Yahoo Tuning Groups Ultimate Backup tuning Re: [tuning] Digest Number 3731

Date: Thu, 20 Oct 2005 10:05:08 -0500
From: Aaron Krister Johnson <aaron@akjmusic.com>
Subject: the history of the quartertone? (was: British Microfest)

On Thursday 20 October 2005 9:54 am, Afmmjr@aol.com wrote:

> In the virgin microtonal world, a quartertone is as sinister an invader
> into norms as any other microtone. In fact, a quartertone is a gateway
> interval, often leading to other distinctive microtonalalia.

it's funny, is the quartertone so popular because of the acedemic popularity
of composers like Carillo and Wyschenegradsky, or is it the multiple of 12
factor, or both, or none of the above?

Johnny: Quartertones have entered the musical public's consciousness since
early music. It could even be the interval between a 5/4 and 81/64 (more
properly an "eighthtone"). The quartertone was the value for anything smaller than
a semitone. It was the difference between the 4/3 and an 11/8, heard clearly
in the natural Swiss alphorn. No need to be reactionary to it just because
it is the negative image of 12-tet. It holds a pedigree with its
identification with the 11th limit (fully explored by Wyschnegradsky).

Aaron: i know that busoni wrote about 18; it thus seems (my tentative
hypothesis, if
you will) that the whole idea of a 'tone' of 1/6 of an octave might be the
culprit: then the explorative mind seeks to divide *it* by simple integer
fractions, instead of exploring different sizes of tone.

Johnny: Actually, Busoni never made music in 18. It was just theory. Maybe
(maybe) he actually built a keyboard, but without being heard or discovered.
The concept of human beings dividing things they are familiar with through
bisection is as basic as human error.

Aaron: ...in this way, this is another aspect of 12-equal being an 'industry
standard'
tuning in a negtive way.

anyone have any other thoughts?

-aaron.

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗monz <monz@tonalsoft.com>

Hi Johnny and Aaron,

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> Aaron: i know that busoni wrote about 18; it thus seems
> (my tentative hypothesis, if you will) that the whole idea
> of a 'tone' of 1/6 of an octave might be the culprit:
> then the explorative mind seeks to divide *it* by simple
> integer fractions, instead of exploring different sizes
> of tone.
>
>
> Johnny: Actually, Busoni never made music in 18. It was
> just theory. Maybe (maybe) he actually built a keyboard,
> but without being heard or discovered.

Busoni wrote about 36-edo as 2 bike-chains of 18-edo,
in his 1906 book _Sketch of a New Aesthic of Music_.

And Johnny is correct that he never had an instrument
for producing that tuning accurately, and he never
composed anything in 36-edo.

That much is certain. Now ... I could be remembering the
rest of this incorrectly, but i think this is the story:
Busoni commissioned a 36-edo piano later in life, but it
wasn't finished until just after he died.

However, Haba befriended Busoni when he moved to Berlin,
and he did indeed compose probably the most significant
body of work in 36-edo:

date .. opus .. piece

1923 .... 15 ... 5th String Quartet
1928 .... 37 ... 6 Pieces for 6th-tone harmonium or string quartet
1937 .... 49 ... Duo for 2 violins, in 6th-tones
1937-42 . 50 ... Prijd Království Tvé (Nezamestnaní)
................ .. [Thy Kingdom Come (The Unemployed)]
................ .. (6th-tone musical drama in 7 scenes)
1952 .... 80 ... 10th String Quartet
1955 .... 85a .. Suite in 6th-tones for violin solo
1955 .... 85b .. Suite in 6th-tones for cello solo
1957-58 . 87 ... 11th String Quartet

Even that isn't much (Haba composed *many* more pieces
in 24-edo), but i don't know of any from other composers.

Carillo did have a 1/6-tone piano, and Gawel used a
19-tone subset of 36-edo, but i know nothing else about
either of them.

As for 18-edo itself, other than Busoni's theory and
Carillo's 1/3-tone piano, the only other person i know
of who used it was Ivor Darreg. Darreg made an 18-edo
guitar (Jonathan Glasier has it now, at Sonic Arts),
and i'm guessing that he composed some music with it,
but i've never seen or heard any.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> > However, Haba befriended Busoni when he moved to Berlin,
> > and he did indeed compose probably the most significant
> > body of work in 36-edo:
> >
> > date .. opus .. piece
> >
> > 1923 .... 15 ... 5th String Quartet
> > 1928 .... 37 ... 6 Pieces for 6th-tone harmonium or string quartet
> > 1937 .... 49 ... Duo for 2 violins, in 6th-tones
> > 1937-42 . 50 ... Prijd Království Tvé (Nezamestnaní)
> > ................ .. [Thy Kingdom Come (The Unemployed)]
> > ................ .. (6th-tone musical drama in 7 scenes)
> > 1952 .... 80 ... 10th String Quartet
> > 1955 .... 85a .. Suite in 6th-tones for violin solo
> > 1955 .... 85b .. Suite in 6th-tones for cello solo
> > 1957-58 . 87 ... 11th String Quartet
>
> It would be interesting to see these performed and recorded.

Someday i hope to use Tonescape to make computer realizations
of the three quartets, or at least one of them.

I meant to point out that one of these really is a major
work: "Thy Kingdom Come", a 1/6-tone opera!

> I wonder if Haba was aware of the 7-limit implications
> of 36-edo?

He probably was, because in 1925 he wrote a weighty tome
on his microtonal tunings and theories:

Neue Harmonielehre des diatonischen, chromatischen, viertel-,
drittel-, sechstel-, und zwöftel-tonsystems

['New harmony-textbook of the diatonic, chromatic (12-ET),
quarter- (24-ET), third- (18-ET), sixth- (36-ET), and
twelfth-tone (72-ET) systems'].

I have a copy of that in German, and also an English
dissertation that explains it in detail ... unfortunately,
i can't find either of them at the moment.

I'm not sure exactly how much Haba knew about the
mathematics of rational tunings, but he apparently
had a very good ear for microtonal inflections.

Here's my webpage about Haba:

http://tonalsoft.com/monzo/haba/haba-worklist.htm

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗monz <monz@tonalsoft.com>

Hi Gene,

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> >
> > I wonder if Haba was aware of the 7-limit implications
> > of 36-edo?
>
>
> He probably was, because in 1925 he wrote a weighty tome
> on his microtonal tunings and theories:
>
> Neue Harmonielehre des diatonischen, chromatischen, viertel-,
> drittel-, sechstel-, und zwölftel-tonsystems
>
> ['New harmony-textbook of the diatonic, chromatic (12-ET),
> quarter- (24-ET), third- (18-ET), sixth- (36-ET), and
> twelfth-tone (72-ET) systems'].
>
> I have a copy of that in German, and also an English
> dissertation that explains it in detail ... unfortunately,
> i can't find either of them at the moment.
>
>
> I'm not sure exactly how much Haba knew about the
> mathematics of rational tunings, but he apparently
> had a very good ear for microtonal inflections.

I still can't find the original German _Neue Harmonilehre_
by Haba, but i did find the English dissertation:

Battan, Suzette Mary. 1980.
Alois Haba's _Neue Harmonielehre des diatonischen,
chromatischen, viertel-, drittel-, sechstel-, und
zwölftel-tonsystems_.
Ph.D. dissertation, Eastman School of Music.

p 22:
"Haba's sixth-tone harmonium was constructed by [August]
Förster [of Bohemia] in 1927. The instrument was patterned
in many ways after the sixth-tone instrument that Busoni
designed in 1924.[footnote 30: Busoni's plans were not
realized by the firm of J. & P. Schiedmayer until a year
after his death.]"

