From: Tuning Digest
To: monz@juno.com
Date: Wed, 25 Nov 1998 10:57:18 -0500 (EST)
Subject: TUNING digest 1592
TUNING Digest 1592
Topics covered in this issue include:
1) Re: TUNING digest 1591
2) Csound card
3) answering machine
4) RE: Erlich's Contest
5) Cognitive limits
6) reply to Lumma's reply to Grady
7) "undertone series"
8) Microtonal Composition Software
9) Reply to Stephen Soderberg
10) reply to Ed Foote on Mozart Tuning
11) Carillon Tuning
12) subharmonic series
13) Re:Reply to Carl Lumma
14) Re:DJWOLF/BABBITT
15) Re: Reply to Paul Erlich
16) pitch-class
17) Re: A strange 9-limit temperament
18) Re: reply to Paul H. Erlich to Ed Foote on Mozart Tuning
19) Re: reply to Paul H. Erlich to Ed Foote on Mozart Tuning
20) Re: Microtonal Composition Software
21) Most 7-limit consonances with 12 pitches
----------------------------------------------------------------------
Topic No. 1
Date: Tue, 24 Nov 1998 12:29:27 -0800
I did miss it. And I disagree with the implied results of the experiment.
I experience a great deal of pleasure from purely-tuned chords, and that
pleasure is absent when the chords are mistuned. In fact, mistuned chords
cause me discomfort if they are sustained for any period of time.
There are plenty of experiments with results just the opposite of the one
you cite, and it shouldn't be surprising since we're talking about people's
subjective likes and dislikes. Also, I think "melodic mistuning" can mean
a lot of things. If you listen to a capella recordings of groups like
the Swingle Singers, The King's Singers, or various Barbershop groups, you
will hear a type of melodic mistuning that I don't think you'll find the
least bit upsetting. In fact, I wish you'd take my advice and get the
following album...
..it is the best single example of singing (yes, in general) I know of.
The fifth degree of the natural minor mode of the diatonic scale is not a
tritone. If you check out the matrices I posted, I am sure you will
understand my questions.
Reality check, folks. Organs are still being built for meantone, and the
idea that there was any kind of standard in Mozart's time is absurd. Back
then, instruments were tuned by ear in a hurry (because you had to tune
them all the time) with little regard for anything written in a book. The
answer is well temperaments, of all sorts imaginable.
Carl
------------------------------
Topic No. 2
Date: Tue, 24 Nov 1998 12:38:39 -0800
Thanks for the info. The URL is giving some sort of 404, however.
Carl
------------------------------
Topic No. 3
Date: Tue, 24 Nov 1998 12:55:11 -0800
Regarding talk about melody vs. harmony, I would like to perform an
experiment.
Pacific Bell has been rather tardy in deleting my voicemail account since I
left California. Hopefully, they won't remedy this in the next 24 hours.
Here's what I propose...
Call (510) 433-7271 and listen to my greeting, which I made on Norman
Henry's 11-limit harpsichord.
It's pretty simple, but you do get a taste of a harmonic series melodic
effect at the end. What do you think? How well did the 7/4 work as a
leading tone?
Carl
------------------------------
Topic No. 4
Date: Tue, 24 Nov 1998 16:20:30 -0500
I have played little tidbits of decatonic music, but since I've obtained
my 22-tone instruments, I've been more drawn to 22's non-decatonic
resources. The idea was a purely theoretical one, in the tradition of
Yasser, Balzano, etc., but with what I feel are more valid criteria.
How about a piano tuned to 12 out of 22 (put 1/22 oct. at e-f and b-c),
or if you want to modulate around all 22 keys, the main keyboard mapping
described in my paper?
The rules I chose capture pretty much all the important features of the
diatonic and pentatonic scales, in my opinion. I have considered many of
the characterizations made by other authors
(MOS, propriety,
unique interval vector, etc.) and come to the conclusion that these are less
important.
I wholeheartedly agree, and would love to find some scales that do
anything like that.
On the many-tones issue, I think the tetrachord structure helps to
reduce the number of independent elements that need to be perceived, and
compositional technique can make at least as much difference as an order
of magnitude difference in the number of tones.
------------------------------
Topic No. 5
Date: Tue, 24 Nov 1998 16:31:30 -0500 (EST)
Carl Lumma posts some interesting questions about cognitive limits. In
particular, the "Miller limit" poses an interesting challenge:
and ...
This doesn't take into account (unless I'm missing something -- a distinct
possibility) the mind's characteristic ability to recognize (and organize
into) patterns. It may not be as "instantaneous" as Miller's tests
suggest (and I admit I don't know the study -- I'm going on the present
description and similar ones I've heard), but seven stones are nearly
immediately organized into four-plus-three and so on. Second, a strictly
"melodic" test doesn't take into account the full power of many musics to
organize material into recognizable, memorable chunks.
