Yahoo Tuning Groups Ultimate Backup tuning [tuning] Digest Number 1439

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There are 25 messages in this issue.

Topics in this digest:

1. Harry Partch on the radio and TV
From: "Michael Saunders" <michaelsaunders7@hotmail.com>
2. Re: mighty weird theory book
From: JoJoBuBu@aol.com
3. Re: Re: comma question
From: <manuel.op.de.coul@eon-benelux.com>
4. Levarie and Levy's "Tone" online
From: "Rosati" <dante.interport@rcn.com>
5. Re: Levarie and Levy's "Tone" online
From: "John F. Sprague" <jsprague@dhcr.state.ny.us>
6. Re: new "equitone" dictionary entry
From: "monz" <joemonz@yahoo.com>
7. Re: Levarie and Levy's "Tone" online
From: "monz" <joemonz@yahoo.com>
8. Re: comma question
From: "Paul Erlich" <paul@stretch-music.com>
9. Re: In search of unison vectors
From: "Paul Erlich" <paul@stretch-music.com>
10. Re: mighty weird theory book
From: "Paul Erlich" <paul@stretch-music.com>
11. Re: Re: In search of unison vectors
From: "D.Stearns" <STEARNS@CAPECOD.NET>
12. Re: In search of unison vectors
From: "Paul Erlich" <paul@stretch-music.com>
13. Re: In search of unison vectors
From: "Paul Erlich" <paul@stretch-music.com>
14. Re: Warped Canon page updated!
From: "Paul Erlich" <paul@stretch-music.com>
15. Re: A neo-Gothic approach to 20-tET (Part 1)
From: mschulter <MSCHULTER@VALUE.NET>
16. Re: A neo-Gothic approach to 20-tET (Part 1)
From: "David J. Finnamore" <daeron@bellsouth.net>
17. Re: Harry Partch on the radio and TV
From: Kraig Grady <kraiggrady@anaphoria.com>
18. Re: Re: mighty weird theory book
From: JoJoBuBu@aol.com
19. Re: Re: Warped Canon page updated!
From: Herman Miller <hmiller@IO.COM>
20. Re: Re: In search of unison vectors
From: "D.Stearns" <STEARNS@CAPECOD.NET>
21. Re: Re: In search of unison vectors
From: "D.Stearns" <STEARNS@CAPECOD.NET>
22. new John Chalmers 19-limit lattice
From: "monz" <joemonz@yahoo.com>
23. 22 + 34 =/= 56 (was: Re: Warped Canon page updated!)
From: "monz" <joemonz@yahoo.com>
24. Re: Re: mighty weird theory book
From: "David Beardsley" <davidbeardsley@biink.com>
25. 22 tet mp3s - up and running
From: Alison Monteith <alison.monteith3@which.net>

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Message: 1
Date: Fri, 22 Jun 2001 11:25:39
From: "Michael Saunders" <michaelsaunders7@hotmail.com>
Subject: Harry Partch on the radio and TV

I don't recall ever seeing/hearing him in the mass
media (except maybe the BBC), but this brings up
some nostalgia. My first exposure to him was at a
night dedicated to "Harry Partch, the hobo genius"
at Club Lower Links in Chicago. They showed "The
Dreamer that Remains", "Daphne of the Dunes", "US
Highball" and possibly some others. I was charmed
to death by the old man.

-m
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Message: 2
Date: Fri, 22 Jun 2001 12:29:18 EDT
From: JoJoBuBu@aol.com
Subject: Re: mighty weird theory book

In a message dated 6/22/2001 2:48:29 AM Eastern Daylight Time,
jpehrson@rcn.com writes:

> Well, I decided to "spring" for the Mathieu _Harmonic Experience_
> theory book and it is, indeed, mighty strange...
>
> If you know *me*, that is not necessarily a criticism...
>
> I've never seen a harmony book that EVER had any references to
> lattices or tuning...
>
> I'm just saying that, in comparison to the other very _standard_
> texts that I've had to ingest over the years, this is rather er..
> ideosyncratic...
>
> I think I'm going to enjoy it, though... when I get the time...
>
> _______ ______ ________
>

Just wait till you get to the strange names that start popping up. You'll see
what I mean prettty soon into the book. I found some of the names bizzare and
I didn't feel the names were important enough to warrant me going through
memorizing them. I am really not sure why he didn't use standard solfege, and
other reasonably standard names, for an american audience. Or at least names
more standard then the ones he chose. (I will leave the actual names in the
abstract cause I dont particularly feel like going through the book and
listing them)

Overall I thought the book was good and I did get something out of reading
it, but its definitely ideosyncratic, and I definitely have my criticisms.

One thing for sure though is that Mathieu is an interesting author and his
voice, text writing voice, has a real flare to it ... my own criticisms
aside.

Cheers,

Andy

[This message contained attachments]

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Message: 3
Date: Fri, 22 Jun 2001 18:55:52 +0200
From: <manuel.op.de.coul@eon-benelux.com>
Subject: Re: Re: comma question

Joseph wrote:
>And, similarly, when you lower the Bb in the same tetrad, you have to
>lower it by 1/6 tone, or 33.3 cents, *two* steps of 72-tET. That way
>the larger *septimal* comma, which has been tempered out in 12-tET
>becomes the "just" Bb of 72-tET... the *septimal* comma "in
>action..."

>So that becomes a clear illustration of the two commas in 72-tET.

>Correct??

Yes, that's right. So when a comma is said to vanish in a certain
ET, it is represented by 0 steps. This is something you can check
with the command DIVIDE/CONSISTENT.

