Re: Adaptive JI/RI tuning and neo-Gothic valleys (Part V)

------------------------------------------------------
Adaptive rational intonation and neo-Gothic valleys
A 24-note scheme a la Vicentino
(Essay in honor of John deLaubenfels)
Part V: Alternative solutions and circular JI system
------------------------------------------------------

For earlier parts of this article, please see:

http://www.egroups.com/message/tuning/16640 (Part I)
http://www.egroups.com/message/tuning/17034 (Part II)
http://www.egroups.com/message/tuning/17339 (Part III)
http://www.egroups.com/message/tuning/17389 (Part IV)

For a step-by-step presentation of neo-Gothic progressions and
flavors, please see the series "A gentle introduction to neo-Gothic
progressions":

http://www.egroups.com/message/tuning/15038 (1/Pt 1)
http://www.egroups.com/message/tuning/15630 (1/Pt 2A)
http://www.egroups.com/message/tuning/15685 (1/Pt 2B)
http://www.egroups.com/message/tuning/16134 (1/Pt 2C)

-----------------------------------------------------
5. Alternative solutions and circular 2-3-7 JI system
-----------------------------------------------------

Having surveyed some of the possibilities for our neo-Gothic adaptive
JI system with two 12-note Pythagorean keyboards tuned a septimal
comma apart, we first consider some alternative solutions to the
problem of combining pure or near-pure ratios of 2, 3, and 7. In a
neo-Gothic setting, such alternatives include septimal schisma
temperaments, regular temperaments with fifths in the vicinity of
704.61 cents, and 22-tone equal temperament (22-tET).

Returning to our 24-note adaptive scheme, we then explore how it could
be enlarged to a circulating 106-note system with two 53-note cycles
of pure fifths a septimal comma apart, and a remarkable property of
near-perfect closure which this system would have. Such a system would
afford a virtually pure realization of the "web of 2, 3, and 7."[29]

---------------------------------------------------------
5.1. Alternative neo-Gothic solutions for ratios of 2-3-7
---------------------------------------------------------

In comparing neo-Gothic tunings which realize or approximate pure
ratios of 2, 3, and 7, we might weigh such factors as accuracy,
evenness or regularity, conceptual simplicity, minimum tuning size,
and simplicity or intricacy for the performer. These last two factors
tend to be related: the larger the tuning, the more likely it is that
commas or dieses are routinely going to complicate -- or enrich -- the
life of the keyboardist.

Especially for larger tunings, the availability of other favored
neo-Gothic ratios can also be a main attraction: for example, regular
major and minor thirds around 14:11 (~417.51 cents) and 13:11 (~289.20
cents), the neo-Gothic "11-favor"; and diminished fourths and
augmented seconds around 21:17 (~365.83 cents) and 17:14 (~336.13
cents), the "17-flavor" of submajor/supraminor thirds.

Together, these factors happily conspire to prevent any one system
from being a "perfect" solution, and to promote a multiplicity of
systems in keeping with the ideals of Ivor Darreg.[30]

------------------------------------------------
5.1.1. Septimal schisma tunings and temperaments
------------------------------------------------

As explained in Section 1, our adaptive JI system grew out of a
regular 24-note Pythagorean or "Xeno-Gothic" tuning with two 12-note
manuals in identical Eb-G# arrangements tuned a Pythagorean comma
apart (531441:524288, ~23.46 cents).

To achieve pure ratios of 7, our adaptive system stretches the fifth
connecting the two manuals by a septimal schisma of 33554432:33480783
(~3.80 cents), increasing their spacing from a Pythagorean comma to a
septimal comma of 64:63 (~27.26 cents). All other fifths remain pure.

Using a carat (^) to show a note raised by a septimal comma, and
Vicentino's "comma" or small interval sign, here an apostrophe ('), to
show a note raised by a septimal schisma above its Pythagorean
position, we can diagram this scheme as follows, with two possible
names for each note on the upper keyboard:

(D#'- A#' - E#'- B#'- F##'-C##'-G##'-D##'-A##'-E##'-B##'- F###')
Eb^- Bb^ - F^ - C^ - G^ - D^ - A^ - E^ - B^ - F#^ - C#^ - G#^

Eb - Bb - F - C - G - D - A - E - B - F# - C# - G#

In principle, we could tune this JI system by ear using only audibly
pure ratios: the usual Pythagorean fifths, fourths, and octaves on
each manual, plus a pure 7-based interval such as a 7:6 minor third or
possibly a 7:4 minor seventh to bridge the transition between the two
manuals.[31]

We might view the result as a chain of 23 fifths: 11 pure fifths on
each keyboard (Eb-G#, Eb^-G#^), linked by the "septimal schisma fifth"
G#-Eb^ or G#-D#' at the complex integer ratio of 16777216:11160261
(~705.76 cents), a 3.80-cent septimal schisma wider than pure.

As a JI system, this scheme therefore also belongs to the family of
septimal schisma tunings and temperaments of a general kind described
and advocated by Graham Breed[32], where one or more fifths in a
Pythagorean chain is slightly widened in order to obtain or very
closely approximate pure 7-based ratios.

More specifically, our system might be described as a "rational
adaptive schisma tuning" (RAST), in which a single fifth bears the
full burden of the septimal schisma adjustment. In regular schisma
temperaments of the type we are about to consider, this burden is
dispersed equally among all fifths along the tuning chain, each
tempered by a very small and irrational quantity.

From the viewpoint of conceptual elegance, our RAST solution might be
said to have the advantage that only a single fifth is "virtually
tempered by ratio," with all intervals remaining integer-based; and
the disadvantage that this fifth represents a slight irregularity in
what would otherwise be a perfectly regular system.

From the viewpoint of accuracy, we obtain pure ratios of 3 and 7
within the base range of our "standard" gamut Eb-G#, but with the
audible compromise of the fifth G#-D#' at around 3.80 cents wide,
about as impure as in 17-tET (~705.88 cents, ~3.93 cents wide).[33]

In a regular septimal schisma temperament, we avoid this slight
irregularity while seeking to keep all fifths and 7-based intervals
within our gamut "virtually pure" to the ear by adjusting each fifth
equally.

To obtain pure 7:4 minor sevenths and 8:7 major seconds, formed from
chains of 14 fifths up or down, we could temper each fifth by 1/14 of
a 3.80-cent septimal schisma; for pure 7:6 minor thirds and 12:7 major
sixths, by 1/15 septimal schisma; and for pure 9:7 major thirds and
14:9 minor sixths, by 1/16 septimal schisma.

Here is a table of these regular temperaments:

------------------------------------------------------------
Chain Pure intervals Fifth Tempering
------------------------------------------------------------
14 fifths 8:7 / 7:4 ~702.227 cents +~0.272 cents
15 fifths 12:7 / 7:6 ~702.209 cents +~0.254 cents
16 fifths 9:7 / 14:9 ~702.193 cents +~0.238 cents
------------------------------------------------------------

Suppose we choose the middle alternative of a 1/15-septimal schisma
temperament with pure 12:7 major sixths and 7:6 minor thirds; fifths
and the other 7-based intervals of our table are alike impure by the
amount of the temperament, about 0.25 cents, remaining "virtually
just."[34]

From a theoretical viewpoint, while our RAST approach leaves the
Pythagorean intervals within each manual unaltered, our 1/15-schisma
temperament causes very subtle changes in the global intonational
fabric. Regular major thirds, for example, are slightly enlarged from
a Pythagorean 81:64 (~407.82 cents) to around 408.83 cents, rather
close to a ratio of 19:15 (~409.24 cents); usual diatonic semitones
contract from a Pythagorean 256:243 (~90.22 cents) to around 88.96
cents.[35]

In practice, the two systems seem musically synonymous, and it is an
open question whether a performer at the 24-note keyboard would notice
any difference of "look and feel" in these two schisma tunings with
their kindred qualities of accuracy -- and intricacy.

From the viewpoint of the performer, either system is large and
relatively intricate: 24 notes are needed to make 7-based intervals
available at the same number of locations as their regular Pythagorean
counterparts in a 12-note tuning, and septimal comma distinctions at
once complicate and diversify the possible range of sonorities and
progressions.

In conclusion, one's choice between a RAST approach and a regular
schisma temperament may reflect one's conceptual taste for "pure JI
ratios" (in theory!) versus pervasive regularity and symmetry; the
musical kinship between these solutions may be more important than
their theoretical differences.[36]

-------------------------------------------------------------
5.1.2. The many-flavored e-based tuning: a 2.65-cent solution
-------------------------------------------------------------

While either our 24-note adaptive scheme or a regular septimal schisma
temperament provides pure or virtually pure ratios of 3 and 7 as a
variation on extended Pythagoraen tuning, another intricate 24-note
system combines close approximations of these intervals with others
much favored in neo-Gothic music: the e-based tuning with fifths at
around 704.61 cents (~2.65 cents wide).

In this tuning, the ratio between the whole-tone and diatonic semitone
is equal to Leonhard Euler's e, ~2.7182818284590452353603, these
steps having sizes of approximately 209.214 cents and 76.965 cents.

From a neo-Gothic perspective, the obvious attractions of this tuning
may be found in its first 12 notes. Regular major and minor thirds at
around 418.43 cents and 286.18 cents approximate ideal neo-Gothic
"11-flavor" ratios of 14:11 and 13:11 or 33:28. Diminished fourths and
augmented seconds, at around 363.14 cents and 341.46 cents, are not
too far from ideal "17-flavor" ratios of 21:17 and 17:14, with the
supraminor third leaning rather in the largish or neutral direction
toward 11:9 (~347.41 cents).

Only after some months of exploring and analyzing the e-based tuning
did I consider the properties of an extended 24-note version, and
discover that in addition to these primary 11-flavor and 17-flavor
intervals, such a larger tuning yields close approximations of
7-flavor intervals, including virtually pure 7:4 minor sevenths and
8:7 major seconds.

In such a 24-note e-based tuning, two keyboard manuals are tuned apart
by a diesis, the amount by which 12 fifths exceed 7 pure octaves
(analogous to the Pythagorean comma), approximately 55.28 cents. Here
an asterisk (*) is used to show a note raised by a diesis:

C#* Eb* F#* G#* Bb*
C* D* E* F* G* A* B* C*
---------------------------------------------------------------
C# Eb F# G# Bb
C D E F G A B C

Canvassing this 24-note system, and using a MIDI-like octave notation
with C4 as middle C and higher numbers showing higher octaves, we find
the following approximations for 7-based intervals:

----------------------------------------------------------------------
Ratio Fifth chain Description Example Size/Variance cents
----------------------------------------------------------------------
9:7 13 5ths down 4th-less-diesis G*3-C4 ~440.11 ~+5.03
14:9 13 5ths up 5th-plus-diesis D3-A*4 ~759.89 ~-5.03
......................................................................
7:6 14 5ths up M2-plus-diesis E3-F#*3 ~264.50 ~-2.37
12:7 14 5ths down m7-less-diesis G*3-F4 ~935.50 ~+2.37
......................................................................
7:4 15 5ths up M6-plus-diesis E3-C#*4 ~969.10 ~+0.28
8:7 15 5ths down m3-less-diesis D*3-F4 ~230.90 ~-0.28
----------------------------------------------------------------------

Not inappropriately, this tuning defined by Euler's famous _e_ yields
a near-pure 7:4 minor seventh and an excellent approximation of the
7:6 minor third, two intervals he documented and championed as a music
theorist in 1764.[37] The 9:7 major third receives a less accurate but
reasonably fair approximation at about 440.11 cents, just over 5 cents
wide.

The special musical appeal of the 24-note e-based tuning is that it
combines these 7-flavor intervals with the more obvious 11-flavor and
17-flavor intervals in a single intonational "package."

Were we interested only in ratios of 2-3-7, then our adaptive JI
system or a septimal schisma temperament would not only yield purer
ratios of 7, but would avoid the compromising of our fifths by some
2.65 cents.

Were we interested only in 11-flavor and 17-flavor intervals, we might
choose a temperament in the range from 29-tET (fifths ~703.45 cents,
~1.49 cents wide) to 46-tET (~704.35 cents, ~2.39 cents wide) or the
almost identical tuning with pure 14:11 major thirds (~704.38 cents,
~2.42 cents wide). These tunings involve somewhat less tempering of
the fifth than the e-based system, and often yield more accurate
approximations of such intervals as the 17:14 supraminor third.

If we seek a single 24-note system uniting 11-flavor, 17-flavor, and
7-flavor intervals, however, then the e-based tuning becomes an
outstanding option, a "2.65-cent solution" made at once intricate and
alluring by the "metachromatic" possibilities of the 55-cent diesis,
the standard cadential semitone in 7-flavor progressions.[38]

-----------------------------------------
5.1.3. Simplicity and circularity: 22-tET
-----------------------------------------

In contrast to these intricate 24-note systems, 22-tET with fifths at
around 709.09 cents (~7.14 cents wide) offers regular or "native"
7-flavor intervals conveniently available in a usual 12-note tuning:

------------------------------------------------------------------
Ratio Regular interval 22-tET steps Size/Variance cents
------------------------------------------------------------------
9:7 M3 (e.g. F3-A3) 8 ~436.36 ~+1.28
14:9 m6 (e.g. A3-F4) 14 ~763.64 ~-1.27
..................................................................
7:6 m3 (e.g. D3-F3) 5 ~272.73 ~+5.86
12:7 M6 (e.g. F3-D4) 17 ~927.27 ~-5.86
..................................................................
8:7 M2 (e.g. D3-E3) 4 ~218.18 ~-12.99
7:4 m7 (e.g. E3-D4) 18 ~981.82 ~+12.99
------------------------------------------------------------------

A hallmark of 22-tET is its dispersal of the septimal comma: the
regular major second at around 218 cents can represent either the
usual Pythagorean interval at 9:8 or the 7-flavor interval at 8:7,
while the 982-cent minor seventh can represent either 16:9 or 7:4.

The price for this simplicity and convenience is a substantial
compromise not only of the 7:4 or 8:7, but of fifths and fourths, our
primary neo-Gothic concords, varying almost 7.14 cents from pure. In
typical timbres, 22-tET may approach the far end of the neo-Gothic
spectrum where this compromise becomes increasingly problematic.[39]

In addition to making 7-flavor intervals available in a 12-note
tuning, 22-tET maximizes melodic evenness by using a single 218-cent
whole-tone for steps of either 9:8 or 8:7, in contrast to the
distinction between these steps in our other systems. Both styles of
intonation -- equal or unequal whole-tone steps -- have their strong
advocates, and like many musical questions this seems one largely of
taste.

Interestingly, diatonic semitones at ~54.55 cents (1/22 octave) are
somewhat smaller than the 28:27 cadential semitones (~62.96 cents)
precisely realized in our adaptive JI scheme and very closely
approximated in a septimal schisma temperament; but almost identical
in size to the 55.28-cent diesis of our e-based tuning used as a
cadential semitone in 7-flavor progressions.

In short, while our other solutions for combining ratios of 3 and 7
maximize accuracy and intricacy, 22-tET optimizes convenience and
simplicity as well as melodic evenness by dispersing the septimal
comma; additionally, if circularity is desired, it offers closure in
only 22 notes.

-----------------------------------------------------------
5.2. Circularity: a 106-note "web of 2-3-7" and the nanisma
-----------------------------------------------------------

In the 24-note version we have explored, our adaptive JI system for
ratios of 2, 3, and 7 has the slight "flaw" of the impure fifth G#-D#'
(G#-Eb^), "tempered by ratio" a 3.80-cent septimal schisma wide.
Curiously, this asymmetry could be "repaired," and virtually perfect
closure achieved, if we extended the system to two 53-note Pythagorean
cycles a septimal schisma apart, or 106 notes per octave in all.

As is well known, a 53-note Pythagorean cycle offers "virtual closure"
from a practical perspective, since 53 pure 3:2 fifths exceed 31 pure
2:1 octaves by only the small quantity sometimes known as Mercator's
comma, 19383245667680019896796723:19342813113834066795298816 or about
3.615 cents.

Such a 53-note Pythagorean tuning therefore features 52 pure fifths,
plus an "odd" 53rd fifth "virtually tempered" in the narrow direction
by this comma, at ~698.340 cents. This odd fifth arises between the
53rd note of the cycle, located 52 fifths up or ~501.660 cents above
the initial note, and the pure octave of this initial note.

Suppose now that we tune two such complete 53-note cycles a septimal
schisma apart -- 33554432:33480783 or ~3.804 cents -- as with our
24-note adaptive JI tuning, obtaining pure ratios of 2-3-7.

To see the consequences for circularity, let us look at what happens
as we approach the conclusion of the twin 53-note cycles. Here, in
addition to the carat sign (^) raising a note by a septimal comma and
the apostrophe (') raising a note by a septimal schisma, I use the
"greater than" sign (>) to raise a note by a Pythagorean comma. Values
in cents for each note are in reference to the first note of the cycle
on the lower or "standard" keyboard, here arbitrarily set as Eb, with
two spellings shown for notes of the upper cycle:

(Eb>>>^ Bb>>>^ F>>>^ C>>>^ G>>>^ D>>>^)
Eb' ... Eb>>>>' Bb>>>>' F>>>>' C>>>>' G>>>>' Eb'
Fifth# 0 48 49 50 51 52 0/53
cents 3.804 97.644 799.599 301.554 1003.509 505.464 1203.804
-----------------------------------------------------------------------
Eb... Eb>>>> Bb>>>> F>>>> C>>>> G>>>> [D>>>>]
Fifth# 0 48 49 50 51 52 [53]
cents 0 93.840 795.795 297.750 999.705 501.660 [1203.615]

Note that the last or 53rd fifth on the lower chain is a hypothetical
note tuned a pure fifth above the 52nd fifth, thus shown in brackets;
actually, the 52nd fifth would be followed by a pure octave to the
opening note of the cycle, here Eb (1200 cents).

In the lower or standard 53-note cycle, the 48th fifth brings us to a
note precisely four Pythagorean commas (~93.840 cents) higher than the
initial Eb, or ~3.615 cents higher than a usual 256:243 diatonic
semitone or limma (~90.224 cents) -- a difference equal to the comma
of Mercator. Five more fifths would take us to the hypothetical 53rd
fifth or 54th note of the cycle at a Pythagorean major seventh above
this note (243:128, ~1109.776 cents), or ~1203.615 cents above the
initial Eb, exceeding a pure octave by the comma of Mercator.

If we compare this hypothetical 53rd fifth of the lower cycle with the
pure octave of the initial note Eb' of the upper cycle at ~1203.804
cents above Eb, we find that they differ by only about 0.189 cents,
the amount by which the septimal schisma exceeds the comma of
Mercator.

Thus while the 52nd fifth or 53rd note of the lower cycle is followed
in this cycle by the pure octave of the initial note (here Eb),
forming a fifth ~3.62 cents narrow, from this 53rd note to the pure
octave of the _upper_ cycle forms a virtually just fifth at about
702.144 cents, our small quantity of ~0.189 cents wider than pure.

For this small difference by which the septimal schisma exceeds the
comma of Mercator, I propose the term _nanisma_ (from Greek _nano_,
"tiny," also used as the prefix for 10^-9, the American "billionth").
The nanisma is a small interval expressed by a large integer ratio:

649037107316853453566312041152512:648966242035284859600333477874109

In practice, of course, 106 notes may seem like a rather large tuning;
but larger systems for JI or near-JI applications are sometimes
discussed, for example 118-tET for ratios of 2-3-5.[40]

Whatever practical uses this 106-note system may invite, and
electronic implementations for use with MIDI sequencers or the like
seem quite feasible, the possibility of a circulating and indeed
almost perfectly circular "web of 2-3-7" based entirely on integer
ratios may be a notable (however novel or often-rediscovered)
conclusion for JI theory.[41]

---------------
Notes to Part V
---------------

29. For this expression I am most indebted to Jose Wurschmidt, who in
1928 writes in a very different musical context based on ratios of
2-3-5 of the "web of fifths and thirds" (_Quinten-Terzengewebe_),
advocating 118-tET as an excellent approximation. See Brian McLaren,
"A Brief History of Microtonality in the Twentieth Century,"
_Xenharmonikon_ 17:57-110 (Spring 1998), at p. 64.

30. See ibid., p. 81, quoting Darreg's statement of 1967: "No one
microtonal system has emerged as the ultimate system, and after trying
out several, I want to work with _all_ of them, each for its unique
qualities."

31. Having placed the lower manual in a usual Pythagorean tuning of
Eb-G#, we might take G4 of this manual (G above middle C) and tune E^4
of the upper manual to a pure 7:6 below it, or possibly A^3 to a pure
7:4 below it. The rest of the upper manual would now be tuned in usual
Pythagorean fashion.

32. See http://www.cix.co.uk/~gbreed/schismic.htm. Since Graham
Breed's discussion focuses mainly on systems combining ratios of 2-3-5
or 2-3-5-7 or 2-3-5-7-11 (with a "major third" often suggesting 5:4),
his viewpoint may be somewhat different from that involved in
neo-Gothic systems based on ratios of 2-3-7 (with a "major third"
typically suggesting 81:64 or 9:7). Here I use the term "septimal
schisma temperament" rather narrowly to mean a regular temperament
where the fifth is widened by around 1/14-1/16 of a septimal schisma
to obtain near-pure ratios of 3 and 7, i.e. a temperament with fifths
in the range of ~702.19-702.23 cents (~0.23-0.27 cents wide). Graham
Breed favors a fifth at 79/135 octave (702.2222... cents, ~0.267 cents
wide), virtually identical to a 1/14-septimal schisma temperament
(pure 7:4 and 8:7).

33. In a neo-Gothic setting, we might relish the impurity of G#-D#' as
a stimulating touch of "modal color" at a location having a certain
affinity to the diminished sixth or "Wolf fifth" G#-Eb. Might this
much gentler and more "domesticated" counterpart with its 17-tET-like
size be called a "poodle fifth"?

34. Intervals formed from 14 fifths up or down (8:7, 7:4) receive
14/15 of their full septimal schisma correction from Pythagorean,
while intervals formed from 16 fifths (9:7, 14:9) receive a slight
overcorrection of 16/15 of the schisma -- in either instance, a
variance of 1/15 schisma or ~0.25 cents. Dave Keenan has suggested
that intervals within about 0.5 cents of pure may be considered as
audibly equivalent to "just."

35. The 1/15-septimal schisma tuning is located on the neo-Gothic
spectrum of regular tunings about midway between Pythagorean with its
pure 3:2 fifths at ~701.955 cents and 41-tET (fifths ~702.439 cents,
~0.484 cents wide). While small, the variances of this 1/15-schisma
tuning from our RAST scheme might sometimes be highly desirable. For
example, in the special sixth sonority with a near-11:8 "superfourth"
between the two upper voices, e.g. B3-Eb4-G#^4 cadencing to A3-E4-A4
(see Part IV, Section 4.3.2), this interval has a RAST tuning of
19683:14336 or ~548.77 cents, ~2.55 cents smaller than pure. In the
1/15-schisma tuning, it is ~550.80 cents, within ~0.52 cents of pure.
For either system, incidentally, this very special superfourth unites
the extreme notes of the 23-fifth chain, Eb-G#^.

36. Analogous choices might include 53-note Pythagorean vs. 53-tET, or
a 31-note cycle of 1/4-comma meantone vs. 31-tET.

37. See http://www.ixpres.com/interval/monzo/euler/euler-en.htm, and
n. 15 (Part III).

38. For a brief discussion of 7-flavor cadences in the e-based tuning,
see "A gentle introduction to neo-Gothic progressions," 1, Part 2C,
http://www.egroups.com/message/tuning/16134. In a forthcoming article
on this tuning, I hope to discuss "metachromatic" sequences moving
between manuals in often surprising ways.

39. For metallophone-like timbres, 27-tET (fifths ~711.11 cents, ~9.16
cents wide) can have a very pleasant effect in a neo-Gothic setting
with its virtually pure 7:6 and 12:7 approximations (~266.67 cents,
~933.33 cents, only ~0.20 cents respectively narrow and wide), and a
somewhat "gamelan-like" ambiance.