The most pertinent example is good old 7-space ME imbedded in 12-space --
the "usual diatonic." It's not exactly a secret that this presents a
"bi-modal" system with three major and three minor
triads. Further, the
two modes mirror one another, each containing what we traditionally have
called a "tonic," "dominant," and "subdominant" triad, linked like this
(using pitch-class
notation, e.g., 0=C, 1=C#, etc.):
And each triple "covers" the scale.
From Introductory Diatony 101 let's now return to the Erlich string
(22@41) discussed in earlier posts, since, as a 22-note scale, it's right
at the outer "focus" limit in Carl Lumma's chart. Let's first list this
scale in its pitch-class version to see just how absurd it would be to
think of an audience (or even an individual) with good enough pitch
retention to make sense out of a context-less melody using this scale...
{0,2,4,6,8,10,12,13,15,17,19,21,23,25,26,28,30,32,34,36,38,40}.
Now, it just so happens that, buried in these 22 notes, are some
interesting ORDERING properties which can be used (compositionally) to
build some (contextual) structures that shouldn't be difficult to remember
and relate to one another, melodically or otherwise.
I noted before that, with a simple trick (a WARP transformation as used in
simple diatonic structures) we can organize this material into a
"quadrimodal" system -- two pairs of inversionally related pentachords. I
also suggested plotting these onto a circle to see their peculiar and
unique arrangement. Those of you who did this can now guess where I'm
going. Taking only one of these chord types -- the one built on the
interval string <87t79>, we find one pentachord that acts like a "tonic"
(on 0), two that act like "dominants" (on 26 and 28) and two that act like
"subdominants" (on 13 and 15). These are listed below. The only chord
in "prime" position is the "tonic" in the middle; the rest are rotated to
demonstrate the smooth (hyper)diatonic voice-leading and common tones:
Note that these five chords (like the three in the usual diatonic) cover
the scale. Each of the other three "mode groups" works the same way,
complete with the double-dominant relations, voice-leading and covering
properties. Furthermore, you can easily slip from one mode to another by
maximal common-tone relationships which appear as common-triads. E.g., in
a different mode, the scale gives us the pentachord {8,15,23,32,40} which
can move easily to {0,8,15,25,32} by holding the common-triad {8,15,32}
and moving the other two voices by (hyper)diatonic step.
My point (beyond maybe tempting someone out there to use this system to
compose) is this: the internal musico-mathematical characteristics
(organizational capabilities) of a given scale might tend to ameliorate
what might otherwise be an insurmountable complexity. In the Erlich
string, I don't see a 22-note scale -- I see a 4-mode division of
pentachord types (and a couple of interesting looking "diminished"
pentachords) each of which forms a very peculiar T-D-SD triangle (and NB:
there are other ways to organize an Erlich string). My mind can't grasp 22
objects until they're built into a cohesive structure, however strange it
might appear at first. Put another way: I can't "grasp" 10,000 bricks,
but I can easily "grasp" a brick house.
Steve Soderberg
------------------------------
Topic No. 6
Date: Tue, 24 Nov 1998 17:10:02 -0500
What's the largest mistuning you'll allow? Did you catch my repost of my
post from Nov. 17th on meantone
vs. just (that is, harmonic mistuning
vs. melodic mistuning)?
------------------------------
Topic No. 7
Date: Tue, 24 Nov 1998 17:18:19 -0500
Partch credits Riemann and many others in preceding his
"utonality"
concept. The concept has an intersting status around here, with a few
giving it little to no importance (e.g., Heinz Bohlen), a few giving it
near-equal status with the otonal
or "overtone series" concept, such as
Daniel Wolf and (implicitly) Bill Sethares, and most of us falling
somewhere in between. Interval-wise, utonalities and otonalities are
equivalent, but there are important harmonic effects due to combinations
of three of more tones that
render otonal chords more "tonal".
------------------------------
Topic No. 8
Date: Tue, 24 Nov 1998 23:16:06 +0100
We are one composer and one programmer from Europe (Lithuania, Germany)
who
are working on a software for composing and producing electronical
microtonal
music.
This software product (for windows platform) being developped by us
combines
two different fields:
- provision of the scales of microintervals down to 1/64 semitone
- production of tonal structures by help of mathematic musical functions
The procedure developped by us could lead to the synthesis of the
traditional
techniques of composition and use of mathematical functions.
We just want to ask you if anybody of you is interested in our project
in any way or
knows about some similar software product or is dealing with
microtonal
electronic composition.
We would be glad to receive an answer from you.
Yours
------------------------------
Topic No. 9
Date: Tue, 24 Nov 1998 17:27:37 -0500
And almost nothing to do with music. Stephen, I couldn't disagree with
this position more, but I have only the highest respect for your
intellectual rigor, and I appreciate the respect you've shown to mine.