Manuel

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Message: 4
Date: Fri, 22 Jun 2001 14:18:15 -0400
From: "Rosati" <dante.interport@rcn.com>
Subject: Levarie and Levy's "Tone" online

The interesting book by Levarie and Levy "Tone: A study in musical
acoustics" is online:

http://www.win.net/~pelerin/music/tone/LLTC.html

Their other book, "Musical Morphology: A Discourse and a Dictionary" is also
excellent. Theres a recent reprint but its expensive: you can find copies of
the original 1983 edition for like $30.

Dante

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Message: 5
Date: Fri, 22 Jun 2001 14:31:23 -0400
From: "John F. Sprague" <jsprague@dhcr.state.ny.us>
Subject: Re: Levarie and Levy's "Tone" online

I have a second hand copy of "Tone" and have read it (which is more than I can
say for most of the music books I have). It is indeed an interesting approach,
more from the Goethean scientific view of phenomenology. However, I found the
explanations about scales rather conventional. But the discussion of
architectural acoustics has some very interesting and (to me) novel material.
I wasn't aware of their other book. Do they still teach in Brooklyn?
>>> dante.interport@rcn.com 06/22/01 02:18PM >>>
The interesting book by Levarie and Levy "Tone: A study in musical
acoustics" is online:

http://www.win.net/~pelerin/music/tone/LLTC.html

Their other book, "Musical Morphology: A Discourse and a Dictionary" is also
excellent. Theres a recent reprint but its expensive: you can find copies of
the original 1983 edition for like $30.

Dante

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

[This message contained attachments]

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Message: 6
Date: Fri, 22 Jun 2001 11:33:56 -0700
From: "monz" <joemonz@yahoo.com>
Subject: Re: new "equitone" dictionary entry

Thanks to Margo Schulter for providing me with a
"first draft" definition for "equitone", which I've
finally added to my Tuning Dictionary:

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

(Sorry it took so long, Margo!)

I'd like to point out one particular thing Margo wrote
here that I find to be very insightful, as is the related
footnote:

> ... from an historical point of view, we may find it
> very convenient to say, "Conventional Western European
> notation has evolved in a setting of equitonal tunings,
> namely Pythagorean and meantone."

This is really a great addition to the dictionary.

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

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Message: 7
Date: Fri, 22 Jun 2001 11:36:45 -0700
From: "monz" <joemonz@yahoo.com>
Subject: Re: Levarie and Levy's "Tone" online

> ----- Original Message -----
> From: Rosati <dante.interport@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, June 22, 2001 11:18 AM
> Subject: [tuning] Levarie and Levy's "Tone" online
>

> The interesting book by Levarie and Levy "Tone: A study in musical
> acoustics" is online:
>
> http://www.win.net/~pelerin/music/tone/LLTC.html

Thanks, Dante!

I found one sentence in the "Preface" that could be altered
by one letter to make many JIers happy: just substitute
"retuning" for "returning". :)

> First, the study of acoustics demonstrates the advantages
> and virtues of returning to fundamentals.

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

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Get your free @yahoo.com address at http://mail.yahoo.com

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Message: 8
Date: Fri, 22 Jun 2001 19:08:33 -0000
From: "Paul Erlich" <paul@stretch-music.com>
Subject: Re: comma question

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

> Oh! I think perhaps I may be getting a "glimmer" of this.
>
> So, this is why, let's say in 72-tET, when you lower the "E" by a
> 1/12 tone from 12-tET(in a simple C:E:G:Bb tetrad) you are getting
> the "just E" 16.6 cents flatter than 12-tET where it has been
> tempered out...
>
> So that, obviously, is the syntonic comma "in action..."
>
> And, similarly, when you lower the Bb in the same tetrad, you have
to
> lower it by 1/6 tone, or 33.3 cents, *two* steps of 72-tET. That
way
> the larger *septimal* comma, which has been tempered out in 12-tET
> becomes the "just" Bb of 72-tET... the *septimal* comma "in
> action..."
>
> So that becomes a clear illustration of the two commas in 72-tET.
>
> Correct??

If you add the observation that 12-tET plays the role of Pythagorean
tuning in 72-tET, then yes, this is correct.

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Message: 9
Date: Fri, 22 Jun 2001 19:18:09 -0000
From: "Paul Erlich" <paul@stretch-music.com>
Subject: Re: In search of unison vectors

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

> I've been looking at a lot of these types of two-dimensional scales
> lately.

Great -- maybe you can help us co-author a paper (go to tuning-math).
You may have missed the hypothesis I posted a while back but this
seems to relate.

> Remember Dave Keenan's 11-tone chain of minor thirds scale?
> Well it could be seen in a similar light by way of the 3:4:5 (the
> unison vectors being 15625/15552

The kleisma.

>and 16/15)

Good show! The Fokker periodicity block with unison vectors
15625/15552 and 16/15 is, in cents,

0
70.672
244.97
315.64
386.31
568.72
631.28
813.69
884.36
955.03
1129.3

with step sizes

70.6724
174.2964
70.6724
70.6724
182.4037
62.5651
182.4037
70.6724
70.6724
174.2964
70.6724

The difference between each pair of similar step sizes is the kleimsa
itself,

8.1073 cents.

So the kleisma is the commatic unison vector of this scale.

> in say 34-tet.

No need to specify an ET embedding, at this point.
>
> Here's the 1/6 comma meantone version

Let's restrict the "meantone" terminology to the meantone cases,
i.e., cases where the commatic unison vector is 81:80, shall we?

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Message: 10
Date: Fri, 22 Jun 2001 19:24:56 -0000
From: "Paul Erlich" <paul@stretch-music.com>
Subject: Re: mighty weird theory book

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

> Just wait till you get to the strange names that start popping up.
You'll see
> what I mean prettty soon into the book. I found some of the names
bizzare and
> I didn't feel the names were important enough to warrant me going
through
> memorizing them. I am really not sure why he didn't use standard
solfege, and
> other reasonably standard names, for an american audience. Or at
least names
> more standard then the ones he chose.

