Yahoo Tuning Groups Ultimate Backup makemicromusic More Sagittal: _O Europae

Hello, everyone, and I'm pleased to report that more music is
available in Sagittal notation: a piece called _O Europae_ which I
composed in the context of this group in 2004, when it was announced
here that the European Union was expanding to 25 members, and that
this might be a fitting subject for some compositions.

<http://www.bestII.com/~mschulter/O_Europae.pdf>
<http://www.bestII.com/~mschulter/O_Europae.mid>

Both the score in PDF format using the new Sagittal-2 font still in
testing, and the MIDI file, were produced using Hudson Lacerda's
microabc in conjunction with other abc utilities and ghostscript (for
converting PostScript to PDF). The temperament is Peppermint 24, in
which this piece was conceived.

By the way, doing some abc notation isn't the worst way to spend the
second day here locally where the temperature has gone over 40 degrees
Celsius (or 104 degrees Fahrenheit).

In addition to demonstrating the flexibility of the Sagittal notation
and microabc in showing microtonal nuances such as direct comma shifts
(see measures 26-27 of score, or listen to the MIDI at around 0:39,
which timidity++ for some reason places at around "0:44" on its time
indicator), this piece raises an interesting point on the relation of
text and music.

As Stephen Szpak and others were discussing this general question, I
would like to make it especially relevant here by focusing on the
topic of verbal and musical rhetoric in a microtonal setting. It is
interesting that Nicola Vicentino, in his treatise of 1555 on _Ancient
Music Adapted to Modern Practice_ which described a keyboard including
a complete meantone cycle of 31 notes per octave (1/4-comma or 31-EDO
temperament?), advocated the view that any dissonant interval might be
useful in order to express the sentiments of a text.

While a fascination with interval qualities and expressive dissonances
became an important aspect of conventional late 16th-early 17th
century practice and theory, the microtonal side of Vicentino's music
and theory may only now be getting full consideration. While
Vicentino's context seems to be meantone temperament, some of his
aesthetic principles might be applied to other tunings, such as the
Peppermint temperament in which _O Europae_ was conceived.

To keep things topically focused, I will make it my policy to tie
discussions on text/tuning issues to specific pieces, with a post
about _O Europae_ to follow soon. First, however, I'd like to give
people who aren't yet familiar with this piece a chance to hear it
and form your own impressions.

The mapping of Peppermint used for this Sagittal version follows this
Scala tuning for an octave of C-C oriented around C on the upper
manual of the 24-note Peppermint keyboard:

! pep24-key1.scl
!
Peppermint mapping with C on upper keyboard as 1/1
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

🔗c.m.bryan <chrismbryan@...>

🔗yahya_melb <yahya@...>

Hi Margo,

--- In MakeMicroMusic@yahoogroups.com, Margo Schulter wrote:
>
> Hello, everyone, and I'm pleased to report that more music is
> available in Sagittal notation: a piece called _O Europae_ which I
> composed in the context of this group in 2004, when it was
announced
> here that the European Union was expanding to 25 members, and that
> this might be a fitting subject for some compositions.
>
> <http://www.bestII.com/~mschulter/O_Europae.pdf>
> <http://www.bestII.com/~mschulter/O_Europae.mid>
>
[snip]

> As Stephen Szpak and others were discussing this general question,
I would like to make it especially relevant here by focusing on the
topic of verbal and musical rhetoric in a microtonal setting.
[snip]
> To keep things topically focused, I will make it my policy to tie
> discussions on text/tuning issues to specific pieces, with a post
> about _O Europae_ to follow soon. First, however, I'd like to give
> people who aren't yet familiar with this piece a chance to hear it
> and form your own impressions.

I played the midi file first, and enjoyed the music. I then
imported the midi file in NoteWorthy Composer, changed the timbres
to all synth voice, set the dynamics to mp (the family is sleeping)
and played it again, enjoying it even more. Then I downloaded the
pdf, extracted the lyrics for the tenor part, pasted them into my
Noteworthy score, adjusted for broken syllables, *put in some slurs
to phrase words at easily breathable lengths*, and played it again.

Only after changing the phrasing to suit the words did I understand
how the rhythms had arisen in your setting! Which for me speaks
volumes about the connections between the music and he text.

Mind you, on my import, I'd lost all subtleties of tuning (NWC
doesn't seem to import pitch bends, unfortunately. So what I heard
(except the first time) was only a 12-EDO approximation of your
music. I now have to work out which ofthe 24 notes you actually
used, so I can bend them correctly. (I didn't like the origianl
instrumentation very much.)

Regards,
Yahya

🔗Margo Schulter <mschulter@...>

On Tue, 26 Jul 2006, c. m. bryan wrote:

[...]

> Secondly, Margo, I really enjoyed "O Europae," and the accidentals
> seem very appropriate because they're not too overwhelming.
>
> I just had a question about the voice-leading, since their are many
> parallel "perfect" intervals, I was wondering if you could explain how
> the linear aspect of this is working. (on-or-off list!) David Bowen
> and I are discussing part-writing issues together, it might be useful
> to pick your brain for that as well. :)

Please let me briefly comment that parallel fifths and fourths are routine
in 13th-century technique, and also in many 14th-century progressions for
three or more voices, although "modern" 14th-century theory discourages
parallel fifths in simple two-voice writings (where they still occur now
and then in various compositions). By the mid-15th century, avoiding
parallel fifths is a fairly consistent rule, and at the same time thirds
are becoming more stable. In short, parallel fifths are a medieval
commonplace -- but here sometimes mixed with some less "common" things, as
your next comment might reflect.