As a starting point for some discussion, perhaps you could tell us how
far you'd go in defending the phrase "regardless of how you tune it" in
the first sentence above. I infer that some would require a Rothenberg
proper 12-tone scale; how about you, Stephen?
------------------------------
Topic No. 10
Date: Tue, 24 Nov 1998 18:09:45 -0500
Why would you want a well-temperament
if the music avoids the keyboard
wolf? There are many more ways to achieve variegation of key color when
one allows the wolf to be present than when one insists on its
disappearance. The "realm of historical possibilities" is perhaps 10%
documented in the literature and if one is making judgments with modern
ears it is foolish to restrict oneself to documented possibilities of
another era.
Last time we had this discussion, weren't there a few people who had
various pieces of evidence for Mozart favoring
meantone? Like his
teaching of two semitone
sizes, diatonic and chromatic? And his reaction
to a 31-tone (obviously, meantone) instrument he played on?
------------------------------
Topic No. 11
Date: Tue, 24 Nov 1998 19:04:24 -0500
Darren Burgess from Gainesville FL here. I have posted a proposed tuning
for the Schulmerich JI carillon at
http://www.interbeing.com/carillon/tuning.htm. If you take a look, you
will note that two pitches are assigned to each bar. Each bar has two
solenoids, one that emphasizes the first harmonic (harp), and one the
second (celeste). This allows for having more than 12 tones per octave (up
to 24). I will provide more information for those who are interested.
Please, any feedback would be greatly appreciated.
Darren
------------------------------
Topic No. 12
Date: Tue, 24 Nov 1998 19:21:13 -0800
from Steve Soderberg:
This was discussed over the course of a few days back around
TD 1350 or so. Partch [Genesis, p 390] notes that Riemann
accepted the concept of an "undertone" series, but derides
Riemann's convoluted explanation of the "minor" triad.
Dualism and Functionalism were the fundamental concepts
in Riemann's original conception of harmonic practice.
However, he himself eventually came to discredit the
belief in an "undertone" series. (sure do wish I had my
books with me, so I could give the citations)
Partch clearly based his entire theory upon dualism
[Genesis, p 88-90, Monophonic Concepts # 2 and 3],
but gives Riemann no further credit than that stated above.
------------------------------
Topic No. 13
Date: Tue, 24 Nov 1998 20:10:55 -0800
It means that whenever we have a 3/2 it is seperated by 7 steps of a 8/7
by two steps. Also it one of its subsets, the major scale you have
fifths occuring every 5 steps, the thirds 3. There is the disjunction of
the tritone if we if we see this scale projected as fifths. For the
most part this closing interval will be unique but will be larger than
the intervals associated with the steps below it (in this case thirds)
and smaller than those intervals of larger etc.
I'm not familiar with the double dekany. I am familiar with dekany and
pentadekany. Perhaps you could be more specific?
it is the 2 out of 5 and 3 out of 5 combined!
I did say that the 12-out-of Stellated Hexany
tuning has the greatest number of consonant intervals of any possible
12-tone subset of the 7-limit. Did you know this? Or is it incorrect?
I
have no proof..
the hexany is always the first structure I rush for when looking for the
most for the least! From there I do my damnest to use as few notes as
possible to make a scale under the guidlines above as implied in Erv
MOS. There is the tanabe cycle which illustrates the pentatonics found
in the diatonic. Erv refers to them as second order MOS and this is
where all the following theorists are silent! I for now interpet these as
working as scales because the "generator" ( the building block of the
scale ) remains consistant in its steps. With the scale F A B C E we find
the disjuction A -C being the atypical 4th.
Fr
Kraig Grady
Could you explain more? You have got my interst up.--
It means that whenever we have a 3/2 it is seperated by 7 steps of a
8/7 by two steps. Also it one of its subsets, the major scale you have
fifths occuring every 5 steps, the thirds 3. There is the disjunctionof
the tritone if we if we see this scale projected as fifths. For the
most part this closing interval will be unique but will be larger than
the intervals associated with the steps below it (in this case thirds)
and smaller than those intervals of larger etc.
Look at the 1-3-5-7-9 double dexany and you will see a 14 tone scale
that
I'm not familiar with the double dekany. I am familiar with
dekany and
it is the 2 out of 5 and 3 out of 5 combined!
I did say that the 12-out-of Stellated Hexany
Fr
Kraig Grady
------------------------------
Topic No. 14
Date: Tue, 24 Nov 1998 21:40:43 -0800
Pardon the misunderstanding I to find many ideas of these individuals
worthy of note. I just chringe though with some of them assumptions that
music is nothing more than the interaction of formal relationships. But
true if you were so inclined the CPS are the way to go!