Sir, the names he uses are the _Indian_ solfege names. Since
Americans are highly outnumbered by citizens of India, and since the
first part of the book concerns intonational practices which are far
closer to Indian than to American practice, I feel this was a good
choice on his part. The book is a good complement to a study of raga
with a teacher of Indian music, in which situation the Indian solfege
names would be memorized within the first few days anyway.

I feel that there are many much more substantive criticisms of the
book that can be made than this (as I've discussed in the past).

This was just my humble opinion and should be considered fairly
irrelevant -- nothing to start a flame war over.

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Message: 11
Date: Fri, 22 Jun 2001 16:00:33 -0700
From: "D.Stearns" <STEARNS@CAPECOD.NET>
Subject: Re: Re: In search of unison vectors

Hi Paul and everyone,

<<You may have missed the hypothesis I posted a while back but this
seems to relate.>>

I guess I must've missed it. What I can do, and I've posted on this
quite a bit in the past, is find unison vectors for any given
two-stepsize scale.

<<Let's restrict the "meantone" terminology to the meantone cases,
i.e., cases where the commatic unison vector is 81:80, shall we?>>

Well that's okay with me, but it is after all a generalization of the
very same principles... so, any suggestions on what to call these
types of temperaments?

--Dan Stearns

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Message: 12
Date: Fri, 22 Jun 2001 20:21:28 -0000
From: "Paul Erlich" <paul@stretch-music.com>
Subject: Re: In search of unison vectors

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Hi Paul and everyone,
>
> <<You may have missed the hypothesis I posted a while back but this
> seems to relate.>>
>
> I guess I must've missed it. What I can do, and I've posted on this
> quite a bit in the past, is find unison vectors for any given
> two-stepsize scale.

Awesome! Now we need to figure out how to do the reverse -- given a
set of unison vectors, one of which is "chromatic" while the other(s)
are "commatic", find the generator and interval of repetition of the
resulting MOS.
>
>
> <<Let's restrict the "meantone" terminology to the meantone cases,
> i.e., cases where the commatic unison vector is 81:80, shall we?>>
>
> Well that's okay with me, but it is after all a generalization of
the
> very same principles... so, any suggestions on what to call these
> types of temperaments?

"Forms of Tonality"???

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Message: 13
Date: Fri, 22 Jun 2001 20:23:16 -0000
From: "Paul Erlich" <paul@stretch-music.com>
Subject: Re: In search of unison vectors

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

> Well that's okay with me, but it is after all a generalization of
the
> very same principles... so, any suggestions on what to call these
> types of temperaments?
>
They actually already have a name . . . linear temperaments.

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Message: 14
Date: Fri, 22 Jun 2001 20:26:10 -0000
From: "Paul Erlich" <paul@stretch-music.com>
Subject: Re: Warped Canon page updated!

Herman,

The new 4:6:7 and 1/7:1/6:1/4 JI version are really cool . . .
very "Mizarian" or something . . . thanks for putting them up.

How about a 56-tET version, since Graham talks about 56-tET on his
diachismic page? It's not quite near-just, but it's certainly
close . . .

-Paul

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Message: 15
Date: Fri, 22 Jun 2001 13:28:54 -0700 (PDT)
From: mschulter <MSCHULTER@VALUE.NET>
Subject: Re: A neo-Gothic approach to 20-tET (Part 1)

---------------------------------------------------
A neo-Gothic approach to 20-tET:
Essay in honor of Brian McLaren and Dan Stearns
Part 1
---------------------------------------------------

Sometime maybe around the end of last summer, the renowned microtonal
composer and theorist Brian McLaren recommended 20-tone equal
temperament (20-tET) as a tuning for neo-Gothic music I hadn't yet
explored, but should.

In fact, this was a brilliant suggestion, most happily enriching my
musical practice and theory alike in all kinds of ways, and opening
the path to other related (or maybe not-so-obviously-related) scales.
Therefore this essay is most warmly dedicated to Brian McLaren, and
also to his revered colleague Ivor Darreg for the insight that all
tunings have musical value, offering a rainbow spectrum of "moods."

Also, this essay is dedicated to mathematician, musician, and virtuoso
scale designer Dan Stearns, who has made the Stern-Brocot Tree
flourish with new and rich ramifications for our art.

Early this year, in addition most patiently to guiding me through a
few of the mysteries of scale generation, Dan compared notes with me,
a newcomer to 20-tET, showing at once his creativity and his eagerness
to exchange viewpoints about a tuning system lending itself to a range
of approaches.

To honor Dan, and also a famous arboreal construction of the perennial
artist acclaimed for his high and branching concepts, Ervin Wilson, I
would call this essay simply a view of 20-tET from one particular
treehouse.

-------------------------------
1. Close encounters with 20-tET
-------------------------------

When Brian McLaren called 20-tET to my attention, pointing out the
great neo-Gothic major third at 420 cents (7/20 octave), my first
reaction was, "Yes, that's an excellent third -- but what about those
720-cent fifths?"

Would fifths at 12/20 octave, a full 18.04 cents wider than pure,
really be ideal for music where fifths and fourths are the main stable
concords?

Curiously, before getting around to tuning 20-tET, I tried an
experiment which took me a step further in confronting that particular
barrier: tuning 23-tET, where fifths and fourths are considerably
further from a pure 3:2.

Having found that yes, in a metallophone-like texture 23-tET fifths
and fourths can sound like fifths and fourths, I was ready to consider
tuning them at 720 cents and 480 cents almost a "mainstream" choice.

This January, I got down to the actual tuning, and had to decide on a
keyboard mapping. That involved questions like: "How do I construct a
diatonic scale, and find the cadences I'm looking for?"