40. See n. 29; Dave Keenan has remarked that 118-tET is the smallest
equal temperament offering approximations of all 5-odd-limit intervals
within 0.5 cents of pure.

41. In this 106-note system, as in our 24-note adaptive JI subset,
pure ratios of 8:7, 9:7, 12:7, 27:14, and 81:56 (the 7-based tritone)
are available with the lower note taken from the lower keyboard/cycle,
and the upper note from the upper keyboard/cycle; pure ratios of 7:4,
14:9, 7:6, 28:27, and 112:81 (the 7-based diminished fifth) involve a
lower note from the upper keyboard/cycle and an upper note from the
lower keyboard/cycle. Within a single 53-note cycle, approximations
for these intervals will be a septimal schisma (~3.80 cents) from
pure.

Most respectfully,

Margo Schulter
mschulter@value.net

Hey people. I'm new here. I've been looking at previous posts, and I admit
that this stuff is a bit over my head. However, I hope to learn stuff from
what goes on. I'm a 19-year-old Music Theory/Composition major at Point
Loma Nazarene University (San Diego, CA).

I just reread Gerald Eskelin's book "Lies My Music Teacher Told Me," and I'm
really interested in the natural acoustics vs. equal temperament debate. I
was told by a guy on the MusicTheory eGroup (hey Paul :P) that Gerald used
to be a member of this tuning list. Paul also said that some of Gerald's
misconceptions were dispelled here, and I was wondering if anyone has his
email address so I could communicate with him. I'd like to ask him how he'd
change his book now that he's adopted different views. Thanks, you guys!

-Brad

--- In tuning@egroups.com, "Brad Beyenhof" <saxman32@s...> wrote:
>I've been looking at previous posts, and I admit
> that this stuff is a bit over my head.
You're not the only one. Sometimes I wonder what the point of all the
complicated math and semantics is (other than it being food for some
intriguing study and discussion of the heart of music).

The sheer complexity of alternative tunings leads me to question
whether we can actually hear this stuff, or if there is a "placebo"
effect among microtonalists. I feel that some research into how finely
the human ear can discriminate intervals is in order. It is also fair
to question how much Western culture's use of a scale with only 12
tones has "brainwashed" us--limited the tonal sensitivity of our ears
through disuse of neurons that would be devoted to smaller intervals.
This is assuming the auditory regions of the brain work on a "use it
or lose it" principle.

engell69@gte.net wrote:
> The sheer complexity of alternative tunings leads me to question
> whether we can actually hear this stuff, or if there is a "placebo"
> effect among microtonalists. I feel that some research into

I'd say a definite "yes" to whether or not we can hear this stuff. I'm
pretty new here, and when I first joined I was going through tons of web
sites trying to figure out what the heck they were talking about here (I've
still got it only half figured out. :)
Anyway, I came across some site (somebody here probably knows the URL) that
had at least three Bach pieces played in some JI tuning in MP3 format. I
decided to listen to them thinking I'd just hear three Bach pieces and think
"Ok, I wonder what the point of that was." I was surprised to discover that
I definitely could hear the difference! I was even more surprised to
discover that I really really don't like that JI tuning that was used. Maybe
I'm just a victim of my ET upbringing, but it was just too wierd the
difference between the perfectly consonant tonic chords versus the terribly
dissonant second and seventh chords.

So yeah, I'd say this stuff is more than just academic.

TOdd

engell69@gte.net wrote,

>The sheer complexity of alternative tunings leads me to question
>whether we can actually hear this stuff, or if there is a "placebo"
>effect among microtonalists. I feel that some research into how finely
>the human ear can discriminate intervals is in order.

This has been well researched -- see any psychoacoustics book like
Roederer's for instance -- it is well-established that the average listener
can distinguish hundreds of notes per octave.

>It is also fair
>to question how much Western culture's use of a scale with only 12
>tones has "brainwashed" us--limited the tonal sensitivity of our ears
>through disuse of neurons that would be devoted to smaller intervals.
>This is assuming the auditory regions of the brain work on a "use it
>or lose it" principle.

It doesn't quite work that way. What the brainwashing does is to force us
into a "categorical" way of hearing intervals, and there are two
manifestations of this. The most common is relative pitch, in which
categorical perception means we hear all intervals as some sort of deviation
from the (usually) nearest 12-tET equivalent, rather than as new intervals
in their own right. The second is perfect pitch -- people with perfect pitch
find it painful to even listen to 12-tET music a quarter-tone sharp. But the
brainwashing can be undone with sufficient exposure. One good way to begin
is with _harmonic_ intervals -- the sensual difference between hearing a
just major third vs. a 12-tET major third _harmonically_ is unmistakeable.

--- In tuning@egroups.com, engell69@g... wrote:
> --- In tuning@egroups.com, "Brad Beyenhof" <saxman32@s...> wrote:
> >I've been looking at previous posts, and I admit
> > that this stuff is a bit over my head.
> You're not the only one. Sometimes I wonder what the point of all
the
> complicated math and semantics is (other than it being food for
some
> intriguing study and discussion of the heart of music).

The quest for beauty is the point for many.

> The sheer complexity of alternative tunings leads me to question
> whether we can actually hear this stuff,

Try this simple test:

Set up your midi keyboard so that you can "a&b" between the following
triads:

0, 300, 700 cents
then:
1/1, 6/5, 3/2

and:

0, 400, 700 cents
then:
1/1, 5/4, 3/2

Make note of the ones that sound the most smooth to your ears, and
please post the results. This is one of my favorite demos of JI
tunings, which I love to show to interested folks, and it always gets
a very strong response.

> or if there is a "placebo"
> effect among microtonalists.

I believe there is certainly a kind of personal conditioning that
happens with repeated exposure to favored tuning systems. I would not
call this a "placebo" effect, since most anyone can recognize
distinctions from 12 tET, with very little exposure to new tuning
sounds.

> I feel that some research into how finely
> the human ear can discriminate intervals is in order.

There are many hypothesis about this, but we find only small
consensus with regard to the audibility of "prime or odd limits".
Most folks might find value in these general descriptions in 3-7
Limit intervals, but even these distinctions dissolve with the
inclusion of higher prime (or odd) intervals. I'm personally finding
this an empty argument these days. The recognizability of limits
fails under many significant demonstrations.

Thanks,

Jacky Ligon

Jacky wrote:
<snip demo of JI vs ET>
> Make note of the ones that sound the most smooth to your ears, and
> please post the results. This is one of my favorite demos of JI
> tunings, which I love to show to interested folks, and it always gets
> a very strong response.

Ahh.. and here is something I found interesting about my first exposure to
JI. I actually DON'T like the "smooth" sound. Again, it might be my
inculcation into the 12-tET world, "brainwashing" if you will, but the
"perfect" intervals are just too boring. Besides, once you start basing
chords on notes that are less consonant with the tonic, like the second and
the seventh, you get these cacophanous sounds that are much more dissonant
than the ET intervals.

To me, it's kinda like a solid-state amp vesus a tube amp. Sure the solid
state amp has less THD and all that jazz, but I actually PREFER the
distortion generated by a few EL-84s and a big honkin transformer. Just
makes things warmer. So it is with my opinions of JI vs. ET, at least so
far.

Let me re-emphasize that I'm new to all this stuff (except the general music
theory and the acoustic principles), so it's just my opinion, and here have
this huge salt lick to go with it. :)

Todd

Todd wrote,

>Ahh.. and here is something I found interesting about my first exposure to
>JI. I actually DON'T like the "smooth" sound. Again, it might be my
>inculcation into the 12-tET world, "brainwashing" if you will, but the
>"perfect" intervals are just too boring.

Yes . . . Dave Keenan and I have talked about how it's nice to have, say, a
1 cent error, just to keep those partials from locking in phase, and thus
interfering, some constructively, some destructively -- with a slight
detuning, all the partials slowly cycle between constructive and destructive
interference.

Personally, although I enjoy the way meantone tuning (_not_ JI) makes
diatonic triadic music sound smoother than in 12-tET, I'm personally of the
opinion that 12-tET implies the 5-limit intervals of the triads well enough
to be recognizable, and so I'm more interested in tuning systems which can
imply 7- and 11-limit chords well enough to be recognizable, like 22-tET,
which is certainly not "smooth" like JI for these chords.

>Besides, once you start basing
>chords on notes that are less consonant with the tonic, like the second and
>the seventh, you get these cacophanous sounds that are much more dissonant
>than the ET intervals.

Well, that depends on what kind of tuning system you use. If you use
_adaptive_ tuning, like John deLaubenfels used, this won't be the case. In
fact, almost none of the JI advocates would use it in the way you described,
with the single exception of Ken Overton.

Paul Erlich wrote:
> Well, that depends on what kind of tuning system you use. If you use
> _adaptive_ tuning, like John deLaubenfels used, this won't be
> the case. In
> fact, almost none of the JI advocates would use it in the way
> you described,
> with the single exception of Ken Overton.

Ahh... so adaptive tuning is when you sorta re-do the scale based on the
root of the chord you're about to play, so that your different chords all
have the same sound? Or am I reading too much into that? That doesn't really
sound very possible, since even if you used a computer, it would be hard to
analytically distinguish the root when inversions are allowed.

Soo... what's adaptive tuning? Boring the old-time list members with an
answer is certainly not necessary, but is there a good URL?

Todd

Todd wrote,

>Ahh... so adaptive tuning is when you sorta re-do the scale based on the
>root of the chord you're about to play, so that your different chords all
>have the same sound?

Basically correct.

>That doesn't really
>sound very possible, since even if you used a computer, it would be hard to
>analytically distinguish the root when inversions are allowed.

Not at all! Why would that be hard? What's the root of C-Eb-Ab? It's Ab!
That's pretty easy, isn't it?

>Soo... what's adaptive tuning? Boring the old-time list members with an
>answer is certainly not necessary, but is there a good URL?

Try the definition here:

http://www.ixpres.com/interval/dict/adaptivetuning.htm

Paul Erlich
> >That doesn't really
> >sound very possible, since even if you used a computer, it
> would be hard to
> >analytically distinguish the root when inversions are allowed.
>
> Not at all! Why would that be hard? What's the root of
> C-Eb-Ab? It's Ab!
> That's pretty easy, isn't it?
>

Yeah, as long as we're not allowing Cm5+ chords, that might work. I could
see neopolitan and augmented sixth chords causing problems also.
On the other hand, after reading the Monzo/Erlich definition of adaptive
tuning, it seems to me it might be possible to create an algorithm that
doesn't care what the root is. Actually, as I read I wonder if that's just
what you've done/are doing. What kind of latency are you guys at in terms of
live performance? 0?

Todd

Todd wrote,

>I could
>see neopolitan and augmented sixth chords causing problems also.

Those chords pose no special problems. The chords which are "interesting"
are augmented, diminished sevenths, and chords built off a chain of three or
more fifths or fourths. These chords are "necessarily tempered" -- you might
want to search the archives for "necessarily tempered".

>What kind of latency are you guys at in terms of
>live performance? 0?

I don't know what you mean by that, but the man you want to talk to is John
deLaubenfels, who actually wrote the adaptive tuning software in question
(with some feedback from my over-sensitive ears). He's on this list, and you
can get to his pages from http://www.adaptune.com.

Paul:
> >What kind of latency are you guys at in terms of
> >live performance? 0?
>
> I don't know what you mean by that, but the man you want to
> talk to is John
> deLaubenfels, who actually wrote the adaptive tuning software
> in question
> (with some feedback from my over-sensitive ears). He's on
> this list, and you
> can get to his pages from http://www.adaptune.com.

Ahh.. well, the latency question would have been clearer if I'd said: "If I
were using this adaptive tuning algorithm live, how much time would there be
between the time I press the keys and the time the retuned chord comes out
of the speakers, in ms?"

But, to digress: I see many many zipped MIDI files on John's web site. I
think I have the technology required to turn these into MP3s, if one would
desire.

Todd

--- In tuning@egroups.com, "M. Schulter" <MSCHULTER@V...> wrote:
> ------------------------------------------------------
> Adaptive rational intonation and neo-Gothic valleys
> A 24-note scheme a la Vicentino
> (Essay in honor of John deLaubenfels)
> Part V: Alternative solutions and circular JI system
> ------------------------------------------------------

Margo,

I want to thank you for this wonderful paper! Just reading through
your methods of scale construction with fifth chains and temperings
has been both fascinating and informative. And as always with your
discussion of the two manual mapping; powerful imagery of nimble
fingers navigating these scales, makes me yearn to hear some of your
improvisations.

I'll add this one to my cherished Schulter Collection. With all your
papers considered together, it looks as though you've got a good
portion of a book here!

>
> While either our 24-note adaptive scheme or a regular septimal
schisma
> temperament provides pure or virtually pure ratios of 3 and 7 as a
> variation on extended Pythagoraen tuning, another intricate 24-note
> system combines close approximations of these intervals with others
> much favored in neo-Gothic music: the e-based tuning with fifths at
> around 704.61 cents (~2.65 cents wide).
>
> In this tuning, the ratio between the whole-tone and diatonic
semitone
> is equal to Leonhard Euler's e, ~2.7182818284590452353603, these
> steps having sizes of approximately 209.214 cents and 76.965 cents.
>
> From a neo-Gothic perspective, the obvious attractions of this
tuning
> may be found in its first 12 notes. Regular major and minor thirds
at
> around 418.43 cents and 286.18 cents approximate ideal neo-Gothic
> "11-flavor" ratios of 14:11 and 13:11 or 33:28. Diminished fourths
and
> augmented seconds, at around 363.14 cents and 341.46 cents, are not
> too far from ideal "17-flavor" ratios of 21:17 and 17:14, with the
> supraminor third leaning rather in the largish or neutral direction
> toward 11:9 (~347.41 cents).

You really inspire me to try the e constant - haven't did much with
this yet (mostly phi so far). Very interesting properties!

>
> Not inappropriately, this tuning defined by Euler's famous _e_
yields
> a near-pure 7:4 minor seventh and an excellent approximation of the
> 7:6 minor third, two intervals he documented and championed as a
music
> theorist in 1764.[37] The 9:7 major third receives a less accurate
but
> reasonably fair approximation at about 440.11 cents, just over 5
cents
> wide.
>
> The special musical appeal of the 24-note e-based tuning is that it
> combines these 7-flavor intervals with the more obvious 11-flavor
and
> 17-flavor intervals in a single intonational "package."

This is like thinking about my favorite ice-creams! A tastey mix!

> -----------------------------------------------------------
> 5.2. Circularity: a 106-note "web of 2-3-7" and the nanisma
> -----------------------------------------------------------
>
> In the 24-note version we have explored, our adaptive JI system for
> ratios of 2, 3, and 7 has the slight "flaw" of the impure fifth G#-
D#'
> (G#-Eb^), "tempered by ratio" a 3.80-cent septimal schisma wide.
> Curiously, this asymmetry could be "repaired," and virtually perfect
> closure achieved, if we extended the system to two 53-note
Pythagorean
> cycles a septimal schisma apart, or 106 notes per octave in all.
>
> As is well known, a 53-note Pythagorean cycle offers "virtual
closure"
> from a practical perspective, since 53 pure 3:2 fifths exceed 31
pure
> 2:1 octaves by only the small quantity sometimes known as Mercator's
> comma, 19383245667680019896796723:19342813113834066795298816 or
about
> 3.615 cents.
>
> Such a 53-note Pythagorean tuning therefore features 52 pure fifths,
> plus an "odd" 53rd fifth "virtually tempered" in the narrow
direction
> by this comma, at ~698.340 cents. This odd fifth arises between the
> 53rd note of the cycle, located 52 fifths up or ~501.660 cents above
> the initial note, and the pure octave of this initial note.
>
> Suppose now that we tune two such complete 53-note cycles a septimal
> schisma apart -- 33554432:33480783 or ~3.804 cents -- as with our
> 24-note adaptive JI tuning, obtaining pure ratios of 2-3-7.

This is an absolutely amazing system Margo! Thanks for this
explanation.

>
> For this small difference by which the septimal schisma exceeds the
> comma of Mercator, I propose the term _nanisma_ (from Greek _nano_,
> "tiny," also used as the prefix for 10^-9, the
American "billionth").
> The nanisma is a small interval expressed by a large integer ratio:
>
> 649037107316853453566312041152512:648966242035284859600333477874109

Call the Guinness Book of Records, and pass me a Guinness Stout while
your at it!

>
> In practice, of course, 106 notes may seem like a rather large
tuning;
> but larger systems for JI or near-JI applications are sometimes
> discussed, for example 118-tET for ratios of 2-3-5.[40]
>
> Whatever practical uses this 106-note system may invite, and
> electronic implementations for use with MIDI sequencers or the like
> seem quite feasible, the possibility of a circulating and indeed
> almost perfectly circular "web of 2-3-7" based entirely on integer
> ratios may be a notable (however novel or often-rediscovered)
> conclusion for JI theory.[41]

Actually I find allot of value in studying large scales and playing
(subsets) from them.

> ---------------
> Notes to Part V
> ---------------
>
>
> 33. In a neo-Gothic setting, we might relish the impurity of G#-D#'
as
> a stimulating touch of "modal color" at a location having a certain
> affinity to the diminished sixth or "Wolf fifth" G#-Eb. Might this
> much gentler and more "domesticated" counterpart with its 17-tET-
like
> size be called a "poodle fifth"?

: )

>
> 38. For a brief discussion of 7-flavor cadences in the e-based
tuning,
> see "A gentle introduction to neo-Gothic progressions," 1, Part 2C,
> http://www.egroups.com/message/tuning/16134. In a forthcoming
article
> on this tuning, I hope to discuss "metachromatic" sequences moving
> between manuals in often surprising ways.

This I will be eargerly awaiting! This would be a wonderful paper to
have some audio examples to accompany the reading (let's do this!).

>
> 39. For metallophone-like timbres, 27-tET (fifths ~711.11 cents,
~9.16
> cents wide) can have a very pleasant effect in a neo-Gothic setting
> with its virtually pure 7:6 and 12:7 approximations (~266.67 cents,
> ~933.33 cents, only ~0.20 cents respectively narrow and wide), and a
> somewhat "gamelan-like" ambiance.

Intervals after my own heart!

Thanks,

Jacky Ligon

Todd Wilcox wrote,

>Ahh.. well, the latency question would have been clearer if I'd said: "If I
>were using this adaptive tuning algorithm live, how much time would there
be
>between the time I press the keys and the time the retuned chord comes out
>of the speakers, in ms?"

Oh, I see . . . well the algorithm in question would require you to play the
entire piece, wait a while, and then hear the retuned piece. This is because
it controls pitch drift over the entire length of the piece, which is of
course impossible to do on the fly. But John also previously developed a
real-time (and obviously inferior) retuning algorithm called JI Relay . . .

>But, to digress: I see many many zipped MIDI files on John's web site. I
>think I have the technology required to turn these into MP3s, if one would
>desire.

That might be valuable, so that we can get more people to hear the results
of John's efforts.

[Paul Erlich wrote:]
>>Well, that depends on what kind of tuning system you use. If you use
>>_adaptive_ tuning, like John deLaubenfels used, this won't be
>>the case. In
>>fact, almost none of the JI advocates would use it in the way
>>you described,
>>with the single exception of Ken Overton.

[Todd Wilcox wrote:]
>Ahh... so adaptive tuning is when you sorta re-do the scale based on
>the root of the chord you're about to play, so that your different
>chords all have the same sound? Or am I reading too much into that?
>That doesn't really sound very possible, since even if you used a
>computer, it would be hard to analytically distinguish the root when
>inversions are allowed.

>Soo... what's adaptive tuning? Boring the old-time list members with an
>answer is certainly not necessary, but is there a good URL?

Hi again, Todd. Adaptive tuning is in its infancy right now, but I may
be the "infant" who's done the most with it to date (as far as I am
aware from this list!).

[Todd:]
>Lets use yet another example:
>Two twins are born and raised in isolation on separate islands. Both
>twins are heavily exposed to recorded music, but are not allowed to
>play or tune any instruments as they grow up. Twin A only listens to
>music recorded on 12-tET instuments. Twin B is only exposed to a JI
>tuning, which may be adaptive for the purposes of this argument, if you
>prefer.

>On their 23rd birthdays, each twin is exposed to the other's tuning
>system. If I understand you correctly, you would wager that the twin
>raised in the ET system might hear the JI recordings and think "ahh..
>that's much easier to listen to," albeit maybe subconciously, while the
>twin raised JI will find the ET recordings at least mildly distasteful.
>*I* would say that both twins would find each other's system equally
>distasteful.

I am the "twin" who was raised on 12-tET, as we pretty much all were.
I started playing with JI in the early '90's, and didn't like 7-limit
chords. Till I heard them enough and DID like them, that is. Now I'm
spoiled to where 12-tET sounds horrible. I doubt that my hypothetical
"twin", exposed from birth to JI, would make a similar transition to
12-tET. IMHO, there is something special to JI, wired into our brains.

Can you play General MIDI (GM) files? If so, please go to

http://www.egroups.com/files/tuning/

change into the JMids directory, and download pearls.zip. Or
caravan.zip. Play them, and tell me if 12-tET still is as natural as
close-to-JI to your ears!

JdL

John wrote:
> Can you play General MIDI (GM) files? If so, please go to
>
> http://www.egroups.com/files/tuning/
>

Well... I'm not sure if I can play GM or not, but if the important part of
GM is that the pitch bend range is +/- 2 semitones, then I can configure a
patch on my synthesiser to work just like that. What other qualities of GM,
if any, are required for these MIDI files?

Todd

Paul:
> >But, to digress: I see many many zipped MIDI files on John's
> web site. I
> >think I have the technology required to turn these into
> MP3s, if one would
> >desire.
>
> That might be valuable, so that we can get more people to
> hear the results
> of John's efforts.

Knowing me, I'll probably convert myself to JI-fandom in the process.. :)

Todd

--- In tuning@egroups.com, "Todd Wilcox" <twilcox@p...> wrote:

> Ahh... so adaptive tuning is when you sorta re-do the scale
> based on the root of the chord you're about to play, so that
> your different chords all have the same sound? Or am I
> reading too much into that? That doesn't really sound very
> possible, since even if you used a computer, it would be hard
> to analytically distinguish the root when inversions are allowed.

No it wouldn't; analyzing the ratios (no matter what the
inversion) makes it easy to find the 1/1, or "root" (or n^0,
as I like to call it).

> Soo... what's adaptive tuning? Boring the old-time list
> members with an answer is certainly not necessary, but is
> there a good URL?

http://www.ixpres.com/interval/dict/adaptivetuning.htm

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'
>
> Todd

[I wrote:]
>>Can you play General MIDI (GM) files? If so, please go to
>>
>> http://www.egroups.com/files/tuning/
>>

[Todd wrote:]
>Well... I'm not sure if I can play GM or not, but if the important part
>of GM is that the pitch bend range is +/- 2 semitones, then I can
>configure a patch on my synthesiser to work just like that. What other
>qualities of GM, if any, are required for these MIDI files?

As you've surmised, the bend range is important. The sequences on my
web page (adaptune.com) are piano-only, and would just need to have
piano programs set for channels 0 thru 15. The sequences in the egroups
file area are multiple-voice, and make use of GM's drum channel
(internal 9); they also specify programs (voices) according to the GM
convention. Because channels are scarce for sequences such as these,
I'm forced to re-assign programs on the fly, so it'd be very hard to
convert these to a non-GM synth.

JdL

Margo Shulter wrote:

> We might view the result as a chain of 23 fifths: 11 pure fifths on
> each keyboard (Eb-G#, Eb^-G#^), linked by the "septimal schisma fifth"
> G#-Eb^ or G#-D#' at the complex integer ratio of 16777216:11160261
> (~705.76 cents), a 3.80-cent septimal schisma wider than pure.

That's the origin of "the septimal schisma" I suppose. I'm generally
dubious of such a complex ratio, when the temperament can be defined using
225:224 and 5120:5103.