--
Kraig Grady
------------------------------
Topic No. 15
Date: Tue, 24 Nov 1998 22:02:45 -0800
Because I wanted consonant tetrads, not just triads. The 7-limit seems
to be the way to go, and 12-tET has poor 7-limit tetrads. In fact, were
it not for this "absurd" desire, I would probably not have developed an
interest in alternate tunings at all!
I applaud and respect your desire! that 's not Absurd! If this tetrad is
good for your uses go ahead. It just I would hope one would say the
sound was right or worked and not put in just mathematical
Justification. The first tuning I worked with was 31 which supplied me
with a good 7 and 11/9 but after a few years of working with it it was
the 9/8 that made it unbearable. It lacks all "asertiveness" this
interval gives us. On the other hand 19 which I have never liked, I
found liking in the hands of Neil Haverstrick (His most recent CD which
surpasses his first) and his live performance of at the micro fest two
years back on a 34 ( Hansons' Baby) sounded better than the math says it
should ( I understand why), Lucys Tuning also sounds better than one
might expect! The desire for consonant tetrads reflects my own desire
for not so much wanting new sounds or chords but new consonances. After
having, these I realized that new structural possibilities that are
nonsense in 12 where possible. But even with your 22 the relationship of
7 are not confused with 9 like they are in 12. I am sure you enjoy these
also!
Kraig Grady
Because I wanted consonant tetrads, not just triads. The 7-limit
seems
I applaud and respect your desire! that 's not Absurd! If this tetrad
is good for your uses go ahead. It just I would hope one would say the
sound was right or worked and not put in just mathematical Justification.
The first tuning I worked with was 31 which supplied me with a good 7 and
11/9 but after a few years of working with it it was the 9/8 that
made it unbearable. It lacks all "asertiveness" this interval gives us.
On the other hand 19 which I have never liked, I found liking in the hands
of Neil Haverstrick (His most recent CD which surpasses his first) and
his live performance of at the micro fest two years back on a 34 ( Hansons'
Baby) sounded better than the math says it should ( I understand why),
Lucys Tuning also sounds better than one might expect! The desire
for consonant tetrads reflects my own desire for not so much wanting new
sounds or chords but new consonances. After having, these I realized that
new structural possibilities that are nonsense in 12 where possible. But
even with your 22 the relationship of 7 are not confused with 9 like they
are in 12. I am sure you enjoy these also!
------------------------------
Topic No. 16
Date: Wed, 25 Nov 1998 01:14:06 -0800
Dan Wolf wrote:
Perhaps eternally lost in a non-octave-scale
harmonic world?
My initial intention in saying that was to be
flippant, but there is a serious truth embedded in
this:
Pitch-class is admittedly an important term,
useful in discussing theoretical points. But
accepting the idea that pitches roughly an
"octave" apart have the same aesthetic effect/affect
leads by extrapolation to the acceptance of the
other prime
(or odd)
affects.
This feeling of similarity is precisely the musical
affect associated with 2, the first prime number,
and is what led the ancient Greeks to divide numbers
between odd and even [see "odd" in my dictionary:
http://www.ixpres.com/interval/monzo/define.htm#odd].
Even if the interval most often perceived as a
consonant "octave" is _not_ precisely a 2:1, I would
argue that 2:1 is the _categorically-perceived_
"octave" interval.
Perhaps concepts similar to "pitch-class" could be
formulated for the affects perceived in other-prime
(or other-odd) relationships.
Perhaps affect is a phenomenon associated only with
primes and not with odd-numbers per se, since 2 is
the only even prime.
Perhaps the unusual affect of _similarity_
in the "octave" occurs only _because_ 2 is the only even
prime.
---------
BTW, I actually _like_ some of Babbitt's music, although
I've long since lost patience with his overly convoluted
prose style.
- Joe Monzo
------------------------------
Topic No. 17
Date: Thu, 26 Nov 1998 00:09:05 +1000
Many thanks to Graham Breed, who finally got me to see this
tuning as a "detempered" 12 of 22-tET. That is, taking 12 of 22-tET
part of the way back towards Just. Not that it was in any way obvious
how to do this profitably.
This would normally mean increasing the accuracy of intervals
(ratios) at the expense of a reduction in the number of sufficiently
accurate intervals. But in this case, while we do lose four 7-limit
intervals, we might be considered to make up for it by gaining some
9-limit ones.
For those who haven't seen it before, and as a new slant for those
who have, it looks like two chains of fifths a half-octave apart,
where the middle fifth of each chain is slightly wider than a 22-tET
fifth and the others are slightly narrower.
As offsets from 12-tET it is
Consider the harmonic resources in each case.
12 of 22-tET has 12 complete 7-limit tetrads.
In 12-tone 7-limit JI, the most we can get appears to be 6 complete
tetrads plus 2 triads (but with no pretense of being a melodic construct).
