Yahoo Tuning Groups Ultimate Backup makemicromusic Something old, something new

Hello, there, everyone, and what a pleasure to be in such a friendly
forum.

As someone with lots of historical inclinations (mainly medieval and
Renaissance/Manneristic European), in a group where _new_ music is
clearly the main point, I've decided on a theme of "something old,
something new."

However, given the focus here, it's appropriate that the "something
new" should come first, so here's a possibly fairly new progression in
22-tET for which I am much indebted to Paul Erlich.

That's to say, Paul, that you called a very striking 22-tET sonority
to my attention; the responsibility for the voice-leading and
resolution remain mine, with whatever cultural roots may have
influenced me in this.

Anyway, here's the progression, maybe an idea for various kinds of
pieces (composed or improvised) that people might come up with: here,
for those following the notation, C4 is middle C, and this is a
conventional 22-tET spelling based on a regular chain of fifths, or as
you say, Paul, a "Pythagorean" style of scale (whole-tone, e.g. C-D,
4/22 octave: usual semitone, e.g. E-F, 1/22 octave):

B4 C5
G4 F4
E4 F4
A3 F3

MIDI example: <http://value.net/~mschulter/22tei003.mid>

The first sonority, quite complex and "different" to my ears but still
somehow on the relatively concordant side, has a ratio close to
4:6:7:9, as you may recall pointing out to me, Paul, when you
introduced me to this sonority on the Alternate Tuning List. It's a
rounded 0-709-982-1418 cents (with 4:6:7:9 at ~0-702-969-1404 cents).

In this resolution, it progresses to an approximation of 1:2:3 --
how's that for "intonational basics" -- a neat and spacious sonority
of octave, twelfth, and upper fourth (0-1200-1909 cents).

A neat thing about this cadence is how it actually combines two more
familiar three-voice cadences in one:

B4 C5 B4 C5
G4 F4 E4 F4
E4 F4 A3 F3

First cadence: <http://value.net/~mschulter/22tei004.mid>
Second cadence: <http://value.net/~mschulter/22tei005.mid>
Both at once again: <http://value.net/~mschulter/22tei003.mid>

The first cadence, in 22-tET, has a near-6:7:9 sonority resolving to a
fifth in the usual manner for this kind of style: the minor third
contracts to a unison, and the near-Just 22-tET major third (almost a
pure 9:7) expands very nicely to a fifth.

The second cadence has a very beautiful near-4:6:9 sonority -- a major
ninth "divided" into two fifths, pleasing in lots of tunings -- with
the outer ninth expanding to that roomy twelfth.

Anyway, 22-tET is a scale very rich with creative ideas, and having
first tried your 4:6:7:9 in this scale (where you recommended it), I'm
using it and assorted variations in a range of tunings.

* * *

Now for the "something old," but also, at least in my view, very new
as well as xenharmonic, and most deserving of a hearing and lots of
use in this 21st century.

In 1618, Fabio Colonna published what I consider one of the hottest
musical figures of all time: a "sliding of the voice" in "enharmonic"
or "fifthtone" steps which he played on his 31-note keyboard, likely
tuned in a meantone with pure 5:4 major thirds -- and a 31-tET guitar
should do very nicely, if someone can work out the tab, so to speak,
not to mention a 31-tone organ a la Vicentino/Fokker.

This example features a sixth sonority, and actually moves through no
fewer than _four_ flavors of sixths before resolving this interval
between the outer voices to the octave. Here it is, with my notation
for the curious using an asterisk (*) to show a note raised by a
diesis or fifthtone:

C5 C*5 C#5 Db5 D5
G4 G4 G4 G4 A4
E4 E4 E4 E4 F#4
E3 E3 E3 E3 D3

<http://value.net/~mschulter/qcmfc001.mid>

Colonna calls this a "sliding of the voice" through "three enharmonic
steps." Vertically, we start with a usual minor sixth or thirteenth
E3-C5, move to what Vicentino in 1555 calls a "proximate minor sixth"
(or in 20th-century terms a neutral sixth) of E3-C*5, then to a usual
major sixth E3-C#5, and finally to Vicentino's "proximate major sixth"
or diminished seventh E3-Db5 (Dave Keenan and others call this a
"supermajor sixth," a fitting name in this kind of style).