A quick and possibly relevant comment on the question of parallels, which
you're welcome of course to share with David Bowen, is that 13th-14th
century cadences very typically involve parallel fifths and/or fourths, in
a context where, however, the impelling or directing two-voice resolutions
involve progressing from an unstable to a stable interval by stepwise
contrary motion (e.g. 3-1, 3-5, 6-8, 2-4, 7-5), or sometimes
"near-conjunct" contrary motion with one voice moving by step and the
other by a third (often 2-5). The main intonational variable is that a
medieval or neomedieval interval aesthetic tends nicely to fit a tuning
system like the historical Pythagorean, or the modern Peppermint, where
fifths and fourths are just or fairly close to it, and thirds and sixths
have rather complex ratios (81:64 and 32:27 in Pythagorean; close to 14:11
and 13:11 in Peppermint).

> If I had to make a criticism, the cadence at measure 30 felt strange
> after 2 listens; if I can I will listen a few more times and see if
> it "settles" in my ear.

That's more than fair enough, and as I'll explain in an article I'm about
to post about words and music in _O Europae_, that passage was meant to be
a bit "unsettling," although for me the effect is moderated by my
familiarity with the basic idioms at play. Not to duplicate that article,
I might mention an intonational point not made there, which might help to
explain a suspension idiom which can apply in more "conventional" (in my
idiom, that is) passages as well.

One thing that George Secor helped get me into around late 2001 or early
2002 is adapting a typical Renaissance idiom, the suspension, to a
neomedieval kind of intonational environment like Peppermint, for example
(which came later than year as a 24-note variation on the Wilson/Pepper
temperament), or a 17-note equal or well-temperament such as his 17-WT.

In a typical Renaissance suspension idiom, we have a fourth above the
lowest voice that resolves to the major third of a sonority at or near
4:5:6, the simplest ratio in a 16th-century JI or meantone style dividing
a fifth into two thirds (here I follow MIDI conventions with C5 for
middle C):

... G5 A5
F5 E5 F5
... C5 F4

Here the suspended voice resolves from the fourth to the major third,
followed by an ascending semitone motion as it moves from major third to
octave with the lowest voice.

In a context like 17-WT or Peppermint, however, an ideal for a "just"
division of a fifth into two thirds based on simple ratios is frequently
6:7:9, with the small minor third placed below the large 9:7 major third.
Thus we have this suspension figure, using conventional accidentals for
the sake of simplicity:

... D5 Eb5
C5 Bb4 Ab4
... G4 Ab4

Here the fourth moves down a large whole-tone (at or near 8:7) to a 7:6
_minor_ third as part of a 6:7:9 sonority that then resolves with the
outer voices ascending by a small semitone (at or near 28:27), and the
middle voice which held the suspension descending in contrary motion by a
whole-tone. In a tuning system like George's 17-WT, this can be realized
with regular steps in the nearer portion of the tuning circle, so the
notation would be just as above (or its Sagittal equivalent using regular
flats).

In Peppermint, it's a bit more complex, because the best septimal
approximations involve mixing notes from two regular 12-note chains. In a
notation oriented to C on the lower keyboard, or C on the upper keyboard
(which is the goal of the cadence), we might have:

G5 G/|\5 ... G\!/5 C5
F5 D/|\5 C/|\5 F\!/5 D5 C5
... C5 C/|\5 or equivalently ... C\!/5 C5

Here "/|\" is the sign for the 58.680-cent step between corresponding
notes on the two keyboards, the interval by which the outer voices ascend
to complete the cadence.

Of course, the parallel fifths between the outer voices, routine in a
13th-14th century setting, would be excluded in conventional Renaissance
technique. Also, a suspended sonority like 6:8:9 is considerably milder in
a medieval kind of context, where major seconds typically play a much
freer role than in a 16th-century technique. It's curious that here either
6:8:9 or the 6:7:9 that follows it can play the role of an "imperfectly
concordant" sonority, relatively euphonious but unstable and leading
eventually to a stable 3:2 fifth or full 2:3:4 sonority or the like.

Thus if you're not familiar with this basic neo-medieval suspension idiom,
it could well sound "strange" itself -- although there are things going on
_O Europae_ that could well make it sound stranger (see my post to follow
in a few minutes).

Also, of course, I'd be delighted to discuss these things in e-mail as
well with you and/or David if it could add to the voice-leading dialogue.

> Also, unless/until sagittal gains wider acceptance, it would be very
> useful to explain the accidentals at the beginning of the score.

That's a fair point, and the way I'm handling it is to make available soon
an archive including the source microabc score files plus some files with
notes on the Sagittal notation. I must admit that some of the equivalences
may invite a bit of orientation, for example

... G\!/5 G5 ... F|||)5 G5
F\!/5 D5 C5 E|)5 D5 C5
... C\!/5 C5 or ... B|)4 C5

The former notation reflects the keyboard arrangement, showing that the
initial F in the middle voice and then the C and G moving us to the 6:8:9
suspension are played on the lower keyboard, and the other notes on the
upper keyboard.