> As a JI system, this scheme therefore also belongs to the family of
> septimal schisma tunings and temperaments of a general kind described
> and advocated by Graham Breed[32], where one or more fifths in a
> Pythagorean chain is slightly widened in order to obtain or very
> closely approximate pure 7-based ratios.

Hey, there's my name! I always pay attention when my name comes up.

That suggests I was describing tunings with fifths wider than Pythagorean.
Although those tend to be the ones I advocate, it's 53-equal that's the
borderline for the 7-based mapping.

> To obtain pure 7:4 minor sevenths and 8:7 major seconds, formed from
> chains of 14 fifths up or down, we could temper each fifth by 1/14 of
> a 3.80-cent septimal schisma; for pure 7:6 minor thirds and 12:7 major
> sixths, by 1/15 septimal schisma; and for pure 9:7 major thirds and
> 14:9 minor sixths, by 1/16 septimal schisma.
>
> Here is a table of these regular temperaments:
>
> ------------------------------------------------------------
> Chain Pure intervals Fifth Tempering
> ------------------------------------------------------------
> 14 fifths 8:7 / 7:4 ~702.227 cents +~0.272 cents
> 15 fifths 12:7 / 7:6 ~702.209 cents +~0.254 cents
> 16 fifths 9:7 / 14:9 ~702.193 cents +~0.238 cents
> ------------------------------------------------------------

That's neat. I didn't realise that you could get fractional schisma
temperaments this way. The meantone equivalent would be the 50.7 cent
septimal comma of 3^10:(2^13*7) or 59049/57344. Then, 7/4 is just in
1/10-septimal comma meantone.

> Suppose we choose the middle alternative of a 1/15-septimal schisma
> temperament with pure 12:7 major sixths and 7:6 minor thirds; fifths
> and the other 7-based intervals of our table are alike impure by the
> amount of the temperament, about 0.25 cents, remaining "virtually
> just."[34]

Although major seconds will be a half cent out from 9:8.

> >From a theoretical viewpoint, while our RAST approach leaves the
> Pythagorean intervals within each manual unaltered, our 1/15-schisma
> temperament causes very subtle changes in the global intonational
> fabric. Regular major thirds, for example, are slightly enlarged from
> a Pythagorean 81:64 (~407.82 cents) to around 408.83 cents, rather
> close to a ratio of 19:15 (~409.24 cents); usual diatonic semitones
> contract from a Pythagorean 256:243 (~90.22 cents) to around 88.96
> cents.[35]
>
> In practice, the two systems seem musically synonymous, and it is an
> open question whether a performer at the 24-note keyboard would notice
> any difference of "look and feel" in these two schisma tunings with
> their kindred qualities of accuracy -- and intricacy.

I found a surprisingly large improvement in 7-limit chords as the tuning
approaches 1/14-septimal schisma. I think a performer would notice the
difference.

> From the viewpoint of the performer, either system is large and
> relatively intricate: 24 notes are needed to make 7-based intervals
> available at the same number of locations as their regular Pythagorean
> counterparts in a 12-note tuning, and septimal comma distinctions at
> once complicate and diversify the possible range of sonorities and
> progressions.

Yes, a meantone tuning can give you much simpler 7-based intervals 19
notes of it go a long way. However, it's a qualitatively different system
melodically, so there's room in the world for both.

> In conclusion, one's choice between a RAST approach and a regular
> schisma temperament may reflect one's conceptual taste for "pure JI
> ratios" (in theory!) versus pervasive regularity and symmetry; the
> musical kinship between these solutions may be more important than
> their theoretical differences.[36]

For me, "conceptual taste" doesn't enter into it. I played with an
almost-Pythagorean tuning for a long time, and was dissatisfied with
7-limit chords in it. Optimising the tuning really makes them sound a lot
healthier. (Keeping the chorus down helps as well.) I'm finding the same
thing today with Kyma, so it probably isn't an artefact of tuning table
inaccuracy. I may look into this more closely.

Now for the footnotes.

> 32. See http://www.cix.co.uk/~gbreed/schismic.htm. Since Graham
> Breed's discussion focuses mainly on systems combining ratios of 2-3-5
> or 2-3-5-7 or 2-3-5-7-11 (with a "major third" often suggesting 5:4),
> his viewpoint may be somewhat different from that involved in
> neo-Gothic systems based on ratios of 2-3-7 (with a "major third"
> typically suggesting 81:64 or 9:7). Here I use the term "septimal
> schisma temperament" rather narrowly to mean a regular temperament
> where the fifth is widened by around 1/14-1/16 of a septimal schisma
> to obtain near-pure ratios of 3 and 7, i.e. a temperament with fifths
> in the range of ~702.19-702.23 cents (~0.23-0.27 cents wide). Graham
> Breed favors a fifth at 79/135 octave (702.2222... cents, ~0.267 cents
> wide), virtually identical to a 1/14-septimal schisma temperament
> (pure 7:4 and 8:7).

I prefer the URL http://x31eq.com/schismic.htm although it
points to the same site. If I ever change ISPs, the cix.co.uk links will
break.

It happens that the best system for 2-3-7 ratios is also the best for
2-3-5-7 ratios. However, in theory it shouldn't make much difference
whether you tune to that optimum or a more pragmatic near-Pythagorean
tuning. The worsening 7:4 should almost be compensated for by an
improving 7:5. However, in practice it makes quite a big difference, so I
go for an easy to remember tuning near the optimum.

> 35. The 1/15-septimal schisma tuning is located on the neo-Gothic
> spectrum of regular tunings about midway between Pythagorean with its
> pure 3:2 fifths at ~701.955 cents and 41-tET (fifths ~702.439 cents,
> ~0.484 cents wide). While small, the variances of this 1/15-schisma
> tuning from our RAST scheme might sometimes be highly desirable. For
> example, in the special sixth sonority with a near-11:8 "superfourth"
> between the two upper voices, e.g. B3-Eb4-G#^4 cadencing to A3-E4-A4
> (see Part IV, Section 4.3.2), this interval has a RAST tuning of
> 19683:14336 or ~548.77 cents, ~2.55 cents smaller than pure. In the
> 1/15-schisma tuning, it is ~550.80 cents, within ~0.52 cents of pure.
> For either system, incidentally, this very special superfourth unites
> the extreme notes of the 23-fifth chain, Eb-G#^.

Ah, the good old 23-fifth chain 11:8. In 1/14-septimal schisma, it's only
about 0.1 cents flat of pure. Unfortunately, an 11:7 comes out as a
37-fifth chain interval!

The other side of 41-equal, there's a simpler 18-fourth chain 11:8. That
would be C/-F# in my notation. I think it's C^-Gb in Margo's. And 11:7
is a mere C-Ab in either system. The optimal 11-limit tuning would be
702.67 cents, where 11:6 and 12:11 are just. Unfortunately, the C-Ab is
still nearly 7 cents out from 11:7.

Graham

John wrote:
> >What other
> >qualities of GM, if any, are required for these MIDI files?
>
> As you've surmised, the bend range is important. The sequences on my
> web page (adaptune.com) are piano-only, and would just need to have
> piano programs set for channels 0 thru 15. The sequences in
> the egroups
> file area are multiple-voice, and make use of GM's drum channel
> (internal 9); they also specify programs (voices) according to the GM
> convention. Because channels are scarce for sequences such as these,
> I'm forced to re-assign programs on the fly, so it'd be very hard to
> convert these to a non-GM synth.

Well, I got cakewalk and some skills, maybe I'll see what I can get.
Certainly the piano ones would not be a problem. I thought the GM drum
channel was 10?

Todd

How would I do that on my Yamaha PSR-730? I know where the tuning change is
on the thing, but to what values do I set each note to arrive at the notes
you mentioned as ratios?

-Brad
-----Original Message-----
From: ligonj@northstate.net [mailto:ligonj@northstate.net]
Sent: Friday, January 19, 2001 2:46 PM
To: tuning@egroups.com
Subject: [tuning] Re: New Guy

--- In tuning@egroups.com, engell69@g... wrote:
> --- In tuning@egroups.com, "Brad Beyenhof" <saxman32@s...> wrote:
> >I've been looking at previous posts, and I admit
> > that this stuff is a bit over my head.
> You're not the only one. Sometimes I wonder what the point of all
the
> complicated math and semantics is (other than it being food for
some
> intriguing study and discussion of the heart of music).

The quest for beauty is the point for many.

> The sheer complexity of alternative tunings leads me to question
> whether we can actually hear this stuff,

Try this simple test:

Set up your midi keyboard so that you can "a&b" between the following
triads:

0, 300, 700 cents
then:
1/1, 6/5, 3/2

and:

0, 400, 700 cents
then:
1/1, 5/4, 3/2

Make note of the ones that sound the most smooth to your ears, and
please post the results. This is one of my favorite demos of JI
tunings, which I love to show to interested folks, and it always gets
a very strong response.

> or if there is a "placebo"
> effect among microtonalists.

I believe there is certainly a kind of personal conditioning that
happens with repeated exposure to favored tuning systems. I would not
call this a "placebo" effect, since most anyone can recognize
distinctions from 12 tET, with very little exposure to new tuning
sounds.

> I feel that some research into how finely
> the human ear can discriminate intervals is in order.

There are many hypothesis about this, but we find only small
consensus with regard to the audibility of "prime or odd limits".
Most folks might find value in these general descriptions in 3-7
Limit intervals, but even these distinctions dissolve with the
inclusion of higher prime (or odd) intervals. I'm personally finding
this an empty argument these days. The recognizability of limits
fails under many significant demonstrations.

Thanks,

Jacky Ligon

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--- In tuning@egroups.com, "Brad Beyenhof" <saxman32@s...> wrote:
> How would I do that on my Yamaha PSR-730? I know where the tuning
change is
> on the thing, but to what values do I set each note to arrive at
the notes
> you mentioned as ratios?
> -Brad

Brad,

Your board very likely will have as a preset, the Just Intonation
Minor, and Just Intonation Major scales. You can set up your board
with the same sound on two separate midi channels - a piano sound is
good for testing this out. Leave one of the channels set to 12 Tone
Equal Temperament, and set the other to the JI minor or major. Then
you can just switch between the two by changing your midi channel;
whilst playing the triads. Please note that these scales usually
require you to play in a single key, and there is likely the ability
to have it be in any of 12 keys. Try "C".

To answer your question though:

The cents values can be set to:

1/1 0 (This is your "C", which should be configuable on your board)
6/5 316 cents for D#
3/2 702 cents for G

1/1 0 (This is your "C", which should be configuable on your board)
5/4 386 cents for E
3/2 702 cents for G

Let me know how it goes,

Jacky Ligon

> Try this simple test:
>
> Set up your midi keyboard so that you can "a&b" between the
following
> triads:
>
> 0, 300, 700 cents
> then:
> 1/1, 6/5, 3/2
>
> and:
>
> 0, 400, 700 cents
> then:
> 1/1, 5/4, 3/2
>
> Make note of the ones that sound the most smooth to your ears, and
> please post the results. This is one of my favorite demos of JI
> tunings, which I love to show to interested folks, and it always
gets
> a very strong response.
>

[I wrote:]
>>As you've surmised, the bend range is important. The sequences on my
>>web page (adaptune.com) are piano-only, and would just need to have
>>piano programs set for channels 0 thru 15. The sequences in
>>the egroups
>>file area are multiple-voice, and make use of GM's drum channel
>>(internal 9); they also specify programs (voices) according to the GM
>>convention. Because channels are scarce for sequences such as these,
>>I'm forced to re-assign programs on the fly, so it'd be very hard to
>>convert these to a non-GM synth.

[Todd wrote:]
>Well, I got cakewalk and some skills, maybe I'll see what I can get.
>Certainly the piano ones would not be a problem. I thought the GM drum
>channel was 10?

When they're numbered from 1 thru 16, it's 10. Down at the bit level,
the MIDI channels are numbered 0 thru 15; that what I'm calling the
"internal" designation. We're talking about the same channel.

JdL

JDL:
> [Todd wrote:]
> >Well, I got cakewalk and some skills, maybe I'll see what I can get.
> >Certainly the piano ones would not be a problem. I thought
> the GM drum
> >channel was 10?
>
> When they're numbered from 1 thru 16, it's 10. Down at the bit level,
> the MIDI channels are numbered 0 thru 15; that what I'm calling the
> "internal" designation. We're talking about the same channel.

Oh.. duh, of course. I rarely hear MIDI channels referred to by their
ordinals. :)

Todd

There's a widespread notion that those with perfect pitch cannot
stand anything that deviates from high-quality 12-tet. I have found
that I am the only exception to this rule that I have ever met. I
have perfect pitch, yet I *love* such departures as hearing 12-tet
music a quarter-tone sharp. In fact, I generally prefer to hear music
that is out of "tune", hence my interest in microtonal tunings.
Another difference is that I've not met anyone with perfect pitch who
can tell the notes of the diatonic scale that someone is speaking on
or that birds chirp on etc. except for myself. Maybe there are
multiple forms of perfect pitch?

-John

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> It doesn't quite work that way. What the brainwashing does is to
force us
> into a "categorical" way of hearing intervals, and there are two
> manifestations of this. The most common is relative pitch, in which
> categorical perception means we hear all intervals as some sort of
deviation
> from the (usually) nearest 12-tET equivalent, rather than as new
intervals
> in their own right. The second is perfect pitch -- people with
perfect pitch
> find it painful to even listen to 12-tET music a quarter-tone
sharp. But the
> brainwashing can be undone with sufficient exposure. One good way
to begin
> is with _harmonic_ intervals -- the sensual difference between
hearing a
> just major third vs. a 12-tET major third _harmonically_ is
unmistakeable.

Jay here,
Well, though "met" may not be the proper word in this medium, you now
"know" of another other than yourself who has "perfect pitch" and, 1.
revels in deviations of tuning and pitch standard and 2, can pick out the
notes in chirping birds, trash cans and such. And, if Pierre Boulez has
anything like the auditory accuity with which he's credited, I betcha he
can do such things, too.
At 04:54 AM 1/23/01 -0000, engell69@gte.net wrote:
>There's a widespread notion that those with perfect pitch cannot
>stand anything that deviates from high-quality 12-tet. I have found
>that I am the only exception to this rule that I have ever met. I
>have perfect pitch, yet I *love* such departures as hearing 12-tet
>music a quarter-tone sharp. In fact, I generally prefer to hear music
>that is out of "tune", hence my interest in microtonal tunings.
>Another difference is that I've not met anyone with perfect pitch who
>can tell the notes of the diatonic scale that someone is speaking on
>or that birds chirp on etc. except for myself. Maybe there are
>multiple forms of perfect pitch?
>
>-John
>
>--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
>> It doesn't quite work that way. What the brainwashing does is to
>force us
>> into a "categorical" way of hearing intervals, and there are two
>> manifestations of this. The most common is relative pitch, in which
>> categorical perception means we hear all intervals as some sort of
>deviation
>> from the (usually) nearest 12-tET equivalent, rather than as new
>intervals
>> in their own right. The second is perfect pitch -- people with
>perfect pitch
>> find it painful to even listen to 12-tET music a quarter-tone
>sharp. But the
>> brainwashing can be undone with sufficient exposure. One good way
>to begin
>> is with _harmonic_ intervals -- the sensual difference between
>hearing a
>> just major third vs. a 12-tET major third _harmonically_ is
>unmistakeable.
>
>
>You do not need web access to participate. You may subscribe through
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>
>
>

--- In tuning@egroups.com, engell69@g... wrote:

http://www.egroups.com/message/tuning/17840

> There's a widespread notion that those with perfect pitch
> cannot stand anything that deviates from high-quality 12-tet.
> I have found that I am the only exception to this rule that I
> have ever met. I have perfect pitch, yet I *love* such
> departures as hearing 12-tet music a quarter-tone sharp. In
> fact, I generally prefer to hear music that is out of "tune",
> hence my interest in microtonal tunings. Another difference
> is that I've not met anyone with perfect pitch who can tell
> the notes of the diatonic scale that someone is speaking on
> or that birds chirp on etc. except for myself. Maybe there
> are multiple forms of perfect pitch?

I'm very right-handed, so I'd hesitate to use the cliche
"I'd give my right arm for...". But yes, I *would* consider
exchanging my left arm for perfect pitch! And I definitely
like microtonal tunings! (so count me in this small club, John).

-monz

Though I do not have perfect pitch, my work with musicians who do has shown
lots of variety in perception.

When I do my Microtonal Bach Christmas radio show, it is always telephone
calls from listeners with perfect pitch that complain that the music is a
semitone lower than the key in their titles. So, when I say D Minor, they
hear C# Minor (because early music is typically performed at A=415. This
semitone difference actually distinguishes the "early music movement." But
it doesn't mean squat when listening to Werckmeister's chromatic temperament.
Since Bach had NO pitch reference outside of the particular organ he was
using, pitch height is not at issue. But for many with perfect pitch, it
blocks the ability to hear the idiosyncratic intervals between scale tones,
let alone particular key qualities and characteristics.

On the other side are my fellow American Festival of Microtonal Music
Ensemblers David Eggar (cello) and Michiyo Suzuki (clarinet). David's
perfect pitch can be turned on and off by will. In my cello concerto
"Odysseus" he must tune in to found metals and woods struck off a Styrofoam
resonator and improvise using these tones. They are beyond description (at
this time) but David zooms in and makes each inharmonic pitch ring true with
his priceless cello.

Michiyo does it one better because she has synaestesia. She can memorize
almost instantly buy memorizing the color produced the notes of the paper.
She is able to play and hear in any tuning, almost immediately. I wrote
Michiyo "Sleep" to take full advantage of her abilities. She gave my an
octave specific scales based on the frequencies she divined in a corner of
"The Room" by van Gogh. As I recall, there was so much color in my choice,
that she notated only arrows from letter names, but she played specific
pitches in the performance, radiantly.

Johnny Reinhard

Hello, there, Graham Breed, and thank you for a very thoughtful
response to my final article in the series on a 24-note neo-Gothic JI
system for ratios of 2, 3, and 7.

> That's the origin of "the septimal schisma" I suppose. I'm
> generally dubious of such a complex ratio, when the temperament can
> be defined using 225:224 and 5120:5103.

While after reading the remainder of your post I'm not sure if this is
still an issue, I should explain that the septimal schisma at its rather
large ratio of 33554432:33480783 (~3.804 cents) isn't as formidable as
it may appear.

It's simply the amount by which, for example, a minor seventh from a
chain of 14 pure fourths up or fifths down differs from a pure 7:4. If
we're addressing ratios of 2-3-7, then this is the relevant schisma;
your ratios involve other factors such as 5 which would, of course, be
relevant in a 7-limit system based on 2-3-5-7, for example.

Using the 3.80-cent schisma is thus the simplest approach in a 2-3-7
system. In practice, of course, the complexity of the integer ratio is
academic: it's a question of taking 3.80 cents and figuring the
closest approximation on a given synthesizer's tuning table, for
example (3/1024 octave for a 1024-tET synthesizer).

If we were hypothetically tuning the 24-note 2-3-7 JI system by ear,
we actually wouldn't even need to know about this schisma or do any
tempering at all: we just tune the first manual in Pythagorean; tune,
say, a D on the second manual to a pure 7:6 below F on the first
manual in the same octave; and tune the second manual in Pythagorean
from there.

>> As a JI system, this scheme therefore also belongs to the family of
>> septimal schisma tunings and temperaments of a general kind
>> described and advocated by Graham Breed[32], where one or more
>> fifths in a Pythagorean chain is slightly widened in order to
>> obtain or very closely approximate pure 7-based ratios.

> Hey, there's my name! I always pay attention when my name comes up.

Actually, I feel like apologizing for rather understating your great
contribution to my RAST (Rational Adaptive Schisma Tuning) solution
for 2-3-7 JI, because your articles last summer really got me
interested both in making those 7-based intervals _pure_, and in the
septimal schisma as a key to the problem.

Please let me add that compared to the kinds of schisma tunings you
discuss, mine is much simpler and less sophisticated, and addresses a
much more rudimentary problem. If one is dealing with multiple prime
factors (2-3-5-7 or 2-3-5-7-11), then your suggested schisma ratios
and methods are indeed the relevant ones.

> That suggests I was describing tunings with fifths wider than
> Pythagorean. Although those tend to be the ones I advocate, it's
> 53-equal that's the borderline for the 7-based mapping.

From my 2-3-7 outlook, I would say that indeed 53-tET is satisfactory
for yielding good approximations of 7 -- but that if we take
Pythagorean (pure fifths) as the starting point, as it is for
neo-Gothic, then 53-tET is moving in the wrong direction to improve
7-based ratios, albeit ever so slightly. From a 7-limit perspective
(2-3-5-7), of course, it is also slightly improving the 5-limit
thirds.

Just to place this question in a bit of context: last summer, you were
commenting that the comma in 53-tET (~22.64 cents, a tad narrower than
the Pythagorean 23.46 cents) was a bit too small to be comfortable for
you as a melodic inflection, so that you tended to favor leaning in
the wide direction, where the comma gets larger. For example, it's
~26.67 cents with your 1/14 septimal schisma tuning with the fifth at
79/135 octave, and ~29.27 cents in 41-tET.

> That's neat. I didn't realise that you could get fractional schisma
> temperaments this way. The meantone equivalent would be the 50.7
> cent septimal comma of 3^10:(2^13*7) or 59049/57344. Then, 7/4 is
> just in 1/10-septimal comma meantone.

This is a neat way of viewing things, and indeed 1/10 of this septimal
comma gives us a temperament of the fifth on the meantone side by
about 5.07 cents, close to 1/4-comma meantone (~5.38 cents) and even
closer to 31-tET (~5.18 cents).

>> Suppose we choose the middle alternative of a 1/15-septimal schisma
>> temperament with pure 12:7 major sixths and 7:6 minor thirds;
>> fifths and the other 7-based intervals of our table are alike
>> impure by the amount of the temperament, about 0.25 cents,
>> remaining "virtually just."[34]

> Although major seconds will be a half cent out from 9:8.

One advantage of the RAST approach -- just "virtually temper" one
fifth by the full 3.80-cent schisma, and have done -- is that apart
from usual Pythagorean-like intervals with that fifth in their chains,
we keep the familiar 3-based ratios pure, including all the 9:8's
within either keyboard.

> I found a surprisingly large improvement in 7-limit chords as the
> tuning approaches 1/14-septimal schisma. I think a performer would
> notice the difference.

This is interesting, and I wonder how 1/14 schisma vs. 1/15 schisma
might work out for 12:14:18:21 or 14:18:21:24 (what might Paul
Erlich's "harmonic entropy" say?).

With a RAST approach, all these ratios are pure -- although we're
talking about minute variations here.

> Yes, a meantone tuning can give you much simpler 7-based intervals
> 19 notes of it go a long way. However, it's a qualitatively
> different system melodically, so there's room in the world for both.

While the meantone indeed offers a shorter chain of fifths for these
intervals, as Dave Keenan points out also, I'd say the choice might be
one between a Gothic style where the regular Pythagorean intervals are
natural, and a Renaissance style where the meantone intervals are
natural -- melodically and vertically.

In a Gothic setting, pure or near-pure fifths are great; in a
Renaissance or later setting, that 5-odd-cents of temperament (in the
narrow direction) also serves the very useful purpose of giving us
pure or near-pure thirds at or close to 5:4 and 6:5.

> For me, "conceptual taste" doesn't enter into it. I played with an
> almost-Pythagorean tuning for a long time, and was dissatisfied with
> 7-limit chords in it. Optimising the tuning really makes them sound
> a lot healthier. (Keeping the chorus down helps as well.) I'm
> finding the same thing today with Kyma, so it probably isn't an
> artefact of tuning table inaccuracy. I may look into this more
> closely.

Here my "conceptual taste" remark was directed to the rather narrow
question of whether to seek those pure 7-based intervals by stretching
a single fifth the full schisma (RAST), or with a regular temperament
(e.g. 1/14 of the schisma for a pure 7:4).

One thing I might have added is that for synthesizers, if one is going
for pure ratios as the ideal, the tuning table and the "nanotempering"
needed to fit its steps can make a difference.

