[Smt-talk] Gravity (Was: Car names)

[Thomas Noll]

Dear Nicolas,

> You may be making too much of Jacques Handschin's ideas.

Handschins had a very wide historical perspective and his ideas were driven by his sharp awareness of open theoretical problems. His act of upgrading the line of fifths to a central music-theoretical concept is the main concern of his book "Der Toncharakter". Remarkably, it starts with a departure from its "boring" role as a vehicle for harmony teachers and piano tuners. At any rate Handschin's ideas really deserve to be reviewed. It is a different question, of course, whether our algebraic approaches go in the right direction. 

> The fact is that a sharpward series of fifths in Pythagorean intonation does raise in pitch, by one Pythagorean comma after twelve steps.

That's a sophisticated perspective. With the same line of argument one could say that five sharpward fifths lower the pitch by a semitone, and that seven sharpward fifths raise it by an augmented prime. But the pitch height direction of those "commata" is not directly concerned with the pitch height directions of the scale steps themselves. It only measures their difference. My concern about directionality is more elementary. 

>     In short, a mode is not a scale.

A mode relates the perfect fifth and perfect fourth to a species of the fifth and a species of the fourth. It further relates the perfect octave to the concatenations of the species of the fifth and the fourth. In the dorian mode, for example, the species of the fourth is Y = TST (Tone, Semitone, Tone) and the species of the fifth is X = TSTT, wherein the species of the fourth is a prefix, i.e. X = YT, with T playing the role the major step as well as the role of the diazeuxis. 
The point where I might be making too much of Jacques Handschin's ideas is the construction of a "species of the major step" T = Y^(-1) X and a "species of the minor step" S = T^(-1)YT^(-1) = X^(-1)YYX^(-1)Y. Handschin doesn't deliberately distinguish between an ascending fifth and a descending fourth. These concepts seem to be algebraically motivated neologisms. But is this historically true? Schenker's "ausgeworfener Grundton" is quite close to that construction and maybe other theorists have also considered the five species of the semitone?

Sincerely
Thomas Noll

> 
> Yours,
> Nicolas Meeùs
> Université Paris-Sorbonne
>  
> 
> 
> Le 1/08/2012 15:08, Thomas Noll a écrit :
>> If we assume a directional markedness in the pitch height dimension (e.g. downwards being unmarked) we might assume an analogous markedness along the line of fifths (e.g. flatward being unmarked). Such an assumption implies an interesting question: How do the two kinds of markedness interrelate? Jacques Handschin argues in favor of an affinity between ascending pitch height and sharpward oriented fifths. That same type of affinity would then hold between descending pitch and flatward oriented fifths. This affinity is contrapuntally supported by the ultimate progression between tenor and bass in the cadence (as well as in the Ursatz). But for modal tone relations Handschin's assumption might nevertheless be wrong. There are good mathematical reasons to postulate that the combination between ascending pitch and flatward oriented fifths is the unmarked one.
>> Sincerely
>> Thomas Noll       
>> 
>>> Curt Sachs writes, in one of his books, that descending motion is more common, in all musics of the world, than ascending one. He does not say, however, how common it is to describe such motion as 'descending'. In general, though, melodies end at the pitch at which they began: they can but descend what they first climbed. the 'descending' effect probably results from the fact that they go up by leaps and come down by conjunct steps.
>>>     There is an interesting paper on the verticalization of pitch in Western music by M. E. Duchez in Acta musicologica 51/1, 1979. She indicates that the verticalization by no means is universal and that it appeared slowly and lately in the West (after the 9th century). The verticalization of pitch may be the consequence (rather than the cause) of the vertical disposition in notation. It does not seem to have existed in Latin (or Greek), where pitches were described as acutus (oxus) and gravis (barus). For some time, no clear distinction was made between pitch and intensity ('musica alta' was loud, not high).
>>>     In harmonic music, singing in just intonation tends to shift pitch. With respect to the cycle of fifths (Pythagorean tuning) taken as reference, the pitch shifts down a comma for each ascending major or descending minor third, and the reverse. Think of a neo-Riemannian network and of the change of line corresponding to 3d-relations: horizontal lines are a comma apart in just intonation. Tonal harmonic progressions tend to shift down – one of the reasons why a capella choirs shift down: they sing too much in tune!
>>> 
>>> Nicolas Meeùs
>>> Université Paris-Sorbonne
>>> 
>>> 
>>> 
>>> Le 30/07/2012 03:23, Christopher Bonds a écrit :
>>>> A quick comment. Seems like success in relating any kind of musical event to gravity depends on the answers to a couple of questions. First, whether descending intervals, stepwise lines, root progressions, etc., generally always create a sense of closure or at least a lessening of tension; and if so, are these style and culture independent? Second, if so, could there be other explanations for this phenomenon? Third, if some sort of relationship could be established between the physical law and gravity, what effect, if any, will Einstein's general theory of relativity have on musical perception, now or in some future time? Finally, is the concept of "up and down" in music universal and innate, or is it something we have learned by association?
>>>> 
>>>> (For the record, my personal thinking is that the musical brain has learned to associate higher and lower pitches with up and down in space. Maybe because low sounds are associated with heavier objects, which seem to be tending downward more seriously than lighter objects (although they accelerate at the same rate when falling.))
>>>> 
>>>> Christopher Bonds
>>>> Wayne State College (retired)
>>>> 
>>>> 
>>>> 
>>>> 
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>> 
>> 
>> 
>> *********************************************************
>> Thomas Noll
>> http://user.cs.tu-berlin.de/~noll
>> noll at cs.tu-berlin.de
>> Escola Superior de Musica de Catalunya, Barcelona 
>> Departament de Teoria i Composició 
>> 
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>> 
>> 
>> 
>> 
>> 
> 



*********************************************************
Thomas Noll
http://user.cs.tu-berlin.de/~noll
noll at cs.tu-berlin.de
Escola Superior de Musica de Catalunya, Barcelona 
Departament de Teoria i Composició 

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