The latter is more "analytical" in a way, letting us know that the notes
on the lower keyboard are, in effect, playing the role of alternative
"versions" of E, B, and F# (F/||\) on the upper keyboard (here the
"standard" one) raised by Peppermint's equivalent of a septimal or 64:63
comma (George's "comma of Archytas," an auspicious name).

As you can see, I have lots to explain <grin>. Your basic counsel is
indeed a prudent one.

> Posted by: "yahya_melb" yahya@... yahya_melb
> >
> > <http://www.bestII.com/~mschulter/O_Europae.pdf>
> > <http://www.bestII.com/~mschulter/O_Europae.mid>
> >
> [snip]
>
> I played the midi file first, and enjoyed the music. I then
> imported the midi file in NoteWorthy Composer, changed the timbres
> to all synth voice, set the dynamics to mp (the family is sleeping)
> and played it again, enjoying it even more. Then I downloaded the
> pdf, extracted the lyrics for the tenor part, pasted them into my
> Noteworthy score, adjusted for broken syllables, *put in some slurs
> to phrase words at easily breathable lengths*, and played it again.
>
> Only after changing the phrasing to suit the words did I understand
> how the rhythms had arisen in your setting! Which for me speaks
> volumes about the connections between the music and he text.

This is fascinating, and of course, I would begin for thanking you both
for the time and effort you devoted to my composition, and for sharing
your impressions.

> Mind you, on my import, I'd lost all subtleties of tuning (NWC
> doesn't seem to import pitch bends, unfortunately. So what I heard
> (except the first time) was only a 12-EDO approximation of your
> music. I now have to work out which ofthe 24 notes you actually
> used, so I can bend them correctly. (I didn't like the origianl
> instrumentation very much.)

Maybe I should note that tastes vary in historically oriented performances
of medieval European repertory also. One school, represented for example
by Christopher Page, often leans toward a vocal rendition of all melodic
lines; a different school seeks contrasting instrumental timbres (mixed
with voices, or sometimes in purely instrumental renditions). Some
ensembles have very nicely used both techniques. Of course, what you did
is much more than merely trying different timbres. I'd be delighted to
help, if I can, in identifying the pitch bends for the notes used so that
you can add them to your edited version.

> Regards,
> Yahya

Peace and love,

Margo

🔗Margo Schulter <mschulter@...>

[This article, which I wrote before reading the helpful comments of Chris
and Yahya, explains more about the interplay of text and music in this
piece, and especially the events of measures 22-32, including the cadence
at measure 30 about which Chris perceptively queried. One fascinating
interaction is that between the composer's intentions or assumptions and
those of a listener diligently encountering the piece from what could
often be a rather different frame of reference.]

In the spring of 2004, a suggestion was offered on the MakeMicroMusic
forum that people consider writing compositions to celebrate the
expansion of the European Union to 25 member nations. Although the
suggestion more specifically proposed that these compositions use
25-tone equal temperament (25-tET or 25-EDO), I happened to compose
the piece _O Europae_ in the Peppermint temperament.

This piece is available as a PDF score using Sagittal notation, and
also a MIDI file:

<http://www.bestII.com/~mschulter/O_Europae.pdf>
<http://www.bestII.com/~mschulter/O_Europae.mid>

In addition to illustrating some features of Sagittal notation (not
used in my initial version, as I recall, but quite apt as I find now),
the piece may show some interesting interactions between text and
music. One term for this might be "microtonal madrigalisms": figures
where, as in the madrigal of the 16th and early 17th centuries,
musical idioms serve rhetorically to express the ideas or emotions of
the words.

The opening section mostly presents the kind of smooth texture often
associated with early 15th-century fauxbourdon, with passages rich in
parallel thirds and sixths (and fourths between the two upper voices)
leading to cadences on stable fifths and octaves. There is a typical
14th-15th century contrast between more inconclusive cadences on A,
involving a semitonal descent from Bb (Sagittal B\!!/) in the lowest
voice, and more definitive cadences on F, the resting note or final of
the mode, with semitonal ascents in the upper voices (E-F, B-C).

At measures 16-18, however as we approach the conclusion of this
section, there is a nuance in the setting of the words _querulae
pacis_, "of the complaint (or cooing) of peace," also an allusion to
the famous essay _Querula pacis_ by the great Erasmus of Rotterdam in
the early 16th century which makes a powerful argument against war
(see O_Europae.pdf for the typeset notation, with C5 here showing
middle C as per MIDI conventions):

16 17 18
| 1 2 3 4 5 6 | 1 2 3 4 5 6 | 1 2 3 4 5 6 |
A5 G5 G\!/5 G5
E5 D5 D\!/5 D5
C5 B\!!/4 A4 G4
que - ru- lae

While the major thirds and sixths in measure 16 have their usual
Peppermint sizes of around 416 and 912 cents, in measure 17 these
intervals are derived in altered form as the difference of a fourth or
minor seventh less the interval (\!/) between the two 12-note
keyboards of about 59 cents, or about 437 and 933 cents, the former
close to 9:7 and the latter a just 12:7. This near-7:9:12 sonority
then resolves to a momentary cadence on G, with the upper voices
ascending by narrow semitones or thirdtones of about 59 cents, in
contrast to the usual 80-cent semitone. In effect, the inflected notes
D\!/ and G\!/ serve as accentuated versions of C# and F# (C/||\,
F/||\), lending emphasis to the text by wider major thirds and sixths
and narrower resolving semitone steps.

