to monz

Here, under Boethius.pdf, you will catch a glimpse of my labour on Boethius's mode transpositions as we agreed:

http://www.ozanyarman.com/anonymous/

Scroll down to page 22 and you'll witness the enormous toil I had to deal with extracting all the Godforsaken symbols out of hundreds of dusty unicode pages (cardo.ttf & new athena unicode.ttf among others) and attempting to organize them in a meaningful way. Why couldn't these people prepare all the characters used by Boethius anyway???

The results, however, are well worth the toil!

(The characters marked with big red X's require your attention, as I have not been able to locate these anywhere, nor could I manipulate the related ones to do the job. Please compare with my colored version of Boethius's table of transpositions prior to this work.)

Ocean blue slots indicate my interpretation of pitches as specified by Boethius. These indeed confirm your suspicions that a sort of temperament was underway back then.

Forest green slots indicate pitches used only once in the entire sequence.

Vocal notation is above per mode register, instrumental notation is below.

Certain notes are colored within each mode register, indicating similar character usage with both vocal and instrumental notations for that mode.

Cordially,
Oz.

Hi Oz,

--- In tuning@yahoogroups.com, <oyarman@o...> wrote:
>
> Here, under Boethius.pdf, you will catch a glimpse of
> my labour on Boethius's mode transpositions as we agreed:
>
> http://www.ozanyarman.com/anonymous/
>
> Scroll down to page 22 and you'll witness the enormous
> toil I had to deal with extracting all the Godforsaken
> symbols out of hundreds of dusty unicode pages (cardo.ttf
> & new athena unicode.ttf among others) and attempting
> to organize them in a meaningful way.

I really appreciate the work you've put into this.
It looks very good.

Can you please make another version of the diagram
where the mese of the lydian mode is "A"? Thanks.
Then i'll compare it to the diagrams i made in my
1996 paper and make comments.

> Why couldn't these people prepare all the characters
> used by Boethius anyway???

Most likely they used Alypius as their source.
As i stated previously, his treatise is considered
to be the main reference on ancient Greek musical notation.

Note also that Aristides Quintilianus gave extensive
diagrams of the Greek notation.

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

Hey there monz, check out `to-monz.pdf` at
http://www.ozanyarman.com/anonymous/

I hope you will find it useful (besides others who are just as interested).

BTW, I'm still expecting you to give me a reference concerning an English
translation of the treatise of Alypius.

It might be possible to unite this pseudo-article with your past article on
modes in order to give both some polish. You may grant this presumptuous
colleague some liberty at editorializing then... what do you think?

Cordially,
Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 29 Kas�m 2005 Sal� 8:49
Subject: [tuning] Re: to monz

> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, <oyarman@o...> wrote:
> >
> > Here, under Boethius.pdf, you will catch a glimpse of
> > my labour on Boethius's mode transpositions as we agreed:
> >
> > http://www.ozanyarman.com/anonymous/
> >
> > Scroll down to page 22 and you'll witness the enormous
> > toil I had to deal with extracting all the Godforsaken
> > symbols out of hundreds of dusty unicode pages (cardo.ttf
> > & new athena unicode.ttf among others) and attempting
> > to organize them in a meaningful way.
>
>
> I really appreciate the work you've put into this.
> It looks very good.
>
> Can you please make another version of the diagram
> where the mese of the lydian mode is "A"? Thanks.
> Then i'll compare it to the diagrams i made in my
> 1996 paper and make comments.
>
>
> > Why couldn't these people prepare all the characters
> > used by Boethius anyway???
>
>
> Most likely they used Alypius as their source.
> As i stated previously, his treatise is considered
> to be the main reference on ancient Greek musical notation.
>
> Note also that Aristides Quintilianus gave extensive
> diagrams of the Greek notation.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>
>
>

monz, breaking news: It has become apparent to me that Boethius has
specified 19 tones per octave. Darn me if this isn't 19 equal.

