RE: Gibson digest 1274

>
>}Gregg Gibson said:
>}> >>The ideal value for the octave itself is of course 1200/19 =3D =
63.16 ;
>}> >>here are the values for the other six consonances.
>}> >>3:2 701.96/11 =3D 63.82
>}> >>4:3 498.04/8 =3D 62.26
>}> >>5:4 386.31/6 =3D 64.39
>}> >>5:3 884.36/14 =3D 63.17
>}> >>6:5 315.64/5 =3D 63.13
>}> >>8:5 813.69/13 =3D 62.59
>}> >
>}> >>If one considers the consonances to be all of equal importance, =
one can
>}> >>simply take the average of the above seven figures, which is =
63.22, to
>}> >>arrive at a figure for the octave of 1201.2.
>
>}Paul Ehrlich said:
>}> >Gregg, this is not correct. You are not giving equal importance to =
the
>}> >intervals above. Since whatever compromise is made in taking the =
average
>will
>}> >be multiplied 14-fold for the 8:5 but only 5-fold for the 6:5, you =
are
>being
>}> >more permissive for tuning errors in the larger intervals. I am =
certain
>}> >Fokker would not have made this mistake, being a brilliant =
physicist. I
>know
>}> >you will probably gloss over this post the way you have dismissed, =
with
>total
>}> >lack of understanding, my other comments. But if you are =
interested, I
>will
>}> >tell you the other things wrong with your calculations here, and =
how I
>}> >arrived at an optimal octave of 1202.7 cents for 19-equal.
>
>}you presume to assert that I have "glossed over"
>
>You have -- for instance, what is your response to my question as to =
why
>26-equal shouldn't be considered as a diatonically usable temperament? =
What
>is your response to my question as to why just intonation is far =
superior to
>53-equal?
>
>}and dismissed
>}your posts with "total lack of understanding"
>
>You have and continue to do so -- here's evidence:
>
>}I advise you to study the cycle of 22-tone equal consonant fifths. See
>}if you can find a consonant third, four fifths above the tonic. If you
>}cannot (and you cannot) your arguments fall to the ground. I repeat =
that
>}when I was a beginner, I made the same mistake you are making.=20
>
>which proves that you don't have an inkling of what my "arguments" are,
>although I have evidently presented them with enough clarity so that =
Graham
>Breed, Paul Hahn, and Steven Rezsutek have understood them.
>
>}1. Fokker's method is as I have stated. Read the references for
>}yourself. If you do not have access to Fokker's original texts, use
>}Mandelbaum.
>
>I have not been able to gain access to Mandelbaum's writings, or to the
>particular ones of Fokker in question. Believe me I have tried to read =
every
>shred of tuning-related literature, including the Yale, Harvard, NYU, =
and NY
>Public libraries, partly in an attempt to see if anyone had discovered =
the
>decatonic scales before me. Surprisingly, no one has, as far as I know.
>However, since the issue is mathematical, not historical, we need not =
appeal
>to the literature. If Fokker was using a convenient approximation to
>illustrate a point, so be it, but we can still do better. I have other
>disagreements with Fokker, such as his use of square rather than =
triangular
>lattices, as well as his use of 31-equal to represent ratios of odd =
numbers
>(such as 13) that are not consistently expressed by the tuning.
>=20
>}2. Fokker could have used _no_ method to achieve equal weighting of
>}deviations of the consonances.
>
>Excuse me, but did you not say in the above that you were treating the
>consonances as equally important, and therefore taking an average of =
the
>figures?
>
>}The most _basic_ principle of
>}temperament, which is taught to all _beginners_ in this discipline, is
>}that there can be _no_ temperament which compromises the consonances
>}equally.
>
>Of course, one cannot make all the errors equal, but one can make them
>equally important in determining a temperament.
>
>}This arises from the mathematics of the case. _Learn_
>}mathematics before you make such statements, which again, only show =
your
>}ignorance.
>
>}Now that I have administered the bitter pill, let me add a large
>}tablespoon of sugar. You are quite bright. You were led into this =
faulty
>}conclusion by assuming that the consonances are independent, and so,
>}vary independently when tempered. I use non-mathematical language here
>}deliberately. But in fact the consonances consist of three pairs, 5:4 =
&
>}8:5, 6:5 & 5:3, and 3:2 & 4:3, each of which pair varies as if it were =
a
>}single interval, so far as temperaments are concerned. Therefore, to
>}seek some system which shall weight deviations from the consonances
>}equally, even in the case in which the octave is itself tempered, is =
the
>}classic pons asinorum of temperament, for no such system can exist.
>
>Again, _you_ were the one who attempted to weight the deviations =
equally,
>which is a perfectly fine thing to attempt to do. I simply pointed out =
that
>you did not do so correctly. If you wish, I will go through the math =
and show
>that you did not find the optimal octave for your initial example. Your =
error
>propagates through your other refinements and the fact that we arrive =
at a
>similar value for the optimal 19-tone octave (1202.7 cents) is either =
sheer
>coincidence or evidence that both of us were listening.
>
>}Finally, let me observe that the value of 1202.7 cents for the octave,
>}while apparently very precise, and possibly indicative that one person
>}may have copied the other without acknowledgement,
