Mailing list post
From: Margo Schulter (2006-07-17)
Subject: Re: Keenan and Secor Honored! -- microabc
On Sat, 15 Jul 2006 "Hudson Lacerda" hfmlacerda@... wrote:
> c.m.bryan escreveu:
> >> <http://www.bestII.com/~mschulter/BlackLaundry.pdf>
> >
> >
> > What does the natural sign stand for in the penultimate measure?
>
> Good question.
> I just noticed that the values in cents shown below the `Shurist' scale
> does not correspond to the pitches defined in the peppermint24 table:
Hi, Chris and Hudson, and first some short answers -- then the longer
explanations.
Chris, that Sagittal natural sign for D in the middle voice and G in the
highest voice means exactly what it says; here the complication is that
our final or center for the piece is G/|\, located about 763 cents or a
near-14:9 above C, the '1/1' or reference note for Scala and the
peppermint.txt microabc tuning table posted by Hudson.
We need to know that in Peppermint Sagittal notation, /|\ shows an
alteration of about 58.680 cents. The the chromatic figure in the middle
voice of C/|\-D-D/|\ divides a usual 208-cent whole-tone into steps of
about 149.512 cents and 58.680 cents. The vertical interval A/|\-D is
equal to a fourth less this 59-cent step, or a near-9:7; and A-G/|\ to a
minor seventh less this step, or a just 12:7 (around 933 cents).
That should give a general idea of what's going on -- more below.
Hudson, the `Shurist' scale has its '1/1' (the basis for the cents values
in the pdf file) at C/|\, Scala note number 1 of the usual peprmint.scl
file and also peppermint.txt. We need to do 'KEY 1' in Scala to see the
intervals available this note (rather than C), which do include those
specified for the 'shurist' set.
Chris and Hudson, your two questions are closely related, because both,
I'd guess, relate at least in part to the situation when we make a note on
the upper Peppermint 12-note keyboard with a Sagittal /|\ modification our
'1/1' or point of reference. The reason for doing this is precisely that
certain intervals are available (in the desired direction) from a note on
the upper rather than lower keyboard. In "Black Laundry," these include
the best 9:7 and 12:7 flavors of intervals (with the 12:7 just) and an
ascending 59-cent step (e.g. D-D/|\) for septimal-type cadences.
In the 'shurist' set, these include the near 8:7 (around 229 cents in
Peppermint) and the just 12:7, important ratios in Shaahin's just tuning,
intervals not listed in peppermint.txt because they are not available
above C (or another note on the lower keyboard).
Now for the longer discussion:
-----------------------------------------------
1. Chris's question on "Black Laundry" naturals
-----------------------------------------------
Chris asks what the natural sign means in the final cadence of "Black
Laundry," which is as follows, with middle C here shown as C5 (since
it's MIDI note 60, five octaves above the lowest C of the MIDI
standard, in a conventional mapping):
1 2 3 4 5 6 | 1 2 3 4 5 6 ||
E/|\6 G6 E/|\6 G/|\6
C/|\6 D6 D/|\6
A/|\5 G/|\5
I'm going to resist the temptation to write a long essay about the
interpretation of the Sagittal notation signs in JI and Peppermint,
since that's included as part of the documentation for my archive to
be released in the next day or so, I hope.
Instead, I'll simply explain that the '/|\' sign in Peppermint shows
an interval of 58.680 cents, equal to the distance between the two
12-note keyboards. From a keyboardist's viewpoint, it might be read
simply to say, "Play this note on the upper manual."
From another point of view, in Peppermint the '/|\' sign can represent
either of two JI ratios: the "11-diesis" of 33:32 (53.273 cents), its
meaning in Sagittal JI notation; and also the "septimal thirdtone"
much favored by Archytas at 28:27 (62.961 cents).
Since all three notes of the first sonority A/|\-C/|\-E/|\ are
inflected by a /|\ symbol, the vertical intervals are equivalent to
those of plain A-C-E. In Peppermint, this means a regular minor third
of about 287.713 cents (a bit smaller than 13:11) and regular major
third of about 416.384 cents (a bit smaller than 14:11), with the
outer fifth at 704.096 cents (2.141 cents wide of 3:2).
Now the middle voice moves chromatically C/|\-D, a step of 149.512
cents (very close to 12:11), going from a regular minor third above
the lowest voice to a large septimal-flavor major third at 437.225
cents, close to 9:7. At the same time, the highest voice moves from
the fifth A/|\-E/|\ to the pure septimal major sixth A/|\-G at 12:7
(933.139 cents), proceeding via a step of 229.033 cents, close to a
large 8:7 tone. Thus we have a vertical sonority of 0-437-933 cents
very close to a just 7:9:12, poised for the usual expansion to fifth
and octave (with the upper voices moving in fourths).
Then the highest voice adds an embellishment to the expected
resolution expanding stepwise from major sixth to octave by first
momentarily returning to the fifth (G-E/|\), producing a brief
penultimate sonority of A/|\-D-E/|\ (about 0-437-704 cents, with a
pure 7:6 between the upper voices, close to a just 14:18:21). From
here we move to the expected G/|\-D/|\-G/|\.
Note that in this resolution, the middle voice has an incisive 59-cent
semitone or thirdtone motion (D-D/|\), which could be said here to
represent the septimal thirdtone of 28:27. In other contexts '/|\' can
also have its Sagittal JI meaning of a 33:32 diesis, since in
Peppermint D-G/|\, for example, is the best representation of 11:8
(i.e. 4:3 plus 33:32), here around 554.584 cents).
Melodically, the middle voice divides the usual tone C/|\-D/|\ at
208.219 cents into an extra large "chromatic semitone" of 149.51 cents
plus a compact 58.680-cent thirdtone, C/|\-D-D/|\, and this is the
kind of thing that happens in the early 14th-century Italian music of
Marchettus of Padua and some others (with the precise intonational
interpretation often debated, and inevitably variable in practice
because the main focus of this practice is free vocal intonation).
Anyway, there are two quick points to be made. The first is that
treating a note on the _upper_ keyboard as the vertical center or
"final" of the piece (here G/|\) makes possible septimal cadences
where one or more voices move upward by the 58.680-cent thirdtone
step. This makes the notation more visually complex if we follow the
convention (as here) of C on the lower keyboard as the reference, for
example with the regular sonority A/|\-C/|\-E/|\.
Also, note the usual Peppermint spellings of a near-9:7 major third as
a fourth less the '/|\' thirdtone (here A/|\-D), and of a pure 7:6
minor third as a major second or regular tone plus a '/|\' (D-E/|\).
-----------------------------------------------------------
2. Hudson's question on the Peppermint "shurist" tuning set
-----------------------------------------------------------
Hudson observes that some of the intervals in my Peppermint "shurist"
11-note set inspired by Shaahin Mohaajeri's just tuning dividing a
string length of 120 don't match the intervals listed in a microabc
tuning reference file with C as the 1/1 -- in contrast to C/|\ here.
C/|\ C/|||\ E\!!/ E(!) F/|\ F/|||\ G/|\
0 128.669 229.033 287.713 495.904 624.574 704.096
G/||\ G/|||\ B\!!/ B(!) C/|\
774.085 832.765 933.139 991.809 1200
12/7
The quick answer is that the 1/1 for "shurist" is indeed C/|\ or Scala
note number 1 (MIDI number 61) rather than C, so that in Scala we can
do a 'KEY 1' command to see Peppermint 24 with C/|\ as the 1/1, with
the "shurist" scale as 0-2-5-6-10-12-14-15-16-19-20-24 (with the first
listed Scala note as '1,' since note 0 or the 1/1 is not listed in a
.scl file):
! peprmint_key1.scl
!
Peppermint with C* or Sagittal C/|\ as 1/1 (24)
24
!
69.98955
128.66924
149.51152
208.19121
229.03349
287.71318
357.70273
416.38243
437.22470
495.90439
565.89395
624.57364
645.41591
704.09561
774.08516
832.76485
853.60713
912.28682
933.12909
991.80879
1061.79834
1120.47803
1141.32031
2/1
Peace and love,
Margo
Full thread (8 messages)
From: Margo Schulter (2006-07-15)
Subject: Keenan and Secor Honored! -- microabc
Hello, everyone, and I am pleased to announce that indeed Dave Keenan
and George Secor have been richly honored by Hudson Lacerda's
microabc, which implements Sagittal notation and now makes it
available for use with a temperament such as Peppermint 24, more
difficult to implement but now made practical and user-friendly by the
extraordinary efforts of this intrepid developer.
Here are a PDF score and MIDI files generated with microabc in
conjunction with abcm2ps and abc2midi for an example of a "shurist"
tuning set in Peppermint inspired by the shurist tuning and piece of
Shaahin Mohaajeri in just intonation, and the complete three-voice
rondeau "Black Laundry" (one PDF file and two MIDI files):
<http://www.bestII.com/~mschulter/BlackLaundry.pdf>
<http://www.bestII.com/~mschulter/pep_shurist_set.mid>
<http://www.bestII.com/~mschulter/BlackLaundry.mid>
For Shaahin's beautiful tuning based on a division of a string length
of 120, and a piece showing how it can be used, visit:
<http://240edo.tripod.com/sitebuildercontent/sitebuilderfiles/shurist.mp3>
Soon I hope to release a zip archive which will document the files and
procedures used to generate these and other forms of output. The PDF
file used the PostScript Type 1 font Sagittal.pfb developed as part of
the microabc project from a sagittal True Type font of the Keenan/Secor
sagittal endeavor. This font makes possible high-quality output of the
kind abcm2ps users might expect with hinting to improve quality on
lower-resolution devices.
Of course, as Hudson often emphasizes, microabc is only one part of
the abc suite of utilities, which have also developed very impressive
features to make it easier, for example, to write multi-voice notation
which can either be posted in ASCII for Usenet or Internet forums in a
score-like format with vertical alignment of voices, or used to
generate typeset PostScript output or MIDI files.
A fun aspect of microabc is that in addition to producing MIDI files
from a Peppermint score file in the expected intonation, it's possible
to generate MIDI files based on a JI interpretation of the Sagittal
symbols. Actually this is a bit easier to implement that the
Peppermint mapping, although Hudson has insulated me as a user from
most of the complications, and a Linux shell script can make the
process user-transparent (mainly the need with a Peppermint reading to
process the score file twice with microabc to get an abc file for
abc2midi).
When read in a JI interpretation, the Peppermint symbols produce a
tuning with two 12-note Pythagorean chains at a 33:32 apart -- making
available some neat variations and shading effects that can give
another pleasant angle to a piece, rather like the many readings of
medieval or Renaissance pieces offered by different performers. Here
are versions of the Peppermint "shurist" set (where reducing the small
neutral second at around 14:13 to a Pythagorean 2187:2048, or from
about 129 to 114 cents, might not exactly fit the original scheme),
and of "Black Laundry" -- the latter of which has many idiomatic
regular Pythagorean intervals for this piece in a more or less
14th-century style, and also exuberant final cadence (using a near-9:7
third and pure 12:7 sixth in Peppermint) which becomes yet more
exuberant with intervals of around 445 cents (128:99) and 943 cents
(512:297), and neat 33:32 dieses (another take on Marchettus of
Padua?).
<http://www.bestII.com/~mschulter/pep_shurist_set2JI.mid>
<http://www.bestII.com/~mschulter/BlackLaundry2JI.mid>
In fact, the "Black Laundry" rendition in JI demonstrates the kind of
thing that Sagittal was especially designed to accomplish: making it
possible to "port" a piece from one tuning system to another with
variations in color (whether taken as a compromise or advantage), but
retaining the basic logic of the music as much as possible.
Thank you, Hudson, for an amazing development effort that gives new
meaning to the felicitous words that may be found on the Sagittal
website: "Keenan and Secor Honored."
Peace, love, and many thanks,
Margo
From: Aaron Krister Johnson (2006-07-15)
Subject: Re: [MMM] Keenan and Secor Honored! -- microabc
Thanks Margo,
It's been on my plate for a while to check out Hudson's efforts---but alas
many a more pressing thing, including planned compositions, get in the
way....
I'd be interested in seeing a source file, perhaps annotated, so we could be
taken through the process--it might make it a bit easier to understand how it
all comes together that way.
All best,
Aaron.
On Friday 14 July 2006 10:16 pm, Margo Schulter wrote:
> Hello, everyone, and I am pleased to announce that indeed Dave Keenan
> and George Secor have been richly honored by Hudson Lacerda's
> microabc, which implements Sagittal notation and now makes it
> available for use with a temperament such as Peppermint 24, more
> difficult to implement but now made practical and user-friendly by the
> extraordinary efforts of this intrepid developer.
>
> Here are a PDF score and MIDI files generated with microabc in
> conjunction with abcm2ps and abc2midi for an example of a "shurist"
> tuning set in Peppermint inspired by the shurist tuning and piece of
> Shaahin Mohaajeri in just intonation, and the complete three-voice
> rondeau "Black Laundry" (one PDF file and two MIDI files):
>
> <http://www.bestII.com/~mschulter/BlackLaundry.pdf>
> <http://www.bestII.com/~mschulter/pep_shurist_set.mid>
> <http://www.bestII.com/~mschulter/BlackLaundry.mid>
>
> For Shaahin's beautiful tuning based on a division of a string length
> of 120, and a piece showing how it can be used, visit:
>
> <http://240edo.tripod.com/sitebuildercontent/sitebuilderfiles/shurist.mp3>
>
> Soon I hope to release a zip archive which will document the files and
> procedures used to generate these and other forms of output. The PDF
> file used the PostScript Type 1 font Sagittal.pfb developed as part of
> the microabc project from a sagittal True Type font of the Keenan/Secor
> sagittal endeavor. This font makes possible high-quality output of the
> kind abcm2ps users might expect with hinting to improve quality on
> lower-resolution devices.
>
> Of course, as Hudson often emphasizes, microabc is only one part of
> the abc suite of utilities, which have also developed very impressive
> features to make it easier, for example, to write multi-voice notation
> which can either be posted in ASCII for Usenet or Internet forums in a
> score-like format with vertical alignment of voices, or used to
> generate typeset PostScript output or MIDI files.
>
> A fun aspect of microabc is that in addition to producing MIDI files
> from a Peppermint score file in the expected intonation, it's possible
> to generate MIDI files based on a JI interpretation of the Sagittal
> symbols. Actually this is a bit easier to implement that the
> Peppermint mapping, although Hudson has insulated me as a user from
> most of the complications, and a Linux shell script can make the
> process user-transparent (mainly the need with a Peppermint reading to
> process the score file twice with microabc to get an abc file for
> abc2midi).
>
> When read in a JI interpretation, the Peppermint symbols produce a
> tuning with two 12-note Pythagorean chains at a 33:32 apart -- making
> available some neat variations and shading effects that can give
> another pleasant angle to a piece, rather like the many readings of
> medieval or Renaissance pieces offered by different performers. Here
> are versions of the Peppermint "shurist" set (where reducing the small
> neutral second at around 14:13 to a Pythagorean 2187:2048, or from
> about 129 to 114 cents, might not exactly fit the original scheme),
> and of "Black Laundry" -- the latter of which has many idiomatic
> regular Pythagorean intervals for this piece in a more or less
> 14th-century style, and also exuberant final cadence (using a near-9:7
> third and pure 12:7 sixth in Peppermint) which becomes yet more
> exuberant with intervals of around 445 cents (128:99) and 943 cents
> (512:297), and neat 33:32 dieses (another take on Marchettus of
> Padua?).
>
> <http://www.bestII.com/~mschulter/pep_shurist_set2JI.mid>
> <http://www.bestII.com/~mschulter/BlackLaundry2JI.mid>
>
> In fact, the "Black Laundry" rendition in JI demonstrates the kind of
> thing that Sagittal was especially designed to accomplish: making it
> possible to "port" a piece from one tuning system to another with
> variations in color (whether taken as a compromise or advantage), but
> retaining the basic logic of the music as much as possible.
>
> Thank you, Hudson, for an amazing development effort that gives new
> meaning to the felicitous words that may be found on the Sagittal
> website: "Keenan and Secor Honored."
>
> Peace, love, and many thanks,
>
> Margo
>
>
>
>
>
> Yahoo! Groups Links
>
>
>
From: c.m.bryan (2006-07-15)
Subject: Re: [MMM] Keenan and Secor Honored! -- microabc
> <http://www.bestII.com/~mschulter/BlackLaundry.pdf>
What does the natural sign stand for in the penultimate measure?
Chris
From: Hudson Lacerda (2006-07-15)
Subject: Re: [MMM] Keenan and Secor Honored! -- microabc
c.m.bryan escreveu:
>> <http://www.bestII.com/~mschulter/BlackLaundry.pdf>
>
>
> What does the natural sign stand for in the penultimate measure?
Good question.
I just noticed that the values in cents shown below the `Shurist' scale
does not correspond to the pitches defined in the peppermint24 table:
{} =============
{} PEPPERMINT-24
{} =============
{}index ASCII Sag name(s) Decimal codes cents JI approximations
0 C C|//| ^/144C . 0.000 1/1
1 C/|\ D!!!) ^/168C _/80D 58.680 28/27 33/32 1053/1024
2 C/||\ . ^/196C . 128.669 14/13
3 C/|||\ D!) ^/220C _/132D 187.349 10/9 392/351 19/17
4 D D|//| ^/144D . 208.191 9/8 44/39 273/242
5 D/|\ E!!!) ^/168D _/80E 266.871 7/6 (just)
6 E\!!/ . _/92E . 287.713 13/11 33/28
7 E(!) D)||| _/116E ^/197D 346.393 11/9 39/32
8 E E|//| ^/144E . 416.382 14/11 33/26
9 E/|\ F!) ^/168E _/132F 475.062 21/16
10 F F|//| ^/144F . 495.904 4/3 117/88 121/91
11 F/|\ G!!!) ^/168F _/80G 554.584 11/8
12 F/||\ . ^/196F . 624.574 56/39
13 F/|||\ G!) ^/220F _/132G 683.253 49/33
14 G G|//| ^/144G . 704.096 3/2 176/117 182/121
15 G/|\ A!!!) ^/168G _/80A 762.775 14/9
16 G/||\ . ^/196G . 832.765 34/21 21/13
17 G/|||\ A!) ^/220G _/132A 891.445 5/3 847/507
18 A A|//| ^/144A . 912.287 22/13 56/33
19 A/|\ B!!!) ^/168A _/80B 970.967 7/4
20 B\!!/ . _/92B . 991.809 16/9 39/22 484/273
21 B(!) A)||| _/116B ^/197A 1050.488 11/6
22 B B|//| ^/144B . 1120.478 21/11
23 B/|\ . ^/168B _/132c 1179.158 63/32 77/39 196/99
--
'-------------------------------------------------------------------.
Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
*N\ufffdo deixe seu voto sumir! http://www.votoseguro.org/
*Ap\ufffdie o Manifesto: http://www.votoseguro.com/alertaprofessores/
== THE WAR IN IRAQ COSTS ==
http://nationalpriorities.org/index.php?option=com_wrapper&Itemid=182
.-------------------------------------------------------------------'
--
_______________________________________________________
Voc\ufffd quer respostas para suas perguntas? Ou voc\ufffd sabe muito e quer compartilhar seu conhecimento? Experimente o Yahoo! Respostas !
http://br.answers.yahoo.com/
From: Margo Schulter (2006-07-17)
Subject: Re: Keenan and Secor Honored! -- microabc
On Sat, 15 Jul 2006 "Hudson Lacerda" hfmlacerda@... wrote:
> c.m.bryan escreveu:
> >> <http://www.bestII.com/~mschulter/BlackLaundry.pdf>
> >
> >
> > What does the natural sign stand for in the penultimate measure?
>
> Good question.
> I just noticed that the values in cents shown below the `Shurist' scale
> does not correspond to the pitches defined in the peppermint24 table:
Hi, Chris and Hudson, and first some short answers -- then the longer
explanations.
Chris, that Sagittal natural sign for D in the middle voice and G in the
highest voice means exactly what it says; here the complication is that
our final or center for the piece is G/|\, located about 763 cents or a
near-14:9 above C, the '1/1' or reference note for Scala and the
peppermint.txt microabc tuning table posted by Hudson.
We need to know that in Peppermint Sagittal notation, /|\ shows an
alteration of about 58.680 cents. The the chromatic figure in the middle
voice of C/|\-D-D/|\ divides a usual 208-cent whole-tone into steps of
about 149.512 cents and 58.680 cents. The vertical interval A/|\-D is
equal to a fourth less this 59-cent step, or a near-9:7; and A-G/|\ to a
minor seventh less this step, or a just 12:7 (around 933 cents).
That should give a general idea of what's going on -- more below.
Hudson, the `Shurist' scale has its '1/1' (the basis for the cents values
in the pdf file) at C/|\, Scala note number 1 of the usual peprmint.scl
file and also peppermint.txt. We need to do 'KEY 1' in Scala to see the
intervals available this note (rather than C), which do include those
specified for the 'shurist' set.
Chris and Hudson, your two questions are closely related, because both,
I'd guess, relate at least in part to the situation when we make a note on
the upper Peppermint 12-note keyboard with a Sagittal /|\ modification our
'1/1' or point of reference. The reason for doing this is precisely that
certain intervals are available (in the desired direction) from a note on
the upper rather than lower keyboard. In "Black Laundry," these include
the best 9:7 and 12:7 flavors of intervals (with the 12:7 just) and an
ascending 59-cent step (e.g. D-D/|\) for septimal-type cadences.
In the 'shurist' set, these include the near 8:7 (around 229 cents in
Peppermint) and the just 12:7, important ratios in Shaahin's just tuning,
intervals not listed in peppermint.txt because they are not available
above C (or another note on the lower keyboard).
Now for the longer discussion:
-----------------------------------------------
1. Chris's question on "Black Laundry" naturals
-----------------------------------------------
Chris asks what the natural sign means in the final cadence of "Black
Laundry," which is as follows, with middle C here shown as C5 (since
it's MIDI note 60, five octaves above the lowest C of the MIDI
standard, in a conventional mapping):
1 2 3 4 5 6 | 1 2 3 4 5 6 ||
E/|\6 G6 E/|\6 G/|\6
C/|\6 D6 D/|\6
A/|\5 G/|\5
I'm going to resist the temptation to write a long essay about the
interpretation of the Sagittal notation signs in JI and Peppermint,
since that's included as part of the documentation for my archive to
be released in the next day or so, I hope.
Instead, I'll simply explain that the '/|\' sign in Peppermint shows
an interval of 58.680 cents, equal to the distance between the two
12-note keyboards. From a keyboardist's viewpoint, it might be read
simply to say, "Play this note on the upper manual."
From another point of view, in Peppermint the '/|\' sign can represent
either of two JI ratios: the "11-diesis" of 33:32 (53.273 cents), its
meaning in Sagittal JI notation; and also the "septimal thirdtone"
much favored by Archytas at 28:27 (62.961 cents).
Since all three notes of the first sonority A/|\-C/|\-E/|\ are
inflected by a /|\ symbol, the vertical intervals are equivalent to
those of plain A-C-E. In Peppermint, this means a regular minor third
of about 287.713 cents (a bit smaller than 13:11) and regular major
third of about 416.384 cents (a bit smaller than 14:11), with the
outer fifth at 704.096 cents (2.141 cents wide of 3:2).
Now the middle voice moves chromatically C/|\-D, a step of 149.512
cents (very close to 12:11), going from a regular minor third above
the lowest voice to a large septimal-flavor major third at 437.225
cents, close to 9:7. At the same time, the highest voice moves from
the fifth A/|\-E/|\ to the pure septimal major sixth A/|\-G at 12:7
(933.139 cents), proceeding via a step of 229.033 cents, close to a
large 8:7 tone. Thus we have a vertical sonority of 0-437-933 cents
very close to a just 7:9:12, poised for the usual expansion to fifth
and octave (with the upper voices moving in fourths).
Then the highest voice adds an embellishment to the expected
resolution expanding stepwise from major sixth to octave by first
momentarily returning to the fifth (G-E/|\), producing a brief
penultimate sonority of A/|\-D-E/|\ (about 0-437-704 cents, with a
pure 7:6 between the upper voices, close to a just 14:18:21). From
here we move to the expected G/|\-D/|\-G/|\.
Note that in this resolution, the middle voice has an incisive 59-cent
semitone or thirdtone motion (D-D/|\), which could be said here to
represent the septimal thirdtone of 28:27. In other contexts '/|\' can
also have its Sagittal JI meaning of a 33:32 diesis, since in
Peppermint D-G/|\, for example, is the best representation of 11:8
(i.e. 4:3 plus 33:32), here around 554.584 cents).
Melodically, the middle voice divides the usual tone C/|\-D/|\ at
208.219 cents into an extra large "chromatic semitone" of 149.51 cents
plus a compact 58.680-cent thirdtone, C/|\-D-D/|\, and this is the
kind of thing that happens in the early 14th-century Italian music of
Marchettus of Padua and some others (with the precise intonational
interpretation often debated, and inevitably variable in practice
because the main focus of this practice is free vocal intonation).
Anyway, there are two quick points to be made. The first is that
treating a note on the _upper_ keyboard as the vertical center or
"final" of the piece (here G/|\) makes possible septimal cadences
where one or more voices move upward by the 58.680-cent thirdtone
step. This makes the notation more visually complex if we follow the
convention (as here) of C on the lower keyboard as the reference, for
example with the regular sonority A/|\-C/|\-E/|\.
Also, note the usual Peppermint spellings of a near-9:7 major third as
a fourth less the '/|\' thirdtone (here A/|\-D), and of a pure 7:6
minor third as a major second or regular tone plus a '/|\' (D-E/|\).
-----------------------------------------------------------
2. Hudson's question on the Peppermint "shurist" tuning set
-----------------------------------------------------------
Hudson observes that some of the intervals in my Peppermint "shurist"
11-note set inspired by Shaahin Mohaajeri's just tuning dividing a
string length of 120 don't match the intervals listed in a microabc
tuning reference file with C as the 1/1 -- in contrast to C/|\ here.
C/|\ C/|||\ E\!!/ E(!) F/|\ F/|||\ G/|\
0 128.669 229.033 287.713 495.904 624.574 704.096
G/||\ G/|||\ B\!!/ B(!) C/|\
774.085 832.765 933.139 991.809 1200
12/7
The quick answer is that the 1/1 for "shurist" is indeed C/|\ or Scala
note number 1 (MIDI number 61) rather than C, so that in Scala we can
do a 'KEY 1' command to see Peppermint 24 with C/|\ as the 1/1, with
the "shurist" scale as 0-2-5-6-10-12-14-15-16-19-20-24 (with the first
listed Scala note as '1,' since note 0 or the 1/1 is not listed in a
.scl file):
! peprmint_key1.scl
!
Peppermint with C* or Sagittal C/|\ as 1/1 (24)
24
!
69.98955
128.66924
149.51152
208.19121
229.03349
287.71318
357.70273
416.38243
437.22470
495.90439
565.89395
624.57364
645.41591
704.09561
774.08516
832.76485
853.60713
912.28682
933.12909
991.80879
1061.79834
1120.47803
1141.32031
2/1
Peace and love,
Margo
From: George D. Secor (2006-07-18)
Subject: Re: Keenan and Secor Honored! -- microabc
--- In [email protected], Margo Schulter <mschulter@...>
wrote:
>
> Hello, everyone, and I am pleased to announce that indeed Dave
Keenan
> and George Secor have been richly honored by Hudson Lacerda's
> microabc, which implements Sagittal notation and now makes it
> available for use with a temperament such as Peppermint 24, more
> difficult to implement but now made practical and user-friendly by
the
> extraordinary efforts of this intrepid developer.
> ...
> Thank you, Hudson, for an amazing development effort that gives new
> meaning to the felicitous words that may be found on the Sagittal
> website: "Keenan and Secor Honored."
May I also add my heartfelt thanks to both Hudson and Dave for their
patience in working through the many details that were required to
bring this to fruition (time not being available lately for me to
take a more active role in the process).
And it's no less a privilege and honor to be a member of this
alternate tunings community. If we keep on making music and
supporting one another, eventually the rest of the world is going to
notice.
+ Love, joy, peace , patience ...
--George
From: yahya_melb (2006-07-23)
Subject: Re: Keenan and Secor Honored! -- microabc
Hi George,
--- In [email protected], "George D. Secor" wrote:
>
[snip]
> And it's no less a privilege and honor to be a member of this
> alternate tunings community. If we keep on making music and
> supporting one another, eventually the rest of the world is going to
> notice.
>
> + Love, joy, peace , patience ...
... and tolerance!
Regards,
Yahya
From: George D. Secor (2006-07-24)
Subject: Re: Keenan and Secor Honored! -- microabc
--- In [email protected], "yahya_melb" <yahya@...> wrote:
>
>
> Hi George,
>
> --- In [email protected], "George D. Secor" wrote:
> >
> [snip]
> > And it's no less a privilege and honor to be a member of this
> > alternate tunings community. If we keep on making music and
> > supporting one another, eventually the rest of the world is going
to
> > notice.
> >
> > + Love, joy, peace , patience ...
>
> ... and tolerance!
>
> Regards,
> Yahya
Hmmm, that one wasn't mentioned in the source I was quoting from, but
here's the complete list:
+ Love, joy, peace, patience, kindness, goodness, faithfulness,
gentleness, self-control
Should we tolerate lies, slander, inflammatory language, or off-topic
messages on this list?
I think that the supreme test of tolerance is to examine one's own
attitude toward those who appear to be intolerant. ;-)
--George
P.S. - Please think carefully before replying to this message. :-)