Cordially,
Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 29 Kas�m 2005 Sal� 8:49
Subject: [tuning] Re: to monz

> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, <oyarman@o...> wrote:
> >
> > Here, under Boethius.pdf, you will catch a glimpse of
> > my labour on Boethius's mode transpositions as we agreed:
> >
> > http://www.ozanyarman.com/anonymous/
> >
> > Scroll down to page 22 and you'll witness the enormous
> > toil I had to deal with extracting all the Godforsaken
> > symbols out of hundreds of dusty unicode pages (cardo.ttf
> > & new athena unicode.ttf among others) and attempting
> > to organize them in a meaningful way.
>
>
> I really appreciate the work you've put into this.
> It looks very good.
>
> Can you please make another version of the diagram
> where the mese of the lydian mode is "A"? Thanks.
> Then i'll compare it to the diagrams i made in my
> 1996 paper and make comments.
>
>
> > Why couldn't these people prepare all the characters
> > used by Boethius anyway???
>
>
> Most likely they used Alypius as their source.
> As i stated previously, his treatise is considered
> to be the main reference on ancient Greek musical notation.
>
> Note also that Aristides Quintilianus gave extensive
> diagrams of the Greek notation.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>
>

Hi Oz,

--- In tuning@yahoogroups.com, <oyarman@o...> wrote:

> monz, breaking news: It has become apparent to me
> that Boethius has specified 19 tones per octave.
> Darn me if this isn't 19 equal.

You're kidding, right?

In my 1996 paper, i tabulated all the notes and
noted that there are 19 per octave. But there's
no way that i can see them as 19-edo. Please explain.

PS -- Thanks for the new diagram based on lydian mese=A.

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

Ach, no it isn't 19-equal, I was mistaken and you are right. What was your
conclusion about the tuning he used then?

Cordially,
Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 30 Kas�m 2005 �ar�amba 8:04
Subject: [tuning] Boethius 19-edo? (was: to monz)

> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, <oyarman@o...> wrote:
>
> > monz, breaking news: It has become apparent to me
> > that Boethius has specified 19 tones per octave.
> > Darn me if this isn't 19 equal.
>
>
> You're kidding, right?
>
> In my 1996 paper, i tabulated all the notes and
> noted that there are 19 per octave. But there's
> no way that i can see them as 19-edo. Please explain.
>
> PS -- Thanks for the new diagram based on lydian mese=A.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>
>

Forgive my own ignorance,

but at the time all the notes were derivable from a 3-limit
interpretation, no? Tempering the 5th may have happened if the 81/64
was more often replaced by 5/4. My guess is a more pythagorean
interpretation. Sharps higher than flats (without reading the 1996
paper) I guess. Did the 19 notes include Bsharp/cflat and esharp/f
flat? Thought subhemitonia were big mediaeval no-no. Not until
renaissance did enharmonic/chromatic genera get use again surely?
>
> You're kidding, right?
>
> In my 1996 paper, i tabulated all the notes and
> noted that there are 19 per octave. But there's
> no way that i can see them as 19-edo. Please explain.
>

I'm the ignorant one here obviously. Forgive my intrusion Mark, but the
scheme of monz requires the Mese of Lydius to be A, which in turn requires a
Cb with Mixolydian (the same as B of Lydius). In my scheme where the
transpositions are done over natural tones, the note names are:

C C(') Db Db' D Eb Eb' E F F' F#(Gb) G G' Ab Ab' A Bb Bb' B

In my opinion, this is a clearer picture. Note that the F# of Lydius is the
enharmonical equivalent of Gb of Mixolydius. In no way can Pythagorean
intonation alone allow for this.

Cordially,
Oz.

----- Original Message -----
From: "Mark" <mark@equiton.waitrose.com>
To: <tuning@yahoogroups.com>
Sent: 30 Kas�m 2005 �ar�amba 13:49
Subject: [tuning] Re: Boethius 19-edo? (was: to monz)

> Forgive my own ignorance,
>
> but at the time all the notes were derivable from a 3-limit
> interpretation, no? Tempering the 5th may have happened if the 81/64
> was more often replaced by 5/4. My guess is a more pythagorean
> interpretation. Sharps higher than flats (without reading the 1996
> paper) I guess. Did the 19 notes include Bsharp/cflat and esharp/f
> flat? Thought subhemitonia were big mediaeval no-no. Not until
> renaissance did enharmonic/chromatic genera get use again surely?
> >
> > You're kidding, right?
> >
> > In my 1996 paper, i tabulated all the notes and
> > noted that there are 19 per octave. But there's
> > no way that i can see them as 19-edo. Please explain.
> >
>
>
>
>
>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
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> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>
>
>
>
>
>
>
>

Hi Oz,

--- In tuning@yahoogroups.com, <oyarman@o...> wrote:

> Ach, no it isn't 19-equal, I was mistaken and you are
> right. What was your conclusion about the tuning he
> used then?