In 31-tET, those "enharmonic steps" (C5-C*5-C#5-Db5) are each 1/31
octave (~38.71 cents); in 1/4-comma meantone with pure 5:4 thirds,
they're very slightly unequal, at ~41.06 cents (128:125) and ~34.99
cents, with the locations of these two sizes depending on the choice
of a tuning chain.

By the way, I play this progression myself (actually a three-voice
version easier to navigate) on a 24-note synthesizer in meantone (two
12-note manuals a 128:125 diesis or fifthtone apart), where it's
available in lots of positions; but with all 31 notes, you get full
transposibility, as both Vicentino and Colonna observe.

Speaking of microtonality in action, I might add that Colonna's
31-note instrument used a kind of "generalized keyboard" with five
ranks of 7 notes each spaced a fifthtone apart, and with some notes
replicated on more than one key.

In theory, as Monz and I have both noted, Colonna also discussed all
kinds of complex integer ratios including some involving higher primes
(e.g. 17:12). In practice, however, he went with something fairly
straightforward, at least for his 31-note keyboard: take a usual
meantone (likely with pure major thirds), and divide the octave into
31 more or less equal parts. That's also Vicentino's approach, and
both use it to make some very radical music.

Anyway, I'd say that in a classic 1/4-comma meantone or on a 31-tET
guitar, this is one hot progression right out of the Neapolitan scene
in 1618, and I hope it gives people lots of ideas.

Celebrating the new and the old, I wish the best to everyone here,
including my "comrades in numerology" Jacky and Monz.

With peace, love, and harmony to all,

Margo

🔗monz <joemonz@...>

🔗nanom3@...

🔗monz <joemonz@...>

> From: mschulter <MSCHULTER@V...>
> Date: Wed Jul 25, 2001 6:43 am
> Subject: Something old, something new
> </makemicromusic/topicId_30.html#30>
>
> ...
> In 1618, Fabio Colonna published what I consider one of
> the hottest musical figures of all time: a "sliding of the
> voice" in "enharmonic" or "fifthtone" steps which he played
> on his 31-note keyboard, likely tuned in a meantone with
> pure 5:4 major thirds -- and a 31-tET guitar should do very
> nicely, if someone can work out the tab, so to speak,
> not to mention a 31-tone organ a la Vicentino/Fokker.
>
> This example features a sixth sonority, and actually moves
> through no fewer than _four_ flavors of sixths before resolving
> this interval between the outer voices to the octave. Here it
> is, with my notation for the curious using an asterisk (*) to
> show a note raised by a diesis or fifthtone:
>
> C5 C*5 C#5 Db5 D5
> G4 G4 G4 G4 A4
> E4 E4 E4 E4 F#4
> E3 E3 E3 E3 D3

> From: nanom3@h...
> Date: Wed Jul 25, 2001 7:20 am
> Subject: Re: Something old, something new
> </makemicromusic/topicId_30.html#34>
>
> How would you write that in ratios or cents? I'd like to
> enter that into FTS and use it for voice training.

Hi Mary,

About a week ago on one of the lists there was a bit of debate
over the usefulness of MIDI-files for audio examples.

As I use MIDI a lot I'm well aware of its limitations. But
one really big advantage it has in a situation such as this
is that it allows one to examine the tuning of the audio
example, because it's a simple matter to open the MIDI-file
in any sequencer and look at the event list, which shows
all the pitch-bends. And the more-or-less standard use of
Cawapus (4096 per Semitone) for pitch-bend gives sufficiently
fine resolution to figure out to a fraction of a cent what
the tuning is.

So I performed surgery on Margo's file of the Colonna example,
and am here presenting several different versions of it.

Margo noted that her example was tuned by Scala in 1/4-comma
meantone. I could provide "ratios" for this, but they'd
be quite inconvenient-looking, so instead I simply notate
the actual meantone values as units of the 1/4-comma meantone
generator, which is (3/2) / ( (81/80)^(1/4) ).