For example, 1024-tET gives almost pure fifths, but the closest
approximation of any of the regular schisma temperaments we've been
discussing is to widen one fifth in every four by 1/1024 octave (~1.17
cents). If we look at the resulting chain of 23 fifths, we find
something like this:

|-----------------------------------------|
s s s L s s s L s s s L s s s L s s s L s s s
|------------------------------------------|

Note over a chain of 14 fifths, we want 11 almost-pure (s) fifths and
three large (L) fifths, for a total correction of 3 tuning units
(~3.51 cents, the best approximation of the schisma). However, what we
get are some chains with 3 L and some with 4 L, so that we can't use
the most accurate approximation for all these intervals.

With a RAST approach, we temper one fifth by 3 tuning units, and
optimize all 7-based intervals (including the 7:4's) to within around
0.32 cents of pure, since all these intervals will have that one fifth
in their chain.

Of course, as the phrase goes, this is a "device-specific" issue. If
we had a synthesizer in 1350-tET, then a regular 1/14-schisma
temperament with all fifths at 790 units would be the way to go.

> I prefer the URL http://x31eq.com/schismic.htm although
> it points to the same site. If I ever change ISPs, the cix.co.uk
> links will break.

Thank you for this information, of which I'll take note.

> Ah, the good old 23-fifth chain 11:8. In 1/14-septimal schisma,
> it's only about 0.1 cents flat of pure. Unfortunately, an 11:7
> comes out as a 37-fifth chain interval!

Yes, 1/14-septimal schisma is right at an optimal 11:8 point. If we
want both 11:7 and 11:8, then the region around 46-tET (pure 14:11
major thirds and 11:7 minor sevenths) is one possibility. We get 11:7
as the regular minor sixth -- a bit languid in a very pleasant way in
neo-Gothic -- and 11:8 as the "Wolf fourth" of 11 fifths up,
e.g. Eb-G# -- a chain 12 fifths shorter than in the Pythagorean zone.

For a pure 11:7 (and 14:11) we have fifths at ~704.38 cents (~2.42
cents wide), just a tad wider than 46-tET. For a pure 11:8 Wolf fourth
or augmented third, we need to go just a tad further than the
"e-based" tuning at 704.61 cents, in fact ~704.665 cents (2.71 cents
wide). With the e-based tuning, our 11:7 is about 0.91 cents narrow,
and our 11:8 about 0.64 cents narrow.

> The other side of 41-equal, there's a simpler 18-fourth chain 11:8.
> That would be C/-F# in my notation. I think it's C^-Gb in Margo's.
> And 11:7 is a mere C-Ab in either system. The optimal 11-limit
> tuning would be 702.67 cents, where 11:6 and 12:11 are just.
> Unfortunately, the C-Ab is still nearly 7 cents out from 11:7.

Yes, I find this fifth for the pure 18-fourth 11:8 at around 702.7046
cents, about halfway between Pythagorean and 29-tET, and I could
indeed describe the interval as A^-Eb, for example, a diminished fifth
less comma (6 + 12 fourths up). From your viewpoint, I suspect, the
regular diminished fifth only about 1.26 cents wide of a pure 7:5 is
also an attraction.

By the way, to wander into the general neighborhood of Paul Erlich's
22-tET country, we get a diminished fifth of 11:8 with a fifth of
around 708.11 cents (~6.16 cents wide), or roughly a cent less
tempering than 22-tET. This is maybe around the middle of the "optimal
paultone zone."

One rational approximation of this fifth is 140:93 (~708.15 cents).

Most appreciatively,

Margo Schulter
mschulter@value.net

Margo Schulter wrote:

> > That's the origin of "the septimal schisma" I suppose. I'm
> > generally dubious of such a complex ratio, when the temperament
can
> > be defined using 225:224 and 5120:5103.
>
> While after reading the remainder of your post I'm not sure if this
is
> still an issue, I should explain that the septimal schisma at its
rather
> large ratio of 33554432:33480783 (~3.804 cents) isn't as formidable
as
> it may appear.

It isn't an issue in this context, but others (specifically Joe Monzo)
do use it as "the" septimal schisma in the full 7-limit context. I
didn't understand its significance until I read your post. I still
have a minor gripe with it in other contexts, but it's not that
important.

> It's simply the amount by which, for example, a minor seventh from a
> chain of 14 pure fourths up or fifths down differs from a pure 7:4.
If
> we're addressing ratios of 2-3-7, then this is the relevant schisma;
> your ratios involve other factors such as 5 which would, of course,
be
> relevant in a 7-limit system based on 2-3-5-7, for example.

This highlights the different ways we view these systems, you see. I
start with my tempered fifth and don't know or care what 14 pure ones
would have been.

> Using the 3.80-cent schisma is thus the simplest approach in a 2-3-7
> system. In practice, of course, the complexity of the integer ratio
is
> academic: it's a question of taking 3.80 cents and figuring the
> closest approximation on a given synthesizer's tuning table, for
> example (3/1024 octave for a 1024-tET synthesizer).

And that's another thing. When you take the 5s out, this is *the*
septimal schisma. To reflect this, I suggest it be called the
"Pythagorean-septimal schisma" or "2-3-7 schisma".

> If we were hypothetically tuning the 24-note 2-3-7 JI system by ear,
> we actually wouldn't even need to know about this schisma or do any
> tempering at all: we just tune the first manual in Pythagorean;
tune,
> say, a D on the second manual to a pure 7:6 below F on the first
> manual in the same octave; and tune the second manual in Pythagorean
> from there.

Yes, for ear tuning you'd work with whatever pure intervals were
relevant. The fact that these intervals are so close to just means
that you don't need to worry about tempering them exactly, and the
tuning as a whole will take care of itself.

But I find it conceptually easier to explain a temperament without
using the complicated "bridge" intervals. I think of schismic
temperament as being about commas. In the 5-limit case, the
Pythagorean and syntonic commas are equivalent. The septimal comma
64:63 then joins the party. If 81:80 decides to leave, that's no
problem!

I don't even know the ratio for a Pythagorean comma offhand. I could
work it out, of course. But all I need to know it that it's the
amount by which 6 whole tones of 9:8 are sharp of a 2:1 octave.

So when you're tuning your keyboard, you'll find an interval that is a
comma flat of the Pythagorean minor third. As all commas are equal,
you know that interval approximates 7:6. So, within the natural
imprecision of acoustic instruments, you're free to tune it likewise.

A small bit of mathematics is needed to know that that interval is a
7:6. The Pythagorean minor third is three octave-reduced fourths.
The denominator then is 27. The numerator must be a power of two, and
32 fits the bill. But we don't even need to know that. call it 1:27.
Flatten it by 64:63, or 1:63, and we get 63:27 which cancels down to
7:3. And that's an octave equivalent of 7:6.

So, when I make casual remarks about "the septimal schisma" being
over-complex, part of my argument is that we don't need a septimal
schisma at all. Only a septimal comma. Which also means I don't care
much what gets called "the septimal schisma" as I rarely talk about
"schismas" only "schismic temperaments".

The situation may be different if you were to tune 13 pure commas and
decide the next one should be tempered. But I'd still rather say "13
pure commas" than whatever ratio it turns out to be.

This also shows my preference for small integers over complex ratios.
As I often use matrix algebra to manipulate those small integers, my
idea of "simplicity" may not tally with that of the general
population, but there you go.

> Actually, I feel like apologizing for rather understating your great
> contribution to my RAST (Rational Adaptive Schisma Tuning) solution
> for 2-3-7 JI, because your articles last summer really got me
> interested both in making those 7-based intervals _pure_, and in the
> septimal schisma as a key to the problem.

Thanks for that. Given your high standard of scholarship, I feel
slightly honoured that you're paying me any attention at all.

> > That suggests I was describing tunings with fifths wider than
> > Pythagorean. Although those tend to be the ones I advocate, it's
> > 53-equal that's the borderline for the 7-based mapping.
>
> From my 2-3-7 outlook, I would say that indeed 53-tET is
satisfactory
> for yielding good approximations of 7 -- but that if we take
> Pythagorean (pure fifths) as the starting point, as it is for
> neo-Gothic, then 53-tET is moving in the wrong direction to improve
> 7-based ratios, albeit ever so slightly. From a 7-limit perspective
> (2-3-5-7), of course, it is also slightly improving the 5-limit
> thirds.

The thing about 53 is that, if the fifth gets any flatter, the best
7-limit approximation doesn't equate the Pythagorean and septimal
commas. So the general "septimal schisma" concept is only valid for
tunings with a fifth wider than that in 53-equal. As an example,
118-equal is a good 7-limit tuning (may even be consistent) and is a
schismic temperament, but it isn't a "septimal schisma" temperament.

In the same way, 12-equal is the borderline between meantone and
schismic temperaments. So "meantone" would usually refer to scales
generated by a fifth flatter than 7/12 octaves (although the
definition is contentious :) and "schismic" to those with fifths sharp
of 5/12 octaves.

I "advocate" sharper fifths for the reasons you outline. Including
the fatter comma:

>Just to place this question in a bit of context: last summer, you
were
>commenting that the comma in 53-tET (~22.64 cents, a tad narrower
than
>the Pythagorean 23.46 cents) was a bit too small to be comfortable
for
>you as a melodic inflection, so that you tended to favor leaning in
>the wide direction, where the comma gets larger. For example, it's
>~26.67 cents with your 1/14 septimal schisma tuning with the fifth at
>79/135 octave, and ~29.27 cents in 41-tET.

Another way of thinking about this is the number of commas that make
up an octave. 1/14 septimal schisma tuning has around 45 commas to
the octave. I tune it to exactly 45. There are around 51.15
Pythagorean commas to an octave, and I found that to be wide enough.
So the cutoff is between 1/51 and 1/53 octaves. It would follow that
64- and 50-equal should also be okay if the single steps are audible.
Although the exact cutoff will likely be a matter of personal taste.

> >> Suppose we choose the middle alternative of a 1/15-septimal
schisma
> >> temperament with pure 12:7 major sixths and 7:6 minor thirds;
> >> fifths and the other 7-based intervals of our table are alike
> >> impure by the amount of the temperament, about 0.25 cents,
> >> remaining "virtually just."[34]
>
> > Although major seconds will be a half cent out from 9:8.
>
> One advantage of the RAST approach -- just "virtually temper" one
> fifth by the full 3.80-cent schisma, and have done -- is that apart
> from usual Pythagorean-like intervals with that fifth in their
chains,
> we keep the familiar 3-based ratios pure, including all the 9:8's
> within either keyboard.

Ah, so that's another subtlety I hadn't taken account of.

> > I found a surprisingly large improvement in 7-limit chords as the
> > tuning approaches 1/14-septimal schisma. I think a performer
would
> > notice the difference.
>
> This is interesting, and I wonder how 1/14 schisma vs. 1/15 schisma
> might work out for 12:14:18:21 or 14:18:21:24 (what might Paul
> Erlich's "harmonic entropy" say?).

If I remember these, I could try them. Although the difference
between 1/14 and 1/15 schisma is likely to be much smaller than
between either and Pythagorean intonation. 12:18 and 14:21 are both
fifths, right? And 12:14 is 6:7. So these are fifth pairs a subminor
third apart.

Usually I go with a 4:5:6:7 for testing, or 4:5:6:7:8 if my fingers
stretch far enough.

I have done some more tests as well. I set up a MIDI knob to fade
between my near-enough optimal 1/45 octave comma, and 41-equal. Then
I extrapolated to take me past Pythagorean.

Now, when I tried it that first evening, I found that the
near-Pythagorean tuning wasn't as bad as I remembered. Or, at least,
it ceased to be as the experiment progressed. Next morning, the
sourness returned, so I think it's that I was coming to recognize the
7-limit harmonies and unconsciously make allowances for their
mistuning.

This is something we have to watch out for. The average audience
member will be less familiar with 7-limit harmony than I am. So, if
you hit them with mistuned 7-limit chords, the first impression will
be "yeek, that's out of tune!" You may think your intonation's fine
if you've been desensitised during rehearsals. So be careful.

Anyway, the results. There is some kind of cut-off where the tuning
gets 110% of the way from 41 to 135. I'm not sure exactly where this
falls, but it sounds uncomfortably close to 1/16-schisma. Going the
other side of 41-equal isn't such a problem. The chords become
blurred, but not sour. So, where there's an uncertainty about how
accurate an instrument may be tuned, I suggest something like
1/14-schisma, or somewhere towards 41-equal, to be on the safe side.

7:9:11 chords, using the simplest approximation for 7:11, start to
sound great half way towards 41-equal. They aren't so sensitive to
tuning, so either side of 41= is okay, althought the theoretical
optimum is the far side of 41= to the 7-limit optimum. If the
equalness of 41 simplifies anything for you, go for it.

This is all done with filtered sawtooth waveforms. Raising the filter
is good for 7:9:11 chords.

> With a RAST approach, all these ratios are pure -- although we're
> talking about minute variations here.

In practical terms, it would be hardware-dependent.

> > Yes, a meantone tuning can give you much simpler 7-based intervals
> > 19 notes of it go a long way. However, it's a qualitatively
> > different system melodically, so there's room in the world for
both.
>
> While the meantone indeed offers a shorter chain of fifths for these
> intervals, as Dave Keenan points out also, I'd say the choice might
be
> one between a Gothic style where the regular Pythagorean intervals
are
> natural, and a Renaissance style where the meantone intervals are
> natural -- melodically and vertically.

I think a lot of the neo-Gothic concepts would work in meantone. You
still have good-enough approximations to the 2-3-7 intervals.

> In a Gothic setting, pure or near-pure fifths are great; in a
> Renaissance or later setting, that 5-odd-cents of temperament (in
the
> narrow direction) also serves the very useful purpose of giving us
> pure or near-pure thirds at or close to 5:4 and 6:5.

It happens that 1/4-comma meantone is both the optimal minimax 5-limit
temperament, and the same optimum for the 7-limit. So there isn't the
7-5 dichotomy you get in schismic temperament where the two are
optimised either side of Pythagorean. However, in meantone, the
fifths are always bad relative to schismic if you optimize to either
of these limits.

I think the fifths in, say, 31-equal are good enough for trines to
function as stable chords. I find the tempering to be noticeable but
tolerable. 7-based chords should be able to resolve onto trines the
same as they do in a schismic temperament.

The near-pure thirds are something of a red-herring. Yes, either 5:4
or 6:5 can be pure in meantone, but so can either 7:6 or 7:4. The
trade-off between meantone and schismic is the same whether you take
2-3-5 or 2-3-7. Schismic temperament will give you much purer
intervals, but with a more complex scale.

I'm interested in how neo-Gothic would work in meantone. I haven't
followed the details of the theory as you outlined it. I tend to
switch off when I see harmonic progressions discussed, because I'm not
familiar with the traditional theory. Perhaps a summary of
characteristic progressions would be useful, or I could go back
through the archives.

If enough intervals with 7 and 11 are involved, it may be possible to
remove the Pythagorean ones altogether. So an 11-limit aware meantone
notation could be used for variable pitched instruments.

I'm also wondering how much Common Practice harmony could work with
9-limit intervals. The occasional 6:7:9 minor triad, or 21:20 leading
tone, could do it a power of good.

> Here my "conceptual taste" remark was directed to the rather narrow
> question of whether to seek those pure 7-based intervals by
stretching
> a single fifth the full schisma (RAST), or with a regular
temperament
> (e.g. 1/14 of the schisma for a pure 7:4).

Ah, right. So this is like a well-temperament for schismic scales.
As such, it would favor some keys over others. Although mostly, yes,
likely a conceptual difference.

> One thing I might have added is that for synthesizers, if one is
going
> for pure ratios as the ideal, the tuning table and the
"nanotempering"
> needed to fit its steps can make a difference.
>
> For example, 1024-tET gives almost pure fifths, but the closest
> approximation of any of the regular schisma temperaments we've been
> discussing is to widen one fifth in every four by 1/1024 octave
(~1.17
> cents). If we look at the resulting chain of 23 fifths, we find
> something like this:
>
> |-----------------------------------------|
> s s s L s s s L s s s L s s s L s s s L s s
s
> |------------------------------------------|
>
> Note over a chain of 14 fifths, we want 11 almost-pure (s) fifths
and
> three large (L) fifths, for a total correction of 3 tuning units
> (~3.51 cents, the best approximation of the schisma). However, what
we
> get are some chains with 3 L and some with 4 L, so that we can't use
> the most accurate approximation for all these intervals.
>
> With a RAST approach, we temper one fifth by 3 tuning units, and
> optimize all 7-based intervals (including the 7:4's) to within
around
> 0.32 cents of pure, since all these intervals will have that one
fifth
> in their chain.

Yes, that sounds like a good approach, if you want to consider such
small details. However, I caution against making too many assumptions
about the way synthesizers do their tuning. You may know the
precision, but not the accuracy. For example, if the tuning is with
1024 steps to the octave, those steps may not all be equal. So you
might have to do a lot of experimentation to fit the tuning to the
hardware. I prefer to choose a temperament that is likely to fail
gracefully however the precise implementation turns out.

If the tuning is done relative to a tonic, you'll probably find it
ends up as some RAST like that when the tuning table's defined whether
or not you oversaw the process.

> Of course, as the phrase goes, this is a "device-specific" issue. If
> we had a synthesizer in 1350-tET, then a regular 1/14-schisma
> temperament with all fifths at 790 units would be the way to go.

You only need 135-tET for that.

> > Ah, the good old 23-fifth chain 11:8. In 1/14-septimal schisma,
> > it's only about 0.1 cents flat of pure. Unfortunately, an 11:7
> > comes out as a 37-fifth chain interval!
>
> Yes, 1/14-septimal schisma is right at an optimal 11:8 point. If we
> want both 11:7 and 11:8, then the region around 46-tET (pure 14:11
> major thirds and 11:7 minor sevenths) is one possibility. We get
11:7
> as the regular minor sixth -- a bit languid in a very pleasant way
in
> neo-Gothic -- and 11:8 as the "Wolf fourth" of 11 fifths up,
> e.g. Eb-G# -- a chain 12 fifths shorter than in the Pythagorean
zone.

I don't like comparisons to 46-equal in this context, because it
belongs to a different family of temperaments, which have different
tuning considerations.

In schismic terms, the 2-3-7 starts to suffer when you optimize this
11:7. But 41-equal works well enough, so this is one way to think
about the 11-limit in 41-equal.

12 note well temperaments work as they do because some parts of the
keyboard favour thirds, and some fifths. This compromise comes from
the ideal tunings for 3:2 and 5:4 being either side of 12-equal. In
the same way, a 41 note RAST might balance the 3 and 7 on one side,
and the 11 on the other. Perhaps you could look at this in the light
of your theories. (Or perhaps you already have.)

> Yes, I find this fifth for the pure 18-fourth 11:8 at around
702.7046
> cents, about halfway between Pythagorean and 29-tET, and I could
> indeed describe the interval as A^-Eb, for example, a diminished
fifth
> less comma (6 + 12 fourths up). From your viewpoint, I suspect, the
> regular diminished fifth only about 1.26 cents wide of a pure 7:5 is
> also an attraction.

The pure 7:5 isn't that important, because the other 9-limit intervals
will be so far out.

In general, it looks like 5 and 11 don't go together. In the same
octave, they compare as 10 and 11. So a chord using both implies an
11:10, which is uncomfortably small, probably within the critical
band. The occasional 15 might turn up, but it'd have to be with a 21
to give a 7:5, and then you have 21:22. As the tuning's optimized for
chords with 11 in them, a 7:5 isn't likely to be at all important. In
this case leaving out 5 altogether looks like a good idea. So we're
in agreement!

Graham

Hi John,

I wonder if you've tried adaptive tuning for C.P.E.Bach?

With all the pure triads, and his transparent and very
mellow "laid back" style, I think it would sound nice adaptively tuned
to 5-limit.

I have a flute + piano sonata that I try out on the recorder,
and I've been practicing the recorder part with just intonation C major
and G major chords today, and it sounds nice. Later on it has
minor chords and will need to think about fingering / tuning for those
too, and though it doesn't wander that far, will
need adaptive tuning to do those in j.i. for instance, has a
d minor chord at start of the next section which doesn't
work in just intonation syntonic scale.

The one I'm practicing is Sonata 1 in C major, Allegretto.

There are several at http://www.prs.net/midi-a-e.html#b
but couldn't see any of his pieces for flute and piano.
There's a nice one there by J.C. Bach (on midi flute + harpsichord).

If you do do it, might be nice to also do a file with the flute part left
out, so one can have a go at playing along with it in adaptive j.i.

Another idea.

You've often explained how the adaptive tuning technique doesn't work
so well in real time because it is impossible to anticipate a chord
until all its notes have been played.

Also your adaptive tuning techniques take into account all the notes
in the whole piece and that extra level obviously isn't going to work in real
time.

However the pieces you adaptively tune are often ones with scores
that the performers play from.

I wonder if there is some way you could do it so that one plays
a piece through with the adaptive tuning program "recording" the
performance.

Then leave it to work out the adaptive tunign fro it, then
play it again, and this time it will know all the notes you
are going to play and so could adaptively tune them correctly.

Can imagine there'd be a fair nubmer of subleties like recognising
ones place if the notes of a "simultaneous" chord are played in another order
from teh one recorded, or if a trill is played with another number
of notes, or if the performer leaves out a repeat, or adds
an extra ornament to a part or whatever.

But seems do-able - performer could cooperate with the program and
if it loses its place it could show a message or something.

Would be interesting as I expect performers would play to
heighten the effect of the adaptive tuning and use it in various
ways.

Just a thought,

Robert

[Robert Walker wrote:]
>I wonder if you've tried adaptive tuning for C.P.E.Bach?

No, but I'd be glad to!

>With all the pure triads, and his transparent and very
>mellow "laid back" style, I think it would sound nice adaptively tuned
>to 5-limit.

Kyool...

>I have a flute + piano sonata that I try out on the recorder,
>and I've been practicing the recorder part with just intonation C major
>and G major chords today, and it sounds nice. Later on it has
>minor chords and will need to think about fingering / tuning for those
>too, and though it doesn't wander that far, will
>need adaptive tuning to do those in j.i. for instance, has a
>d minor chord at start of the next section which doesn't
>work in just intonation syntonic scale.
>
>The one I'm practicing is Sonata 1 in C major, Allegretto.
>
>There are several at http://www.prs.net/midi-a-e.html#b
>but couldn't see any of his pieces for flute and piano.
>There's a nice one there by J.C. Bach (on midi flute + harpsichord).

I'll take a look.

>If you do do it, might be nice to also do a file with the flute part
>left out, so one can have a go at playing along with it in adaptive
>j.i.

Understood. Ideally, the flute part would be considered in the
analysis, but would be stripped out at the end.

>Another idea.
>
>You've often explained how the adaptive tuning technique doesn't work
>so well in real time because it is impossible to anticipate a chord
>until all its notes have been played.
>
>Also your adaptive tuning techniques take into account all the notes
>in the whole piece and that extra level obviously isn't going to work
>in real time.
>
>However the pieces you adaptively tune are often ones with scores
>that the performers play from.
>
>I wonder if there is some way you could do it so that one plays
>a piece through with the adaptive tuning program "recording" the
>performance.
>
>Then leave it to work out the adaptive tunign fro it, then
>play it again, and this time it will know all the notes you
>are going to play and so could adaptively tune them correctly.

Yes. One of the things I want to do! The idea came up in the "fantasy
grand" discussion earlier this year.

>Can imagine there'd be a fair nubmer of subleties like recognising
>ones place if the notes of a "simultaneous" chord are played in another
>order from teh one recorded, or if a trill is played with another
>number of notes, or if the performer leaves out a repeat, or adds
>an extra ornament to a part or whatever.

Or if the performer makes a mistake, will the program get completely
lost, messing up the rest of the performance? Doing it right is quite
a challenge, but I agree that it's doable.

>But seems do-able - performer could cooperate with the program and
>if it loses its place it could show a message or something.

Perhaps the performer could define markers in the score, and instruct
the program where to re-synchronize if it gets lost.