I've already stated it repeatedly -- Boethius himself
explains the monochord division for the diatonic genus
as the standard pythagorean tuning. However, i discovered
that if Didymus's 5-limit tuning is used for the diatonic
genus, it agrees perfectly with the Greek-letter notation.

That's not to say that no other tunings will agree with
it -- i haven't explored any others. I just know that
pythagorean tuning does *not* agree with the Greek letters,
but Didymus tuning does.

I'll try to quickly post a tabulation of the Didymus
tuning as it correlates to Boethius's Greek-letter notation.
After that, my voice in this thread is going to die down
-- i'm going out of town until December 12, to work
intensively on Tonescape.

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

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> Hi Oz,
>
> --- In tuning@yahoogroups.com, <oyarman@o...> wrote:
>
> > Ach, no it isn't 19-equal, I was mistaken and you are
> > right. What was your conclusion about the tuning he
> > used then?
>
>
> I've already stated it repeatedly -- Boethius himself
> explains the monochord division for the diatonic genus
> as the standard pythagorean tuning. However, i discovered
> that if Didymus's 5-limit tuning is used for the diatonic
> genus, it agrees perfectly with the Greek-letter notation.
>
> That's not to say that no other tunings will agree with
> it -- i haven't explored any others. I just know that
> pythagorean tuning does *not* agree with the Greek letters,
> but Didymus tuning does.
>
> I'll try to quickly post a tabulation of the Didymus
> tuning as it correlates to Boethius's Greek-letter notation.
> After that, my voice in this thread is going to die down
> -- i'm going out of town until December 12, to work
> intensively on Tonescape.

I explained the Didymus tuning here:
/tuning/topicId_62290.html#62531

Didymus specified this reference tetrachord for the
diatonic genus, descending:

. A ......... G ............ F .......... E (modern equivalents)
mese ..... lichanos .... parhypate .... hypate
...... 9/8 ........ 10/9 ......... 16/15

I was hoping to find the time to give the entire table
of pitches, but i don't and won't, so i'll just quickly
post the entire table of cents-values and 3,5-monzos,
and hopefully you can figure out how they correspond to
the diagrams you just made for me. My table is given
in descending order:

.. A ... [ 0, 0> ...... 0
.. Ab .. [-3, -1> .. 1108
.. Ab .. [-7, 0> ... 1086
.. G ... [ 2, -1> .. 1018
.. G ... [-2, 0> .... 996
.. F# .. [ 3, 0> .... 906
.. Gb .. [-5, -1> ... 904
.. F ... [ 0, -1> ... 814
.. F ... [-4, 0> .... 792
.. E ... [ 1, 0> .... 702
.. Eb .. [-2, -1> ... 610
.. Eb .. [-6, 0> .... 588
.. D ... [-1, 0> .... 498
.. Db .. [-4, -1> ... 406
.. Db .. [-8, 0> .... 384
.. C ... [ 1, -1> ... 316
.. C ... [-3, 0> .... 294
.. B ... [ 2, 0> .... 204
.. Cb .. [-6, -1> ... 202
.. Bb .. [-1, -1> ... 112
.. Bb .. [-5, 0> ..... 90
.. A ... [ 0, 0> ...... 0

From message 62531 again, here are the skhisma-related
notes which have the same Greek-letter symbol:

mode ...... note-name ..... modern.. 2,3,5-monzo ... ratio . cents

hypolydian .paramese .......... F#. [-5 3, 0> ..... 27/32 .. -294
dorian .....trite synemmenon .. Gb. [10 -5, -1> . 1024/1215. -296
mixolydian .parhypate meson ... Gb. [10 -5, -1> . 1024/1215. -296

hypolydian .nete diezeugmenon . B . [-3 2, 0> ...... 9/8 .... 204
lydian .....paramese .......... B . [-3 2, 0> ...... 9/8 .... 204
mixolydian .trite synemmenon .. Cb. [12 -6, -1> . 4096/3645.. 202

Hopefully that table will help you see how the cents-values
correspond to the modern letter notation.

