Response to PAULE

Your response clarified your position in some detail; it will be useful if
certain other features in your approach are spelled out (I am writing in
parallel to re-reading your text):

(1) Does your central pitch processor depends on harmonic partials? Real
instrumental sounds deviate significantly from a ideal series. Does your
processor make tolerance decisions at both the individual instrument
(pitch) and the instrumental ensemble (chord) levels? It was for precisely
this complication that I made my initial assumptions of a sine wave
orchestra.

(2) Are amplitude and phase differences among the partials ignored?

(3) Would it be terribly difficult to couple your root-finding function
with some harmonic distance function in order to address chord
progressions?

(4) The limits on amplitude and durational aspects limit the algorithm to a
part of the world�s music; would you define this more precisely? In
general, I find this to be the most difficult part of your work (and of
other research along these lines) in that you have reified aspects
particular to a small musical repertoire as psychoacoustical facts.

Some comments:

(1) Naturally, if a triad is tuned 5:6:7, the fundmental frequency of the
series on 1 is reinforced;
what happens, when it is tuned /7:/6:/5, or in a temperament where the
approximation of 7 is poor? If I recall correctly, Boomsliter and Creel
demonstrated that in harmonic contexts both trained and untrained subjects
had a preference for the real interval of 225/128 over 7/4, thus showing
that a lower position within a harmonic series was not necessarily
preferable to some other, more complex relationship.

(2) My musical experience suggests, however, that diminished, augmented,
and other intervallically symmetrical pitch complexes function in tonal
music as ambiguous - neither major nor minor - structures. For this reason,
I introduced the _neutral_ characterization for pitch spacings that are
neither harmonic nor subharmonic.

(3) 54:64:81 is a chord that I am able to identify immediately in
relationship to a previously known tonic of 2^n. I recognize it in both
terms of harmonic distance from 2^n, from the size of the melodic intervals
which I have learned to distinguish (thus at least part of my recognition
is cultural), and from beating. Moreover, my recognition of this chord cues
me in on the entire field of relationships including this chord and the
chord proceeding it. It is this field that seems to determine musically
dynamic characteristics: chord _progression_; tonicity; _resolution_;
surprise, etc..

(4) The melodic difference between 9/8 and 10/9 is too real to be dismissed
as something "handled on paper". Even if the listener doesn�t get the
melodic difference immediately (something heard all the time in good string
playing or unaccompanied vocal music), eventually the comma difference will
either manifest itself in a _bad_ fifth, which is immediately _heard_ as
such, or a _return_ to a tonic that has missed its mark by a comma (the
ear is much faster at picking this up than the eye anyways).

(5) Which interpretation does this support? Your own analysis of the minor
triad prefers a subharmonic description. You can not have it both ways. For
this reason, I find it sufficent to base my spacing description upon
fundamental frequencies and a single calculated fundamental or guiding
tone.

(6) The harmonic and subharmonic series are two transfinite series with
different memberships; the second may be constructed from the first, but a
one to one mapping of the second onto the first is not possible. This is
however, coincidental to my point, that we process subharmonic structures
less well than harmonic due to conceptual and computational difficulties.
Example: it is much easier to compare three objects with one object than it
is to compare one object with thirds of an object.

(7) Prof. Hennix has worked specifically with musical issues; most closely
with the late John Myhill and with La Monte Young. (Her closest purely
mathematical collaborations were with Myhill and with A.S. Yesinin-Volpin.)
She may represent a different school of mathematical foundations from your
own, but her work is anything but drivel; indeed intuitionist proof demands
are the most rigorous.

Daniel Wolf

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Date: Sun, 29 Sep 1996 08:26:03 -0700
Message-Id: <199609291719.RAA18439@teaser.teaser.fr>
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There was at the end of september, in the Abbaye of Royaumont (near Paris,
France)an important 'colloque' on microtonality organized by "Voix=
Nouvelles"=20
(Marc Texier, director).=20

Here is the programm of the differents events:

*09/19 =20
Marcel PERES (Directeur de l'ensemble Organum): Le probleme du temperament=
=20
dans l'interpretation de la musique gregorienne.

Pedro MEMELSDORFF (Directeur de l'ensemble Mala Punica): Microintervalles=20
dans l'oeuvre de Matteo da Perugia.

Klaus HUBER (compositeur): Le tiers de ton chez Guillaume Costeley et de nos
jours.

Pierre CAZES (claveciniste): Echelles et temperaments =E0 l'epoque baroque.

Marc TEXIER (Directeur de Voix Nouvelles): Modalite, timbre :=20
les deux vecteurs d'un depassement du temperament egal au XXe siecle.

Pascale CRITON (musicologue): Les approches ultrachromatiques de la premiere=
=20
moitie du XXe siecle (Wyschnegradsky, Carrillo, Haba).

At the end of this first day there was a presentation of the followings=20
instruments : Clavicytherium, Piano-Carrilo in 1/16 of tone, microtonal=20
clavicembalo of Alain Louvier and microinterval midi keyboard by=20
Fran=E7ois Paris.

After Dinner, the public presentation of the "Theorie de la Pansonorite" of=
=20
Wyschnegradsky realised by Franck Jedrzejewsky and edited by Contrechamps,
Geneve.


*09/20
Makis SALOMOS (musicologue): Xenakis et la recherche hors-temps.=20
Theorie des Cribles. Echelles non-octaviantes.

Pierre-Abert CASTANET (musicologue)/ Alain LOUVIER (compositeur):
L'ecole microtonale en France (Bancquart, Louvier, Barbaud, Philipot,=
Ballif,
Marie, Levinas...).

Didier ASCHOUR (guitariste) : Guitares microtonales.

James TENNEY (compositeur): Les nouveaux temperaments aux Etats-Unis.

Christian POCHE (ethnomusicologue)/Klaus HUBER: Les maqams arabes et leur=20
utilisation par Klaus Huber.

Fran=E7ois PICARD (musicologue)/XU SHUYA (compositeur): Echelles dans la=20
musique chinoise et leur utilisation par Xu Shuya.

Pascal GALLOIS (bassoniste): Les nouvelles techniques du basson illustrees
par des extraits d'oeuvres de Berio, Hersant et Taira.

Harry STARREVELD (fl=FBtiste): La flute en 1/4 de ton.


*09/21
Philippe LEROUX (compositeur): De l'action sonore au processus.

Fran=E7ois PARIS (compositeur): "Anamorphose et oblique dans la musique
d'aujourd'hui". Vers de nouveaux temperaments. Claviers midi microtonaux.

Marc TEXIER: Temperaments, echelles sonores, microintervalles : une nouvelle
frontiere de la musique.

Brian FERNEYHOUGH (compositeur)/Trio Contrechamps (I.Magnanat,vl; J.Sulem,=
alto;
D.Haefliger, vlc): Analyse du Trio =E0 cordes de Brian Ferneyhough.
Oeuvre en 1/8 de ton. Execution commentee de cette oeuvre en avant premiere.


This "colloque" was, at my knowledge, the first big event on microtonality=
=20
in France with such a diversity of approaches.
I wish it is the beginning of a real interest for other tunings...

Didier Aschour