Thanks for that, Carl Lumma.
In the 7-limit, my temperament is intermediate, with 8 complete 7-limit
tetrads and 4 others that have a broken 7:4 (and so become 8 triads).
However these bad 7:4's are actually good 16:9's which occur as 9:4's
in extending other tetrads to 9-limit pentads. So nothing is wasted relative
to 12 of 22-tET. In fact when 9-limit is considered, my temperament has
*more* usable intervals than 12 of 22-tET. Notably, 9:5's essentially do
not exist in 22-tET.
Here's a comparison of the errors:
This is the version with 706 and 712 cent fifths. Whether you use
maximum error or RMS there is a minimum in the vicinity of this pair
of fifth sizes.
Note that only in the 7:6's, and in 2 of the 10 fifths, is there a
significant increase in error. The minor thirds, the other 8 fifths,
and the 9-limit intervals except the 9:7, are significantly improved.
So we've gained some accuracy with little loss of 7-limit harmonic
resources (no loss at 9-limit).
This temperament can be seen as simultaneously approximating the
following Just tunings.
Then there's the question of modulation. Paul Erlich's decatonic
scales would presumably occur in only one or two positions in a suitable
7-limit 12-tone JI. They occur in 4 positions in 12 of 22-tET. They also
occur in 4 positions in my temperament, however two of these have the
transmuted 7:4's in the otonalities while the other two have them in
the utonalities.
Regards,
------------------------------
Topic No. 18
Date: Wed, 25 Nov 1998 09:15:17 -0500 (EST)
On Tue, 24 Nov 1998, Paul H. Erlich wrote:
I suspect the historic literature provides more than 50% of what happened
in particular composer's tunings. There is much information, after all.
It may not be "foolish" to focus there when trying to perform the music as
the composer would have desired. I see little evidence of meantone in
Mozart, if any. His father mentions Werckmeister foremost in his Violin
treatise (no someone endorsing meantone). For Mozart to distinguish
between 2 sizes of semitones is simply a variant of Werckmeister I tuning
(or just intonation as it is derived precisely from the overtone series).
And could someone run by again with his supposed reaction to a
hypothetical 31 -tone instrument?
Johnny Reinhard
------------------------------
Topic No. 19
Date: Wed, 25 Nov 1998 16:19:23 +0100
I posted this 13-aug-1994 and again 9-jul-1996. I think Kelletat makes
a rather big leap with his conclusion there.
-------------------------
On my holiday this summer I was in Vienna and paid a visit to the
collection of musical instruments of the museum of art history.
There was a beautiful 31-tone Harmoniehammerfluegel built by Johann
Jakob K"onnicke in Vienna and finished in July 1796.
It has 6 rows of 37 white keys and a range of F1-g'''. The keys of the
C columns have a large dot on it and the keys of the F and G columns
three small dots. The layout of the five upper rows is as follows:
The keys of the bottom row are coupled to other keys. This layout
enables an easy shift by a chromatic semitone of 77.4 cents by
changing a row.
Beethoven and Haydn have played on this piano, which was tuned in
31 tET. K"onnicke built it with instructions of the Domkapellmeister
of Linz, Johann Georg Roser who had ordered a similar instrument in
Brussels ten years earlier for Mozart. Roser had several meetings
in Linz with Mozart, who allegedly composed two little pieces for the
instrument (according to the manuscript of Roser's biography), and
which were regrettably lost.
This Harmoniehammerfluegel shows the importance meantone temperament
still had at the end of the 18th century in Vienna.
According to Herbert Kelletat had Mozart meantone temperament in
consideration when he chose the keys for his keyboard compositions.
Kelletat analysed 230 compositions with employment of a keyboard
instrument or organ and found that more than 80% is in C, G, D, F, A
and B flat major, exactly the same keys that have pure thirds in
meantone temperament. E flat and E major are exceptions and B major is
absent. Moreover in 45 symphonies Mozart used only 8 different main
keys among which only a few minor.
The museum also has a 12-tone harmonium with a von Jank'o keyboard
from around 1900, built in Vienna. It has 3 rows of 25 and 3 rows of
24 keys. When you press one key, two more go down, so there are only
two independent rows. The purpose is easy fingering, although I
imagine that it would take time to get used to.
The rest of the museum makes a visit very worthwhile too. You are
allowed to play on modern copies of a spinettino and a clavichord.
They also hand out wireless headphones to hear musical examples
depending on where you stand in the room.
Reference: Herbert Kelletat: Zur musikalischen Temperatur, Teil II,
"Wiener Klassik". Berlin: Merseburger Verlag, 1982, pp. 22-32.
Manuel Op de Coul coul@ezh.nl
------------------------------
Topic No. 20
Date: Wed, 25 Nov 1998 16:32:56 +0100
It looks like we are doing similar work, so I'll make a plug for my
software: http://www.tiac.net/users/xen/scala/
Please tell us more about your project and perhaps we can share ideas or
code.