This will have to be my last post on this until i return
home.

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

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

> Didymus specified this reference tetrachord for the
> diatonic genus, descending:
>
> . A ......... G ............ F .......... E (modern equivalents)
> mese ..... lichanos .... parhypate .... hypate
> ...... 9/8 ........ 10/9 ......... 16/15
>
>
> I was hoping to find the time to give the entire table
> of pitches, but i don't and won't, so i'll just quickly
> post the entire table of cents-values and 3,5-monzos,
> and hopefully you can figure out how they correspond to
> the diagrams you just made for me.

That is, the lydian mese is A = 1/1 ratio = 0 cents.

> My table is given in descending order:
>
> .. A ... [ 0, 0> ...... 0
> .. Ab .. [-3, -1> .. 1108
> .. Ab .. [-7, 0> ... 1086
> .. G ... [ 2, -1> .. 1018
> .. G ... [-2, 0> .... 996
> .. F# .. [ 3, 0> .... 906
> .. Gb .. [-5, -1> ... 904
> .. F ... [ 0, -1> ... 814
> .. F ... [-4, 0> .... 792
> .. E ... [ 1, 0> .... 702
> .. Eb .. [-2, -1> ... 610
> .. Eb .. [-6, 0> .... 588
> .. D ... [-1, 0> .... 498
> .. Db .. [-4, -1> ... 406
> .. Db .. [-8, 0> .... 384
> .. C ... [ 1, -1> ... 316
> .. C ... [-3, 0> .... 294
> .. B ... [ 2, 0> .... 204
> .. Cb .. [-6, -1> ... 202
> .. Bb .. [-1, -1> ... 112
> .. Bb .. [-5, 0> ..... 90
> .. A ... [ 0, 0> ...... 0

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

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

> That's not to say that no other tunings will agree with
> it -- i haven't explored any others. I just know that
> pythagorean tuning does *not* agree with the Greek letters,
> but Didymus tuning does.

Can you explain why Pythagorean tuning does not agree with the Greek
letters?

I would like to see the entire scale, if that was possible.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 01 Aral�k 2005 Per�embe 1:22
Subject: [tuning] Re: Boethius 19-edo? (was: to monz)

> Hi Oz,
>
> --- In tuning@yahoogroups.com, <oyarman@o...> wrote:
>
> > Ach, no it isn't 19-equal, I was mistaken and you are
> > right. What was your conclusion about the tuning he
> > used then?
>
>
> I've already stated it repeatedly -- Boethius himself
> explains the monochord division for the diatonic genus
> as the standard pythagorean tuning. However, i discovered
> that if Didymus's 5-limit tuning is used for the diatonic
> genus, it agrees perfectly with the Greek-letter notation.
>
> That's not to say that no other tunings will agree with
> it -- i haven't explored any others. I just know that
> pythagorean tuning does *not* agree with the Greek letters,
> but Didymus tuning does.
>
> I'll try to quickly post a tabulation of the Didymus
> tuning as it correlates to Boethius's Greek-letter notation.
> After that, my voice in this thread is going to die down
> -- i'm going out of town until December 12, to work
> intensively on Tonescape.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

I see you have already given the cent values for the entire scale. Splendid!
I'll look into this and tell you what I think...

Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 01 Aral�k 2005 Per�embe 1:55
Subject: [tuning] monz speculation: Didymus tuning for Boethius modes (was:
Boethius 19-edo?)

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> >
> > Hi Oz,
> >
> > --- In tuning@yahoogroups.com, <oyarman@o...> wrote:
> >
> > > Ach, no it isn't 19-equal, I was mistaken and you are
> > > right. What was your conclusion about the tuning he
> > > used then?
> >
> >
> > I've already stated it repeatedly -- Boethius himself
> > explains the monochord division for the diatonic genus
> > as the standard pythagorean tuning. However, i discovered
> > that if Didymus's 5-limit tuning is used for the diatonic
> > genus, it agrees perfectly with the Greek-letter notation.
> >
> > That's not to say that no other tunings will agree with
> > it -- i haven't explored any others. I just know that
> > pythagorean tuning does *not* agree with the Greek letters,
> > but Didymus tuning does.
> >
> > I'll try to quickly post a tabulation of the Didymus
> > tuning as it correlates to Boethius's Greek-letter notation.
> > After that, my voice in this thread is going to die down
> > -- i'm going out of town until December 12, to work
> > intensively on Tonescape.
>
>
>
> I explained the Didymus tuning here:
> /tuning/topicId_62290.html#62531
>
>
> Didymus specified this reference tetrachord for the
> diatonic genus, descending:
>
> . A ......... G ............ F .......... E (modern equivalents)
> mese ..... lichanos .... parhypate .... hypate
> ...... 9/8 ........ 10/9 ......... 16/15
>
>
> I was hoping to find the time to give the entire table
> of pitches, but i don't and won't, so i'll just quickly
> post the entire table of cents-values and 3,5-monzos,
> and hopefully you can figure out how they correspond to
> the diagrams you just made for me. My table is given
> in descending order:
>
> .. A ... [ 0, 0> ...... 0
> .. Ab .. [-3, -1> .. 1108
> .. Ab .. [-7, 0> ... 1086
> .. G ... [ 2, -1> .. 1018
> .. G ... [-2, 0> .... 996
> .. F# .. [ 3, 0> .... 906
> .. Gb .. [-5, -1> ... 904
> .. F ... [ 0, -1> ... 814
> .. F ... [-4, 0> .... 792
> .. E ... [ 1, 0> .... 702
> .. Eb .. [-2, -1> ... 610
> .. Eb .. [-6, 0> .... 588
> .. D ... [-1, 0> .... 498
> .. Db .. [-4, -1> ... 406
> .. Db .. [-8, 0> .... 384
> .. C ... [ 1, -1> ... 316
> .. C ... [-3, 0> .... 294
> .. B ... [ 2, 0> .... 204
> .. Cb .. [-6, -1> ... 202
> .. Bb .. [-1, -1> ... 112
> .. Bb .. [-5, 0> ..... 90
> .. A ... [ 0, 0> ...... 0
>
>
> >From message 62531 again, here are the skhisma-related
> notes which have the same Greek-letter symbol:
>
> mode ...... note-name ..... modern.. 2,3,5-monzo ... ratio . cents
>
> hypolydian .paramese .......... F#. [-5 3, 0> ..... 27/32 .. -294
> dorian .....trite synemmenon .. Gb. [10 -5, -1> . 1024/1215. -296
> mixolydian .parhypate meson ... Gb. [10 -5, -1> . 1024/1215. -296
>
> hypolydian .nete diezeugmenon . B . [-3 2, 0> ...... 9/8 .... 204
> lydian .....paramese .......... B . [-3 2, 0> ...... 9/8 .... 204
> mixolydian .trite synemmenon .. Cb. [12 -6, -1> . 4096/3645.. 202
>
>
> Hopefully that table will help you see how the cents-values
> correspond to the modern letter notation.
>
> This will have to be my last post on this until i return
> home.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
> >
>
>

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> > That's not to say that no other tunings will agree with
> > it -- i haven't explored any others. I just know that
> > pythagorean tuning does *not* agree with the Greek letters,
> > but Didymus tuning does.
>
> Can you explain why Pythagorean tuning does not agree with
> the Greek letters?

I won't have time to do it now, because i'm going
out of town tomorrow. But if you want to do it yourself,
you can use the diagram Ozan made: 'to-monz.pdf' at

http://www.ozanyarman.com/anonymous/

(the "mese" of the lydian mode = "A" = 1/1 = 0 cents,
so the lydian "G" = 16/9, the lydian "B" = 9/8, etc.),
and calculate the ratios and cents values, and you'll
see that pythagorean tuning doesn't correlate in
any special way with the Greek-letter notation.

Didymus tuning, OTOH, does allow those notes which our modern
notation renders as the pairs F#/Gb and B/Cb (a skhisma apart),
to have the same Greek-letter symbol.

As i just wrote earlier, certainly there are also other
tunings which will fit the Greek symbols like this, but
i only discovered more-or-less by accident that Didymus
tuning "worked" like this, and haven't checked any other
tunings.

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