Haba MIDI & Monzo quarter-tone notation

Here are some thoughts on my MIDI sequence of the
opening of Alois Haba's _2nd Quartet_, and on a
quarter-tone notation I created to re-notate Haba's
music so that I could better understand what he is
doing.

SIGNIFICANT QUARTER-TONE MUSIC
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I just uploaded a refined version of my MIDI sequence
of the opening of Haba's _2nd Quartet_:
http://www.ixpres.com/interval/monzo/haba/2qt.mid

and would love to get some feedback.
(hope you have good string sounds...)

I know many microtonalists out there are not crazy
about 24-ET (hi Paul), but I think this piece really
deserves a plug.

I'm really warming to Haba's music - I think this
is a great piece, and this is only the very beginning.

As Partch argued so much, no amount of theory can
replace the function of *significant music* in changing
one's willingness to accept an alternative tuning system.

QUARTER-TONE ACCIDENTALS: HABA'S, AND MY ASCII CONVENTION
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Haba used a symbol like this

|
>

(but with the stem and the lower part connected)
to represent a quarter-tone sharp: I use ^, and

|
(

(again, the two parts connected, the lower part more round)
to represent a quarter-tone flat: I use v.

HABA'S DIFFERENT USES OF QUARTER-TONES
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Haba's use of quarter-tones in this particular piece
falls into three distinct categories:

1) The notes of the 12-eq chromatic scale are 'targets',
and the quarter-tones above and below (more often above)
are used as appogiaturas which resolve to the 12-eq pitch.
The appogiaturas are usually of longer duration than the
resolving note.

2) Melodic passages of successive quarter-tone [50=cent]
intervals which can be considered subsets of the 24-eq
(ultra-)chromatic scale.

3) Melodic passages, sometimes in parallel harmony, of
successive '3/4-tone' [150-cent] intervals, which can
be considered subsets of octatonic scales comprised
entirely of conjunct 3/4-tone steps, i.e.:

ratio cents cents between degrees

2^(21/24) 1050
> 150
2^(18/24) 900
> 150
2^(15/24) 750
> 150
2^(12/24) 600
> 150
2^( 9/24) 450
> 150
2^( 6/24) 300
> 150
2^( 3/24) 150
> 150
2^( 0/24) 0

Later, as can be heard in the opening of the _14th Quartet_
(also on my website), he used pentatonic scales with essential
5/4-tone [= 1 & 1/4-tone = 250 cent] intervals. (I'll shortly
be sending a posting on that piece.)

MONZO QUARTER-TONE NOTATION
---------------------------

I've invented a nice quarter-tone notation which
eliminates all accidentals. It makes it easy to
visualize all three of Haba's characteristic uses
of quarter-tones in the _2nd Quartet_: the quarter-tone
appogiaturas, the 'little steps' (i.e., conjunct
quarter-tone passages) in the melodic shapes, and
best of all, the odd-sized melodic steps in the frequent
places where Haba uses subsets of '3/4-tone scales'.

The essentials of the notation work like this:

Each pitch in the 12-eq scale occurs on a line.
Thin lines represent pitches in the C-major diatonic
scale, analagous to the 'white keys' on the piano
keyboard, and bold lines represent the 'black keys'.
(In this ASCII version, '===' represents a bold line.)

Spaces represent the quarter-tone pitches in between
all the 12-eq pitches.

Each staff represents an 'octave', with the line
representing 'C' on each staff missing - 'C' when
necessary is written on a ledger-line.

In this example, the ratio 2^(0/24) [= n^0] is
given to 'C'. The letter-name notation uses my
ASCII convention.

ratio cents letter

2^( 0/24) 0 C ---
2^(23/24) 1150 B^/Cv
2^(22/24) 1100 B ------------------------------
2^(21/24) 1050 Bv
2^(20/24) 1000 Bb/A# ==============================
2^(19/24) 950 A^
2^(18/24) 900 A ------------------------------
2^(17/24) 850 Av
2^(16/24) 800 Ab/G# ==============================
2^(15/24) 750 G^
2^(14/24) 700 G ------------------------------
2^(13/24) 650 Gv
2^(12/24) 600 Gb/F# ==============================
2^(11/24) 550 F^
2^(10/24) 500 F ------------------------------
2^( 9/24) 450 Fv/E^
2^( 8/24) 400 E ------------------------------
2^( 7/24) 350 Ev
2^( 6/24) 300 Eb/D# ==============================
2^( 5/24) 250 D^
2^( 4/24) 200 D ------------------------------
2^( 3/24) 150 Dv
2^( 2/24) 100 Db/C# ==============================
2^( 1/24) 50 C^
2^( 0/24) 0 C ---

(The idea of representing the black-and-white layout
of the piano keys on the musical staff was adapted from
the notational system presented by Max Meyer, _The
Musician's Arithmetic_.)

By stacking these one on top of the other, on a regular
8 & 1/2 " x 11 " sheet of paper I can represent an
8-octave span from 2^-4 to 2^4, where 2^0 [= n^0] = 'middle-C'.

For the Haba Quartet, I can simply write all 4 of the
parts right onto this score, which is really a sort of
huge 'great staff', and see all the polyphonic lines at once,
without the cumbersome quarter-tone notation used by Haba
himself (altho his is better than some others). It works
beautifully.

When I can figure out how to get Finale to create this
notation, I'll put it on my Haba page.

SOME QUARTER-TONE MANUSCRIPT PAPER TO CALL MY OWN
-------------------------------------------------

Here's a sample you can print out and use for your
own quarter-tone manuscript paper. I made my actual
paper using Microsoft Word's line-drawing tool.

The numbers with exponents in the 'C' spaces, delineating
the 'octave' registers, can be considered clefs.

Try it - you'll like it!

2^3
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2^2
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2^1
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n^0
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2^-1
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2^-2
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2^-3

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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