streams’ of notational data in the same bar. Sibelius, MuseScore, and (as far as I can tell) most other apps all use the term Voices, with no regard for chords.
Only Finale uses Layers, and even that is an addition to the original feature, called Voices, which still exists, of course. And you could still have a chord in the same voice if you wanted.
Whatever merits there may be in trying to avoid any contrapuntal confusion, that ship has sailed.
3 Likes
The ship has sailed all right, the Titanic.
Now I am going to work on a “song” by Beethoven, the Hammerklavier Sonata.
1 Like
I can agree with that, though I’ve never met a composer who used the term voice for a chord. It is proper to discuss how a chord is “voiced”- i.e., which individual notes are placed where. But, I certainly agree that a voice is an individual entity- in virtually any musical context🙂
In German, the Term „Satz“ can mean phrase, part of a phrase, the arrangement (as in how the instruments relate to each other) and movement. Probably I forgot something. Only thing „Satz“ cannot be used for is voice, though…
klafkid, in the US, the term “song” is now applied to any musical composition, be it a pop tune or a symphony by Brahms, and not just among the untutored. I used to inform my students that a “song” was obviously something sung by the human voice and that the term “piece” was used for instrumental music. But that ship also sailed along with the term “voice” for a single melody line.
And as fine distinctions are lost, so is clear communication. Which leads us to the state we are now in.
1 Like
I’ve been reading up on this over the past few days and it seems diminished unison has always been the byproduct of a particular view on tonal organization.
From what I could find, the spatial system (augmented is higher - diminished is lower) from the days of Rousseau, was replaced with the size system (larger / smaller) that had been used for interval inversions. Diminished unison was ok in one system but not in another. The two are nearly identical in every other respect.
The articulated rejection of diminished unison, combined with the particular way of semitone counting appears to have become widespread in the US and in Europe by the time of Schoenberg and tone rows. I have owned a first edition harmony book from 1897 for more than 40 years and I discovered only yesterday that it described diminished unison in some sort of middle ground terms as exception.
In the 1930s, Russian theorists (Yavorsky) propose to merge major and minor modes into a single tonal system. His pupil (Ogolevets) in the 1940s claims linear counting of semitones is a misrepresentation because sections of a standard 12 tone system always get “overlayed” with each other, thus enabling modulation, borrowed chords, etc - and it happens in all tonal music and throughout CP period. The overlays expand the boundaries of 12TET, and the hard stop at 0 artificially chops it off. I suspect the crazy old man who taught me was at least aware of this as it some parts sound familiar.
In the 1980s in the US, Lewin proposes the neo-Riemannian theory, according to which the tonal organization in music is not linear but geometrical. Chords, voice leading and modulations are explained by following units inside 3D objects (transformations). This has been conceptualized in circles, networks, cubes and a “Fourier phase space” - whatever that is! What seems to be the common element is the idea of a 3D shape instead of a line/size as a better way to understand intervals.
The prominent “geometry” theorists who are active in the field today do not appear to be rejecting diminished unison at all: Cohn (Yale), Yust (Boston), Tymoczko (Princeton) and others. Most use it without much explanation, but Klumpenhouwer (Eastman School of Music) clarified just in 2019 that
- diminished unison is indeed not possible in a flat size system (he calls it “magnitude system”),
- a descending augmented unison is a non-mainstream attempt to bring back spatiality,
- negative values are meaningful for spatial relationships, and
- linear “magnitude system” remains the institutional orthodoxy for now (though for reasons to do with teaching rather than science, it seems to me)
Yet, Tymoczko has been teaching the double-diminished unison in his class in Princeton for a while now (see page 5). His famous book (which I could never finish) is used in Math and Music course today at Northwestern, for example, and many many others.
Update: @Michael_Cook says below that the definitions used by Tymoczko are conventional, contradictory and problematic. I think the chapter by Klumpenhouwer in this book is brilliant and will explain what’s going on with various counting systems much better than a non-scholar like me. I could read most of it in previews, please scroll to page 40. Michael, I hope you don’t mind me responding here, I really wouldn’t want to make Derrek even more upset than he is with the length of the thread.