>Would be interesting as I expect performers would play to
>heighten the effect of the adaptive tuning and use it in various
>ways.

Yeah, it'd be something! Do you want to tackle the synchronization
functionality, to be bolted together with my stuff?

JdL

>But seems do-able - performer could cooperate with the program and
>if it loses its place it could show a message or something.

>Perhaps the performer could define markers in the >score, and instruct
>the program where to re-synchronize if it gets lost.

>Would be interesting as I expect performers would play >to
>heighten the effect of the adaptive tuning and use it >in various
>ways.

>Yeah, it'd be something! Do you want to tackle the >synchronization
>functionality, to be bolted together with my stuff?

>JdL

Perhaps you could hook up the audio source to some kind of controller which pitch shifts the sound and amplifies it loud enough to drown out the original source (a foot pedal attached to a computer perhaps)
(or maybe muffle it so the audience cant hear it or something)

That way the performer could control the pitch with there foot, or whatever, with out worrying about synchronizing up a program. Guitarists do this sort of thing all the time for special effects.

Andy

--- In tuning@y..., JoJoBuBu@a... wrote:

/tuning/topicId_17672.html#22194

> Perhaps you could hook up the audio source to some kind of
> controller which pitch shifts the sound and amplifies it loud
> enough to drown out the original source (a foot pedal attached
> to a computer perhaps) (or maybe muffle it so the audience cant
> hear it or something)
>
> That way the performer could control the pitch with there foot,
> or whatever, with out worrying about synchronizing up a program.
> Guitarists do this sort of thing all the time for special effects.

Just thought I'd mention that my old buddy who's here at UCSD,
Rand Steiger, has always been interested in composing for mixed
ensembles of live instruments and electronically-recorded sounds,
and has recently been getting more and more interested in
just-intonation.

A couple of years ago Rand wrote a piece for a small wind
ensemble where the computer took the pitches of the bass
clarinet as fundamentals and adjusted in real-time the pitches
of all the other instruments that sounded above that fundamental,
so that they would all be harmonics of it.

And Andy, since you're new to the list, you should definitely
give a listen to John deLaubenfels's incredible adaptive-tuning
rendtions of various MIDI-files provided by others.

And John, please email me at
joemonz@yahoo.com
so I can send you some new MIDI-files.

-monz
http://www.monz.org
"All roads lead to n^0"

In a message dated 5/6/2001 10:26:56 PM Eastern Daylight Time,
joemonz@yahoo.com writes:

> And Andy, since you're new to the list, you should definitely
> give a listen to John deLaubenfels's incredible adaptive-tuning
>

Thanks for the suggestion. Where is it available? I pulled up his name on
google.com but didn't see it.

Andy

--- In tuning@y..., JoJoBuBu@a... wrote:

/tuning/topicId_17672.html#22218

> In a message dated 5/6/2001 10:26:56 PM Eastern Daylight Time,
> joemonz@y... writes:
>
>
> > And Andy, since you're new to the list, you should definitely
> > give a listen to John deLaubenfels's incredible adaptive-tuning
> >
>
> Thanks for the suggestion. Where is it available? I pulled up
> his name on google.com but didn't see it.

Go to
www.adaptune.com
and click on "Studio J".

BTW, Andy's post here came up with my full email address
on it. What gives? I've always seen the domain names
x'd out.

-monz
http://www.monz.org
"All roads lead to n^0"

[Andy wrote:]
>Perhaps you could hook up the audio source to some kind of controller
>which pitch shifts the sound and amplifies it loud enough to drown out
>the original source (a foot pedal attached to a computer perhaps)
>(or maybe muffle it so the audience cant hear it or something)

I'm aware that sound can be pitch-shifted after generation, but my
preference would be to decide the pitch, and realize it, using pitch
bend messages or tuning table sysex, from the synth itself.

Like you, I'm excited about what could be done by the performer in
real-time using foot pedals. At one extreme, the computer could become
a mere slave to the performer's explicit instructions, and make no
tuning decisions itself.

[Monz wrote:]
>>And Andy, since you're new to the list, you should definitely
>>give a listen to John deLaubenfels's incredible adaptive-tuning
>>rendtions of various MIDI-files provided by others.

Thanks for the plug, Monz! ;-> My site is fairly bare right now; I
purged out all the older stuff a while back and haven't added much.
Soon to come, however: a majorly hot Chopin sequence in several hot
tunings...

[Andy:]
>Thanks for the suggestion. Where is it available? I pulled up his name
>on google.com but didn't see it.

I'm in google. Perhaps you misspelled my name? A space between "de"
and "L" could be a killer, for example... They list both my
adaptune.com page and my idcomm.com page.

[Monz:]
>BTW, Andy's post here came up with my full email address
>on it. What gives? I've always seen the domain names
>x'd out.

Yeah, that's strange. Andy, I'm guessing you're sending mail in one
of the more "advanced" forms. Somehow this is defeating the privacy
filter. I'm getting an odd font from your posts as well. Could you
possibly send plain text?

JdL

Hi John,

I'd really like to get involved in some way. Sounds like the kind of thing where
say, user could record to midi, then your program in batch mode could analyse
the midi and make an output file which could be used by another program
to adaptively re-tune the performance.

At first sight seems like it might be quite an elaborate thing to do, but
maybe if we hit on some idea to make it work, could turn out to be easy
after all.

I'm all for leaving an idea for a while and mull over it, and hope for
the "one line" solution. Well, that's surely an exageration here, but maybe
there will be a really neat way to do it. I'll give it some thought.

Practicing is going to be a big challenge I see. What happens if one
wants to try a particular section / phrase several times? One wants to
be able to set a cue point to the start of that section very easily, and
then the adaptive tuning has to key in immediately on the first note played.

One point to bear in mind. If all the right notes are played, but the speed
varies from the original recording, that would be less of a problem
as it wouldn't add any tracks or anything to it, but just retune the notes as they
are played.

Would just need to go:

"
expecting an A at some time in the future as the next note - here it
comes, so it needs to be pitch bent by ....

Now expecting a Bb,...
"

To take account of chords, would need to do something like
"Expecting a C and an E in some order for the next 2 notes"

- maybe a look ahead buffer of maybe a dozen or so notes + their
tunings would be the way to do it, and one would just use the next
one in the list with the right midi note number.

With that sort of approach, and if one doesn't try to adaptively tune
at all if one loses ones place, could be fairly robust and simple, and not
demand much on the play back program.

Ideally one would want to integrate it with a program that could show the
position in the score as one played, as that would make the setting and
placing of cue points much easier and more intuitive I expect.

I'm not sure how that might work - I'd love to write a microtonal
score editor, but that is so much work to contemplate, and at present I'm using
a standard score editor (NWC) with the output retuned using FTS,
which works rather well.

Hope someone gets inspired to write a purpose built score editor some day!

FTS does have a very basic kind of "score" that it shows, but it isn't
that far developed, and I think perhaps not up to this at present.

One way to get it started would be to start with something reasonably
simple that actually worked and was interesting and worthwhile for
players to experiment with, and didn't take much in the way of programming.

I'll keep it in mind.

Robert

Hi John,

> Understood. Ideally, the flute part would be considered in the
> analysis, but would be stripped out at the end.

Yes indeed, and have two versions, one with and one without.

One could then try playing with the flute in unison, and then
on ones own, to get the idea of what it is like to really play in
adaptive j.i.

Robert

--- In tuning@y..., "Robert Walker" <robert_walker@r...> wrote:

/tuning/topicId_17672.html#22257

> I'd really like to get involved in some way. Sounds like the
> kind of thing where say, user could record to midi, then your
> program in batch mode could analyse the midi and make an output
> file which could be used by another program to adaptively
> re-tune the performance.

In fact, Robert and John, I'd like JustMusic to interface
not only with Scala, CSound, standard MIDI sequencers, and
FTS, but also with John's adaptive tuning software. I think
manipulating prime-limits, etc., on a lattice would be a
great way of specifying the JI parameters for a retuning
of a pre-existing MIDI file.

Robert, I definitely like the idea of making JustMusic a
sort of modular interface. Back in the 1980s, when I first
started formulating the ideas for it, I wanted it to be
the all-inclusive music software that I wished I had and
no-one made.

Now, programs like Scala and FTS can do a lot of what I
would have programmed JustMusic to do, so its very sensible
now to think of JustMusic as a nice lattice-oriented GUI
that ties together the computing power of a lot of other
applications.

Robert, sorry if there was any misunderstanding... I didn't
mean to convey the impression that you should or would
"take over" the project (did I use those words?...), simply
that I knew you were very interested, and you seem to have
he skills and enthusiasm that could actually get the darn
thing "up on its feet".

-monz
http://www.monz.org
"All roads lead to n^0"

[Robert Walker wrote:]
>I'd really like to get involved in some way. Sounds like the kind of
>thing where say, user could record to midi, then your program in batch
>mode could analyse the midi and make an output file which could be used
>by another program to adaptively re-tune the performance.

Yep! And/or, I might could make a DLL of my stuff that could bolt
directly onto some other program, or visa versa.

>At first sight seems like it might be quite an elaborate thing to do,
>but maybe if we hit on some idea to make it work, could turn out to be
>easy after all.

I already have a program, JI Relay, that receives MIDI messages,
reassigns channels, inserts tuning bends, and plays in real-time. So
all that's missing is the smarts to synchronize to a sequence which has
already been tuned.

>I'm all for leaving an idea for a while and mull over it, and hope for
>the "one line" solution. Well, that's surely an exageration here, but
>maybe there will be a really neat way to do it. I'll give it some
>thought.

By all means, let it kick around in the ol' brain, and see what pops
out. I really think there might be some elegant solutions to the
challenge which, once a tuned sequence was loaded, would allow the
performer to skip around anywhere in the piece, with the program quickly
figuring out where he is. Well... depending upon the piece: if there
are passages which begin as an exact repeat, then deviate, the program
would be confused till the point of deviation, but it COULD in principle
sense its own confusion and gradually discard the erroneous connections.

JdL

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_17672.html#22214

>
> Just thought I'd mention that my old buddy who's here at UCSD,
> Rand Steiger, has always been interested in composing for mixed
> ensembles of live instruments and electronically-recorded sounds,
> and has recently been getting more and more interested in
> just-intonation.

Hi Joe!

I had no idea that you knew Rand Steiger! Steiger is really an
amazing composer, in my personal opinion one of the best composers
out on the Internet. He's become quite a "known" entity as well,
that's for sure, with many orchestral performances...

Here is his mp3.com link for those interested. I love this stuff...

http://artists.mp3s.com/artists/35/rand_steiger.html

_________ ____ _ _____
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

> Hi Joe!
>
> I had no idea that you knew Rand Steiger!

Just hung out with him a couple of hours ago! (Concert
at UCSD featuring computer music of Jean-Claude Risset,
who's been in residence here for a couple of weeks.)

> Steiger is really an amazing composer, in my personal opinion
> one of the best composers out on the Internet. He's become
> quite a "known" entity as well, that's for sure, with many
> orchestral performances...
>
> Here is his mp3.com link for those interested. I love this stuff...
>
> http://artists.mp3s.com/artists/35/rand_steiger.html

One of the reasons I cultivated my friendship with Rand so
strongly is because I recognized, way back then when I was
just a young buck in college, that he was indeed an extremely
talented composer. His work made a very strong impression
on me, at a time when I was particularly impressionable.

His graduation piece for Manhattan School of Music, the
marimba concerto _Dialogues II_, really knocked my socks off...
and he dismisses it as "juvenilia" now. My roomate at the
time, Dan Palkowski, was hired by Rand to copy the parts for
the performance, and I ended up with the copy of the manuscript
score, which I still have and treasure. We had an unusually
cold winter here in San Diego this year, and when I told Rand
a couple of months ago that I had the score, he suggested I
"hold on to it for use as kindling on one of those cold nights"...
his humility is not only notable, but funny too.

Rand was "volunteered" by Elias Tanenbaum to set up the computer
interface for the Electronic Music Studio at Manhattan, back
in 1980. Everything had been analog up to that time. The
computer was the awesome (I'm being facetious here) Commodore
Pet. Rand wrote the interface in Machine Language, which means
pages and pages of 5-digit numbers. Dan and I would hang out
in the studio with Rand until 3:00 in the morning, helping
him out by reading the numbers to him as he typed them in.
That's mainly how we became friends. He was always impressed
by my compositions too (particularly _Romeo's Death_), so I
guess we're a "mutual admiration society".

We unfortunately only knew each other for one year, because
Rand was a senior the year that I was a freshman. He came
out to California right after Manhattan, studied at Cal Arts,
and became closely associated with Morton Subotnick. He's been
teaching composition on the music faculty at UCSD for 14 years,
and held the rotating music department chair for a few years a
little while back. (Microtonalist and Ben Johnston student
John Fonville is the current chair.) But I see him a lot these
days, so we're catching up on lost time pretty well...

BTW, I had another close friend at Manhattan who turned out
to be a very successful and talented composer: Aaron Jay Kernis.
He graduated the year after Rand, so I knew him for one year
longer, and we were quite good friends. Unfortunately, we
haven't seen each other since.

Dan Palkowski is *also* a very talented composer,
but hasn't yet found quite as much fame as those two.
Dan did his graduate work at Columbia, and is still in
New York, teaching at Tisch School of the Arts at NYU.
I used to have a link to his webpage (with some terrific
audio samples), but it seems to be dead now. He's also
a fantastic artist (painter).

Those really were some great years at Manhattan.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_17672.html#22303

> ... Steiger is really an amazing composer, in my personal
> opinion one of the best composers out on the Internet.
> He's become quite a "known" entity as well, that's for
> sure, with many orchestral performances...
>
> Here is his mp3.com link for those interested.
> I love this stuff...
>
> http://artists.mp3s.com/artists/35/rand_steiger.html

Just thought I'd point out a minor thing that makes this
a little more "on-topic": The photo of Rand was taken
by Betty Freeman, who had close associations with Partch
and took most of the published photos of Partch that I've seen.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_17672.html#22317

> Rand was "volunteered" by Elias Tanenbaum to set up the computer
> interface for the Electronic Music Studio at Manhattan, back
> in 1980. Everything had been analog up to that time. The
> computer was the awesome (I'm being facetious here) Commodore
> Pet. Rand wrote the interface in Machine Language, which means
> pages and pages of 5-digit numbers. Dan and I would hang out
> in the studio with Rand until 3:00 in the morning, helping
> him out by reading the numbers to him as he typed them in.
> That's mainly how we became friends.

Rand has some pictures on his site relating to this story:

Rand in the studio:
http://www.earunit.org/rands/images/arp.html

Tanenbaum in California with Rand, and in the studio:
http://www.earunit.org/rands/images/eli.html

Rand, David Lang, and Aarron Jay Kernis:
http://www.earunit.org/rands/images/lang.html

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_17672.html#22317

> [Rand Steiger]
> We unfortunately only knew each other for one year, because
> Rand was a senior the year that I was a freshman. He came
> out to California right after Manhattan, studied at Cal Arts,
> and became closely associated with Morton Subotnick. He's been
> teaching composition on the music faculty at UCSD for 14 years,
> and held the rotating music department chair for a few years a
> little while back. (Microtonalist and Ben Johnston student
> John Fonville is the current chair.) But I see him a lot these
> days, so we're catching up on lost time pretty well...
>

Speaking of which, my 1991 article by John Fonville in Perspectives
of New Music arrived. I will be anxious to probe deeper into the Ben
Johnston system... and it seems this article is about the only place
to do so at present (to my knowledge!)

Of course, Johnson's system, if I understand it correctly, is VERY
predicated on a C-major just tonality and, additionally, BEGINS the
alteration process from what is ALREADY a two-dimensional rather than
a one-dimensional lattice... adding to the "complexity."

However I will study the Johnston system with great interest!

By the way, in deference to Kyle Gann and other Johnston
supporters... I haven't really detected any kind of anti-Johnston
bias on this list!

In fact, everybody (well at least *me*)has been "raving" about the
wonderful MIDI realizations of Ben Johnston's music that Joe Monzo
has somehow been able to do...

The questions were more just practical ones of notation and debating
the merits of the Johnston just notation system against other
possible ones (HEWM, AKA "Monzowolfellholtz"), nothing personal to do
with either Johnston or his impressive music!

__________ _______ _____
Joseph Pehrson

In a message dated 5/9/2001 1:15:48 PM Eastern Daylight Time,
jpehrson@rcn.com writes:

> Of course, Johnson's system, if I understand it correctly, is VERY
> predicated on a C-major just tonality and, additionally, BEGINS the
> alteration process from what is ALREADY a two-dimensional rather than
> a one-dimensional lattice...

Hi. I am working with Ben on his notation, among other things, as we speak
(write? :). We were discussing this yesterday. To the best of my
understanding if you base the lattice off a one dimensional system you have
to notate whether you want a just third or not(meaning 5/4 against 1/1),
adding to the complexity of the notated score(correct me if this is not quite
accurate) In other words C = 1/1, 3/2 = G, and 5/4 = E -. The minus makes
this more complicated on the score then with Ben's notation in the same
situation.

On the other hand, yes, a two dimensional lattice is more complex than a one
dimensional, but the same chord is less complex notationally. C = 1/1, G =
3/2, E = 5/4. No minus is required. I'm sure to most people on this list this
is not new stuff, but I'm just attempting to show a brief comparison. I see
this as a give or take. It would seem good to understand both points of view,
but the choice of what notation to use doesn't seem as important as just
working on the sound of the intervals or the ear training aspect of
microtonality in general, no matter what system you are working in. For
another point of view, with a similar idea, here is an excerpt from an
article by Adam Silverman entitled "Notation Styles for Microtonal Just
Intonation." (page 19) (sorry if you all have already read this - and alot of
this info really comes from this source)

The primary advantage of of Wolf's notation is that it provides a consistency
of accidental in chromatic music that wanders freely from one limit to
another. Johnston's advantage is that it provides fewer diacritical marks in
music that remains anchored to the center of the lattice.

Anyway both systems are good but for slightly different situations.

>Speaking of which, my 1991 article by John Fonville in Perspectives
>of New Music arrived.  I will be anxious to probe deeper into the Ben
>Johnston system... and it seems this article is about the only place
>to do so at present (to my knowledge!)\

Just so you know there are also a few other articles,whatnot, that deal with
Ben's notation. This Silverman article talks about it some, and Ben has some
articles he wrote that discuss either the notation or other general JI topics
which might be helpful if your trying to get to know his notation. I think
some of this stuff is in perspectives in the 60's. There is also an article
about his fourth quartet(not written by him), 70's?, that MIGHT discuss some
of it. (I haven't read that one yet so no promises) Lets see, what else.
There is a masters thesis written by one of his students which discusses his
notation(if you want to try and read it I will se if I can find the name for
you - I've read it but I forget who wrote it!). Also there is a copy of
"Daphne of the Dunes" floating around which has partch's notation translated
into Bens. This might be helpful if you know Partch's notation,at least his
notation at that time, well but not Ben's. This was done by Glenn Hackbarth.
Or there are scores available and they might be helpful in and of themselves.
I will ask Ben on friday to see if I forgot any others that might be useful.
Also if you are want it I could throw a little list together for you?

Cheers hopefully this helps some,

Andy Stefik

Joseph!
If you will notice that the notation that Erv Wilson has proposed in Xenharmonikon and
elsewhere can have the same bias as Johnson. The difference is that Erv notion implies that the
scale being used in a Constant Structure. From that point, the notation is based on the melodic
consistency (or linear series) of the tuning as opposed to the harmonic, not that this necessarily
an opposition. The further advantage of his notation is that the logic holds true from tuning to
tuning and is consistent with a Bosanquet keyboard. Not perfect, if such a thing was possible, it
still is the only keyboard construction that offers any promise for moving forward. Of course we
can all sit around and reinvent the wheel as many times as possible even though it was sitting in
front of us 25 years ago. Also a a learning tool it far surpasses in simplicity the use of
matrixes to see the unison vectors in any tuning. One has only to learn the basic template in a
tuning and visually pick them out. Also when taking a given structure (such as a diamond) and
wanting to fill it out until it forms a constant structure it is easy and simple to see what tones
can be added. Matrixes are not simpler of doing this at all. One picture is worth a 100 words or
in this case, numbers.

jpehrson@rcn.com wrote:

> Of course, Johnson's system, if I understand it correctly, is VERY
> predicated on a C-major just tonality and, additionally, BEGINS the
> alteration process from what is ALREADY a two-dimensional rather than
> a one-dimensional lattice... adding to the "complexity."

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., JoJoBuBu@a... wrote:

/tuning/topicId_17672.html#22332

> Hi. I am working with Ben on his notation, among other things,
> as we speak (write? :). We were discussing this yesterday

Hi Andy - good to see you on the Tuning List! Ben had told
me about you a while back, and I was hoping to eventually get
in touch with you. Ben and I have been on quite friendly terms
since we met in 1996... I just hope that my tirade against
his notation here on the list hasn't messed that up...

> On the other hand, yes, a two dimensional lattice is more
> complex than a one dimensional, but the same chord is less
> complex notationally. C = 1/1, G = 3/2, E = 5/4. No minus
> is required. I'm sure to most people on this list this
> is not new stuff, but I'm just attempting to show a brief
> comparison. I see this as a give or take. It would seem good
> to understand both points of view, ...
>
> <snip>
>
> ... The primary advantage of of Wolf's notation is that it provides
> a consistency of accidental in chromatic music that wanders
> freely from one limit to another. Johnston's advantage is that
> it provides fewer diacritical marks in music that remains
> anchored to the center of the lattice.
>
> Anyway both systems are good but for slightly different
> situations.

Exactly the point I've made. Since my main concern in tuning
theory is to try to relate *all* quantizations of the pitch
continuum together on a lattice, the HEWM notation (i.e.,
my version of Wolf's notation) works much better for me.

But I've pointed out in my posts to Joe Pehrson that Ben's
notation works just fine for a composer who deal extensively
in 5-limit JI. (pun intended) Kyle Gann, Glenn Hackbarth,
John Fonville, and David Doty are just four of the JI luminaries
who like it. (pun intended again)

> Just so you know there are also a few other articles,whatnot,
> that deal with Ben's notation.

I've already given all the complete citations in posts here,
many of them just a few weeks ago. Actually there are a
few others too... stuff of Ben's that appeared in ASUC, etc.
I'll get around to making a webpage bibliography of stuff
on Ben.

> Also there is a copy of "Daphne of the Dunes" floating around
> which has partch's notation translated into Bens. This might
> be helpful if you know Partch's notation,at least his notation
> at that time, well but not Ben's. This was done by Glenn
> Hackbarth.

Wow, the synchronicity of this is just too weird! (and OK,
I'll stop with the "just" puns, because there would be too many)

You're talking about Glenn Hackbarth's 1982 dissertation on
_Daphne of the Dunes_. I just it for the first time at the
UCSD library a couple of weeks ago, while researching Schoenberg.
I had never known about it before.

Then just yesterday I was talking about the _Dapne_ score
with Jon Szanto, and he mentioned Hackbarth's dissertation!
I just got my copy of it this evening - and now on checking
my emails I see you bring it up!! Bizarre...

So, OK, now I mentioned that I have it before I wanted to,
so I might as well add that I plan to do a book or webpage
about _Daphne_, scored in HEWM notation, with Hackbarth's
harmonic analysis shown on lattices. Someone prod me about
this if too much time goes by and it doesn't appear...

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_17672.html#22303

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_17672.html#22214
>
> >
> > Just thought I'd mention that my old buddy who's here at UCSD,
> > Rand Steiger, has always been interested in composing for mixed
> > ensembles of live instruments and electronically-recorded sounds,
> > and has recently been getting more and more interested in
> > just-intonation.

> Here's the mp3.com ... <snip>

Since I'm saying all this stuff about Rand here on the
Tuning List, thought I'd point to a little of his microtonal
work. Check out the freaky sounds coming out of the trombones
and oboes starting about 0:47 into the "Odontogriphus" movement
of _The Burgess Shale_:
http://artists.mp3s.com/artist_song/159/159876.html

This whole piece is awesome.