This gesture might be taken as a kind of prelude to the middle section
(measures 22-32), where another cadence featuring septimal-flavor
intervals and 59-cent steps introduces the words _Ex dumeto_ "Out of
the thicket":

22 23 24
| 1 2 3 4 5 6 | 1 2 3 4 5 6 | 1 2 3 4 5 6 |
E5 E5 E\!/5 E5
A4 A4 B4 A4
A4 A4 A\!/4 A4
Ex du- me- to

Here the sonority at measure 23 is a near-6:7:9, with a pure 7:6 minor
third and the near-9:7 major third, or 0-267-704 cents, again
resolving with some ascending 59-cent semitones (here in the outer
voices). The next words tell us that this "thicket" is more
specifically the "entangling" (_illaqueante_) thicket "of war"
(_belli_).

25 26 27
| 1 2 3 4 5 6 | 1 2 3 4 5 6 | 1 2 3 4 5 6 |
F5 F5 F5 E5 F5 E|)5
D\!/ D\!/ D\!/4 D\!/5 D\!/ D5
A4 A4 A4 A4 A4 A|)4
Il- la- que- an- te bel-

28 29 30
| 1 2 3 4 5 6 | 1 2 3 4 5 6 | 1 2 3 4 5 6 |
F5
C5 B|) C5 B\!!/4
B\!!/4
li

At measures 25-26, we have mostly a sonority of A4-D\!/4-F4 or
0-437-784 cents, close to 7:9:11. The rhythm of _illaqueante_ or
"entangling" in the second half of measure 25 presents a pair of
duplets, each equal to a 3/8-note in this prevailing 6/4 meter.
The declamatory style might suggest something more around 1600 than
1400, and as in a composer such as Monteverdi, can lead to a dramatic
vertical sonority.

In a neomedieval style, the 7:9:11 is often followed by a sonority
with a fourth and a fifth above the lowest note, actually somewhat
concordant in its regular form of 6:8:9, leading in turn to some
cadence. Here, however, we have A|)-D-E|), 0-475-704 cents or a
near-16:21:24 with a narrow 16:21 type of fourth.

Melodically, the lowest voice arrives at this sonority by a motion of
A-A|) -- a direct step of a Peppermint comma, around 21 cents, in
ascent, while the upper voice descends F-E|), a 59-cent step. Thus we
have a progression between these outer voices from regular minor sixth
to fifth by contrary motion, if one considers the comma a distinct step!
Both the melodic and vertical rhetoric here might amplify the word
_belli_, "of war."

Resolving the tension of the near-16:21:24, the middle voice descends
from the narrow fourth to a pure septimal minor third above the lowest
voice (near-6:7:9), then momentarily to an embellishing major second
(near 8:9:12), and then returns to the 7:6 third, followed by a
typical resolution of the near-6:7:9 to a stable fifth (B\!!/4-F5).

As a transition bringing us to the final and more tranquil section, we
have the entreaty _ducite nos_, that is, "lead us" out of the
entangling thicket of war we have just aurally surveyed:

31 32
| 1 2 3 4 5 6 | 1
F5 F5 G5 A5
D5 D5 D5 E5
B\!!/4 B\!!/4 B\!!/4 A4
du- ci- te nos

This entreaty or exclamation leads us back to the more familiar and
ebullient style of the final section or coda on the words _Ut
praevaleat concordia_, "so that concord may prevail."

It might be added, of course, that one does not need the stimulus or
occasion of a dramatic text in order to use a neomedieval sonority
like 7:9:11 or 16:21:24; however, the situation of wedding words and
music can, as in the rhetorical program of a Vicentino or a Monteverdi,
lead to some striking passages which might then be expressively
emulated in instrumental music also.

In peace and love,

Margo

🔗Hudson Lacerda <hfmlacerda@...>

Hi Margo and all.

I would like to share some thoughts about microtonalismo, Peppermint scale and Margo's composition ``O Europae''.

> On Tue, 26 Jul 2006, c. m. bryan wrote:
> [...]
>>Secondly, Margo, I really enjoyed "O Europae," and the accidentals
>>seem very appropriate because they're not too overwhelming.
[...]

I should first to say that I really liked ``O Europae'' too.

I think that the way Margo uses of Peppermint scale is consistent in several ways. The scale is designed for ``neomedieval'' music, and that ``neomedieval'' music is composed with Peppermint scale in mind. Reducing that music to extraneous scales (like 12-EDO or a meantone) would not work, since essential harmonic traits would vanish.

There are always various aesthetical issues raised by any ``neo-something'' practices. ``Neo-baroque'', ``neo-classic'', ``neo-tonal'', ``neo-romantism'', ``neo-serialism'', ``neo-atonalism'', ``neo-microtonalism''... What are the justifications to use old music (or art, or life style...) as a model for today? In what senses can be that approaches actual, contemporary, and tied/suitable to our current sensibility(ies)?

While I have mainly questions rather than answers, I think that there are some real contributions in the Margo's ``neomedieval''/microtonal approach.