----------------------------------
1.1. Keyboard mapping and spelling
----------------------------------

In my kind of neo-Gothic approach to 20-tET, the two 12-note manuals
look like this, with a "+" sign showing a note raised by 120 cents or
2/20 octave, an interval which I term an apotome or chromatic
semitone, arbitrarily taking a C-C octave as a point of reference,
with C4 as middle C:

300 420 780 900 1080
C#+4/ Eb+4/ F#+4/ Ab+4/ Bb+4
Eb4 E4 Ab4 A4
C+4 D+4 E+4 F+4 G+4 A+4 B+4 C+5
120 360 540 600 840 1020 1260 1380
240 180 60 240 180 240 60
-----------------------------------------------------------------
180 300 660 780 960
C#4 Eb4 F#4 Ab4 Bb4
C4 D4 E4 F4 G4 A4 B4 C5
0 240 420 480 720 900 1140 1200
240 180 60 240 180 240 60

In this "regularized keyboard" layout, each keyboard has identical
steps and intervals, arranged in a pattern which might be described as
a kind of "quasi-syntonic diatonic."

This patterns features a limma or diatonic semitone at 60 cents (1/20
octave), and alternating large and small whole-tones at 240 cents
(4/20 octave) and 180 cents (3/20 octave).

Accidentals are added to each keyboard so as to provide diatonic
semitones of 60 cents (e.g. C#-D, Eb-D, F#-G, Ab-G). This divides a
large whole-tone (e.g. C-D) into steps of 180-60 cents (e.g. F-F#-G),
and a small whole-tone into steps of 60-120 cents (e.g. D-Eb-E).

People may note that while I usually choose a range of Eb-G# for
accidentals, here I've preferred Ab-C# in this arrangement, for
reasons having to do with cadences (see Part 2, Section 3.1).

Of course, since the tuning includes all 20 notes, our "G#4," here
spelled G+4 (840 cents above C4), is available also. Likewise, if we
want a "G#+" at 840 cents above C+, that's available at Bb4.

For some of my favorite modes, I can proceed more or less as if 20-tET
were a regular diatonic tuning, especially in a purely melodic context
or a polyphonic style after a 13th-century Western European manner
with lots of cadences in modes such as Mixolydian where all voices
move by whole-tones (e.g. major thirds contracting to unisons or minor
sixths expanding to octaves).

Here are F Lydian and G Mixolydian, for example, with T for large
tone, t for small tone, and S for semitone:

T t T s T t s
F3 G3 A3 B3 C4 D4 E4 F4
0 240 420 660 720 960 1140 1200
240 180 240 60 240 180 60

MIDI example: http://value.net/~mschulter/20tly001.mid

t T s T t s T
G3 A3 B3 C4 D4 E4 F4 G4
0 180 420 480 720 900 960 1200
180 240 60 240 180 60 240

http://value.net/~mschulter/20tmx001.mid

In these neo-Gothic modes of 20-tET, a major third of 420 cents is
formed from a large tone of 240 cents and a small tone of 180 cents.

This arrangement results in a "quasi-syntonic comma" equal to 60
cents, also the size of the usual diatonic semitone: the difference
between our major third at 420 cents, and four 720-cent fifths up less
two octaves, (2880-2400) or 480 cents. This comma is also equal to the
difference between our two sizes of whole-tones at 240 and 180 cents.

As in the syntonic diatonic of Ptolemy as applied to 16th-century
European polyphony by Fogliano and Zarlino, so here, this type of
comma causes special complications for the fifth spelled D-A in a
regular tuning.

Maybe as a kind of homage to Ben Johnston, a 720-cent fifth here is
spelled C#-A or D-Bb! The keyboard spelling D-A yields an interval of
660 cents, also the size of a usual augmented fourth (e.g. F-B, C-F#).

This produces three variations on the Dorian mode at D-D -- or, for
one variation, actually C#-C#:

"Hard Dorian" (C#-C#)

T s T t T s t
C#4 E4 F4 G4 A4 B4 C5 C#5
0 240 300 540 720 960 1020 1200
240 60 240 180 240 60 180

http://value.net/~mschulter/20tdr001.mid

"Soft Dorian" (D-D)

T s T T t s T
D4 E4 F4 G4 Bb4 B4 C5 D5
0 180 240 480 720 900 960 1200
180 60 240 240 180 60 240

http://value.net/~mschulter/20tdr002.mid

"Natural Dorian" (D-D)

T s T t T s T
D4 E4 F4 G4 A4 B4 C5 D5
0 180 240 480 660 900 960 1200
180 60 240 180 240 60 240

http://value.net/~mschulter/20tdr003.mid

The "soft Dorian" version on D has a very curious effect at the point
where we have two successive large whole-tones, F-G-Bb, where I am
somewhat reminded of the slendro scale for gamelan (close to 5-tET).
This effect seems a kind of meeting between neo-Gothic and gamelan
mediated through 20-tET's connection with 5-tET (compare the remarks
of Dan Stearns at the conclusion of this section).

The "natural Dorian" interestingly sounds quite pleasant to me as a
melodic scale featuring a 660-cent "fifth" at D-A; in a polyphonic
setting, one might modify either note to get a 720-cent vertical
interval (C#-A or D-Bb).

The "hard Dorian" at C#-C# has an interval C#-G of 540 cents (a
diminished fifth in size and also here in spelling) in place of a
usual fourth above the final or note of repose C#, and permits
interesting versions of some standard 13th-century cadences in three
or four voices (Part II, Section 3.2).

Here I might add that both for Dan Stearns and me, Mixolydian is an
especially beloved mode in 20-tET, with our interpretations and styles
suggesting some of the versatility of this tuning. Something like my
"soft Dorian" might suggest words which Dan has used about other types
of 20-tET patterns:

"What's special about scales like these is that they bath[e]
the familiar in pungent hues of the new and the exotic.

"Speaking very broadly, the sound of these modes is like that
of 7-limit diatonic scales bent through the unique mood of
20 equal with its ancestral genealogy in 5 equal."[1]

---------------------------
2. Intervals and categories
---------------------------

With 20-tET, as with more "conventional" tunings such as 29-tET or
46-tEt, how one maps scale steps into intervals and categories may
depend a great deal upon the desired style.

Here is a table of 20-tET intervals which may provide some overview of
my own neo-Gothic approach, with explanatory comments following:

=====================================================================
Interval Cents Example ~Ratio Cents Variation
---------------------------------------------------------------------
1 0 C3-C3 1:1 (exact) 0.00 0.00
---------------------------------------------------------------------
limma 60 E3-F3 28:27 62.96 - 2.96
or min2 G3-Ab3
---------------------------------------------------------------------
apotome 120 Eb3-E3 2187:2048 113.69 + 6.31
or dim3 G3-G+3/G#3 15:14 119.44 + 0.56
C#3-Eb3 14:13 128.30 - 8.30
---------------------------------------------------------------------
small 180 D3-E3 65536:59049 180.45 - 0.45
Maj2 G3-A3 10:9 182.40 - 2.40
---------------------------------------------------------------------
Large Maj2 240 C3-D3 8:7 231.17 + 8.83
quasi-min3 D3-F3 15:13 247.74 - 7.74
G3-Bb3 7:6 266.87 -26.87
---------------------------------------------------------------------
min3 300 C3-Eb3 32:27 294.13 + 5.87
E3-G3 19:16 297.51 + 2.49
---------------------------------------------------------------------
Neutral3 360 E3-Ab3 16:13 359.47 + 0.53
C3-D+3/D#3 21:17 365.83 - 5.83
D3-F+3
---------------------------------------------------------------------
Maj3 420 C3-E3 14:11 417.51 + 2.49
E3-G+3/G#3 23:18 424.36 - 4.36
---------------------------------------------------------------------
4 480 D3-G3 4:3 498.04 -18.04
Bb3-D4
---------------------------------------------------------------------
dim5 540 B3-F4 15:11 536.95 + 3.05
Super4 A3-D4 11:8 551.32 -11.32
---------------------------------------------------------------------
demi8 600 C3-F3+ 24:17 597.00 + 3.00
12:17 603.00 - 3.00
---------------------------------------------------------------------
Aug4 660 C3-F#3 16:11 648.68 +11.32
sub5 D3-A3 22:15 663.05 - 3.05
---------------------------------------------------------------------
5 720 C3-G3 3:2 701.96 +18.04
D3-Bb3
C#3-A3
---------------------------------------------------------------------
min6 780 C3-Ab3 11:7 782.49 - 2.49
D3-A+3
---------------------------------------------------------------------
Neutral6 840 F#3-Eb4 34:21 834.17 + 5.83
D3-Bb+3 13:8 840.53 - 0.53
G+3-F4
---------------------------------------------------------------------
Maj6 900 G3-E4 27:16 905.87 - 5.87
A3-F+4
---------------------------------------------------------------------
small min7 960 G3-F4 12:7 933.13 +26.87
Quasi-Maj6 A3-F#4 26:15 952.26 - 7.74
E3-C#4 7:4 968.83 - 8.83
---------------------------------------------------------------------
large min7 1020 A3-G4 9:5 1017.60 - 2.40
E3-D4 59049:32768 1019.55 - 0.45
---------------------------------------------------------------------
Aug6 1080 Eb3-C#4 13:7 1071.70 - 8.30
28:15 1080.56 - 0.56
15:8 1088.27 - 8.27
---------------------------------------------------------------------
Maj7 1140 F3-E4 27:14 1137.04 + 2.96
A3-G#4
---------------------------------------------------------------------
8 1200 F3-F4 2:1 (exact) 1200.00 0.00
_____________________________________________________________________
---------------------------------------------------------------------

As Brian McLaren pointed out to me, 20-tET has an excellent neo-Gothic
major third at 420 cents, somewhere between 14:11 (~417.51 cents) and
a suggested region of maximum "entropy" or complexity around 422-423
cents.[2]

Regular minor thirds at 300 cents, and major sixths at 900 cents, are
not too far from their usual Pythagorean ratios, although a bit
"subdued" or "mild"; these intervals have the same size as in 24-tET
or 36-tET (or more generally 12n-tET). However, when combined as they
typically are with the ebullient 420-cent major third, they can have a
most pleasantly active and shimmering quality.

A delightful ramification of our two sizes of whole-tones in
quasi-diatonic modes (240 cents and 180 cents) is the use of
"quasi-thirds" at 240 cents spelled and treated vertically like minor
thirds contracting to unisons, and likewise "quasi-sixths" at 960
cents spelled and treated like major sixths expanding to octave.
In other contexts, these same interval sizes also serve as usual major
seconds or minor sevenths.

To introduce the quasi-minor-third (q3 for short) at 240 cents, let us
first consider a routine two-voice progression with a "regular" minor
third at 300 cents. Here numbers in parentheses show vertical
intervals, and signed numbers show ascending (+) or descending (-)
melodic intervals in each voice:

D4 -- -240 -- C4 -- -60 -- B3
(720) (300) (0)
G3 -- +180 -- A3 -- +240 -- B3

5 - m3 - 1

http://value.net/~mschulter/20tq3000.mid

This typical 13th-century progression from fifth to minor third to
unison takes on an engagingly different "modal color" at positions
where the 240-cent quasi-third is the natural minor third:

C4 -- -240 -- Bb3 -- -60 -- A3
(720) (240) (0)
F3 -- +240 -- G3 -- +180 -- A3

5 - q3 - 1

http://value.net/~mschulter/20tq3001.mid

Here my impression is that the 240-cent quasi-third _acts_ like a
usual minor third, and so I tend to hear it in this way.