I suppose having George Lewis as a cohort at UCSD gives him
at least a little inspiration for these bizarre trombone parts.
Lewis is really incredible - I've never heard such things from
*any* kind of horn! His discography of the 90 albums he's
recorded is here:
http://orpheus.ucsd.edu/dept.music/musicdept/lewis_disco.html

You La Monte Young fans who don't already know might be interested
to find out that Charles Curtis is also now on the faculty
at UCSD.

This is really a good sign: at UCSD Fonville is the music
department chair, and Curtis, Steiger, and Chinary Ung (all
microtonalists to varying degrees) are currently on the faculty,
and Ferneyhough was here until recently. And in Montréal
the 96-tET piano has been installed at the university, and
Kyle teaches tuning history at Bard. Seems like tuning is
finally creeping into the curriculum. And it's about time.

-monz
http://www.monz.org
"All roads lead to n^0"

Kraig wrote:

> If you will notice that the notation that Erv Wilson has
> proposed in Xenharmonikon and
> elsewhere can have the same bias as Johnson.

Not in "On Linear Notations..." he doesn't. He has the same bias as
Monzowolfellholtz.

> The difference is that Erv
> notion implies that the
> scale being used in a Constant Structure. From that point, the notation
> is based on the melodic
> consistency (or linear series) of the tuning as opposed to the
> harmonic, not that this necessarily
> an opposition.

I don't think they are. What do you intend by drawing the distinction?
The Bosanquet layout ensures the two are not in opposition.

> The further advantage of his notation is that the logic
> holds true from tuning to
> tuning and is consistent with a Bosanquet keyboard.

Of course it's consistent with a Bosanquet keyboard, it's designed for a
Bosanquet keyboard. It certainly is not consistent from tuning to tuning.
In positive notation, a 4:5:6 triad is C E- G. In negative notation it's
C E G. That's an inconsistency and it's a problem.

> Not perfect, if
> such a thing was possible, it
> still is the only keyboard construction that offers any promise for
> moving forward.

What do you mean the only construction. You said before: "One of the
things that really got Erv excited about Hanson' s keyboard is that it
handles 72 where as the Bosanquet does not."

So Bosanquet can't handle 72. Whereas a keyboard constructed around a
10+1 "Miracle" scale could, along with 31 and 41. Why does that not offer
any promise for moving forward?

If you haven't been following the Miracle discussion, I urge you to look
back though it. If there's something you don't understand, please ask.
The theorists have done their work, now it's time for composers and
instrument builders to move the revolution forward.

> Of course we
> can all sit around and reinvent the wheel as many times as possible
> even though it was sitting in
> front of us 25 years ago.

Where did this come from?

> Also a a learning tool it far surpasses in
> simplicity the use of
> matrixes to see the unison vectors in any tuning.

I assume that's a swipe at me, as I'm the one who uses matrixes. So how
does this negative notation help me to see the unison vector (4 -1)h? It
rather looks designed to stop me seeing it.

> One has only to learn
> the basic template in a
> tuning and visually pick them out.

Yes, it's a good idea, no question about that.

> Also when taking a given structure
> (such as a diamond) and
> wanting to fill it out until it forms a constant structure it is easy
> and simple to see what tones
> can be added.

Yes, because that's what generalised keyboards show. If you want to fill
in the harmony, a lattice would be simpler. You don't have to throw away
one because you use the other.

> Matrixes are not simpler of doing this at all.

Of course they aren't. What fool would suggest otherwise?

> One
> picture is worth a 100 words or
> in this case, numbers.

Look, mathematicians tend to fall into one of two groups. Those who think
in terms of pictures, and those who think in numbers or symbols. Erv
looks like he's in the former group, and so are you. I'm in the latter.
That doesn't stop me drawing diagrams, or Erv using numbers. We can have
a discussion without either of us having to be wrong.

Graham

[Robert Walker wrote:]
>I wonder if you've tried adaptive tuning for C.P.E.Bach?
>With all the pure triads, and his transparent and very
>mellow "laid back" style, I think it would sound nice adaptively tuned
>to 5-limit.

>I have a flute + piano sonata that I try out on the recorder,
>and I've been practicing the recorder part with just intonation C major
>and G major chords today, and it sounds nice. Later on it has
>minor chords and will need to think about fingering / tuning for those
>too, and though it doesn't wander that far, will
>need adaptive tuning to do those in j.i. for instance, has a
>d minor chord at start of the next section which doesn't
>work in just intonation syntonic scale.
>
>The one I'm practicing is Sonata 1 in C major, Allegretto.
>
>There are several at http://www.prs.net/midi-a-e.html#b
>but couldn't see any of his pieces for flute and piano.
>There's a nice one there by J.C. Bach (on midi flute + harpsichord).

I've downloaded the tuned all the C.P.E. Bach I could find. All quite
pleasant stuff, nothing with flute or recorder and piano. I'm not quite
clear which J.C. Bach piece you mean, but I downloaded and will tune
a bunch of them as well.

>If you do do it, might be nice to also do a file with the flute part
>left out, so one can have a go at playing along with it in adaptive
>j.i.

I've made that enhancement to my retuning program (still largely
untested for BUGS). I decided to make the stripping out of voices
(=programs, =patches) a separate run from the tuning itself. That way,
there are guaranteed to be both a sequence with all voices and a
separate one with one or more voices removed, but the rest in the same
tuning as before.

Would you like to pick a sequence and sample the output? Wish we had
the particular C.P.E. Bach piece you've been practicing!

JdL

--- In tuning@y..., JoJoBuBu@a... wrote:

/tuning/topicId_17672.html#22332

> Hi. I am working with Ben on his notation, among other things, as
we speak (write? :). We were discussing this yesterday. To the best
of my understanding if you base the lattice off a one dimensional
system you have to notate whether you want a just third or not
(meaning 5/4 against 1/1), adding to the complexity of the notated
score(correct me if this is not quite accurate) In other words C =
1/1, 3/2 = G, and 5/4 = E -. The minus makes this more complicated
on the score then with Ben's notation in the same situation.
>
> On the other hand, yes, a two dimensional lattice is more complex
than a one dimensional, but the same chord is less complex
notationally. C = 1/1, G = 3/2, E = 5/4. No minus is required. I'm
sure to most people on this list this is not new stuff, but I'm just
attempting to show a brief comparison.

Hello JoJoBuBu!

This is just "Jo," so you're a "Jo" and two boo boos ahead of me!

Well, what you say makes sense, but, on the other hand, if I am
understanding things correctly, a simple tried even on D minor has
a "D" with a minus sign, so things get pretty complex fast!

That is, unless one really is centering around C major continuously.

I have some reservations about the primacy of the key of C major in
ANY intonational inflection... just or otherwise.

Why center on that? OK, there is a certain historical precedent, but
why not go back "all the way" to good ol' Pythagoras (who possibly
didn't exist) and take it from there...?

>I see this as a give or take. It would seem good to understand both
points of view,

I think there is no question but that "Monzowolfellholtz," partially
invented by our own Monz, is decidedly superior as a notation.

> but the choice of what notation to use doesn't seem as important as
just working on the sound of the intervals or the ear training aspect
of microtonality in general, no matter what system you are working
in.

Well, this is a very good point, which was emphasized (gently... not
quite :) ) by Paul Erlich and David Doty himself (a user, of course,
of the system...)

However, MY point in some of my prior posts is that NOTATION REALLY
DOES make a difference, and that it even LEADS people to write in a
certain way.

I could see a person using Johnston's notation to want to "gravitate"
toward the key of C Major, for instance, just because it was a
notational breeze...

For
> another point of view, with a similar idea, here is an excerpt from
an article by Adam Silverman entitled "Notation Styles for Microtonal
Just Intonation." (page 19) (sorry if you all have already read this -
and alot of this info really comes from this source)

Nope. And, in fact Monz asserts he gave all these citations, but I
DO NOT believe he gave any Silverman citation...

Silverman, by the way, I believe has now relenquished microtonality,
so I would be careful about the "ease of use" of his notational
systems.... NOTA BENE.

>
> The primary advantage of of Wolf's notation is that it provides a
consistency of accidental in chromatic music that wanders freely from
one limit to another.

d'accord!

Johnston's advantage is that it provides fewer diacritical marks in
> music that remains anchored to the center of the lattice.
>

If one is to confirm that C MAJOR is the center. I am not
convinced... In fact, to me it is a rather "sickening" idea at the
moment...

> Anyway both systems are good but for slightly different situations.
>

I believe it can be definitively proven that Monzowolfellholtz is a
superior notational system, in the overall...

It's already *BEEN* proven on this Tuning List... a search will find
the path. This is how advances are made!

>Also there is a copy of "Daphne of the Dunes" floating around which
has partch's notation translated into Bens. This might be helpful if
you know Partch's notation,at least his notation at that time, well
but not Ben's. This was done by Glenn Hackbarth.

Glenn Hackbarth is no hack. He is a truly incredible composer...
I've met him and I would love to present his music soon. He is
a "hidden treasure..." He presented one of the finest electronic and
acoustic pieces here in New York recently that I have ever heard...

> I will ask Ben on friday to see if I forgot any others that might
be useful. Also if you are want it I could throw a little list
together for you?
>
> Cheers hopefully this helps some,
>
> Andy Stefik

It helps a LOT, and, indeed, if you can cull such a list I would
greatly appreciate it. I'm hoping to get quite a bit out of the
Fonville article, as well, especially as this topic has been
discussed in detail on ye Tuning List...

_______ ______ _ ____
Joseph Pehrson

Hi John,

Hadn't realised you could retune files so easily.

I'd love to hear all the cpe Bach you've retuned if it isn't too large a file
as I like his style a lot, and I think adaptive tuning will bring it out.
Would be interesting to see if it does.

I'll keep an eye out and see if I can find the midi file for c.p.e.
Bach flute sonatas anywhere. They are lovely pieces, to my taste
anyway,... So relaxed and gentle. Some time since I heard the
others, just really know the one I have and practice, but
I've heard the others in the past in a very beautiful
recording, and liked them as well. I remember it was played on
baroque flute. Of course there is no baroque flute
standard midi patch, but people do re-do midi files as mp3s or
whatever using appropriate patches.

I've greatly enjoyed the chopin you posted recently, and I thnk the
adapitive tuning bring out his singing melodies wonderfully, and make
the counterpoint clearer too. I htink he is a natural to adaptively
tune to j.i. because of his wonderful singing melodies, whatever
one might say about authenticity.

Pehaps the counterpoint is brought out most clearly in the
7-limit one. I certainly like that one, so join the club of those
who you say must have something seriously wrong with them.

I don't hear this thing about equal semitones and find the chromatic
scales very exciting. Perhaps I do notice a kind of evenness about
the chromatic passages in 12-tet, but not so sure, more notice
the exciting variety of colour in the adaptively tuned ones.

There is a kind of "mistyness" about the 12-tet discords that is rather
suited to Chopin however.

(See for example the discord on the repeated note just after the end
of the lovely slow melody that ends the piece, just before the
closing bars, which changes to a much crisper chord and the
whole resolution is much stronger in the adaptively tuned versions.
I like both, but actually, prefer the adaptively tuned resolutions
really).

I wonder what tuning he actually used for his pianos?

I experimented playing as a cycle with the 12-tet version first.
It was a nice way to hear them.

The original un-retuned version has no patches in it - playing
it first, got some interesting renderings of Chopin on recorder
:-) then on a second try after playing a bit of one of the others,
recorder + piano (recorder playing the sustained base notes
of course not fading away at all, and arpeggiated accompaniment)!

Of course, that's not going to be anything to do with
your program.

Now if only one could adaptively tune a real acoustic piano
(as in the fantasy grand)!

I've also been gradually mulling over the cue points idea for
adaptive tuning, but not getting very far with it. It would be
easy to set them if the notes for chords were always played
in the same order I expect, - one would just need to go through
the entire midi file and make a search tree from it, each time
indexing a note by the following sequence of notes. So when a
particular sequence of notes is played, one uses that to key into
the search tree, and go instantly to right part of the file.

(
search tree entry would be:
key = note sequence sufficiently long to uniquely identify the cue point
+ data = pointer to relevant place in the midi file
)

Then idea would be, by default starts at beginning of piece.

If you stop and re-start, moves to whatever point you re-started
at. First time it does this you would expect some sliding of pitch.
but then having cued it in to where you want to start from, it will
then keep starting from that point, until you move to another practice
cue point, and so on.

Seems quite workable and wouldn't need one to use a score editor
to set the cue points. The search tree could be reasonably fast
and not too large memory wise, except possibly for large
repeated secitons, which might be a problem.

But, how will one ever deal with chords that could be started
with the notes in any order (at level of milliseconds).

I think could be hard to do.

If one could recognise all the chords, then one could order
the notes of a chord,say, from lowest to highest, and ignore
the time order for those, and then it would work okay I
imagine.

Anyway, will continue to keep it in mind.

Robert

In a message dated 5/11/2001 10:55:50 PM Eastern Daylight Time,
jpehrson@rcn.com writes:

>

LOL. I've had this silly little name for a while. Its definately silly, but
it keeps me entertained :)

>Why center on that?  OK, there is a certain historical precedent, but
>why not go back "all the way" to good ol' Pythagoras (who possibly
>didn't exist) and take it from there...?

Well if you are going to center the lattice you have to center it on
something. C is as good as any. C major is a simpler key to base it on as
opposed to B triple sharp major. It is a better choice than any other key
since it has no sharps or flats. On the other hand if you really want to base
a lattice off B triple sharp major,or any other key, thats ok too. if you
want to base off pythagoras I wont complain.

One important thing to remember with Bens actual music itself is that he
often wants a 5/4.(not always of course but at least this would be fair to
say for some of the string quartets) In other words he had in mind the very
music he was intending to write. This doesn't mean his notation is better it
just means different notations cane have different purposes. If you look at
his string quartet scores in depth its pretty clear why he did it the way he
did it, at least from my point of view. If you look at the ninth or tenth
this should be very clear. Like I said though I'm not saying its a better OR
worse on the whole in ALL situations, cause thats just not an issue I'm
concerned with, if its even possible for a notation to have that cabability
(meaning being better in all situations).

>I think there is no question but that "Monzowolfellholtz," partially
>invented by our own Monz, is decidedly superior as a notation.

>However, MY point in some of my prior posts is that NOTATION REALLY
>DOES make a difference, and that it even LEADS people to write in a
>certain way.

>I could see a person using Johnston's notation to want to "gravitate"
>toward the key of C Major, for instance, just because it was a
>notational breeze...

Well I see your point for sure. Notation does make a difference thats a
reasonable statement. On the other hand Look at Toby Twinings music. He uses
JI in an EXTREMELY complicated way, with Bens notation, and by no means
whatsoever tends to gravitate towards C major. Have a look if you can get a
hold of a score and you will, hopefully see what I mean. Sure notation is
important but to say one notation is superior in this particular case seems
more an academic argument then a viable advancement.

> another point of view, with a similar idea, here is an excerpt from
>an article by Adam Silverman entitled "Notation Styles for Microtonal
>Just Intonation." (page 19) (sorry if you all have already read this -
>and alot of this info really comes from this source)

>Nope.  And, in fact Monz asserts he gave all these citations, but I
>DO NOT believe he gave any Silverman citation...

I am actually not sure if the article I mentioned is published because Ben
just had it lying around the house. Its a pretty good article if you can find
it check it out. (probably available through silverman, although I dont know
him personally)

>Silverman, by the way, I believe has now relenquished microtonality,
>so I would be careful about the "ease of use" of his notational
>systems.... NOTA BENE.

I didn't mean silverman had a notational system, if thats what you thought I
meant(did I understand what you just said correctly?). His article is an
exploration of different notation systems including Bens, wolfmonz, Lou
Harrison, and some others.

>If one is to confirm that C MAJOR is the center.  I am not
>convinced... In fact, to me it is a rather "sickening" idea at the
>moment...

LOL. Well no reason to be sickened or convinced I am trying to do neither
(convince you of anything or make you puke). I am on the other hand just
TRYING to objectively discuss the two concepts as objectively as I can .

> Anyway both systems are good but for slightly different situations.
>

>I believe it can be definitively proven that Monzowolfellholtz is a
>superior notational system, in the overall...

>It's already *BEEN* proven on this Tuning List... a search will find
>the path.  This is how advances are made!

Soon I will prove once and for all that honey roasted chicken tastes better
than garlic chicken.

I really dont think it matters.

Some people like one and some the other. However I will OF COURSE check out
the old posts to see how this was proven. Do you have any suggestions as a
good post to look at that would clearly explain the methodology involved for
proving that one notation is superior than the other? How was this tested?
Was there spot polls of giving the different notations to performers to see
how they handled it or something of that nature? Did people add up all the
marks on different scores and come up with some statistics suggesting the
simplicity of one notation over the other in certain circumstances? In what
cirumstances? Those types of studies could be very interseting and convincing
if the methodology is reasonable. Hopefully thats the kind of thing you are
referring too.

Or on the other hand do you mean that subjectively people on the list seem to
like one system over the other(which is not proof)?

Ben is a close friend of mine but I am by no means saying his notation is
superior or inferior to other notations. You said

(this was in reference to me saying I just focus on ear training instead of
the superiority of a notation )

>Well, this is a very good point, which was emphasized (gently... not
>quite :) ) by Paul Erlich and David Doty himself (a user, of course,
>of the system...).

Well if thats what they emphasized, I just joined the list and have missed
those posts, but if what you said accurately portrays their point of view
then I'd agree with them. I will search those out...

I was attempting to objectively enter a discussion in which I missed the
first
835658639986982364982364028346203462034720348760283469283476293846239846239846

293846 emails. (hehe) Sorry if I am reinventing the wheel.

>It helps a LOT, and, indeed, if you can cull such a list I would
>greatly appreciate it.  I'm hoping to get quite a bit out of the
>Fonville article, as well, especially as this topic has been
>discussed in detail on ye Tuning List...

Sure no problem. I will have to search out the fonville as well as I havent
read it. Hopefully I wont just be duplicating what monz has done with my
little list, but I'll see what I can find. I know Ben Had contact with Monz
and so he might have all the articles Ben knows about, except for perhaps the
silverman which I mentioned but I will look. I had forgotten about about that
when I mentioned it, but I'll look and send something off as soon as possible.

Thanks for the very interesting conversation!!!!!!!!

ANdy

--- In tuning@y..., JoJoBuBu@a... wrote:
> In a message dated 5/11/2001 10:55:50 PM Eastern Daylight Time,
> jpehrson@r... writes:
>
>
> >
>
> LOL. I've had this silly little name for a while. Its definately
silly, but
> it keeps me entertained :)
>
> >Why center on that?  OK, there is a certain historical precedent,
but
> >why not go back "all the way" to good ol' Pythagoras (who possibly
> >didn't exist) and take it from there...?
>
> Well if you are going to center the lattice you have to center it
on
> something. C is as good as any. C major is a simpler key to base it
on as
> opposed to B triple sharp major.

HEWM notation is also centered on C major.

> It is a better choice than any other key
> since it has no sharps or flats.

How about A minor? Would anyone claim that D-A is dissonant in A
minor? Even Bruckner?
>
> One important thing to remember with Bens actual music itself is
that he
> often wants a 5/4.(not always of course but at least this would be
fair to
> say for some of the string quartets) In other words he had in mind
the very
> music he was intending to write. This doesn't mean his notation is
better it
> just means different notations cane have different purposes.

HEWM is great for seeing where the 5/4s are. They always look the
same on the staff -- an extra + on the lower note or an extra - on
the higher note. In Johnston's notation, the pattern of +s and -s in
a 5:4 will depend which notes are involved.

> If you look at
> his string quartet scores in depth its pretty clear why he did it
the way he
> did it, at least from my point of view.

I've looked at the fourth and every measure involved minuted of head-
scratching, and muttering, "oh, why couldn't he have notated this
like Helmholtz-Ellis, Barbour, and Blackwood would"? Then I would
have known _immediately_ what the chords were, and what the melodic
steps were.

On the other hand Monz claims that Johnston prefers to modulate by
5:4s . . . this would involve fewer accidentals in his notation . . .
but does he compose that way _because_ of his notation?

In a message dated 5/12/2001 3:13:42 AM Eastern Daylight Time,
paul@stretch-music.com writes:

> HEWM is great for seeing where the 5/4s are. They always look the
> same on the staff -- an extra + on the lower note or an extra - on
> the higher note. In Johnston's notation, the pattern of +s and -s in
>

Thats only true between a D and an F# for a 5/4. D would be D and F# would be
F#+. Furthermore this is true for any kind of D. So if you have D# And Fx it
would actually be D# and Fx+ if you are denoting a 5/4 between the two
intervals.

So the syntonic comma difference occurs in any kind of D and any kind of F.
This is not difficult to remember when you are referring to a 5/4.
(see the lattice below)

If adding a note above any kind of D on the spine of fifths, or a note to the
right, but not the left, of any kind of D on the spine of thirds, add a
comma.

If adding a note above any kind of B on the spine of fifths add a comma. If
adding a note to the spine of thirds in either direction do not add a comma.

This applies to the following lattice (hopefully this picture comes out)

[Unable to display image]

You have to show the difference of syntonic comma somewhere. Think about it
from this point of view for a moment. On a standard tempered piano the notes
B to F require a Sharp on the F or a flat on the B to make it a perfect fith.
With Bens notation between D and F# requires a comma to notate a major
third(5/4), between D and A+ a comma is required to notate a perfect fifth,
and between B and F#+ a comma is required.

And thats all that needs to be remembered for 5 limit JI. This is not
complicated!!!

In equal temperament between D and F requires a sharp on the F or flat on the
D. Band F requires the same for a perfect fifth. Bens rules are really not
complicated at all.

>I've looked at the fourth and every measure involved minuted of head-
>scratching, and muttering, "oh, why couldn't he have notated this
>like Helmholtz-Ellis, Barbour, and Blackwood would"? Then I would
>have known _immediately_ what the chords were, and what the melodic
>steps were.

I would guess you werent familiar with Bens notation at the time and were
familiar with the other. I have no trouble at all understanding the chords in
the fourth quartet. If you understand bens notation its quite easy to put any
of the notes into its ratio equivilant or to understand it harmonically.

> It is a better choice than any other key
> since it has no sharps or flats.

>How about A minor? Would anyone claim that D-A is dissonant in A
>minor? Even Bruckner?

Ok you have missed the point entirely. For starters the 1/1 is on C, neither
major nor minor. The center is only one note not a collection of notes like
major or minor... If in your hypothetical situation, and keeping in the vein
of Ben's notation, the lattice was instead based on A then the notes Ben
would choose for the comma difference would be B, D#+ and F#+. If you dont
understand look at the above lattice and just put A in the middle and draw it
again from there with the commas in the same spot. Now heres why you have
missed the point and this comes directly from Bens mouth. The choice to have
the syntonic comma difference between D and A+ IS ARBITRARY. Other notes
could have been chosen for sure, but you have to notate the syntonic comma
difference SOMEWHERE in the lattice and therefore he chose D to A+. D in this
case being (3/2)2 and A+ being (3/2)3. To say that D and A are dissonant is
to clearly show a misunderstanding of the notation. The point is not that D
to A is dissonant but that between D and A is where Ben arbitrarily put the
syntonic comma difference. The comma has to go somewhere...

His point is not that the notes D and A are mystically dissonant, but instead
that thats where he chose to show the difference of syntonic comma. A+ in his
notation is a 3/2 above D.

Hopefully this clears up a misconception or two.

Cheers
Andy

Thanks Andy. I agree with almost everything you say, and I'm sure Ben's notation has become
very logical for many of its users, but HEWM is very logical for a lot of JI thinkers . . . again,
notation ultimately shouldn't matter.

But the rules for Ben's notation get more and more complicated the more primes you add in. For
example, G-F is a 9:16, while C-Bb is a 9:5 . . . and D wasn't involved in either of those!