Margo also noted that 31-EDO gives results very close to
the 1/4-comma meantone. I have included these as well.

Analysis of tuning of Margo Schulter's MIDI-file of
Colonna "fifth-tone" example:

Cawapus (Cakewalk pitch-bend units, 4096 per Semitone):

C5 0 C5 +1682 C#5 -981 Db5 +701 D5 -280
G4 -140 G4 -140 G4 -140 G4 -140 A4 -420
E4 -561 E4 -561 E4 -561 E4 -561 F#4 -841
E3 -561 E3 -561 E3 -561 E3 -561 D3 -280

Cents (C = 0):

0.0 41.1 76.0 117.1 193.2
696.6 696.6 696.6 696.6 889.7
386.3 386.3 386.3 386.3 579.5
386.3 386.3 386.3 386.3 193.2

1/4-comma meantone generators (C = 0):

0 -12 7 -5 2
1 1 1 1 3
4 4 4 4 6
4 4 4 4 2

31-EDO degrees (C = 0):

0 1 2 3 5
18 18 18 18 23
10 10 10 10 15
10 10 10 10 5

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

🔗nanom3@...

likely tuned in a meantone with
> > pure 5:4 major thirds --

Is that the same as saying 1/4 comma meantone?

so instead I simply notate
> the actual meantone values as units of the 1/4-comma meantone
> generator, which is (3/2) / ( (81/80)^(1/4) ).

This is actually a very funny statement to anyone other than a
microtuning enthusiast :-)

>
> Do you have an Excel spreadsheet that does these conversions for
you, especially the pitchbend to cents? Or do you know them by
heart. If you have a spreadsheet could I have a copy?

But thank you very much for doing the calculating work. Someday I'm
sure it will seem "simple" to me but it isn't yet, so I really value
your nuts and bolts contribution. And its ok if you even call me
a "moria" numerologist when you answer . I don't mind :-) And I
agree with you midi files definately are useful, especially if you
are on a slow connection.

Thanks
moria maria
>
> Cawapus (Cakewalk pitch-bend units, 4096 per Semitone):
>
> C5 0 C5 +1682 C#5 -981 Db5 +701 D5 -280
> G4 -140 G4 -140 G4 -140 G4 -140 A4 -420
> E4 -561 E4 -561 E4 -561 E4 -561 F#4 -841
> E3 -561 E3 -561 E3 -561 E3 -561 D3 -280
>
>
> Cents (C = 0):
>
> 0.0 41.1 76.0 117.1 193.2
> 696.6 696.6 696.6 696.6 889.7
> 386.3 386.3 386.3 386.3 579.5
> 386.3 386.3 386.3 386.3 193.2
>
>
> 1/4-comma meantone generators (C = 0):
>
> 0 -12 7 -5 2
> 1 1 1 1 3
> 4 4 4 4 6
> 4 4 4 4 2
>
>
> 31-EDO degrees (C = 0):
>
> 0 1 2 3 5
> 18 18 18 18 23
> 10 10 10 10 15
> 10 10 10 10 5
>
>
>
> -monz
> http://www.monz.org
> "All roads lead to n^0"

🔗monz <joemonz@...>

Hi Mary,

--- In MakeMicroMusic@y..., nanom3@h... wrote:
/makemicromusic/topicId_30.html#38

> > > likely tuned in a meantone with pure 5:4 major thirds --
>
> Is that the same as saying 1/4 comma meantone?

Yep. 1/4-comma meantone is the only version of "meantone"
that actually literally has *the* mean whole-tone (right
between 10/9 and 9/8) and also the only one which has
"pure 5:4 major thirds".

All other varieties of "meantone" have something close to
a 5:4, but not exactly a 5:4.

> > Do you have an Excel spreadsheet that does these
> > conversions for you, especially the pitchbend to cents?
> > Or do you know them by heart.

Yes and no. I did them on an Excel spreadsheet, but I'm
so used to doing the conversions that I often don't even
bother to save the spreadsheet when I'm finished putting
the numbers into a list posting. I didn't save this one,
but it's actually very easy.

To convert what I call "cawapus" to cents is simple:

1) Replace the MIDI-note name with the cents-value; i.e.,
if C = 0 cents, C#/Db = 100, D = 200, etc.;

2) Divide the cawapu value by 40.96 (because there are
40.96 cawapus in 1 cent) -- this gives the cents "correction";
i.e., -140 cawapus becomes -~3.4 cents;

3) Add the converted cawapu-to-cents value to that; i.e.,
"G -140" becomes 700 - ~3.4 = ~696.6.

> If you have a spreadsheet could I have a copy?

Sure... I can make another one and send it to you.

It's quite a bit more difficult to calculate the
1/4-comma meantone values, but even these are a piece
of cake after you know how to do it.

-monz

🔗monz <joemonz@...>

🔗mschulter <MSCHULTER@...>

Hello, there, Mary -- and Monz.

One advantage of a group like this is that we can share different
approaches to a question like ways that a singer might get acquainted
with the intervals of Colonna's "sliding of the voice" in fifthtones.

It's exciting that you share my enthusiasm for this progression, and
to use it for ear/voice training is a very special and fitting kind of
compliment to Colonna.

Mary, please let me lend you lots of encouragement. In 1555, Vicentino
predicted that singers would come to sing the most difficult leaps as
easily as they customarily sang a perfect fifth, and he offered some
tips for singing difficult intervals such as sevenths. Mainly his
advice was to train with his _archicembalo_ or "superharpsichord" with
its 31 steps per octave; and 446 years later, that might still be the
best of advice, with a bit of help from high technology and computers.

Monz, your tuning information looks it might be just what's needed to
set up this sequence in a program like Scala or FTS or whatever.

Maybe I might just add a perspective focusing on how the melodic
fifthtone steps for a singer tie in with some of the vertical
intervals like the different kinds of sixths.

Please let me emphasize that this is only one possible "road map," and
that hearing and singing are the main things.

Here I'll give cents for 1/4-comma meantone with pure 5:4 major
thirds, and for 31-tET, which was first to my knowledge precisely
defined by Lemme Rossi in 1666. In practice, especially on instruments
tuned by ear, the real-world variations might well be greater than any
theoretical differences between these two mathematical models -- not
to speak of the fluidity of the human voice once a singer enters the
picture.

I'll take the lowest note of a sonority as "0 cents," and show the
simultaneous or vertical intervals in parentheses above that, plus the
melodic steps of the highest voice in positive (ascending) or negative
(descending) cents. Here the steps of this voice are all upward, so
all the values are positive. Let's see what happens when we move
through those fifthtone steps in 1/4-comma meantone, with the signed
numbers above the notes of the highest line showing the "total
distance travelled" from the starting note:

+41 +76 +117 +193
C5 -- +41 -- C*5 -- +35 -- C#5 -- +41 -- Db5 -- +76 -- D5
(2014) (2055) (2090) (2131) (2400)
G4 ------------------------------------------- +193 -- A4
(1510) (1897)
E4 ------------------------------------------- +193 -- F#4
(1200) (1586)
E3 ------------------------------------------- -193 -- D3

By the way, although Colonna repeats the notes of the lower three
voices each time the upper voice moves, you could also treat the lower
voices as a kind of a drone, moving only for the concluding cadence,
against which you could sing the rising fifthtone steps.

Mary, one way for a singer to approach this is to focus on the
intervals that the fifthtone steps make with the lowest voice;
Vicentino says that the bass determines the modal organization of a
piece, and Tomas de Santa Maria (1565) takes the two outer voices as
most important. Here I'll ignore octaves, and treat E3-C5 as a minor
sixth at a pure 8:5 (meantone) or around 814 cents, for example,
rather than as the actual interval of 16:5 or a minor thirteenth at a
rounded 2014 cents:

+41 +76 +117 +193
C5 -- +41 -- C*5 -- +35 -- C#5 -- +41 -- Db5 -- +76 -- D5
(814) (855) (890) (931) (1200)
E3 ------------------------------------------- -193 -- D3

Here you start out at C5 on a usual minor sixth, a pure 8:5 in
1/4-comma meantone (major thirds and minor sixths are pure).

Now you move up to the first step of the "slide," a fifthtone higher
-- about 41 cents higher, C*5, and land on a "proximate minor" or
neutral sixth at around 855 cents. As Dan Stearns might say, feel free
to "take in" that neutral sixth, which Vicentino mentions in 1555 (he
finds neutral thirds quite consonant). From a JI viewpoint, it's close
to 18:11.

Next you move up by a slightly smaller fifthtone of 35 cents -- at
least in theory, or on a synthesizer's tuning table -- to a usual
major sixth at C#5, slightly wider than a pure 5:3 (884 cents) in this
meantone, or about 890 cents. You're now a small or chromatic meantone
semitone higher than where you started (C5-C#5), about 76 cents.

Next you move up by a 41-cent fifthtone to the "proximate major sixth"
or diminished seventh of E3-Db4, which Vicentino finds a rather tense
interval leaning toward dissonance, not an unlikely judgment in this
kind of style where it sounds very different than an expected major
sixth at or near 5:3. It's around 931 cents, actually very close to a
pure 12:7 -- a great 21st-century concord, but in this context a more
"special" interval.

In the concluding cadence, that wide major sixth expands to the octave
as you move Db5-D5, a small or chromatic semitone in meantone of
around 76 cents, in contrast with the more usual diatonic semitone
like C#5-D5 at around 117 cents. A JI-oriented person might compare
these steps to ratios of 25:24 (around 71 cents) and 16:15 (around 112
cents).

The vocal steps and vertical intervals are almost the same in 31-tET,
where those three ascending fifthtones are precisely equal at ~38.71
cents

+39 +77 +116 +194
C5 -- +39 -- C*5 -- +39 -- C#5 -- +39 -- Db5 -- +77 -- D5
(2013) (2052) (2090) (2129) (2400)
G4 ------------------------------------------- +194 -- A4
(1510) (1897)
E4 ------------------------------------------- +194 -- F#4
(1200) (1587)
E3 ------------------------------------------- -194 -- D3

Here are your intervals in 31-tET above the lowest voice, with the
different flavors of sixths almost identical to 1/4-comma meantone:

+39 +77 +116 +194
C5 -- +39 -- C*5 -- +39 -- C#5 -- +39 -- Db5 -- +77 -- D5
(813) (852) (890) (929) (1200)
E3 ------------------------------------------- -194 -- D3

Monz, your information might actually be more helpful in setting this
up with a software program, since such programs tend to map things in
terms of pitches rather than vertical intervals (at least Scala
does).

Anyway, Mary and anyone else who might be interested, this kind of ear
training is a really interesting side of making microtonal music: the
best of success to you, and I'd love to hear about experiences with
this kind of learning.

In peace and love,

Margo

🔗nanom3@...

Hi guys

In trying out Monz's suggestion I hack the midi file to discern the
tunings I realized that it was "simple" for me to to make an audio
file of this glorious progression.

. First I opened it in Logic, slowed the tempo and isolated the
voice I was planning to sing. I used Baroque Strings on the K2500
with some KDFX reverb and eq and recorded it into protools. Then I
added my voice.

> Mary, please let me lend you lots of encouragement. In 1555,
Vicentino
> predicted that singers would come to sing the most difficult leaps
as
> easily as they customarily sang a perfect fifth,

He is right. It isn't. But I also have the advantage of AutoTune 3,
which was very easy to set up using Monz's cents. And I am proud my
worst deviation was about 10 cents. Given a lttle more time, using
the Autone feedback I think I could get it better.

So here is a fruitful collaboration between artists theorists and
mathematicians and may it be the first of many more on this civil
list. I kept it real short (that was the hardest part for me :-))
becasue of bandwidth but plan to expand upon it tonight.

Gotta run but thanks everyone.

>
> In peace and love,
>
Mary