Similarly, a major sixth may be realized by either the usual interval
of 900 cents, or a "quasi-major-sixth" (Q6 for short) at 960 cents.
Here is a routine 13th-14th century progression from fifth to major
sixth to octave, given first with the usual 900-cent major sixth:

D4 -- +180 -- E4 -- +60 -- F4
(720) (900) (1200)
G3 --------------- -- -240 -- F3

5 - M6 - 8

http://value.net/~mschulter/20tq6000.mid

We might observe that while the _vertical_ intervals are routine, the
upper voice moves melodically through a quasi-third (D4-E4-F4) made up
of a small 180-cent major second or whole-tone plus a usual 60-cent
semitone.

Here is a version of the same basic progression with a resolution of
quasi-sixth to octave (Q6-8):

E4 -- +240 -- F#4 -- +60 -- G4
(720) (960) (1200)
A3 --------------- -- -180 -- G3

5 - Q6 - 8

http://value.net/~mschulter/20tq6001.mid

The same type of Q6-8 progression, this time featuring a descending
semitonal motion, occurs naturally in the mode of E Phrygian:

C4 -- +240 -- D4 -- +180 -- E4
(720) (960) (1200)
F3 --------------- -- -60 -- E3

5 - Q6 - 8

http://value.net/~mschulter/20tq6002.mid

Thus the frequent interchangeability of quasi-thirds and quasi-sixths
with usual minor third and major sixths is one charming feature of
neo-Gothic "diatonicity" in 20-tET.

------------------------
2.1. A bit of philosophy
------------------------

Neo-Gothic tuning systems such as 29-tET, and also 24-tET when used in
a neo-Gothic setting, feature intervals about midway between a regular
whole-tone and minor third, or between a major sixth and minor
seventh. In 29-tET, intervals of 6/29 octave (~248.28 cents) and 23/29
octave (~951.72 cents) admirably fill this role, closely approximating
15:13 (~247.74 cents) and 26:15 (~952.26 cents). In 24-tET, intervals
of 250 cents and 950 cents lend themselves to the same treatment.[3]

In two ways, we might say that 20-tET goes these systems one better.

First, in 29-tET or 24-tET, the applicable intervals are about equally
poised between a large major second and a small minor third, or
between a large major sixth and a small minor seventh. In 20-tET,
however, 240 cents is decidedly closer to a major second, and 960
cents to a minor seventh -- yet they can also serve as minor thirds or
major sixths.[4]

Secondly, in 20-tET these quasi-thirds and quasi-sixths are an
integral part of "diatonic" scale structure, in contrast to a system
like 29-tET where they play more of a supplementary role to the
regular intervals and cadences.[5]

Both as vertical intervals, and as routine melodic intervals in
various modes, quasi-thirds and quasi-sixths may illustrate how usual
diatonic patterns are "bent," as Dan Stearns puts it, when mapped into
a system such as 20-tET -- definitely not a regular diatonic tuning,
but a most intriguing one for neo-Gothic music.

-----
Notes
-----

1. See </tuning/topicId_24348.html#24348>.

2. See Margo Schulter and David Keenan, "The Golden Mediant: Complex
ratios and metastable intervals," TD 810:3 (17 September 2000):
</tuning/topicId_12915.html#12915> -- with the term
"Noble Mediant" now preferred for the Phi-based mediant described in
that paper. As estimated by the Noble Mediant, the region of maximum
complexity between 5:4 (~386.81 cents) and 9:7 (~435.08 cents) may be
located around 422.48 cents; Paul Erlich's "harmonic entropy" approach
similarly suggests a region around 423 cents.

3. In neo-Gothic theory, these intervals around 15:13 or 26:15 --
along with wide major thirds around 13:10 (~454.21 cents), e.g. 11/29
octave in 29-tET (~455.17 cents) or 9/24 octave in 24-tET (450 cents)
-- are known as "13-flavor" intervals. In 1318, Marchettus of Padua
provides a _possible_ precedent for their use when he describes a
cadential major sixth (typically expanding to an octave) equally
distant in size from the 3:2 fifth and 2:1 octave, differing by "six
diesis" from either interval. If we take his division of the 9:8
whole-tone into five dieses to be an equal division, then he may be
describing a system of adaptive tuning for singers approximately
modelled by 29-tET on a fixed-pitch instrument, with the cadential
major sixth close to 23/29 octave. However, while this interpretation
very nicely fits his description of this sixth, it is only of the
various readings considered by various scholars. See, for example, my
recent paper
http://value.net/~mschulter/marchetmf.txt (ASCII text);
http://value.net/~mschulter/marchetmf.zip (zip, text and PostScript)
See also Joseph L. Monzo, _Speculations on Marchetto of Padua's
"Fifth-Tones"_ (1998),
<http://www.ixpres.com/interval/monzo/marchet/marchet.htm>;
and Jay Rahn, "Practical Aspects of Marchetto's Tuning," _Music Theory
Online_ 4.6 (1998),
<http://boethius.music.ucsb.edu/mto/issues/mto.98.4.6/mto.98.4.6.rahn.html>.

4. At 240 cents, the large major second and quasi-minor-third is
considerably closer to 8:7 (~231.17 cents) than to 7:6 (~266.87
cents); at 960 cents, the small minor seventh and quasi-major-sixth is
likewise closer to 7:4 (~968.83 cents) than to 12:7 (~933.13 cents).
See also the table of intervals in Section 2.