Manuel Op de Coul coul@ezh.nl
------------------------------
Topic No. 21
Date: Wed, 25 Nov 1998 09:49:45 -0600 (CST)
On Tue, 24 Nov 1998, Paul H. Erlich wrote:
I think Carl's talking about JI, i.e. no mistuning at all. But Carl, I
hate to break it to you, but I think you're wrong. The scale you
describe has 30 7-limit consonances, but consider this 3^2 * 5 * 7
genus:
By my count this has 31 7-limit consonances.
------------------------------
End of TUNING Digest 1592
I welcome feedback about this webpage: corrections, improvements, good links.
by Carl Lumma
by Carl Lumma
by Carl Lumma
by "Paul H. Erlich"
by Stephen Soderberg
by "Paul H. Erlich"
by "Paul H. Erlich"
by Saxarba
by "Paul H. Erlich"
by "Paul H. Erlich"
by "Darren Burgess"
by monz@juno.com
by Kraig Grady
by Kraig Grady
by Kraig Grady
by monz@juno.com
by Dave Keenan
by Johnny Reinhard
by Manuel.Op.de.Coul@ezh.nl
by Manuel.Op.de.Coul@ezh.nl
by Paul Hahn
From: Carl Lumma
To: Tuning Forum
Subject: Re: TUNING digest 1591
Message-ID: <19981124172858593.AAA165@nietzsche>
any sensitivity to mistuning in melody (making comma
adjustments) must be at least an order of magnitude rougher than the
acoustic pleasure tolerance of 1-4 cents.
Carl, did you miss my post to TD 1585, on Tuesday Nov. 17th, where I
Isn't it amazing how many definitions the word "interval" has? Here, I
meant a (number of scale steps, acoustic magnitude) pair. So no, the
usual diatonic is not an example; the tritone is not a type of fifth in the
natural minor.
What do you mean?
I think it's been mentioned on this list before (or was it on HPSCHD-L,
where we have frequent temperament wars also?) that organs were built
which were tuned in meantone well into the 19th century, particularly in
England.
From: Carl Lumma
To: Tuning Forum
Subject: Csound card
Message-ID: <19981124173810593.AAA376@nietzsche>
Website: http://www.analog.com/support/systems/audio/csound.html [doesn't work]
It is in some sense a developer's card, but it does do what you asked,
realtime synthesis on a card.
I am not saying it is necessarily a solution to your needs, but it is
a data point. I declare a mild interest in that I have assisted in
the software for this card, and taken airfares etc from Analog Devices.
From: Carl Lumma
To: Tuning Forum
Subject: answering machine
Message-ID: <19981124175442031.AAA186@nietzsche>
From: "Paul H. Erlich"
To: Tuning Forum
Subject: RE: Erlich's Contest
Message-ID: <85B74BA01678D211ACDE00805FBE3C050B6530@MARS>
While the argument for the 10-of-22 scale is thorough, well-presented,
and
very compelling, it remains to be proven or disproven only through a
body
of music, since that is what the theory is for.
Unfortunately, the only reasonable instrument for
decatonic music that exists at the moment is the
guitar, which is simply not my can of worms...
Can't work for what? The specific set of rules you chose to generalize
diatonicity? There must be other sets of rules that capture the
essence of
G.D. just as well:
And I don't think that we have to rotate through major and minor
to achieve diatonicity. We could rotate through higher and lower
identities, or all sorts of things.
From: Stephen Soderberg
To: Tuning Forum
Subject: Cognitive limits
Message-ID:
>
> tones effect propriety music
> -----------------------------------------------------------------------------
> 2-4 too easy little importance chant
> less interesting ritual song
> more "join in" potential
>
> 5-12 tracking starts to slip most important polyphony
> mind has fun trying to parallel harmony
> keep its place melody over chords
>
> 11-22 tracking the entire scale some importance parallel harmony
> impossible: mind "chunks" melody over chords
> scale into proper subsets melody over drone
> and tracks within/between
> those
>
> 23-34 inability to focus or no importance conceptualism
> and up mind begins to fuse
> individual simuli and
> re-interprets as if
> hearing 5-9 tone scale
(a) It's been shown that average dudes from all over can count how many
stones you toss on the ground almost instantly- so long as you don't toss
more than six stones at a time. Since a good deal of the interest of G.D.
scales comes from the interaction between parts in polyphonic composition,
it seems that we'll lose something if we go above the
11-limit.