>
>That is so absurd as to be laughable. I calculated that number for the =
first
>time just before I posted it, and I clearly indicated its derivation, =
which
>again is quite different than yours.=20
>
>}> > Gregg Gibson is posting such a lot of highly opinionated material,
>}> > it is difficult not to join in the argument.
>bil said:
>}> Or wish my mailer had a filter function -- such a flood of junk.
>
>}For those who have been eager to attack me as uncivil, I give this as =
an
>}example of true incivility. It is not uncivil to say a tuning is =
without
>}value.
>
>Imagine telling an oboist that the oboe is a worthless instrument. If =
that
>were a civil thing to say, you wouldn't need to protect yourself from =
an
>incoming double reed. To describe yourslef as "meekly humble" only =
shows that
>you are hiding behind the impersonal screen of the Internet while =
firing off
>your insulting material. Evidently you find my tone objectionable as =
well --
>I'd be happy to just discuss tuning and not make personal remarks, if =
only
>you'd attempt to understand, rather than dismiss as beneath your
>consideration, the counterarguments that I and others offer.
>
>}As I have abundantly shown in previous posts, this temperament (and
>}analogous ones such as 29- 41- & 53-tone equal,) is impossible for the
>}diatonic, as well as for the chromatic modes (see the four chromatic
>}modal genera or scales I have contributed; these include several of =
the
>}forms of the 'minor' of the West) which obviously require thirds and
>}sixths vis-=E0-vis the tonic, it being granted that the fifth and/or
>}fourth must also be present.=20
>
>On the contrary, you have not shown anything, while I have shown that =
three
>of your four "chromatic" genera are indeed adequately represented in
>non-meantone temperaments.
>
>}The case of the enharmonic is less clear-cut, and requires more =
detailed
>}consideration. For after all, one might ask, surely the divers
>}enharmonic modes have fewer thirds or sixths vis-=E0-vis the tonic, =
and so
>}the inconsistency between the fifth cycle and those of the thirds =
would
>}appear to be less troublesome; in certain enharmonic modes it might
>}never arise at all.=20
>
>That's right -- just as it never arises in three of your four =
"chromatic"
>genera.
>
>}For example, take one form of the enharmonic:
>}C C# Db F G G# Ab C (not the 22-tone equal notation)
>}or in 22-tone equal:
>}0 55 109 491 709 764 818 1200
>
>}There is a consonant major third between Db & F, and another between =
Ab
>}& C, and a consonant minor third between F & Ab.=20
>
>}In reality, of course, the notation of the 22-tone differs from the
>}above notation:
>}C Db B# F G Ab Fx C
>}which BTW is not a mere artefact of notation, but on the contrary
>}explains very succinctly the utterly non-diatonic and non-chromatic
>}nature of this system,
>
>Which is why I would use a decatonic rather than heptatonic notation =
for
>22-equal.
>
>}The effect of this particular Greek enharmonic mode - the most famous =
of
>}them as I recollect - is in 22-tone not wholly dissimilar to its =
effect
>}in 19-tone equal, except that the latter is much more singable because
>}of the wider 63.3 cent interval.
>
>But which is closer to the ancient Greek tuning of this mode?
>
>}Other enharmonic modes in 22-tone equal such as:
>}C D D# F G G# Ab C (not 22-tone equal notation)
>}0 218 273 491 709 764 818 1200
>}have problems however. Here D-F is dissonant, and this would tend to
>}disagregate the already weak tonality of the enharmonic. If D is =
lowered
>}to make D-F consonant, D-G becomes dissonant. This is similar to the
>}break in the fifths that besets just intonation itself. This is not a
>}trivial matter; it is very noticeable to the ear.
>
>Does this mode have any practical or theoretical importance?
>
>}The difference of 9 cents between
>}54.5 and 63.3 cents is very important, because it occurs near the
>}melodic threshold or limen of perception.
>
>So if you go down 54 cents, and then up 63 cents, you've gone down an
>imperceptible interval, and then up a perceptible interval, so you're =
up a
>perceptible interval. Therefore, 9 cents is a perceptible melodic =
interval by
>your logic. You see why we don't think your limen makes much sense? =
Context
>and training are far more important for what can or cannot be =
distinguished
>in melody than any precise cents value.


SMTPOriginator: tuning@eartha.mills.edu
From: "Paul H. Erlich"
Subject: Reply to Bob Lee
PostedDate: 23-12-97 14:45:34
SendTo: CN=coul1358/OU=AT/O=EZH
ReplyTo: tuning@eartha.mills.edu
$MessageStorage: 0
$UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH
RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH
RouteTimes: 23-12-97 14:43:21-23-12-97 14:43:22,23-12-97 14:42:53-23-12-97 14:42:53
DeliveredDate: 23-12-97 14:42:53
Categories:
$Revisions:

Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2
9-3-1997)) with SMTP id C1256576.004B5F64; Tue, 23 Dec 1997 14:45:12 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA24159; Tue, 23 Dec 1997 14:45:34 +0100
Date: Tue, 23 Dec 1997 14:45:34 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA24312
Received: (qmail 9976 invoked from network); 23 Dec 1997 05:44:33 -0800
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 23 Dec 1997 05:44:33 -0800
Message-Id:
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu