Yahoo Tuning Groups Ultimate Backup tuning Re: [tuning] Digest Number 1164

> From: "Mats ï¿½ljare" <oljare@hotmail.com>
> Subject: Yet another MIDI
>
> http://www.angelfire.com/mo/oljare/images/dream.mid
>
> "Dream Tone"uses various 22tet decatonic scales.

This is the wrong URL, I believe.

>
> New demo from a little southern band called The Obese Firemen. The demo,
> "white Trash seeks same" is the weirdest stuff your ever hear in your
> life.
> Includes the hit "The Columbien High Anthem"
> Go to www2.msstate.edu/~jle10/OBESE_FIREMEN for Mp3 samples or
> Email jason1275@juno.com
> Only 7.00 for a 14 song CD.

Sure would like to hear it, but I am denied access. I can get to Amazing
Grace, though. I bet it's just a matter of setting permissions.

> Basically, it is a single stringed movables capo system that we install into
> guitars. Each string gets a tiny bead which slides up and down the string,
> and is held at any fret it is left at. All six beads slide over the nut, so
> any combination can be used from zero to all six. This lets the player set
> up any chord as a base. Not true down tuning, more like 'uptuning', when
> used in combination, the limits are set only by the players imagination.
> There are photos and details of our guitar at the super easy to remember
> address of www3.sympatico.ca/abacuscapo
> Our guitars have only been played by a handful of players, and seeing as
> though we are always striving to make it better, we'd love to hear any
> comments you may have.
> Thank You
> Jonathan Sims
> Abacus Capo

Looks like something that could be very useful, and could be used with
microtonal guitars also. Plus, it appears that the beads could be placed
anywhere behind the fret so that the pitch is not necessarily tied to
the pitch dictated by the fret.

--
John Starrett
"We have nothing to fear but the scary stuff."
http://www-math.cudenver.edu/~jstarret/microtone.html

🔗Daniel Wolf <djwolf1@matavnet.hu>

Joseph Pehrson wrote:

"I have here a simple FAQ answer to Robert Walker's "Newbie" question.
Is it dumb enough? I think probably so..."

It's dumb enough, and beginners catch some of the information, but it's
historically not quite right. The question is: should we use a historical
fiction to get people going, or should we start off with as being as truthful as
possible (all the while knowing every history is in necessarily fictional)?

"Q. Why does the 12 tone scale have 12 notes, and why are there "black
and white" keys on the piano?

A. Our "common" 12 note system, such as one would see on a modern
piano, stems from a "Pythagorean" system which uses a string of
"pure," (unbeating) fifths. This system was developed in the Middle
Ages, in response to the use of pure fifths as a basic consonance."

This confuses two different systems: they keyboard (and that fabled organ in
Halberstadt) system which does stem from the middle ages, but only slowly
settled down into a 7-5 arrangement, and pythagorean intonation, which is
ancient.

"A cycle of fifths will go "once around" 11 times before, eventually,
approximating an octave at the 12th fifth. (It doesn't quite.
see "Pythagorean comma")"

Better to say something like "one can stack fifths on top of each other" instead
of "cycle", and "by the time one reaches the 12th fifth from the bottom it comes
very close to seven octaves".

"If one were to transpose the pitches of this chain to within one
octave, one gets the 12 notes we presently use. The "closest" fifths
to the starting point were given "white" keys and those further away
and generally less used, were given "black keys.""

This only works if we're in D-dorian.

********

Joseph: perhaps starting out with the number 12 is a mistake; for notation and
keyboarding, 7 is really the key number and 12 is a consequence of a particular
way of working with 7. Maybe an approach like the following would work, much of
which is cribbed from the Josquin chapter in Diether de la Motte's counterpoint
textbook _Kontrapunkte_. The following is not really a draft, but a very rough
sketch of how I'd handle the topic, which I don't really want to do.

"Q. Why does the 12 tone scale have 12 notes, and why are there 5 black
and 7 white keys and why do we notate music the way we do?

A: Let's go back arbitrarily about 500 years, to central Europe around the year
1500, an era associated with the composer Josquin des Prï¿½s. The principal tonal
material available to composers was derived from the series of eight fifths:

B - F - C - G - D - A - E - H

of which composers usually used either these seven tones:

F - C - G - D - A - E - H

or these:

B - F - C - G - D - A - E

(B, a perfect fifth below F, is equivalent to Bb in modern English notation, H
is equivalent to B natural).

Since the composer only need to manage seven tones at a time, a staff with seven
places and a keyboard with seven keys were reasonable and compact frameworks
with which to work. To keep it compact, these seven tones were assigned to
consecutive places on the staff and keyboard:

C - D - E - F - G - A - H

When the composer wanted to use the the second collection, a symbol, the flat,
indicating a tone a chromatic semitone lower, was added to the staff on the line
or space associated with H, thus showing the singer or player that the composer
wanted the tone B (or, in English terms, Bb) instead of H (English: B natural),
giving this scalar collection:

C - D - E - F - G - A - B(b)

(There are in fact, illustrations of early instruments showing keyboards with
exactly seven + one keys to accomodate precisely these two collections.)

In Josquin's time, tones not properly belonging to these two collections were
also used. These tones were not necessarily notated, but the players were
expected to provide them. The _subsemitonium_ (semitone below), a pitch
neighboring one of the proper tones in the collections above, was featured
especially in the _clausula_, stock melodic formulae associated with the ends of
musical phrases.

In the first collection, there were already semitone intervals available below F
and C, but extra tones needed for _clausula_ below

D, that is, D - C# - D
G, this is, G - F# - G
and
A, that is, A - G# - A

In the second collection, there were already semitones below F and Bb, and these
additional tones were incorporated for _clausula_ below:

G, this is, G - F# - G
D, that is, D - C# - D
and
C, that is, C - B natural - C

In addition, Josquin and his contemporaries would sometimes expect in the second
collection that E would be replaced by an Eb. Composers would not explicitly
notate this, but singers and players would have known when to make the
substitution in order to avoid an augmented fourth or diminished fifth between
Bb and E .

In this manner, musician were managing a total collection of these twelve tones:

C c# D eb E F f# G g# A Bb B C

which happened to fit nicely onto a keyboard in the familiar 7 + 5 arrangement,
which may have been implemented as early as February 23, 1361, in Nicholas
Haber's Halberstadt organ:

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

(The familiar keyboards today color-code the front row with ivory or white keys
and the back row in ebony or black; using different materials or colors for the
different rows of keys is an old practice, but the present white-black
combination became fixed only around the turn of the nineteenth century).

Up to this point, we've not mentioned anything about how these pitches were
tuned. The initial string of perfect fifths could have been tuned in pure 3:2
intervals, which is called, to honor one of the possible ancient discoverers of
this sequence, pythagorean tuning (see PYTHAGOREAN). Subsequently, someone
noticed that the additional tones (c#, eb, f#, g#) could also be added to this
series of fifths:

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

Indeed, one could continue adding fifths indefinitely in either direction and
this would be accomodated in the notation through the appropriate addition of
flats or sharps.

...Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F# - C# - G# - D# - A#
... etc.

Each added tone allowed one to play music at an additional pitch height, a
procedure now known as tranposition.

For most musical repertoire in the 16th through 18th centuries, however, a
collection of 12 fixed pitches for keyboards and fretted instruments seemed to
be a powerfully attractive economy as music was growing increasingly consumptive
of tonal resources. The problem became how to tune a set of 12 pitches in a way
that would satisfy ever new, multiple, and often contradictory requirements.

One of the requirements was for increased vertical consonance. The thirds of
pythagorean tuning were generally considered to be not pleasant enough to serve
as stable consonances in music, while real musical repertoire increasingly used
thirds as consonances. The initial solution, probably derived from Islamicate
tuning practices, used an the pythagorean interval created by eight consecutive
perfect fifths as a close approcimation of a just major third (see PYTHAGOREAN).
A later solution to this problem came in the form of Meantone temperament (MT,
see MEANTONE) where the difference between a major third and of an octave
reduced series of four perfect fifths (the SYNTONIC COMMA) was distributed over
the series of fifths, a process known as temperament (see TEMPERAMENT). 12
pitches in MT allows one to play satisfactory major triads on eight tones, and
to transpose to perhaps six tonalities.