--- In tuning@y..., JoJoBuBu@a... wrote:

> Ok you have missed the point entirely. For starters the 1/1 is on C, neither
> major nor minor. The center is only one note not a collection of notes like
> major or minor...

If the note C is in the center _note_, then why is two steps to the right G, while two steps to the
left is Bb- (with a minus sign)? Maybe the C note is not really in the center after all.

> Now heres why you have
> missed the point and this comes directly from Bens mouth. The choice to have
> the syntonic comma difference between D and A+ IS ARBITRARY. Other notes
> could have been chosen for sure, but you have to notate the syntonic comma
> difference SOMEWHERE in the lattice and therefore he chose D to A+. D in this
> case being (3/2)2 and A+ being (3/2)3. To say that D and A are dissonant is
> to clearly show a misunderstanding of the notation. The point is not that D
> to A is dissonant but that between D and A is where Ben arbitrarily put the
> syntonic comma difference.

If you look at the very recent archives, that's not the view Kyle Gann was espousing, and it was
to Kyle that I directed those comments.
>
> His point is not that the notes D and A are mystically dissonant,

But Kyle said Bruckner thought they were (in C major). That's what I was reacting against, not the
idea of D-A as an arbitrary place to make the "break". Of course, neither D-A nor G-D gives the
lattice perfect symmetry, so it is an arbitrary choice.

I wrote,

> But the rules for Ben's notation get more and more complicated the more primes you add in.
For
> example, G-F is a 9:16, while C-Bb is a 9:5 . . . and D wasn't involved in either of those!

And I didn't even add in any primes!!!

I wrote,
>
> If the note C is in the center _note_, then why is two steps to the right G,

Oops . . . that should be D, of course . . .

--- In tuning@y..., JoJoBuBu@a... wrote:

/tuning/topicId_17672.html#22563

> This applies to the following lattice (hopefully this picture
> comes out)
>
> [Unable to display image]
>

Andy, you can only post plain ASCII text to the list, because a
lot of subscribers get it as plain text email and don't view it
on the web.

If you have other types of files for us to see, you can create
a folder for yourself in the "files" section of Yahoo Groups
and put them there, then refer to them here.

> You have to show the difference of syntonic comma somewhere.
> Think about it from this point of view for a moment. On a
> standard tempered piano the notes B to F require a Sharp on
> the F or a flat on the B to make it a perfect fith. With Bens
> notation between D and F# requires a comma to notate a major
> third(5/4), between D and A+ a comma is required to notate a
> perfect fifth, and between B and F#+ a comma is required.
>
> And thats all that needs to be remembered for 5 limit JI. This
> is not complicated!!!

Hmmm... that's the first explanation of this aspect of Ben's
notation which has really made sense to me. It *is* analagous
to the # or b added to the diatonic pitches to create a
"perfect 5th" when one occurs at either end of the diatonic
cycle.

In fact, this observation therefore relates Ben's notation to
the procedure used in the famous Babylonian "tuning tablet"
(CBS 10996, a collection of math problems for use in schools,
now in the University Museum in Philadelphia), which I believe
is the oldest existing musical score. For more on that, see:
/tuning/topicId_11624.html#11624

> ... Now heres why you have
> missed the point and this comes directly from Bens mouth.
> The choice to have the syntonic comma difference between
> D and A+ IS ARBITRARY. Other notes could have been chosen
> for sure, but you have to notate the syntonic comma
> difference SOMEWHERE in the lattice and therefore he
> chose D to A+. D in this case being (3/2)2 and A+ being
> (3/2)3. To say that D and A are dissonant is to clearly
> show a misunderstanding of the notation. The point is
> not that D to A is dissonant but that between D and A
> is where Ben arbitrarily put the syntonic comma difference.
> The comma has to go somewhere...
>

Of course Paul and I (and I think Joe Pehrson too) know this.
I think Paul was pointing out the fact that the notation makes
it *look* like there was a dissonance, an inconsistency,
in the actual tuning of the music.

The very reason we prefer the HEWM notation is because there
is *no arbritrary* decision to be made. The entire system
follows a set of logical rules which don't bring up the
need to make an arbitrary decision of where to notate the
comma. The comma arises naturally as the difference between
a Pythagorean and a 5-limit "major 3rd", so that's where
it's notated.

As I've pointed out, Ben's system uses these logical rules
for all prime-factors higher than 5, and in fact it was the
inspiration for the HEWM notation I developed. It's the
fact that he chose to include that arbitrary decision for
prime-factor 5 that I, and the others, don't like.

And I pointed out, and was echoed recently by Joe Pehrson,
that Ben's notation seems to encourage in his writing the
tendency to modulate by 5:4s over 3:2s. Then again, perhaps
it's the other way around - maybe he chose to develop his
notation in this way because he alreaded tended to *think*
this way when he composed.

-monz
http://www.monz.org
"All roads lead to n^0"

In a message dated 5/12/2001 3:37:54 PM Eastern Daylight Time,
paul@stretch-music.com writes:

> Thanks Andy. I agree with almost everything you say, and I'm sure Ben's
> notation has become
> very logical for many of its users, but HEWM is very logical for a lot of
> JI thinkers . . . again,
> notation ultimately shouldn't matter.

I agree completely!!

>
> But the rules for Ben's notation get more and more complicated the more
> primes you add in. For
> example, G-F is a 9:16, while C-Bb is a 9:5 . . . and D wasn't involved in
>

Yes and thats why in the notation there are no comma differences notated
between the two intervals you mentioned. Theres no comma differences notated
there BECAUSE the intervals I mentioned were not involved(D to F#+, Bb to F+,
or D to A+)

Also realize that you are talking about two intervals which go in different
directions on the lattice. C to Bb- is a 16/9 but C to Bb a 9/5 and they both
denote something different and different ways to get to that location on the
lattice. In other words those intervals are a comma apart and the notation
shows that. Notice G to F+ is a 9/5 because it goes through D on the lattice
(or you could go through Bb to F+ of course)

(sorry my lattice picture didn't go through last post)

F+ A+
Bb D
G
C
F
Bb-

In the end though I really couldn't agree more that between the these two
notations it isn't completely important which one is chosen to be used ...
assuming of course that one chose to use either.

Cheers,
Andy

In a message dated 5/12/2001 3:39:46 PM Eastern Daylight Time,
paul@stretch-music.com writes:

> If the note C is in the center _note_, then why is two steps to the right G,
> while two steps to the
> left is Bb- (with a minus sign)? Maybe the C note is not really in the
>

I'm not sure what you mean exactly. Ben usually draws his fifths up and down,
although thats not important obviously, but if you are taking fifths as right
and left G is one space to the right with no comma because the intervals I
mentioned are not used. To the left two places Bb- is used because it DOES
use one of the intervals I mentioned which are either D to F#+ (5/4), D to
A+(3/2) or Bb- to F(3/2)

>But Kyle said Bruckner thought they were (in C major). That's what I was
reacting >against, not the
>idea of D-A as an arbitrary place to make the "break". Of course, neither
D-A nor G->D gives the
>lattice perfect symmetry, so it is an arbitrary choice.

One could perhaps say that he made his arbitrary choice of D to A+, and the
other intervals, by thinking in terms of C major AND C minor because if you
look on the lattice the commas start to appear right outside of that ... kind
of. In other words I, IV and V of major and minor dont have commas .... kind
of and depending on how you look at the lattice. But this doesn't wholly fit
because with the commas theres a Bb- very close to the original C. In fact
the Bb, 9/5 Bb, is farther away to the center of the lattice than the 16/9
which leads me to believe it was more the arbtrary choice I mentioned than a
way of thinking in C major.

In other words I think at best you could say its based on i iv V in C major
and C minor, but I dont think that really covers how the lattice is
contructed either or how the notation really works. Even with the concept of
C major and minor it doesn't tell you where exactly to put the commas on the
lattice or where to make the comma break. C major cant tell you to put the
comma in the notation between D an A+(and the other intervals)... Unless I'm
missing something important...

Maybe it would help more if I drew out a complete lattice how Ben would do
it. Heres an attached file of the way Bens lattice looks. Maybe this will
help explain it better.

Cheers,

Andy

--- In tuning@y..., JoJoBuBu@a... wrote:
>
> >
> > But the rules for Ben's notation get more and more complicated the more
> > primes you add in. For
> > example, G-F is a 9:16, while C-Bb is a 9:5 . . . and D wasn't involved in
> >
>
> Yes and thats why in the notation there are no comma differences notated
> between the two intervals you mentioned. Theres no comma differences notated
> there BECAUSE the intervals I mentioned were not involved(D to F#+, Bb to F+,
> or D to A+)

Somehow that fails to make me happier. There are no comma differences notated, and yet the
intervals differ by a comma.
>
> Also realize that you are talking about two intervals which go in different
> directions on the lattice. C to Bb- is a 16/9 but C to Bb a 9/5 and they both
> denote something different and different ways to get to that location on the
> lattice. In other words those intervals are a comma apart and the notation
> shows that. Notice G to F+ is a 9/5 because it goes through D on the lattice
> (or you could go through Bb to F+ of course)

OK . . . it's all about what you go "through" on the lattice. Again, this seems a great complication
for a JI thinker trying to compose using this notation. What if you accept a 9-limit of consonance
and want to use these intervals without going "through" anything?
>
> In the end though I really couldn't agree more that between the these two
> notations it isn't completely important which one is chosen to be used ...

Well, good . . . Monz and I just happen to find the other one a lot more obvious and intuitive . . .

--- In tuning@y..., JoJoBuBu@a... wrote:
>
> > If the note C is in the center _note_, then why is two steps to the right G,
> > while two steps to the
> > left is Bb- (with a minus sign)? Maybe the C note is not really in the
> >
>
> I'm not sure what you mean exactly. Ben usually draws his fifths up and down,
> although thats not important obviously, but if you are taking fifths as right
> and left G is one space to the right with no comma because the intervals I
> mentioned are not used. To the left two places Bb- is used because it DOES
> use one of the intervals I mentioned which are either D to F#+ (5/4), D to
> A+(3/2) or Bb- to F(3/2)

I corrected myself immediately and said I meant D, not G, is two spaces to the left. But you see
how C is really not the center of symmetry, because of the arbitrary choice to have the
"anomalous" intervals you name above.

>. Even with the concept of
> C major and minor it doesn't tell you where exactly to put the commas on the
> lattice or where to make the comma break. C major cant tell you to put the
> comma in the notation between D an A+(and the other intervals)... Unless I'm
> missing something important...

I think you're exactly right.
>
> Maybe it would help more if I drew out a complete lattice how Ben would do
> it. Heres an attached file of the way Bens lattice looks. Maybe this will
> help explain it better.

Can't see it right now, but the lattice of Ben's notation of the 5-limit lattice is displayed on the
cover of my latest paper, _The Forms of Tonality_.

In a message dated 5/12/2001 6:27:48 PM Eastern Daylight Time,
paul@stretch-music.com writes:

> I corrected myself immediately and said I meant D, not G, is two spaces to
> the left. But you see
> how C is really not the center of symmetry, because of the arbitrary choice
> to have the
>

Yes I think I see what you mean. You mean that when you look at the lattice
its not symetrical per se around C and instead the commas make this diagonal
looking sort of thing as its structure governed by the intervals which Ben
based it on. (this is really obvious when you make a gigantic lattice). On
the other hand C is the 1/1 and everything does relate to that whether its
looks symetrical or not. I dont necesarily think that the diagonal lattice
makes the notation worse or better, and I dont think that is what you are
saying, but I would agree that it is an interesting thing to notice about the
lattice, the diagonal nature of the commas, which governs the notation.

Lastly If thinking about JI music, at least whenever I've seen him do it, Ben
doesn't look at the lattice of course he just has the "rules" so to speak of
how the intervals work in his notation in mind and therefore the lattices
aren't even needed. This is why I brought up the analogy of the 12TET
keyboard. You just remember that B to F is not a perfect fifth. So in this
context its a really simple way to think about notation because theres only a
few simple rules to memorize and then lattices become less important.

Thanks for the interesting discussion Paul!

Andy

[Robert Walker wrote:]
>Hadn't realised you could retune files so easily.

Yes. It's quite easy. I can even batch tune many files in one swell
foop. It does suck a fair amount of juice out of the computer while
it's running, due to the repetitive internal calculations. Each retuning
takes approximately as long as the sequence does to play.

>I'd love to hear all the cpe Bach you've retuned if it isn't too large
>a file as I like his style a lot, and I think adaptive tuning will
>bring it out. Would be interesting to see if it does.

I don't think it'll be large. Do you want soft or rigid vertical
springs, and dom7ths at 8/9 of root (my older practice for 5-limit) or
9/10 of root ("tuning file free", or what Paul E calls "true 5-limit")?

>I'll keep an eye out and see if I can find the midi file for c.p.e.
>Bach flute sonatas anywhere.

Please do!

>I've greatly enjoyed the chopin you posted recently, and I thnk the
>adapitive tuning bring out his singing melodies wonderfully, and make
>the counterpoint clearer too. I think he is a natural to adaptively
>tune to j.i. because of his wonderful singing melodies, whatever
>one might say about authenticity.

Kyool!

>Pehaps the counterpoint is brought out most clearly in the
>7-limit one. I certainly like that one, so join the club of those
>who you say must have something seriously wrong with them.

;->

>I don't hear this thing about equal semitones and find the chromatic
>scales very exciting. Perhaps I do notice a kind of evenness about
>the chromatic passages in 12-tet, but not so sure, more notice
>the exciting variety of colour in the adaptively tuned ones.

It's funny, I've got sequences where uneven step sizes do bother me,
but not this one.

>I wonder what tuning he actually used for his pianos?

This piece is on Ed Foote's latest CD, "Six Degrees of Tonality". He
uses a De Morgan temperament, a kind of backward Well temperament (i.e.,
F# major is more consonant than C major). But as I recall, the liner
notes express uncertainty as to what Chopin himself used.

>The original un-retuned version has no patches in it - playing
>it first, got some interesting renderings of Chopin on recorder
>:-) then on a second try after playing a bit of one of the others,
>recorder + piano (recorder playing the sustained base notes
>of course not fading away at all, and arpeggiated accompaniment)!

Funny! It's amazing how many good midi files of piano works have no
patch command(s). I run a GM reset file before I play anything, as a
matter of habit, so I usually don't notice.

>Now if only one could adaptively tune a real acoustic piano
>(as in the fantasy grand)!

Oh yeah! Some day I'm gonna throw a pot of money at that challenge, if
at all possible...

>I've also been gradually mulling over the cue points idea for
>adaptive tuning, but not getting very far with it. It would be
>easy to set them if the notes for chords were always played
>in the same order I expect, - one would just need to go through
>the entire midi file and make a search tree from it, each time
>indexing a note by the following sequence of notes. So when a
>particular sequence of notes is played, one uses that to key into
>the search tree, and go instantly to right part of the file.

My program uses a construct called a "pseudo-simultaneous event" (PSE),
which collects up MIDI transitions within a preset period of time
(default 64 msec), and does further analysis as if they had all happened
together. This would be very useful for synchronization, I think: one
does not expect everything to happen in a particular order within the
PSE, but one DOES expect to go into the PSE with a particular set of
notes playing, and to come out of the PSE with some other set of notes
playing. I would base tracking on these successive sets of expected
notes.

>Anyway, will continue to keep it in mind.

Please do! This challenge can wait to be solved, if necessary. But
it'll be fun once somebody gets it up and running. Wish I was a better
keyboard player myself!

JdL

--- In tuning@y..., graham@m... wrote:

> The theorists have done their work, now it's time for composers and
> instrument builders to move the revolution forward.

Got it, Graham! Let's hope it ends up working for me... but it's
certainly worth a try! And thanks to everybody for providing a new
direction and incentive for me...

Of course, I still have to "tune up" this scale and listen to
it...that might be nice...

_________ _______ ______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

billions of miracles served?

Joseph - are you becoming the Carl Sagan of the TL? He he!

> Of course, I still have to "tune up" this scale and listen to
> it...that might be nice...

Now why would you want to do that - this might just result in some of
that icky byproduct of theory - the dreaded *music*.

JL

--- In tuning@y..., JoJoBuBu@a... wrote:

/tuning/topicId_17672.html#22524
>

This is a message for Andy (JoJoBuBu) (Two Joes & a couple of boo
boos)

Sorry I haven't answered this sooner, but, as people are more than
aware, I've had severe computerese...

> Well if you are going to center the lattice you have to center it
on something. C is as good as any.

Well, Margo Schulter really did this point of view up in a "recent"
post... (somewhere around 22400 I suspect)... so one can definately
make a case for it... She just did it!

>If you look at the ninth or tenth string quartet

Ummm, by the way, how many string quartets has Ben Johnston
written?? Sounds like he could still outdo Haydn!

> Well I see your point for sure. Notation does make a difference
thats a reasonable statement. On the other hand Look at Toby Twinings
music. He uses JI in an EXTREMELY complicated way, with Bens
notation, and by no means whatsoever tends to gravitate towards C
major. Have a look if you can get a hold of a score and you will,
hopefully see what I mean.

I'm assuming you are implying that Toby Twining uses Ben Johnston
notation?? Yes?? I happen to be a Twining "fan." I've heard his
music live at Bang on a Can, and he is exceptionally talented.

He even posted to our very list... at least a couple of times...
perhaps he is still a member.

>
> >I believe it can be definitively proven that Monzowolfellholtz is
a
> >superior notational system, in the overall...
>
> >It's already *BEEN* proven on this Tuning List... a search will
find the path.  This is how advances are made!
>

> Soon I will prove once and for all that honey roasted chicken
tastes better than garlic chicken.
>

Now there you go... here's some really PRACTICAL advice for Tuning
List members...

> Well if thats what they emphasized, I just joined the list and have
missed those posts, but if what you said accurately portrays their
point of view then I'd agree with them. I will search those out...
>
> I was attempting to objectively enter a discussion in which I
missed the first
>
8356586399869823649823640283462034620347203487602834692834762938462398
46239846293846 emails.

It may *be* that some day, at the rate we're going...

What happened is this. I went to the MicroFest in Los Angeles and
was very intrigued by the compositions of both Kyle Gann and David
Doty, particularly with respect to the way they notated things in Ben
Johnston's notation.

When I got back, around April 13 or so, we started a discussion on
this list about the Johnston notation, and it has been going on in
various manifestations ever since.

The post number to start with on this is #20931

Read through the next couple of weeks after that...

Don't "chicken out" or I'll call Colonel Sanders!

________ _____ _ _____
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_17672.html#22791

> What happened is this. I went to the MicroFest in Los Angeles
> and was very intrigued by the compositions of both Kyle Gann
> and David Doty, particularly with respect to the way they
> notated things in Ben Johnston's notation.
>
> When I got back, around April 13 or so, we started a discussion
> on this list about the Johnston notation, and it has been going
> on in various manifestations ever since.

In fact, Joe, your questions about Ben's notation are exactly
what started the ball rolling on the MIRACLE temperaments.

So Ben is, indirectly, the cause of what many of us here
feel may be the most important development in tuning theory
since Partch's work.

(In fact I'd stick my neck out and make the claim that MIRACLE
is *more* important!)

-monz
http://www.monz.org
"All roads lead to n^0"

In a message dated 5/14/2001 10:37:13 PM Eastern Daylight Time,
jpehrson@rcn.com writes:

> The post number to start with on this is #20931
>
> Read through the next couple of weeks after that...
>
> Don't "chicken out" or I'll call Colonel Sanders!
>
> ________ _____ _ _____
>

LOL I wont. Just give me some time to sift through everything(I have some
other committments for the next little while). Yes Twining, at least the
scores I have seen uses either Ben's notation or slight modifications of
Ben's notation. I can't say this is true for everything because I dont have
any idea, but at least for the chunks of of his scores I have seen he
definately does use it.

Ben Johnston has 10 quartets, since you asked. The tenth has never been
performed to the b best of my knowledge,, and a few others have never been
recorded. The others, 1,2,3,4,5, 6, and 9, are recorded. I just finished
digitally remastering all of the available recordings. (which was pretty
tough because some of the old tapes had eroded quite a bit - hurray for
digital magic)The ninth was not touched digitally by me because it was
recorded digitally originally and therefore didn't need remastering.

Cheers I'll read those posts soon

Andy

Joe,

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> So Ben is, indirectly, the cause of what many of us here
> feel may be the most important development in tuning theory
> since Partch's work. (In fact I'd stick my neck out and make the
> claim that MIRACLE is *more* important!)

Careful, the collar on your lab coat doesn't extend high enough to
protect your neck! :) Before declaring the next Champeeen and Heavy-
Weight Tuning Title Holder of the universe, why don't you wait 50 or
100 years to see if a significant body of work will exist utilizing
the M scale: music (or something along those lines) that has the
power to change people's lives, make them think, transport them --
any and all the things good music can do.

Because, after all, until then it is just a theory, it is just raw
material. It just sits there, waiting...waiting.....waiting.......

Cheers,
Jon

--- In tuning@y..., JSZANTO@A... wrote:

/tuning/topicId_17672.html#22819

> Joe,
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> > So Ben is, indirectly, the cause of what many of us here
> > feel may be the most important development in tuning theory
> > since Partch's work. (In fact I'd stick my neck out and make
> > the claim that MIRACLE is *more* important!)
>
> Careful, the collar on your lab coat doesn't extend high enough
> to protect your neck! :) Before declaring the next Champeeen
> and Heavy-Weight Tuning Title Holder of the universe, why don't
> you wait 50 or 100 years to see if a significant body of work
> will exist utilizing the M scale: music (or something along
> those lines) that has the power to change people's lives, make
> them think, transport them -- any and all the things good music
> can do.
>
> Because, after all, until then it is just a theory, it is just
> raw material. It just sits there, waiting...waiting.....
> waiting.......

So true, Jon, so true. Please understand that I did not intend
in any way to belittle Partch or his work with that remark.

In fact, the effort Partch put into achieving absolutely
"pure" just-intonation notwithstanding, I daresay that the
MIRACLE family could render his compositions in a form which
would be audibly indistinguishable from the originals in
all but the slowest and most baldly-exposed sections, and
maybe even then too.

I recognize Partch as one of the most important 20th Century
composers and like (and listen often to) a lot of his work.
I felt that I was paying him an honor by comparing the importance
of the discovery of MIRACLE to the path-breaking work he did.

Now, with all that out of the way... The main point I wanted
to make is that there's such an excitement about the work
we're doing right now on MIRACLE that I simply cannot see it
ending up on a dusty library shelf.

These tunings are going to be mapped to new instruments;
papers, books, and webpages are going to be written about
them (the tunings *and* the instruments); and most importantly,
a *lot* of new music is going to be composed using them.

I really think Joe Pehrson was closest to the mark when he
talked about MIRACLE taking the place that 12-EDO used to
(... OK, still does) have.

And I swear: as soon as I get my MIRACLE Ztar, I'm taking a
sabbatical from this list and I'm going to compose my *butt*
off! There's a pile of music in my mind that's been waiting
for the suitable instrumental medium to come along so it
can let itself out!

(Hmmm... that sounds pretty shamanistic... guess I *do* need
to scoot on over to that other list...)

-monz
http://www.monz.org
"All roads lead to n^0"

> --- In tuning@y..., JSZANTO@A... wrote:
>
> >
> > Because, after all, until then it is just a theory, it is just
> > raw material. It just sits there, waiting...waiting.....
> > waiting.......
>

Jon,

You must have missed all the music by Mary Beth Ackerly, and Graham
Breed's progression as sequenced by Joe Monzo.

Pretty soon Joseph's going to be making some music with it -- that's
a guarantee.

And I promise, next chance I get I'm going to doodle around with my
Blackjack! :)

Thanks for the prodding!

Paul

P.S. I don't agree with Monz that the MIRACLE scales have anything to
do with Partch's music, though they have everything to do with his
theories. You could play Partch's music in 72-tET, but we knew that
already.

Paul,

--- In tuning@y..., paul@s... wrote:
> You must have missed all the music by Mary Beth Ackerly

Um, nope. Unless I missed it though, isn't just the one ("Nada Clue")
using the M? And I got the distinct impression (trying to understand
without a lot of time) that is was utilized in a very general
fashion, not either a deep exploration or exemplar of the unique
qualities of M.