The keyboard had 3 manuals, two of which contain
the entire 36-edo tuning: the top manual is a
duplicate of the bottom, structured thus:

* the thin raised white and black keys on each manual
contain the 12-edo notes;

* the larger white keys on the top and bottom manuals
contain the subset of 36-edo which is the 12-edo notes
raised by 1/6-tone;

* the larger white keys on the middle manual contain
the subset of 36-edo which is the 12-edo notes lowered
by 1/6-tone (or equivalently, raised by 2/6-tone, which
is how Battan describes it).

In my ASCII diagram of the keyboard below, i use
slashes to represent the coloring of the black keys,
and accidentals from my 72-edo HEWM notation:

* ">" = raise a 12-edo note by 1/6-tone (33.&1/3 cents)

* "<" = lower a 12-edo note by 1/6-tone (33.&1/3 cents)

(click the "Reply" button to see it formatted properly
on the Yahoo web interface)

-------------------------------------------------
| | | | | | | | | |//| | |//| | |//| | | |
| | | | | | | | | |//| | |//| | |//| | | |
| | | | | | | | | |//| | |//| | |//| | | |
|C | | |D | | |E | | |F#| | |G#| | |A#| | |C |
'--' | '--' | '--' | '--' | '--' | '--' | '--'
| | | | | | | | | | | | |
| C> |C#>|D>|D#>|E>|F> |F#>|G> |G#>|A> |A#>| B> |
-------------------------------------------------
| |//| | |//| | | | | | | | | | | | | |
| |//| | |//| | | | | | | | | | | | | |
| |//| | |//| | | | | | | | | | | | | |
| |C#| | |D#| | |F | | |G | | |A | | |B | |
| '--' | '--' | '--' | '--' | '--' | '--' |
| | | | | | | | | | | | |
|C#< |D< |D#<|E<|F<|F#<|G< |G#<|A< |A#<|B< |C< |
-------------------------------------------------
| | | | | | | | | |//| | |//| | |//| | | |
| | | | | | | | | |//| | |//| | |//| | | |
| | | | | | | | | |//| | |//| | |//| | | |
|C | | |D | | |E | | |F#| | |G#| | |A#| | |C |
'--' | '--' | '--' | '--' | '--' | '--' | '--'
| | | | | | | | | | | | |
| C> |C#>|D>|D#>|E>|F> |F#>|G> |G#>|A> |A#>| B> |
-------------------------------------------------

After describing Haba's microtonal instruments,
Battan first discusses his earliest theoretical
writings (all small booklets or unpublished manuscripts).

p 29:
" One of Haba's basic theories, discussed in his writings
about the half-tone system [i.e., 12-edo], deals with the
interrelationship of horizontal and vertical structures.
Haba considers the horizontal (melodic) presentation of a
group of tones to be comparable to the vertical (harmonic)
presentation of the same group of tones. Therefore, the
"basic form" (the term used by Haba) of any group of tones
is neither a scalar nor a chordal structure but both a scalar
and a chordal structure; for example, the "basic form" of
the tones C D E F G A B is the C-major scale or a secundal
chord consisting of the tones of the C-major scale.
Furthermore, Haba regards the C-major scale to be the
"basic scale" and because of this, the secudnal chord
consisting of its tones to be the basic harmony in the
half-tone system (rather than a tertian structure derived
from the tones fothe C-major scale, C E G B D F A)."

Battan notes that Haba conceived of 24-edo as "bichromatic",
that is (in my terminology), as 2 bike-chains of 12-edo
a semitone apart. This is exactly in keeping with
Moellendorf's theory, which is what originally inspired
Haba to work with microtonality. See my webpages on M.:

http://www.sonic-arts.org/monzo/moellendorf/book/contents.htm

p 35:
" A significant amount of Haba's early theoretical work
deals with acoustics, specifically with the relationships
between the overtones and the twelve notes of the
equal-tempered scale and among the overtones themselves.
Most of his work in this area is at a very elementary level,
never progressing beyond a presentation of simple acoustical
data such as the interval ratios between the fundamental and
each overtone and the fractional amounts that the frequencies
of overtones deviate from the tones of the equal-tempered
system.
Haba's early theoretical writing focuses on the quarter-tone
system rather than on the third-tone, the sixth-tone, and the
twelfth-tone systems, which are first discussed by Haba in
_Neue Harmonielehre_."

Battan describes a 2-string "monochord" which Haba had
in his home and on which he apparently made acoustical
experiments. It has 7 sets sets of numbers written on it
which essentially are the 1-udentity (i.e., the whole string)
of the subharmonic scales beginning on 22, 24, 26, 28,
32, 36, and 40, then the numbers which correspond to
the 4/3, 2/1, and 4/1 ratios above these marked of
one each quarter of the string.

So it does indeed seem that he was at least familiar
with some basic JI theory.

Finally moving on to _Neue Harmonielehre_ itself ...

p 74:
"In the treatise, he states that the use of microtones,
particularly quarter-tones, is justified for two basic
reasons, acoustical considerations and historical
precedence. Haba writes: 'The quarter-tone system is
principally based on the inherent law of divisions shown
by the overtones in the sixth octave of the overtone series.'
[p 194 of _Neue Harmonielehre_]"

Battan discusses Haba's 24-edo theory in some detail, then
describes his theories on 18-, 36-, and 72-edo on only p 83-84.

p 84:
"He points out that the sixth-tone system is a synthesis
of the half-tone and third-tone systems and that the
twelfth-tone system is the synthesis of the four other
systems. Haba's discussion of the third-tone, sixth-tone,
and twelfth-tone systems proves to be little more than a
cataloging of some of the possible sonorities available.
Haba believes that it is the reader's responsibility, rather
than the writer's, to decide how to use these constructions
in actual composition.
Despite its impressive listing of chordal and scalar
constuctions, the discussion of the microtonal systems sheds
little light on the actual function of microtones within a
microtonal system. Clearly, in Haba's conception, microtones
serve as much more than embellishing tones with[in] a
composition, but how and when they should be integrated
into the melodic and harmonic texture is not clarified."

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗monz <monz@tonalsoft.com>

Hi Aaron and other Chicago-area list members,

I meant to include this in my last (big) post about
Haba and 36-edo ... but actually perhaps it's better
that it appears here by itself.

There's an unpublished manuscript by Haba from 1939 in the
manuscript collection at the Newberry Library in Chicago,
which i (and probably you and a few others here) would
like very much to read: _Die Musik im Sechsteltonsystem_.

It's a typewritten manuscript composed of 5 articles:

I:
Die Musik im Sechsteltonsystem
[Music in the 1/6-tone system]

Ia:
Vierteltonmusik und Sechsteltonmusik
[1/4-tone music and 1/6-tone music]

II:
Die ersten Komposition für Viertelton-piano
[The first compositions for 1/4-tone piano]

IIa:
Harmonische Grundlagen des Zwölftonsystem: Der thematische
und der unthematische Musikstil
[Harmonic basis of the 12-tone system: The thematic and
athematic musical style]

IIb:
Musikalische und geisteswissenschaftliche Grundlagen des
thematischen und unthematischen Musikstils und neuer Musikformen
[Musical and spirit-scientific basis of the thematic and athematic
musical styles and new music forms]

Not quite sure how to translate "geisteswissenschaftliche"
... my attempt with "spirit-scientific" is probably a
little off.

So can anyone in Chicago get their hands on these?

-monz
http://tonalsoft.com
Tonescape microtonal music software

Re: [tuning] Digest Number 3731

🔗Afmmjr@aol.com

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗monz <monz@tonalsoft.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗monz <monz@tonalsoft.com>

🔗monz <monz@tonalsoft.com>

🔗monz <monz@tonalsoft.com>

🔗klaus schmirler <KSchmir@online.de>

🔗threesixesinarow <CACCOLA@NET1PLUS.COM>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗threesixesinarow <CACCOLA@NET1PLUS.COM>