Finally, I have only a couple of entry-level college textbooks at home that are recent and in use currently (Laitz, Aldwell, Schachter) but they do not mention diminished unison - at least I haven’t found it. They do all use the traditional explanations for the rest. I have also not found any reputable theorist claiming that there are two kinds of octaves, a simple and a compound one, for the purpose of semitone counting, although I spent almost no time on that. One example I did see describes it as an exception.
Update: searching textbooks online, Takesue (3rd ed) and Kostka (8th ed) do specifically say “no diminished unisons”. Takesue is extremely brief, not even a full sentence. Kostka is rather emphatic.
Update: I have seen two reports online from a teacher conference from mid or late 1990s IIRC where diminished unison was proposed as a debate topic for classroom use, as opposed to a hard dismissal. And on the other end of the spectrum, I read extracts from a Cohn article that concedes geometric model of chords and intervals is hard and can alienate a lot of students (I know I wouldn’t go anywhere near it!). He says the model is also applicable to rhythm (e.g. pop music rhythm) and is more intuitive. This is to say that the issue of teaching is a serious one and not to diminish it in any way.
Obviously, all of the above is superficial observations based on two days’ worth of speed-reading, and the geometry school certainly has its critics.
Still, it’s good not to feel like a flat-earther. And also, to learn where the dogma comes from and see it sitting on rather shaky ground. Of course, Dorico will use whatever its developers want and users demand, which is as it should be. But it’s not impossible it is simply being a bit ahead of its time.
7 Likes
@ebrooks All I can say is that I appreciate you doing our homework. This was very interesting to read and took you no little time to synthesize. Thank you.
Yes, it was a lot of research, but insofar as using Dorico productively, this very lengthy thread seems to have started to look like a discussion of how many angels can fit on the head of a pin. Hasn’t Daniel already said he would give the matter some thought?
2 Likes
The problem with Tymoczko’s use of the term “diminished unison” can be seen right there in the table on page 5. The second column is labelled “Chromatic Distance”. Distance by definition cannot be negative, so claiming that the chromatic distance of a diminished unison is -1 semitones makes no sense. Note that the word “distance” is used extensively throughout the article, and it is clear that Tymoczko is using it in the accepted way: an absolute magnitude.
Read the "additional rules " under the table and it gets worse. The first rule states:
- an interval one chromatic semitone smaller than a diminished interval is “doubly diminished”
Having defined C-Cb as a diminished unison, a doubly diminished unison should be one chromatic semitone smaller than that. What does that make it?
After the additional rules, we see this statement:
I’ve used ascending intervals here; descending intervals work the same way.
So C-Cb, the “diminished unison”, is an ascending interval, according to Tymoczko. And he says the descending intervals “work the same way”. So we can have a “descending diminished unison”…
2 Likes
I don’t know if you geek out on Music Theory/Notation Twitter like I do, but there are some pretty amusing accounts and rabbit holes to go down there LOL
1 Like
I’m reluctant to throw any more fuel on this fire but intervals larger than an octave are often called compound (and always called that in ABRSM exams). Thus C4 to E5 is a compound major third. That means C4 to C#5 is not an augmented octave but a compound augmented unison. At least in ABRSM speak.
Inverting a compound interval doesn’t make sense. You can only invert a simple interval, i.e. one less than an octave.
Having said that, and despite teaching music at University for 15 years, I still call a M9 a M9, not a Compound M2.
Strikes me that a good team name for three musicologists might be “The Four Opinions”…
2 Likes
From the existential angst in this thread, I’m inclined to believe you actually meant “the four horsemen!”
Michael Cook is right that my undergraduate handout used language in a sloppy way, I was really talking about one-dimensional vectors rather than absolute distances. Personally, I think the meaning of exotic interval terms like “doubly diminished unison” is undetermined by musical practice, and a place where we just have to make a decision. I remember discussing this issue with Michael Cuthbert, who had to figure out how to program it into music21.
I guess I would be inclined to define a doubly diminished unison as the transposition that preserves letter names while transposing all notes down two semitones, so sending E4 to Ebb4. I have to go get my COVID booster so can’t think any more about it though!
8 Likes