5. Possibly 24-tET is something of an intermediate case: while the
usual 12-tET intervals offer a reasonable approximation of Pythagorean
intonation, I would say that the intervals of 250 cents and 950 cents
(and also the large major third at 450 cents) are a main attraction of
this tuning, at least for me. The dramatic contrast between these
"ultra-Gothic" intervals and the regular "subdued Pythagorean" ones
gives 24-tET, at least for me, a certain 20th-century modernistic
flavor to which I take a special affection.

Most respectfully,

Margo Schulter
mschulter@value.net

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Message: 16
Date: Fri, 22 Jun 2001 22:17:10 -0000
From: "David J. Finnamore" <daeron@bellsouth.net>
Subject: Re: A neo-Gothic approach to 20-tET (Part 1)

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:
> octave), and alternating large and small whole-tones at 240 cents
> (4/20 octave) and 180 cents (3/20 octave).

Happy little coincidence having a 4:3 ratio of large to small step!

David Finnamore

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Message: 17
Date: Fri, 22 Jun 2001 16:41:40 -0700
From: Kraig Grady <kraiggrady@anaphoria.com>
Subject: Re: Harry Partch on the radio and TV

The "Dreamer that Remains" was shown repeatedly on PBS after it was made. It
those days such
things were normal. Now they call it experimental. It shows you how much we have
moved backwards.

So much of the recent "fad" for Harry seems to have done more to water his
message down as
much as possible. "He really didn't mean that when he said that " seems to be
the basic
reactionary newspeak being used to turn him into "one of the boys".

It seems there are those, either independently or as members of a group, who
can explain the
non necessity of elements of Partch's music that really aren't essential
elements. Here is the
formula for his deconstruction!

We need not build new instruments
We need not use Just intonation
We need not have music composed out the the movements of the human body.
We need not have any visual element of any kind
We need not have to have human beings on stage
We need not have a stage
We need not have something that is comprehensible to human listeners.
We need not avoid abstraction regardless of how it sounds.

We have omitted the above elements because we have found them "inconvenient".

It seems these followers have omitted Harry Partch

Michael Saunders wrote:

> I don't recall ever seeing/hearing him in the mass
> media (except maybe the BBC), but this brings up
> some nostalgia. My first exposure to him was at a
> night dedicated to "Harry Partch, the hobo genius"
> at Club Lower Links in Chicago. They showed "The
> Dreamer that Remains", "Daphne of the Dunes", "US
> Highball" and possibly some others. I was charmed
> to death by the old man.
>
> -m

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

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

[This message contained attachments]

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Message: 18
Date: Fri, 22 Jun 2001 20:35:27 EDT
From: JoJoBuBu@aol.com
Subject: Re: Re: mighty weird theory book

In a message dated 6/22/2001 6:49:56 PM Eastern Daylight Time,
paul@stretch-music.com writes:

> Sir, the names he uses are the _Indian_ solfege names. Since
> Americans are highly outnumbered by citizens of India, and since the
> first part of the book concerns intonational practices which are far
> closer to Indian than to American practice, I feel this was a good
> choice on his part. The book is a good complement to a study of raga
> with a teacher of Indian music, in which situation the Indian solfege
> names would be memorized within the first few days anyway.
>
> I feel that there are many much more substantive criticisms of the
> book that can be made than this (as I've discussed in the past).
>
> This was just my humble opinion and should be considered fairly
>

Flame Flame Flame Flame. hehe(just kidding)

Surely we're outnumbered but that does not mean those words are not wierd to
americans. I do not think it was a good choice because it does not reflect
his target audience which is americans AND beginners. Microtones can be
difficult enough for a beginning student. Using standard terminology that
students already know is essential and reduces the learning curve by not
forcing unnecessary memorization. Besides I was talking about more than just
the solfege. There are plenty of other nonstandard terms he uses, some of
which are a little bizzarre. Using all of those terms I think could have
been, and should have been, avoided.

ALso the title of this message was "mighty weird theory book" not "what is
wrong with harmonic experience?" I was therefore not giving an in depth
criticism of the book but instead doing as the title indiciates and saying
what I considered "weird" about the book. And in this case I thought the
terminology, solfege and otherwise, was a rather weird choice for an american
audience. If I was giving a criticism I would have written a paper, not a
short few line post about one very small aspect of the book.

(not a flame)

/ \
/ \
/ \ (a poorly drawn flame - kind of) :)

Andy

[This message contained attachments]

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Message: 19
Date: Fri, 22 Jun 2001 22:20:10 -0400
From: Herman Miller <hmiller@IO.COM>
Subject: Re: Re: Warped Canon page updated!

On Fri, 22 Jun 2001 20:26:10 -0000, "Paul Erlich" <paul@stretch-music.com>
wrote:

>How about a 56-tET version, since Graham talks about 56-tET on his
>diachismic page? It's not quite near-just, but it's certainly
>close . . .

Hmm ... I didn't really "get" diaschismic scales before, but I took another
look at the page, and I think I have a better understanding of them now. I
went through my list of ET's less than 100 to figure out which ones were
diaschismic, and it looks like there's about as many of them as schismic
scales. There are some interesting tunings here. 56-TET sounds very nice.
Its minor sevenths aren't quite low enough to put them in the category of
tunings that suggest 7-limit harmony, but they still sound pretty good. A
bit of the 5-limit goodness of 34 and the 7-limit goodness of 22 (since 56
= 22 + 34). 32-TET also falls into this category, and one of the tunings I
previously tried for 32-TET (not the one that originally ended up on the
page) happens to fit the diaschismic tuning. The 17-limit-consistent 58-TET
is also diaschismic!