By the way, I have mailed a composer which was a colleague of mine at the university, talking about microtonalism. He have heard the my studies and exercises I did with microabc, as well as the examples of Peppermint cadences by Margo. He enjoyed (found interesting) the Peppermint cadences.

I do not know details of Peppermint, but I know that there are two 12-tone chains 7/6 apart, wide major thirds and small intervals which can be used to form appealing leading tones.

I have noted that the Margo's cadences use those leading tones in septimal harmonic sonorities. Such septimal sonorities are apt to generate the tension which preceds the 5th/8th resolutions:

... G\!/5 G5 ... F|||)5 G5
F\!/5 D5 C5 E|)5 D5 C5
... C\!/5 C5 or ... B|)4 C5

Sonorities like B|)4 : D5 : F|||)5 are the main contribution of Margo's piece(s). They are not simply stressed leading tones: they are ``new'' sonorities, with a characteristic effect not present in /musica ficta/ (or other genera). The septimal intervals assure a harmonic consistency, and, no less, yield very interesting sorts of beatings and difference tones, which are a characteristic feature of Peppermint.

>>If I had to make a criticism, the cadence at measure 30 felt strange
>>after 2 listens; if I can I will listen a few more times and see if
>>it "settles" in my ear.

I have also found that passage a bit strange too. But part of the issue is that we heard a MIDI file, with no phrasing or articulation, as Yahya pointed out. Depending on the timbres, you can hear the sonority A|) : C : E|) as a hard ``septimal'' dissonance solving into the consonant sonority B\!!/ : B\!!/ : F .

By the way, I feel the fifths somewhat unstable in Peppermint. Would they be too large? It seems that they are only 2 cents wider than 3/2? I have experienced a bit of aural fatigue after listen to Peppermint pieces, and suspected of the fifths, comparing with the JI versions. However, that fatigue can be actually a result of the beatings and difference tones of the tempered septimal intervals.

>> Posted by: "yahya_melb" yahya@... yahya_melb
[...]
>>Only after changing the phrasing to suit the words did I understand
>>how the rhythms had arisen in your setting! Which for me speaks
>>volumes about the connections between the music and he text.
[...]
>>Mind you, on my import, I'd lost all subtleties of tuning (NWC
>>doesn't seem to import pitch bends, unfortunately. So what I heard
>>(except the first time) was only a 12-EDO approximation of your
>>music. I now have to work out which ofthe 24 notes you actually
>>used, so I can bend them correctly. (I didn't like the origianl
>>instrumentation very much.)

It is a shame to lost the tuning information, but I have a comment on the original timbres: they are heterogeneous, and some of the tuning characteristics would be more apparent when using more homogeneous timbres.

[Margo]
> Maybe I should note that tastes vary in historically oriented performances
> of medieval European repertory also. One school, represented for example
> by Christopher Page, often leans toward a vocal rendition of all melodic
> lines; a different school seeks contrasting instrumental timbres (mixed
> with voices, or sometimes in purely instrumental renditions). Some
> ensembles have very nicely used both techniques. Of course, what you did
> is much more than merely trying different timbres. I'd be delighted to
> help, if I can, in identifying the pitch bends for the notes used so that
> you can add them to your edited version.

Maybe a good interpretation could use three human voices (homogeneous part) supported by three contrasting instrumental timbres. I would like to hear real interpretations of that piece or other Margo's pieces. By the way, I noticed that the piece in ``ForShaahin_Shur001.ogg'' is a lively human interpretation.

Best wishes,
Hudson

_______________________________________________________ Novidade no Yahoo! Mail: receba alertas de novas mensagens no seu celular. Registre seu aparelho agora! http://br.mobile.yahoo.com/mailalertas/

🔗yahya_melb <yahya@...>

Hi Margo,

--- In MakeMicroMusic@yahoogroups.com, Margo Schulter wrote:
>[snip]
> > Posted by: "yahya_melb" > > >
> > > <http://www.bestII.com/~mschulter/O_Europae.pdf>
> > > <http://www.bestII.com/~mschulter/O_Europae.mid>
> > >
> > [snip]
> >
> > I played the midi file first, and enjoyed the music. I then
imported the midi file in NoteWorthy Composer, changed the timbres
to all synth voice, set the dynamics to mp (the family is sleeping)
and played it again, enjoying it even more. Then I downloaded the
pdf, extracted the lyrics for the tenor part, pasted them into my
Noteworthy score, adjusted for broken syllables, *put in some slurs
to phrase words at easily breathable lengths*, and played it again.
> >
> > Only after changing the phrasing to suit the words did I
understand how the rhythms had arisen in your setting! Which for me
speaks volumes about the connections between the music and he text.
>
> This is fascinating, and of course, I would begin for thanking you
both for the time and effort you devoted to my composition, and for
sharing your impressions.
>
> > Mind you, on my import, I'd lost all subtleties of tuning (NWC
doesn't seem to import pitch bends, unfortunately. So what I heard
(except the first time) was only a 12-EDO approximation of your
music. I now have to work out which ofthe 24 notes you actually
used, so I can bend them correctly. (I didn't like the origianl
instrumentation very much.)
>
> Maybe I should note that tastes vary in historically oriented
performances of medieval European repertory also. One school,
represented for example by Christopher Page, often leans toward a
vocal rendition of all melodic lines; a different school seeks
contrasting instrumental timbres (mixed with voices, or sometimes in
purely instrumental renditions). Some ensembles have very nicely
used both techniques. Of course, what you did is much more than
merely trying different timbres. I'd be delighted to help, if I can,
in identifying the pitch bends for the notes used so that you can
add them to your edited version.