(SD) 5 9 0 2 5 9
(T) 0 4 7 9 0 4
(D) 7 11 2 4 7 11
[example by Monzo]
/ 38 4 13 21 <28
"SD"
\ 40 6 15 23 30
"T"= 0 8 15 25 32
/ 0 10 17 26 34
"D"
\ 2 12 19 28> 36
From: "Paul H. Erlich"
To: Tuning Forum
Subject: reply to Lumma's reply to Grady
Message-ID: <85B74BA01678D211ACDE00805FBE3C050B6531@MARS>
said you didn't. I did say that the 12-out-of Stellated Hexany
tuning has the greatest number of consonant intervals of any possible
12-tone subset of the 7-limit. Did you know this? Or is it incorrect?
I have no proof...
From: "Paul H. Erlich"
To: Tuning Forum
Subject: "undertone series"
Message-ID: <85B74BA01678D211ACDE00805FBE3C050B6532@MARS>
From: Saxarba
To: Tuning Forum
Subject: Microtonal Composition Software
Message-ID: <365B3026.68A5EA69@gmx.net>
Dr. Kabelis
A. Hemprich
From: "Paul H. Erlich"
To: Tuning Forum
Subject: Reply to Stephen Soderberg
Message-ID: <85B74BA01678D211ACDE00805FBE3C050B6533@MARS>
So to
malign 12tET (so I assume)
is to malign its effects on the ear, not its
12-space compositional-theoretic properties, which are quite potent
regardless of how you tune it. Likewise, arguments about how the
diatonic
scale should *really* be tuned (for psycho-acoustic or historical or
any
other reason) are mostly irrelevant to its basic 7-space
(compositional-theoretic) properties which carry over to any tuning
that
closes (or pretends to close) at the octave.
In the end, things like
n-tone theory or ME theory or hyperdiatonic theory are abstract and
have
nothing to do with tuning.
From: "Paul H. Erlich"
To: Tuning Forum
Subject: reply to Ed Foote on Mozart Tuning
Message-ID: <85B74BA01678D211ACDE00805FBE3C050B6539@MARS>
From: "Darren Burgess"
To: Tuning Forum
Subject: Carillon Tuning
Message-ID: <0551a14220019b8KHAFRE@acceleration.net>
From: monz@juno.com
To: Tuning Forum
Subject: subharmonic series
Message-ID: <19981124.192115.-148507.0.monz@juno.com>
Joe Monzo:
The "subharmonic scale" can be characterized as a
utonal
progression, in Partch's terms. It is the
exact inverse of the "harmonic series" of overtones
above a fundamental. In the case of subharmonics,
the "fundamental" is the highest note in the series,
with the subharmonics in reciprocal integer ratios
below it.
I keep forgetting to bring this up to see if any of you
can shed some light, so now is as good a time as any...
It's my understanding that in the 19th century Riemann,
partly as an effort to acoustically justify the minor
triad, postulated the "undertone series" which, of course,
was attacked as being a strictly theoretical (non-acoustic)
construct. I haven't got a copy of Partch handy, but
does he credit Riemann at any point, or is Partch's version
a "rediscovery"? Or am I missing a significant distinction?
From: Kraig Grady
To: Tuning Forum
Subject: Re:Reply to Carl Lumma
Message-ID: <365B8330.736208D2@anaphoria.com>
The construction of Centaur (1977) fulfills the property that each
interval that occurs is subtended by the same number of steps. This
preserves and allows the possibility of recognizable melodic
transpositions.
Could you explain more? You have got my interst up.--
Look at the 1-3-5-7-9 double dexany and you will see a 14 tone scale
that
is truly a scale.
North American Embassy of Anaphoria Island
http://www.anaphoria.com
--------------0F1A443F1436DD5251B172E1
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>The construction of Centaur (1977) fulfills the property that each
interval >that occurs is subtended by the same number of steps.
This
preserves and >allows the possibility of recognizable melodic transpositions.
is >truly a scale.
pentadekany. Perhaps you could be more specific?
tuning has the greatest number of consonant intervals of any possible
12-tone subset of the 7-limit. Did you know this? Or
is it incorrect? I
have no proof..
.
the hexany is always the first structure I rush for when looking for
the most for the least! From there I do my damnest to use as few notes
as possible to make a scale under the guidlines above as implied in Erv
MOS. There is the tanabe cycle which illustrates the pentatonics found
in the diatonic. Erv refers to them as second order MOS and this is where
all the following theorist are silent! I for now interpet these as workings
as scales because the "generator" ( the building block of the scale ) remains
consistant in it steps. With the scale F A B C E we find the disjuction
A -C being the atypical 4th.
North American Embassy of Anaphoria Island
http://www.anaphoria.com
--------------0F1A443F1436DD5251B172E1--
From: Kraig Grady
To: Tuning Forum
Subject: Re:DJWOLF/BABBITT
Message-ID: <365B982F.5EAA873A@anaphoria.com>
North American Embassy of Anaphoria Island
http://www.anaphoria.com
From: Kraig Grady
To: Tuning Forum
Subject: Re: Reply to Paul Erlich
Message-ID: <365B9D55.3681FC5D@anaphoria.com>
--------------DCD5F42D0D93E36AC58701E1
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The notion of accepting
intervals because they are not any worst than the triad in
12 et is
absurd. why not stay with 12 then!