The limited number of triads and tonalities available in a MT with only 12 tones
per octave provoked a search for alternative tempering schemes. Given a sequence
of 12 tones separated by perfect fifths: a thirteenth tone, twelve fifths above
the first, will overshoot the tone seven octaves above the first tone by a very
small interval, the _pythagorean comma_ (ratio: 531441:524288, about 23.5 cents,
see PYTHAGOREAN). If this small interval is divided and distributed among each
of the 12 fifths, one arrives at twelve collections of seven pitches with
identical intervallic content, differing only in pitch height. This twelve-tone
equal temperament (see _12tet_) has been, at least in theory, the principal
tuning system for western music for approximately the last 150 years, and longer
for fretted stringed instruments. In the late stages of the MT era and prior to
the the rise of 12tet, many alternative well- or circulating temperaments (see
WELL TEMPERAMENT) were in use, each having their distributive own strategies.

DJW

🔗jpehrson@rcn.com

--- In tuning@y..., "Daniel Wolf" <djwolf1@m...> wrote:

/tuning/topicId_19843.html#19862

Thank you, Daniel Wolf, for your interesting FAQ answer on our
present system of 12 pitches... Most probably this will work quite
nicely. Hopefully the "newbie" would be able to work with this. I had
no trouble getting through it, myself (but then again, I have a
DMA in music... :) :)

Seriously, though, it probably will be fine for the intelligent
beginner, and, obviously more historically accurate than the short
portrayal I presented...

I did have a question about it, though.

(you write:)
> In Josquin's time, tones not properly belonging to these two
collections were also used. These tones were not necessarily notated,
but the players were expected to provide them. The _subsemitonium_
(semitone below), a pitch neighboring one of the proper tones in the
collections above, was featured especially in the _clausula_, stock
melodic formulae associated with the ends of musical phrases.
>
> In the first collection, there were already semitone intervals
available below F and C, but extra tones needed for _clausula_ below
>
> D, that is, D - C# - D
> G, this is, G - F# - G
> and
> A, that is, A - G# - A
>
> In the second collection, there were already semitones below F and
Bb, and these
> additional tones were incorporated for _clausula_ below:
>
> G, this is, G - F# - G
> D, that is, D - C# - D
> and
> C, that is, C - B natural - C
>

I guess the question I would ask is how the singers knew what pitch
to sing for the "semitone...?" It seems as though you are saying
that this process or the neighboring tones in the clausula came
BEFORE
the realization of the additional pitches derived from a chain of
fifths...(??)

Is this true?? And, if so, what did they go by?? Did they just try
to divide the tones in half??

If so, then, it's somewhat just "coincidence" that an "extended"
circle of fifths would result in these pitches (??) That seems to be
the "implication" in your description...

>Subsequently, someone noticed that the additional tones (c#, eb, f#,
g#) could also be added to this series of fifths:
>
> Eb - Bb - F - C - G - D - A - E - B - F# - C# - G#
>
> Indeed, one could continue adding fifths indefinitely in either
direction and this would be accomodated in the notation through the
appropriate addition of flats or sharps.
>
> ...Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F# - C# -
G# - D# - A#... etc.
>

So is seems this "realization" really came AFTER the "semitonal"
practice was already underway...

In a way, the concept rather appeals to me, since it again
illustrates the "linearity" of music over, possibly, theoretical,
considerations....

I enjoyed the rest of the essay, but do you realize you managed to
fit in Meantone, 12-tET, transposition, and almost everything most
important to music theory in ONE essay?? That might be a bit much
for just one entry, yes??

In any case, I think this entry, pretty much as you have written it,
should be included in the FAQ, as should the entry you did on
meantone...

With a little "cleaning up" would you accept that they be included??

In any case, I'm really enjoying this FAQ process already... I'm
learning something new in just about every stage of it!

Thanks so much again, and I hope you'll agree to letting these
materials be used, if in only slightly modified form...

_______ _____ _____ _
Joseph Pehrson

Re: [tuning] Digest Number 1164

🔗Robert Walker <robert_walker@rcwalker.freeserve.co.uk>

🔗jpehrson@rcn.com

🔗John Starrett <jstarret@carbon.cudenver.edu>

🔗Daniel Wolf <djwolf1@matavnet.hu>

🔗jpehrson@rcn.com

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>