Margo,
I'd appreciate the tuning of the scale notes you used, either as
ratios or in cents. From those, I can easily enough calculate the
MIDI pitch bends required - in NWC, there are 2^13 = 8192 divisions
per semitone - and enter those in the NWC score.

Regards,
Yahya

🔗Hudson Lacerda <hfmlacerda@...>

🔗Margo Schulter <mschulter@...>

> Posted by: "Hudson Lacerda" hfmlacerda@... hfmlacerda

> I would like to share some thoughts about microtonalismo, Peppermint
> scale and Margo's composition ``O Europae''.

Dear Hudson and All,

Thank you so much for your thoughtful, sensitive, and fascinating
response to neo-medieval music in the Peppermint temperament. I'm
delighted that you enjoyed the piece, and will try here to keep my
reply reasonably brief to a very rich and stimulating set of comments,
maybe in that way making the dialogue a bit more flexible and
accessible, as you have nicely done.

> By the way, I have mailed a composer which was a colleague of mine
> at the university, talking about microtonalism. He have heard the my
> studies and exercises I did with microabc, as well as the examples
> of Peppermint cadences by Margo. He enjoyed (found interesting) the
> Peppermint cadences.

Please let me add that your very creative MIDI realizations and
instrumentations of those cadences I posted in an article here are
very attractive, and I enjoy them a great deal. Thank you for sharing
these things with other colleagues.

> I do not know details of Peppermint, but I know that there are two
> 12-tone chains 7/6 apart, wide major thirds and small intervals which
> can be used to form appealing leading tones.

You have nicely summed up the septimal resources of Peppermint, and
maybe I should just clarify that the two 12-note chains are placed about
58.680 cents apart, with this interval plus the regular major second
forming a pure 7/6 third, of which there are ten. In the following
diagram, these 7/6 thirds are shown as diagonal lines, with the two
chains shown as horizontal lines with note names in Sagittal notation:

F/|\ - C/|\ - G/|\ - D/|\ - A/|\ - E/|\ - B/|\ - F/|||\ - C/|||\ - G/|||\
/ / / / / / / / / /
E\!!/ - B\!!/ - F - C - G - D - A - E - B - F/|\

Thus the tuning does in effect include two 10-note chains a 7/6 apart,
and the just tuning of these 7/6 thirds is one of the defining traits of
the system. In trying further to clarify the tuning structure, I would
emphasize that your remarks nicely sum up its musical qualities.

> Sonorities like B|)4 : D5 : F|||)5 are the main contribution of
> Margo's piece(s). They are not simply stressed leading tones: they are
> ``new'' sonorities, with a characteristic effect not present in
> /musica ficta/ (or other genera). The septimal intervals assure a
> harmonic consistency, and, no less, yield very interesting sorts of
> beatings and difference tones, which are a characteristic feature of
> Peppermint.

Your remarks tie in with the important point that while it possible that
"stressed leading tones" in a 14th-century style _might_ sometimes have
been sung to produce septimal or near-septimal ratios, the deliberate
use of these ratios seems a modern rather than medieval approach.

(Quoting Chris)

>>If I had to make a criticism, the cadence at measure 30 felt strange
>>after 2 listens; if I can I will listen a few more times and see if
>>it "settles" in my ear.

> I have also found that passage a bit strange too. But part of the
> issue is that we heard a MIDI file, with no phrasing or articulation,
> as Yahya pointed out. Depending on the timbres, you can hear the
> sonority A|) : C : E|) as a hard ``septimal'' dissonance solving into
> the consonant sonority B\!!/ : B\!!/ : F .

Two quick points here. The first is that a 7:6 third or 6:7:9 sonority
can have different effects on different listeners, and we might want to
explore this question more, maybe in part through more musical examples.
Certainly the resolution, as you note, is a central part of the style.

The second point is that indeed phrasing and articulation might make a
difference, so I'll try a keyboard rendition and post it here.

> By the way, I feel the fifths somewhat unstable in Peppermint. Would
> they be too large? It seems that they are only 2 cents wider than 3/2?
> I have experienced a bit of aural fatigue after listen to Peppermint
> pieces, and suspected of the fifths, comparing with the JI versions.
> However, that fatigue can be actually a result of the beatings and
> difference tones of the tempered septimal intervals.

The fifths are indeed about 704 cents, or 2 cents wider than 3/2 --
impure by about the same amount as in 12-EDO, but in the opposite
direction. Another possible explanation for your aural fatigue: could it
be the regular Peppermint thirds at around 416 and 288 cents, which like
Pythagorean thirds are rather complex and active? Comparing different
kinds of styles and textures might help in exploring this question.

[In response to Yahya's experiment of importing "O Europae" into a
composition program and adding phrasing and new registration, etc.]

> It is a shame to lost the tuning information, but I have a comment on
> the original timbres: they are heterogeneous, and some of the tuning
> characteristics would be more apparent when using more homogeneous
> timbres.

This is an interesting point, and I'm considering some synthesizer
versions of pieces including this one with more homogenous textures.

> Maybe a good interpretation could use three human voices (homogeneous
> part) supported by three contrasting instrumental timbres. I would
> like to hear real interpretations of that piece or other Margo's
> pieces. By the way, I noticed that the piece in
> ``ForShaahin_Shur001.ogg'' is a lively human interpretation.

Yes, this is a very important point. While programs like microabc,
abc2midi, Scala, and timidity++ support the very valuable feature of
MIDI files playable in alternative tunings, your remarks and Yahya's
remind me that this is not a substitute for my actually playing on
keyboard, or some performance by an ensemble. This is why I should try
to record actual keyboard versions of the pieces to go with the microabc
scores and MIDI versions. Also, of course, as Yahya is doing, one might
use certain computer and MIDI tools to produce a more "customized" and
refined version.

Again, thank you for a most gracious and valuable post!

Peace and love,

Margo

🔗yahya_melb <yahya@...>

--- In MakeMicroMusic@yahoogroups.com, Hudson Lacerda
<hfmlacerda@...> wrote:
>
> yahya_melb escreveu:
> > I'd appreciate the tuning of the scale notes you used, either as
ratios or in cents. From those, I can easily enough calculate the
MIDI pitch bends required - in NWC, there are 2^13 = 8192 divisions
per semitone - and enter those in the NWC score.
>
> Hi Yahya.
>
> Are you sure about that tuning resolution? With MIDI, the
resolution for pitchbends (pitchwheel) is 4096 semitone divisions,
and the standard range is +/-8192 (that is, a whole tone up/down).

Hi Hudson,

Yes, I'm sure. It also exactly matches the specification of the
pitch bend message for the Roland E-28 keyboard.

The retuning range is -8192 to +8191; the value -8192 corresponds
to -(Pitch bend sensitivity); and (Pitch bend sensitivity) defaults
to 2 semitones = 200 cents = a whole tone.

Roland:
Pitch bend change message:
.. Status . Second . Third
.. EnH .... ppH .... mmH
n=MIDI channel number
mm, pp Value: 00 00H - 40 00H - 7F 7FH (-8192 - 0 - +8191)

The interpretation of the value sent in mm, pp depends on the Pitch
bend sensitivity (RPN parameter MSB=00H LSB=00H, data byte MSB=ssH,
LSB=00H). Although the sensitivity defaults to two semitones, it
can range from 0 to 24 semitones, by setting ss to from 00H to 18H.
So you can set it to 0, to prevent retuning via pithbends; or to 1
semitone, to get the maximum possible resolution, 1/8192 semitone.

The master fine tuning (RPN parameter MSB=00H LSB=01H) can be
adjusted similarly, from -1 to +1 semitone, with resolution of -8192
steps per semitone.

> NWC does sound synthesis or another approach rather than use MIDI?

Not at all; it's straight MIDI.

Regards,
Yahya

🔗Hudson Lacerda <hfmlacerda@...>

🔗Margo Schulter <mschulter@...>

🔗yahya_melb <yahya@...>

--- In MakeMicroMusic@yahoogroups.com, Margo Schulter wrote:
>
> Dear Yahya,
>
> Please let me offer this link to a text version of a MIDI file
for "O Europae" showing the MIDI note number, regular or Sagittal
note symbol, tuning in cents, and pitchbend modification of each
note in each of the three voices. As I'll explain, there are some
cautions:
> <http://www.bestII.com/~mschulter/yahyatune.txt>
>
> The most important caution is that if your composition program is
simply reading the MIDI note number of each note without taking into
account the pitchbend, it may be mapping a Bb (Sagittal B\!!/) to
the step A, for example. This is because microabc, as I found, is
actually defining Bb as the note A (e.g. MIDI number 69) plus a
pitchbend.
>
> This way for each voice (one on each MIDI channel), I have given
the MIDI note number and pitchbend (up or down) for each note. It
seemed to me maybe the least confusing method, and I hope it helps.
>
> The pitchbends follow microabc in using units of 1/4096 semitone,
with 8192 as the reference point. The text file includes the
pitchbend numbers from the MIDI file as well as relative pitchbends
(up or down from 8192) using this scale, equivalent to 49152-EDO.
>
> Also, I should say that microabc was helpful in showing the
pitchbend for each note of the scale.
>
> With many wishes for success,
> Peace and love,

Margo,

Thanks for this! I've examined the file you sent, and have noted,
and abstracted a list of, 15 different octave-equivalent pitch
classes, as follows:

Cn 0000.000c +0000u where 1c=4096u
C# 0149.512c +2028u given as D -2068u D\!/
Dn 0208.191c +0336u
D# 0357.703c +2364u given as E -1732u E\|/ - should be E\!/ ?
En 0416.382c +0671u
E# 0437.225c -0168u? given as F\!/, but u units = those for F
Fn 0495.904c -0168u
F# 0645.416c +1860u given as G -2236u G\!/
Gn 0704.096c +0168u
G# 0853.607c +2196u given as A -1900u A\!/
An 0912.287c +0503u
Aq 0933.139c +1357u given as A|)
Bb 0991.809c -0336u given as A+3760u B\!!/
Bn 1120.488c +0839u
Bq 1120.488c? +1692u given as B|), but c units = those for Bn

Names in the first column are mine, for convenience of formatting.
(They do not necessrily imply a particular melodic function.)
n=natural, q=quarter, b=flat, #=sharp

There are, I think, three possible errors in my table above, each
marked by a ? If you would be so kind as to correct those errors,
I'll have a shot at incorporating them in my NWC score.