I added a section on diaschismic tunings and put up the new 32-TET and
56-TET retunings. See what you think.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

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Message: 20
Date: Fri, 22 Jun 2001 22:30:15 -0700
From: "D.Stearns" <STEARNS@CAPECOD.NET>
Subject: Re: Re: In search of unison vectors

I wrote,

"What I can do is find unison vectors for any given two-stepsize
scale."

That actually should've read,

"What I can do is find unison vectors for any given single generator
two-stepsize scale."

A simple example of this would be, say, the [4,3] neutral third 7-tone
scale which has been written about by Graham Breed and many others in
the past. The unison vectors that seem most in line with what people
interpret this scale as would be 59049/58564 and 729/704. But many
others such as 28672/28561 and 52/49 work as well.

More difficult, or convoluted examples would be those with fractional
or non-octave periodicity.

A familiar non-octave example would be the [5,4] Bohlen-Pierce scale.
A beautiful set of unison vectors for this scale are 118098/117649 and
343/324 (the 1/6th comma "meantone" version of this being a personal
favorite that I've posted about several times in the past).

An example of fractional periodicity would be Messiaen's [8,2] 10-tone
scale (AKA Paul Erlich's symmetrical decatonic). One possible set of
unison vectors for this scale, notable for their relative simplicity,
are 27/25 and 352/351 where P = 1:(sqrt(2)).

--Dan Stearns

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Message: 21
Date: Fri, 22 Jun 2001 22:55:01 -0700
From: "D.Stearns" <STEARNS@CAPECOD.NET>
Subject: Re: Re: In search of unison vectors

Hi Paul and everyone,

<<Now we need to figure out how to do the reverse -- given a set of
unison vectors, one of which is "chromatic" while the other(s) are
"commatic", find the generator and interval of repetition of the
resulting MOS.>>

I really never think in these terms, periodicity blocks and vectors,
but I'll see if I can't reverse what I do know and try to duplicate
the same sort of thing backwards.

"Forms of Tonality" would be way too vague for what I'm specifically
doing here. In a certain sense, not calling it meantone is like not
calling any non 12-et an equal temperament because that is usually
what is thought of and meant when one says equal temperament --
present company excluded!

But I agree with you; calling them "meantone" is too confusing.
However, they are just a generalization of the meantone method of
scale construction -- hasn't anyone given this specific class of
scales a name before?

--Dan Stearns

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Message: 22
Date: Fri, 22 Jun 2001 23:26:29 -0700
From: "monz" <joemonz@yahoo.com>
Subject: new John Chalmers 19-limit lattice

John Chalmers just emailed me a terrific lattice diagram
he made of the 1.3.5.7.11.13.17.19 Euler genus. I put it
at the bottom of the "John Chalmers Lattice Diagrams" page:

http://www.ixpres.com/interval/chalmers/diagrams.htm

Awesome!

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

_________________________________________________________
Do You Yahoo!?
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Message: 23
Date: Fri, 22 Jun 2001 23:33:48 -0700
From: "monz" <joemonz@yahoo.com>
Subject: 22 + 34 =/= 56 (was: Re: Warped Canon page updated!)

> From: Herman Miller <hmiller@IO.COM>
> To: <tuning@yahoogroups.com>
> Sent: Friday, June 22, 2001 7:20 PM
> Subject: Re: [tuning] Re: Warped Canon page updated!
>
>
> ... 56-TET sounds very nice.
> Its minor sevenths aren't quite low enough to put them in the category of
> tunings that suggest 7-limit harmony, but they still sound pretty good. A
> bit of the 5-limit goodness of 34 and the 7-limit goodness of 22 (since 56
> = 22 + 34).

Umm... Herman, there's no real substance to this claim.
Just because 56 = 22 + 34, it doesn't mean that 56-EDO
will have pitches or intervals in common with 22- or
34-EDO. The logarithmic division of the 2:1 is different
for all three tunings, and not many of the degrees really
match up.

Here's a graph I made comparing all three:
/tuning/files/monz/22-34-56edo.jpg

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

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

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Message: 24
Date: Sat, 23 Jun 2001 03:31:03 -0400
From: "David Beardsley" <davidbeardsley@biink.com>
Subject: Re: Re: mighty weird theory book

American? English speaking!

I read a few chapters and quickly found that I already
know this sort of material. I'll work my way through
the book someday....can't be "bad".

I'm fine with sa re ga ma...

I stopped in to my favorite guitar store to pick a gtr
in for a set up and the salesman told me he got this book as
a cut out. He used to make fun of my JI guitar because
of a seasonal set up and now he's reading this book.

This afternoon I treked (traffic is bad in NJ/NY on a weekday
in the afternoon) over to the "local" Guitar Center to get a back
up Line 6 DL4. I was telling the salesman about how the Line 6 filter
doesn't have the resolution to be in tune. At some point we discussed
the tuning fundamental - a=440. I use 426.7 and he asked me
if it was lower than a=440. "It's a'bout a 3 quarter tone flat".
"Like a Micotone?"---and then he explains how
his girlfriend is playing in the new Montclar
Partch Ensemble

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Message: 25
Date: Sat, 23 Jun 2001 09:44:47 +0100
From: Alison Monteith <alison.monteith3@which.net>
Subject: 22 tet mp3s - up and running

I have two mp3s up and running, having overcome the problems I was
having with file formats. Fingers crossed here they are :-

http://homepages.which.net/~alison.monteith3/JVguit.mp3
http://homepages.which.net/~alison.monteith3/Satyricalfile.mp3

The first mp3 is an excerpt. The full score is on two pages at :-

http://homepages.which.net/~alison.monteith3/JVimage1.gif

and

http://homepages.which.net/~alison.monteith3/JVimage2.gif

I'll keep these up for a week and then post the rest of the pieces.

Best Wishes.

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[tuning] Digest Number 1439

🔗Justin White <justin.white@davidjones.com.au>