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The notion of accepting
>intervals because they are not any worst than the triad in 12 et
is
>absurd. why not stay with 12 then!
to be the way to go, and 12-tET has poor 7-limit tetrads. In fact,
were
it not for this "absurd" desire, I would probably not have developed
an
interest in alternate tunings at all!
Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
From: monz@juno.com
To: Tuning Forum
Subject: pitch-class
Message-ID: <19981125.011408.-137027.0.monz@juno.com>
I mean, where would we be if Babbitt hadn't
invented the term pitch class?
monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
From: Dave Keenan
To: Tuning Forum
Cc: gbreed@cix.compulink.co.uk
Subject: Re: A strange 9-limit temperament
Message-ID: <3.0.2.32.19981126000905.00968d70@uq.net.au>
Eb -706- Bb -706- F -712- C -706- G -706- D
|
600
|
A -706- E -706- B -712- F# -706- C# -706- G#
C C# D Eb E F F# G G# A Bb B
+6 +12 +18 -18 -12 -6 +6 +12 +18 -18 -12 -6
Intvl 3:2 5:4 6:5 7:4 7:5 7:6 9:4 9:5 9:6 9:7
-------------------------------------------------------------------------
22-tET 7.1 -4.5 11.6 13.0 17.5 5.9 14.3 18.8 7.1 1.3
Keenan 4.0 -4.3 8.4 13.2 17.5 9.1 8.1 12.4 4.0 -5.1
10.0 1.7 8.4
1 15/14 9/8 7/6 5/4 21/16 10/7 3/2 45/28 5/3 7/4 15/8
1 21/20 9/8 7/6 49/40 21/16 7/5 3/2 63/40 49/30 7/4 147/80
1 21/20 28/25 7/6 5/4 4/3 7/5 3/2 8/5 5/3 7/4 28/15
-- Dave Keenan
http://uq.net.au/~zzdkeena
From: Johnny Reinhard
To: Tuning Forum
Subject: Re: reply to Paul H. Erlich to Ed Foote on Mozart Tuning
Message-ID:
Why would you want a well-temperament if the music avoids the keyboard
wolf? There are many more ways to achieve variegation of key color when
one allows the wolf to be present than when one insists on its
disappearance. The "realm of historical possibilities" is perhaps 10%
documented in the literature and if one is making judgments with modern
ears it is foolish to restrict oneself to documented possibilities of
another era.
Last time we had this discussion, weren't there a few people who had
various pieces of evidence for Mozart favoring meantone? Like his
teaching of two semitone sizes, diatonic and chromatic? And his reaction
to a 31-tone (obviously, meantone) instrument he played on?
AFMM
From: Manuel.Op.de.Coul@ezh.nl
To: Tuning Forum
Subject: Re: reply to Paul H. Erlich to Ed Foote on Mozart Tuning
Message-ID:
And could someone run by again with his supposed reaction to a
hypothetical 31-tone instrument?
Fx Gx Ax Bx Cx Dx Ex Fx Gx Ax ...
F# G# A# B# C# D# E# F# G# A# ...
F G A B C D E F G A ...
Fb Gb Ab Bb Cb Db Eb Fb Gb Ab ...
Fbb Gbb Abb Bbb Cbb Dbb Ebb Fbb Gbb Abb ...
From: Manuel.Op.de.Coul@ezh.nl
To: Tuning Forum
Subject: Re: Microtonal Composition Software
Message-ID:
This software product (for windows platform) being developped by us
combines two different fields:
- provision of the scales of microintervals down to 1/64 semitone
- production of tonal structures by help of mathematic musical functions
From: Paul Hahn
To: Tuning Forum
Subject: Most 7-limit consonances with 12 pitches
Message-ID:
[Carl Lumma wrote:]
[T]he 12-out-of Stellated Hexany
tuning has the greatest number of consonant intervals of any possible
12-tone subset of the 7-limit. Did you know this? Or is it incorrect? I
have no proof...
What's the largest mistuning you'll allow?
35:24-------35:16------105:64
.-'/ \'-. .-'/ \'-. .-'/
5:3--/---\--5:4--/---\-15:8 /
/|\ / \ /|\ / \ /| /
/ | / \ | / \ | /
/ |/ \ / \|/ \ / \|/
/ 7:6---------7:4--------21:16
/.-' '-.\ /.-' '-.\ /.-'
4:3---------1:1---------3:2
--pH
*************************
or try some definitions.
Let me know if you don't understand something.