Regards,
Yahya

🔗Margo Schulter <mschulter@...>

> Margo,

> Thanks for this! I've examined the file you sent, and have noted,
> and abstracted a list of, 15 different octave-equivalent pitch
> classes, as follows:

> Cn 0000.000c +0000u where 1c=4096u
> C# 0149.512c +2028u given as D -2068u D\!/
> Dn 0208.191c +0336u
> D# 0357.703c +2364u given as E -1732u E\|/ - should be E\!/ ?
> En 0416.382c +0671u
> E# 0437.225c -0168u? given as F\!/, but u units = those for F
> Fn 0495.904c -0168u
> F# 0645.416c +1860u given as G -2236u G\!/
> Gn 0704.096c +0168u
> G# 0853.607c +2196u given as A -1900u A\!/
> An 0912.287c +0503u
> Aq 0933.139c +1357u given as A|)
> Bb 0991.809c -0336u given as A+3760u B\!!/
> Bn 1120.488c +0839u
> Bq 1120.488c? +1692u given as B|), but c units = those for Bn

> Names in the first column are mine, for convenience of formatting.
> (They do not necessrily imply a particular melodic function.)
> n=natural, q=quarter, b=flat, #=sharp

> There are, I think, three possible errors in my table above, each
> marked by a ? If you would be so kind as to correct those errors,
> I'll have a shot at incorporating them in my NWC score.

Dear Yahya,

Please let me thank you and hasten to let you know that actually I
made an error on the value in cents for the note you list as "Bq",
and also in the pitchbend units for the note you list as "E#," as well
as a Sagittal confusion you correctly queried of "E\|/" for the
intended "E\!/" sign, which you helpfully supplied. Also, as you
noted, the cents value I gave for "Bq" is wrong, and corrected in my
new version below. Further, I made a small error in the cents value
for regular B, fixed below -- 1120.488c for the correct 1120.478c.

Why don't I first simply offer a corrected version using your names
for the most part:

Cn 0000.000c +0000u where 1c=4096u
C# 0149.512c +2028u given as D -2068u D\!/
Dn 0208.191c +0336u
D# 0357.703c +2364u given as E -1732u E\!/
En 0416.382c +0671u
E# 0437.225c +1525u given as F\!/
Fn 0495.904c -0168u
F# 0645.416c +1860u given as G -2236u G\!/
Gn 0704.096c +0168u
G# 0853.607c +2196u given as A -1900u A\!/
An 0912.287c +0503u
Aq 0933.139c +1357u given as A|)
Bb 0991.809c -0336u given as A+3760u B\!!/
Bn 1120.478c +0839u
Bq 1141.320 +1692u given as B|)

Of course, as long as the pitchbends are correct, we could name these
notes in various ways. For example, if we want to have pitches a
regular fifth or fourth apart have similar notations, the following is
one possibility using your "q" sign for a note higher by a Peppermint
comma (about 20.842 cents or 853u -- sometimes rounded to 854u) than a
regular natural or sharp:

Cn 0000.000c +0000u where 1c=4096u
C#q 0149.512c +2028u given as D -2068u D\!/
Dn 0208.191c +0336u
D#q 0357.703c +2364u given as E -1732u E\!/
En 0416.382c +0671u
Eq 0437.225c +1525u given as F\!/
Fn 0495.904c -0168u
F#q 0645.416c +1860u given as G -2236u G\!/
Gn 0704.096c +0168u
G#q 0853.607c +2196u given as A -1900u A\!/
An 0912.287c +0503u
Aq 0933.139c +1357u given as A|)
Bb 0991.809c -0336u given as A+3760u B\!!/
Bn 1120.478c +0839u
Bq 1141.320c +1692u given as B|)

Thus the value of q itself -- or Sagittal |) -- is about 20.842c or 853u,
sometimes rounded up to 854u. The value of #q is about 149.512c, which
together with a /|\ of about 58.680c makes up a regular Peppermint tone
of about 208.191c.

One lesson of this exercise is that lots of proofreading can help,
including yours, which caught a number of my errors in adding notes to
microabc MIDI output (itself accurate!).

Peace and love,

Margo

More Sagittal: _O Europae_ (PDF, MIDI)

🔗Margo Schulter <mschulter@...>

🔗c.m.bryan <chrismbryan@...>

🔗yahya_melb <yahya@...>

🔗Margo Schulter <mschulter@...>

🔗Margo Schulter <mschulter@...>

🔗Hudson Lacerda <hfmlacerda@...>

🔗yahya_melb <yahya@...>

🔗Hudson Lacerda <hfmlacerda@...>

🔗Margo Schulter <mschulter@...>

🔗yahya_melb <yahya@...>

🔗Hudson Lacerda <hfmlacerda@...>

🔗Margo Schulter <mschulter@...>

🔗yahya_melb <yahya@...>

🔗Margo Schulter <mschulter@...>