Hi Lukas,
Am Donnerstag, den 09.07.2020, 10:08 +0200 schrieb Lukas-Fabian Moser:
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> > > But seriously, do you have a suggestion what to do
> > > when the
> > > "item" the
> > >
> > > command is referencing *is* a function?
> > >
> > >
> >
> >
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> > Another good synonym for "function", especially if you
> > passing it as an argument, is "callback"
> >
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> I think there's a misunderstanding here that is worth pointing
> out.
>
> The "functions" Urs is working on are not functions in the
> computer science sense (and neither in the mathematical sense,
> although some theorists disagree). It's about "harmonic
> functions"
> in the sense of a certain theory of harmony that is common
> especially in German-speaking countries.[1]
Which is one more argument for *not* naming the command \function.
Thank you for the following explanations which should make it clear for
everyone what we are talking about.
I have the impression I have no choice but to follow Carl's suggestion
and add a clarifying adjective, although that makes for quite
"expansive" user interface. E.g. \harmonicFunction might be the best
bet so far.
The next question would be how to name the corresponding commands in
the other planned modules (roman numerals analysis and "Bassstufen",
another system obviously tied to German-speaking music theory - I
didn't even find an English reference on Google. It is a system
originally devised by E.A. Förster around 1800 (
https://en.wikipedia.org/wiki/Emanuel_Aloys_F%C3%B6rster) and heavily
built upon in certain very influential streams of German music theory
since about 2000.)
I think "Bassstufe" could be translated to "scale step" or "scale
degree" and could therefore be used as a command like \scaleDegree.
However, people having written roman numeral analysis code (I know of
David Nalesnik and Malte Meyn so far) used \scaleDegree for the roman
numerals.
Maybe this set? * \harmonicFunction
* \romanNumeral
* \bassStufe
The latter would handle the fact that it's used in German contexts only
anyway. And it would nicely deal with the triple "s" ;-)
However, since we're still in a computing environment I'm afraid the
reference to roman numerals might be similarly problematic as
"function". What do you think?
Best
Urs
> General idea
>
>
> In that theory, some of the chords usually denoted by Roman
> numerals have special namens and symbols (now called
> "Funktionen"
> = functions): I is "T" (for "tonic"), IV is "S" (for
> "subdominant"), V is "D" (for "dominant"). But the more
> important
> half of the story is that in this theory, these three
> "functions"
> are the _only_ basic chords, from which all other chords are
> derived in some way. For instance, a vii° is regarded as a D⁷
> with
> root omitted, a ii⁶ is (most often) interpreted as a S with its
> fifth replaced by a sixth, and so on.
> The term "function" can, I think, be interpreted in two different
> ways here:
>
> - In the mathematical sense that these functions map from the
> set
> of key areas to the set of actual chords ("dominant(f major) =
> c
> major-triad") [but this applies for roman numerals as well!]
>
> - In the musical sense that chords tend to express a "function"
> for the harmonic progression of a piece: tonic chords have the
> function of "being at home", so to speak, while dominant chords
> express the function of "being only one step away from home",
> and
> so on.
>
>
> Strenghts and weaknesses
>
>
> As can be expected, a theory with such a strong focus on harmonic
> interpretation of chords has its strengths and weaknesses.
> For an example of what I consider a strengh, if you compare
> cadence formulas ii⁶ V I and IV V I, it can be argued that it
> might make more sense to "hear" the ii⁶ as a "kind of major"
> chord
> since the major third f-a is the same in both progressions.
> "German" function theory caters for this by writing S⁶.
> For examples of what I consider as weaknesses:
> - While a vii°⁶ quite often has the "function" of "wanting to
> resolve to a tonic", it's highly awkward to explain it as a
> "dominant seven with root omitted". First, from a historical
> perspective, V and vii°⁶ both occur much earlier than an actual
> V⁷, so the theory explains an old and well-known phenomenon
> from
> (at the latest) early baroque music as being derived from
> something basically unknown at that point in time. Second, from
> the point of view of classical voice-leading, the seventh of a
> V⁷
> has restrictions for its voice leading (the rule of moving
> downwards by a step, for instance) that are completely unknown
> for
> the same note as part of a vii°6. (And let's not forget that
> even
> the standard designation of vii°⁶ in roman numeral analysis has
> the flaw of explaining a very old "primary" phenomenon as being
> the first inversion of another phenomenon virtually unknown at
> that time.)
>
>
> - A mediant iii (in a major key context) has to be explained
> either as a relative of V or as leading-tone exchange chord of
> I
> (the corresponding German function theory symbols are "Dp =
> Dominantparallele" and "Tg = Tonikagegenklang"), but more often
> than not, if a iii actually occurs somewhere, it gets its
> peculiar
> and interesting sonic quality from being in some sense "neither
> tonic nor dominant".
> Where is this used?
> In German-speaking countries, some very popular
> (mid-20th-century) textbooks made this "Funktionstheorie"
> standard
> - to such a degree that "harmonic analysis of music" was
> considered equivalent to "using the theory of functions" (and
> this
> notion can still be found up until today sometimes).
> For other countries, the situation is different: As far as I can
> see, in English-speaking countries, it seems to be standard to
> use
> roman numerals (which itself comes in different flavors, just
> think of ii⁶ vs. IIb!). But in my teaching (at an Austrian
> music
> university with lots of international students), I always ask
> my
> students about the harmonic theories they have learned in their
> native countries; my impression is that in eastern-european,
> northern-european and far-asian countries, there are harmonic
> theories being used the are to a certain degree a mixture
> between
> "German" function theory and "international" Roman Numeral
> analysis. (A Chinese student once explained to me that he had
> learned to write something like S-ii-56, which means: function
> theory, roman numerals, thoroughbass, all in one.)
>
>
> Lukas
>
>
> [1] This theory was basically invented by 19th century
> musicologist Hugo Riemann, but has been simplfied and
> streamlined
> very much during the first half of the 20th century. Funnily,
> the
> word "theory of functions" also appears in the mathematical
> field
> of complex analysis, with one of its most important
> contributors
> being Bernhard Riemann. The two Riemanns are not related (as
> far
> as I know), and the theories are completely unrelated. :-)
>
>
>
>