All of that, however, is *entirely* beside the point: I am smitten
mightily with MBs work...very! I plan on downloading all of her
stuff, and plan on chatting with her as well...in two weeks when I
have the time.

> and Graham Breed's progression as sequenced by Joe Monzo.

Nope, didn't listen to that one.

> Pretty soon Joseph's going to be making some music with it --
> that's a guarantee.

OK, I'll give it a try.

> And I promise, next chance I get I'm going to doodle around with my
> Blackjack! :)

You better!

> Thanks for the prodding!

Didn't even have the batteries charged... :)

> P.S. I don't agree with Monz that the MIRACLE scales have anything
> to do with Partch's music, though they have everything to do with
> his theories. You could play Partch's music in 72-tET, but we knew
> that already.

Yeah, I think Monz is just in a state of high excitation right now.

Cheers,
Jon

Joe,

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> So true, Jon, so true. Please understand that I did not intend
> in any way to belittle Partch or his work with that remark.

No problem, I didn't feel it as a belittlement at all, in any way. I
understand where you are coming from (I just told Paul I thought you
were in a high state of excitation), so I'm just helping clarify the
butter.

> In fact, the effort Partch put into achieving absolutely
> "pure" just-intonation notwithstanding, I daresay that the
> MIRACLE family could render his compositions in a form which
> would be audibly indistinguishable from the originals in
> all but the slowest and most baldly-exposed sections, and
> maybe even then too.

But you don't need to, you have Partch's 43-tone scale. Use the new
one for new music. Besides, every one that lives on Theory Street
keeps forgetting that for HP the theory and the scale were a means to
an end: communicate using musical materials. I hope that is where the
M business is headed.

> These tunings are going to be mapped to new instruments;
> papers, books, and webpages are going to be written about
> them (the tunings *and* the instruments); and most importantly,
> a *lot* of new music is going to be composed using them.

Papers and books can come later. 12-tET theory books and treatises
(treatii?) didn't *precede* the practice, did they? (Hell, that's
actually an honest question, and I probably won't be around to read
the answer!)

> I really think Joe Pehrson was closest to the mark when he
> talked about MIRACLE taking the place that 12-EDO used to
> (... OK, still does) have.

Oh, shit, I hope *that* doesn't happen! What? Replace one monolith
with another??? How about just adding a new resource, and be done
with it?

> And I swear: as soon as I get my MIRACLE Ztar, I'm taking a
> sabbatical from this list and I'm going to compose my *butt*
> off! There's a pile of music in my mind that's been waiting
> for the suitable instrumental medium to come along so it
> can let itself out!

That sounds swell, and I wish you the best.

Cheers,
Jon

--- In tuning@y..., JSZANTO@A... wrote:
> Paul,
>
> --- In tuning@y..., paul@s... wrote:
> > You must have missed all the music by Mary Beth Ackerley
>
> Um, nope. Unless I missed it though, isn't just the one ("Nada
Clue")
> using the M?

_Lament 3-9-11_ uses the Blackjack scale.

> And I got the distinct impression (trying to understand
> without a lot of time) that is was utilized in a very general
> fashion, not either a deep exploration or exemplar of the unique
> qualities of M.

Much as Partch often used his scale. On the other hand, _Lament 3-9-
11_ was more of an attempt to use the patterns inherent in the scale -
- though Mary was actually trying to use 1-3-7 -- she was still
making use of patterns inherent in the scale, if I understand
correctly.

Wouldn't a conscious, deep exploration or examplar of the unique
qualities of M come out sounding like a technical exercise, rather
than music? And isn't that something you "hate"?

Monz wrote,

> > I really think Joe Pehrson was closest to the mark when he
> > talked about MIRACLE taking the place that 12-EDO used to
> > (... OK, still does) have.

Now that's crazy talk. Joseph just meant taking that place in his
composing life. You been hanging out with Herbert lately?

Paul,

--- In tuning@y..., paul@s... wrote:
> _Lament 3-9-11_ uses the Blackjack scale.

Yes, I'll download that while I go out onto the patio (seriously, at
midnight now) and fire up the table saw (I'm not kidding, I've got a
gong rack to build before tomorrow's rehearsal...).

> > And I got the distinct impression (trying to understand
> > without a lot of time) that is was utilized in a very general
> > fashion, not either a deep exploration or exemplar of the unique
> > qualities of M.

> Much as Partch often used his scale.

Right, right, but I'm interested right now in *hearing* things that
give me an inkling as to the 'miraculous' qualities of the tuning.

> Wouldn't a conscious, deep exploration or examplar of the unique
> qualities of M come out sounding like a technical exercise, rather
> than music? And isn't that something you "hate"?

Wait, don't get me wrong!!! As I said above, I'm just trying to hear
what all the excitement was about. My point, which I semi-elaborated
on, was that Mary Beth's stuff hadn't struck me as all that different
than her ealier pieces, and so I wasn't necessarily 'seeing' what it
was about M that was going to alter the course of music history.

Yes, I'm not fond of musical exercises, but they have their place *as
examples*. And there isn't much in the universe I hate. But if I
really dislike it, I suppose "hate" (in quotes) will have to do,
though I'll work to excise this as well.

I'll just enjoy the pieces as they start to flow out of the petri
dish of latice development!

Cheers,
Jon

Paul,

--- In tuning@y..., paul@s... wrote:
> Monz wrote,
>
> > > I really think Joe Pehrson was closest to the mark when he
> > > talked about MIRACLE taking the place that 12-EDO used to
> > > (... OK, still does) have.
>
> Now that's crazy talk. Joseph just meant taking that place in his
> composing life. You been hanging out with Herbert lately?

OK, I didn't see the original, and misunderstood Monz's quote of the
material. No harm, no foul...

--- In tuning@y..., JSZANTO@A... wrote:

> Right, right, but I'm interested right now in *hearing* things that
> give me an inkling as to the 'miraculous' qualities of the tuning.

Track down the Graham Breed progression that Monz sequenced (I can't
seem to find it right now). This wasn't intended to be a composition
at all, or much of a demonstration of the 'miraculous' qualities of
the blackjack tuning, but merely a paper example Graham posted of a
2401:2400 pump, when Graham tried (successfully) to show me that his
lattice diagram didn't miss out on any progressional possibilities.
There are myriad such progressions in this tuning, doubtless many
that are more beautiful than this one. The only thing miraculous
about the tuning is how many quasi-JI consonances it contains. Joseph
Pehrson wanted a scale with lots of quasi-JI consonances, so we gave
it to him.

> I wasn't necessarily 'seeing' what it
> was about M that was going to alter the course of music history.

It's going to alter the course of Joseph Pehrson's musical history,
that's all. Me, I'm not that interested in classical performance, so
the question of subsets of 72-tET isn't likely to come up in my music
anytime soon.

Hey Jon, you of course have as much of a right to post to this list
as anyone else, but to be perfectly frank, most of what I see from
you is complaining about someone else's theory and someone else's
practice -- not complaining as in providing good, harsh, constructive
criticism, but complaining as in wishing it didn't even exist. I'm
sure you've been involved in a good deal of microtonal theory and/or
practice of your own -- why not share that instead of just sitting
around telling people what they should and shouldn't do?

Now, I know I can be a schmuck here sometimes, and I think I've
benefitted greatly from you and other people having a negative
reaction toward me, and I think I've made a lot of progress in my
attempts to relate to and communicate with others on the internet as
a result. So I hope you will take my comment in the same light.

CREATE!

-Paul

--- In tuning@y..., JSZANTO@A... wrote:
> Paul,
>
> --- In tuning@y..., paul@s... wrote:
> > Monz wrote,
> >
> > > > I really think Joe Pehrson was closest to the mark when he
> > > > talked about MIRACLE taking the place that 12-EDO used to
> > > > (... OK, still does) have.
> >
> > Now that's crazy talk. Joseph just meant taking that place in his
> > composing life. You been hanging out with Herbert lately?
>
> OK, I didn't see the original, and misunderstood Monz's quote of
the
> material. No harm, no foul...

Jon, that wasn't directed toward you. Do you see the name "Jon
Szanto" anywhere in the above quote?

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_17672.html#22827

> P.S. I don't agree with Monz that the MIRACLE scales have
> anything to do with Partch's music, though they have
> everything to do with his theories. You could play Partch's
> music in 72-tET, but we knew that already.

Paul, MIRACLE is too new to me for me to understand a lot
of what it's really capable of. I haven't done any serious
study into how well Partch's music might be represented in
it. I was simply referring to the lattice that Graham made
here <http://x31eq.com/decimal_lattice.htm#partch>.

Since "You could play Partch's music in 72-tET, but we knew
that already", and MIRACLE scales are all subsets of 72-EDO
[= 72-tET], is there any reason to assume that it would work?

-monz
http://www.monz.org
"All roads lead to n^0"

Paul,
--- In tuning@y..., paul@s... wrote:
> Track down the Graham Breed progression that Monz sequenced (I
> can't seem to find it right now).

Yep, I'll do that (just won't be for a few days).

> It's going to alter the course of Joseph Pehrson's musical history,
> that's all.

OK by me.

> Hey Jon, you of course have as much of a right to post to this list
> as anyone else, but to be perfectly frank, most of what I see from
> you is complaining about someone else's theory and someone else's
> practice -- not complaining as in providing good, harsh,
> constructive criticism, but complaining as in wishing it didn't
> even exist.

Hey, I don't mean it in that sense, and a lot of the past couple of
rounds of posting (which included mentions that I have grown to
understand the value of such endeavors, and I guess you either didn't
read those parts or are just skipping over them) have related to
the "Practical" issue. I sincerely was asking, for someone who
doesn't sit down and read lattices or other diagramatic explanations,
if there were examples of a musical nature (not even finished pieces)
that could shed some light.

I don't mean it to be negative, though I am sorry and imagine that it
might come off like that. For a moment, look at how I feel: too dumb
to look at those enormous number of posts on the M scale and get
anything out of it. If I can't ask you, or anyone else on the list,
about a different way to view/hear/determine the interesting
qualities of a theoretical concept, what would you suggest?

> I'm sure you've been involved in a good deal of microtonal theory
> and/or practice of your own

I'm a performer first, composer second, theorist...not. Short of
basic understandings, that is.

> -- why not share that instead of just sitting
> around telling people what they should and shouldn't do?

I don't think I told anyone anything, save for asking Monz to wait a
couple of decades, which frankly was in jest. I asked about the audio
examples. That's all. And when I've shared, it has been on matters of
musical structure and performance, but I don't think that interests
you, which is OK too.

> So I hope you will take my comment in the same light.

Sure do. Sorry if I came off to you, or anyone for that matter, as a
schmuck.

Jon

Paul,

--- In tuning@y..., paul@s... wrote:
> > OK, I didn't see the original, and misunderstood Monz's quote of
> the
> > material. No harm, no foul...
>
> Jon, that wasn't directed toward you. Do you see the name "Jon
> Szanto" anywhere in the above quote?

I guess I was in "full defensive mode" and since I had just written
on that message I thought it was directed at me. Once again, a
misunderstanding and another apology. How's that?

--- In tuning@y..., JSZANTO@A... wrote:

/tuning/topicId_17672.html#22832

> > [me, monz]
> >
> > In fact, the effort Partch put into achieving absolutely
> > "pure" just-intonation notwithstanding, I daresay that the
> > MIRACLE family could render his compositions in a form which
> > would be audibly indistinguishable from the originals in
> > all but the slowest and most baldly-exposed sections, and
> > maybe even then too.
>
> But you don't need to, you have Partch's 43-tone scale. Use
> the new one for new music. Besides, every one that lives on
> Theory Street keeps forgetting that for HP the theory and the
> scale were a means to an end: communicate using musical
> materials. I hope that is where the M business is headed.

First, I want to add that I am well aware of your feelings
concerning Partch's work, and that indeed music is only a
part of it. His endeavor to achieve a truly corporeal
experience in his work entails a lot of other domains
along with the music.

But to me, MIRACLE is *very* much a means to an end.
I don't have much hope of playing any Partch instruments,
with the single exception of the replica Harmonic Canon
at the Sonic Arts Gallery.

But if/when I get my MIRACLE Ztar, I will finally be able
to play Partch's music on my own instrument, at my own leisure,
and can study it thoroughly. The Ztar can be programmed to
play either Partch's actual 43-tone JI scale, or any of the
MIRACLE scales, or any other tuning I care to put on it
(within its own physical limitations, which really aren't much).

So I'm looking forward to using MIRACLE to compose new music
*and* to study the work of others that I really haven't had
the ability to analyze *and play*.

> Papers and books can come later. 12-tET theory books and treatises
> (treatii?) didn't *precede* the practice, did they? (Hell, that's
> actually an honest question, and I probably won't be around to read
> the answer!)

I've mentioned this before (last year?). There are two
different kinds of theory: proscriptive and descriptive.

A theory like Schoenberg's _Harmonielehre_ was descriptive,
because he was simply describing what he saw already
happening in his music and that of others. Partch's
theories in _Genesis_ are *certainly* descriptive of his
own musical practice. A theory like Yasser's or Schillinger's
is proscriptive, because it is a complete ready-made system
looking for a "user".

Schoenberg's case is particularly interesting in this respect,
because I feel that his attitude changed to a proscriptive
one by the time he invented the 12-tone Method.

>
> > I really think Joe Pehrson was closest to the mark when he
> > talked about MIRACLE taking the place that 12-EDO used to
> > (... OK, still does) have.
>
> Oh, shit, I hope *that* doesn't happen! What? Replace one monolith
> with another??? How about just adding a new resource, and be done
> with it?

Well, that's not exactly what I meant. What I meant was:
if we're going to have any kind of monolithic tuning around,
I'd much prefer MIRACLE to 12-EDO.

Hell, I still write 12-EDO music. But as time goes on, I'm
retuning more and more of it...

My real point was that I see MIRACLE as being capable of
being so many things to so many people that it could easily
usurp the role that 12-EDO has had for about a century
or more... and that would be a real good thing.

-monz
http://www.monz.org
"All roads lead to n^0"

Joe,

Excellent points, all! You are in a good space right now, with
materials coming at you at the same time the creative juices are
flowing. I also know that you are savvy enough about the various
Partch issues, so that certainly wasn't pointed in your direction (or
anyone in particular, for that matter).

Good post, well done, off to work now (me, that is)...

Cheers,
Jon

-
-- In tuning@y..., paul@s... wrote:

/tuning/topicId_17672.html#22841

> --- In tuning@y..., JSZANTO@A... wrote:
>
> > Right, right, but I'm interested right now in *hearing*
> > things that give me an inkling as to the 'miraculous'
> > qualities of the tuning.
>
> Track down the Graham Breed progression that Monz sequenced
> (I can't seem to find it right now).

Here's the mp3:
http://www.ixpres.com/interval/monzo/blackjack/breedpmp.mp3

And here's the message explaining what it is:
/tuning/topicId_22433.html#22686

> This wasn't intended to be a composition at all, or much of
> a demonstration of the 'miraculous' qualities of the blackjack
> tuning, but merely a paper example Graham posted of a
> 2401:2400 pump, when Graham tried (successfully) to show me
> that his lattice diagram didn't miss out on any progressional
> possibilities.

And for the benefit of myself, Joe Pehrson, and now Jon Szanto
(and everyone else), now it's also an audio example.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_17672.html#22835

> Monz wrote,
>
> > > I really think Joe Pehrson was closest to the mark when he
> > > talked about MIRACLE taking the place that 12-EDO used to
> > > (... OK, still does) have.
>
> Now that's crazy talk. Joseph just meant taking that place in his
> composing life. You been hanging out with Herbert lately?

yuck, yuck!

Drat, I have to "work" at "work" today.... list is getting good...
________ ______ _____
Joseph Pehrson

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> Since "You could play Partch's music in 72-tET, but we knew
> that already", and MIRACLE scales are all subsets of 72-EDO
> [= 72-tET], is there any reason to assume that it would work?
>
Graham showed that you need a chain of 45 notes in a miracle chain to
get Partch's scale. I guess we've been focusing on 21- and 31-tone
scales mostly, so the Partch scale didn't seem like it particularly
fit within those limits . . .

--- In tuning@y..., JoJoBuBu@a... wrote:

/tuning/topicId_17672.html#22801

> Ben Johnston has 10 quartets, since you asked. The tenth has never
been performed to the b best of my knowledge,, and a few others have
never been recorded. The others, 1,2,3,4,5, 6, and 9, are recorded. I
just finished digitally remastering all of the available recordings.
(which was pretty tough because some of the old tapes had eroded
quite a bit - hurray for digital magic)The ninth was not touched
digitally by me because it was recorded digitally originally and
therefore didn't need remastering.
>
> Cheers I'll read those posts soon
>
> Andy

Congrats to you, Andy, for this VERY important work!
_____________ _____ ___
Joseph Pehrson

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_17672.html#22841

> >
> Track down the Graham Breed progression that Monz sequenced (I
can't seem to find it right now).

/tuning/topicId_22433.html#22686

This wasn't intended to be a composition
> at all, or much of a demonstration of the 'miraculous' qualities of
> the blackjack tuning, but merely a paper example Graham posted of a
> 2401:2400 pump, when Graham tried (successfully) to show me that
his
> lattice diagram didn't miss out on any progressional possibilities.
> There are myriad such progressions in this tuning, doubtless many
> that are more beautiful than this one. The only thing miraculous
> about the tuning is how many quasi-JI consonances it contains.
Joseph Pehrson wanted a scale with lots of quasi-JI consonances, so
we gave it to him.

And I greatly appreciate it! The progression was one of the most
astonishing things I have ever heard, when I realize the potential
for developing a whole new language.

I'm just a "baby" with it, though, and haven't even learned to walk.
Probably I could use some "formal" training if I could get it and
afford it. I need to go through the entire "progression" (literally)
in the same way I developed my 12-tET "chops."

____________ ______ _____ ___
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

> I'm just a "baby" with it, though, and haven't even learned to
walk.
> Probably I could use some "formal" training if I could get it and
> afford it. I need to go through the entire "progression"
(literally)
> in the same way I developed my 12-tET "chops."

Ear-training: perhaps someone could write a program to play random
Blackjack-fabric intervals, harmonically and melodically, and you
have to name the interval. The possibilities would be

semitones approx. JI interval
1/3
2/3
5/6
1 1/6
1 1/2 12:11
1 5/6 10:9
2 9:8
2 1/3 8:7
2 2/3 7:6
3
3 1/6 6:5
3 1/2 11:9
3 5/6 5:4
4 1/6 14:11
4 1/3 9:7
4 2/3
5 4:3
5 1/3
5 1/2 11:8
5 5/6 7:5
6 1/6 10:7
6 1/2 16:11
6 2/3
7 3:2
7 1/3
7 2/3 14:9
7 6/5 11:7
8 1/6 8:5
8 1/2 18:11
8 5/6 5:3
9
9 1/3 12:7
9 2/3 7:4
10 16:9
10 1/6 9:5
10 1/2 11:6
10 5/6
11 1/6
11 1/3
11 2/3
12 2:1

That's 41 types of intervals, within an "octave", from the 21-tone
scale. Not too daunting, considering that Partch's 43-tone scale has
340 types of intervals within an "octave"! Familiarity with the
harmonic series will help in identifying the ones labeled with ratios.

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_17672.html#23144

> Ear-training: perhaps someone could write a program to play random
> Blackjack-fabric intervals, harmonically and melodically, and you
> have to name the interval. The possibilities would be
>

Hi Paul!

This is a great post, which I saved right away.

Might it be possible for you to repost it with Monzo ascii 72-tET
notation as well??

I could probably figure it out, but I bet you could do it 20 times
faster than I could....

Maybe Monz could work up some ear-training sound files based on this
when he gets time...

I hope to do something of the same myself...

Thanks again!

__________ _______ ____ ___
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

>
> Might it be possible for you to repost it with Monzo ascii 72-tET
> notation as well??

I don't see how . . . these are intervals, not pitches . . . the pitch of the lower note should be
randomly chosen for the ear-training exercise.

See Harry's Boogie for another take on adaptive tuning:

http://vms.cc.wmich.edu/~code/groven/compare.html

John Starrett

--- In tuning@y..., "jdstarrett" <jstarret@c...> wrote:

> http://vms.cc.wmich.edu/~code/groven/compare.html

This uses three pianos tuned 1/8 tone apart, all controlled by a master piano. The same system could, I presume, allow for six pianos tuned 1/12 tone apart, and we would have the 72-et.

> From a message with Chris, I had found that I had made the mistaken
> assumption that "adaptive" tuning trys to allow modulations to other
> keys (tonal centers), while adjusting the tuning relationships to a "new
> tonal center". (I would think that it still could be used for this purpose.)

>>i think that *is* what it does, but in a more clever way than
>>a "naive" just intonation analysis would suggest (imho).

What I meant was that it's constantly making adjustments, even within
passages that are all within a given "key," so, yes, it does allow you to
modulate, but it's operating on a much more fine-grained level than
simply adjusting the tuning once every time you modulate.

You had suggested that you could play an adaptuned piece using a pedal
that would switch the tuning every time you modulated. . . my response was
to say, sorry, but the tuning's gonna change a lot more often than that.

I *think* I'm right about that. . . ?

I know that in my piano sonata, it changes every note, pretty much.

cb

HI Wermer,

Nice to see posts from you on the list :-).

YOu may be interested to know that I'm exploring another approach in my
FTS program, real time. It is strict adaptive tuning with diesis shifts,
uncompromising. If you have a comma pump then it will spiral up or down
the pump. If you have a diminished seventh and play overlapping diads
you will get a major diesis shift at the octavae - at least
if one uses the strong dovetailing option.

So it isn't really meant for performance of common practice harmony
particularly in its present form. It is best for exploring the diesis
and comma shifts, and for composing and improvising pieces that work with the
shifts, and maybe even exploit them as features. It does also have
options to somewhat soften the tuning and make the connection of notes
with previous ones looser, but this isn't much developed at all.

I plan to put up a page soon about this with retuned examples.
Meanwhile you can find a few if you scroll down in the bug fixes
and what is new page:

http://www.robertinventor.com/bug_fixes.htm

http://www.robertinventor.com/whats_new.htm

You will find some examples in the bug fixes page which show
that leisure tuning can find better tunings for some pieces
at least for strict adaptive just intonation tuning
than any real time system could possibly
achieve.

Is that the same for Hermode tuning - can it also be
used for leisure time retuning as well?

I have also used it though for retunign the fractal tunes
in FTS and it seems to work well for many of those.
Also for retuning some C.P.E. Bach and J.S. Bach
flute pieces that I practice on the recorder for my
practice sessions, and those too worked really well to my ears. They
have many diesis shifts though so it is rather dependent
on how tolerant one is of those - I seem to be
exceedingly tolerant of them except in a few situations
as to my ears diesis shifts have a tendency to sound like really tiny
semitones in many contexts, indeed sometimes I hardly
realise that it is a shift and not a proper scale
step if I don't listen closely to what is going on.

Anyway I have some midi clips there of those too but
I'll probably do some recordings later with my playing too, as I think
that may bring out what they are like for someone
playing along with them, maybe they will make more
sense that way.

It seems to me that real time and leisure time could
work together so that you play a piece in real time
and also record it in midi or some such and
process that file after the event in order to
get another retuning that looks forwards as well
as backwards.

Incidentally it has no connection with hermode tuning and
wouldn't infringe on your patent I'm sure. I use a method
of searching through all the notes currently in play to
maximise the number of consonant diads between the
currently played note and previous notes in the chord.

Another thing about this is that the tuning of a chord
may depend on the exact order in which you play the notes,
as it has no look ahead. Is this the same for Hermode
tuning or is it independent of the order of the notes,
or maybe somewhere in between?

Anyway it is a fascinating field to be involved in.
Wish you all the best for your Hermode tuning systm,
and I have enjoyed my visits to your site to find
out about what you are doing.

Thanks,

Robert

http://www.robertinventor.com