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Septenarius webpage up

🔗Tom Dent <stringph@gmail.com>

12/3/2006 1:11:32 PM

Here:

http://www.rzuser.uni-heidelberg.de/~tdent/septenarius.html

quite specialised! I have included an image of a small section of the
monochord from 1691.

~~~T~~~

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

12/4/2006 2:35:03 AM

Hi all

Werckmeister IV (the Septenarius tuning) <http://en.wikipedia.org/wiki/Werckmeister_temperament#Werckmeister_IV_.28VI.29:_the_Septenarius_tunings> is a good reason that EDL systems which are based on length divisions are used not only by greek musicians like Ptolemy as john Chalmers mentioned <http://pages.google.com/draft/240edo/John_chalmers_notes_on_EDL.doc?authtoken=6768b02d432c154f06bea5594bcc8f005d869fa8> , but other music theorists like Andreas Werckmeister <http://en.wikipedia.org/wiki/Andreas_Werckmeister> had a glance at it.Septenarius is a subset of 196-EDL , which shows usage of EDL systems to show irregular tunings.

You can see this excel spreadsheet <http://240edo.googlepages.com/196-EDLandseptenarius.xls> for Septenarius tuning to see :

* Interval matrix

* Deviation of interval matrix with 12-EDO

* Graphical presentation of interval matrix

* Frequency of notes in a range of one octave (from C)

* Frequency of beats

* Circle of fifths and fourths

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.tripod.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Tom Dent
Sent: Monday, December 04, 2006 12:42 AM
To: tuning@yahoogroups.com
Subject: [tuning] Septenarius webpage up

Here:

http://www.rzuser.uni-heidelberg.de/~tdent/septenarius.html <http://www.rzuser.uni-heidelberg.de/~tdent/septenarius.html>

quite specialised! I have included an image of a small section of the
monochord from 1691.

~~~T~~~

🔗Tom Dent <stringph@gmail.com>

12/4/2006 8:07:46 AM

For reasons explained in my article, I would recommend the use of 175
rather than 176. Look carefully at the EDL marked out on the 1691
monochord illustration...

Looking at the length differences it becomes clear that this note may
be a problem, compared to expected sizes of semitones and tones in
well-temperament.

The successive differences of length with 176 are:

(C) 10, 10 (D) 11, 9 (E) 9 (F) 8, 8 (G) 7, 7 (A) 7, 6 (B) 6 (c)

which would make C-C# and C#-D similarly narrow, but D-Eb much the
widest semitone. Also C-D would be 196:176 which is almost a minor
tone 10:9 = 200:180, whereas D-E would be 176:156 which is wider than
the major tone 180:160! Not much sense in dividing the major third
into two tones if one of them is *wider* than 9:8.

(C) 10, 11 (D) 10, 9 (E) 9 (F) 8, 8 (G) 7, 7 (A) 7, 6 (B) 6 (c)

now the tones C-D and D-E are much more even.

Equal temperament would be

196, 185, 174.6, 164.8, 155.6, 146.8, 138.6, 130.8, 123.5, 116.5, 110,
103.8, 98.

~~~T~~~

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:
>
> Hi all
>
>
> Werckmeister IV (the Septenarius tuning)
<http://en.wikipedia.org/wiki/Werckmeister_temperament#Werckmeister_IV_.28VI.29:_the_Septenarius_tunings>
is a good reason that EDL systems which are based on length divisions
are used not only by greek musicians like Ptolemy as john Chalmers
mentioned
<http://pages.google.com/draft/240edo/John_chalmers_notes_on_EDL.doc?authtoken=6768b02d432c154f06bea5594bcc8f005d869fa8>
, but other music theorists like Andreas Werckmeister
<http://en.wikipedia.org/wiki/Andreas_Werckmeister> had a glance at
it.Septenarius is a subset of 196-EDL , which shows usage of EDL
systems to show irregular tunings.
>
> You can see this excel spreadsheet
<http://240edo.googlepages.com/196-EDLandseptenarius.xls> for
Septenarius tuning to see :
>
> * Interval matrix
>
> * Deviation of interval matrix with 12-EDO
>
> * Graphical presentation of interval matrix
>
> * Frequency of notes in a range of one octave (from C)
>
> * Frequency of beats
>
> * Circle of fifths and fourths
>
>
>
> Shaahin Mohajeri
>
> Tombak Player & Researcher , Microtonal Composer
>
>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

12/4/2006 8:08:04 PM

hi
yes , by D=28/25 we have at least two better fifth than D=49/44 , i corrected my file.

but what do you mean by:
.....Equal temperament would be

196, 185, 174.6, 164.8, 155.6, 146.8, 138.6, 130.8, 123.5, 116.5, 110,
103.8, 98........
just ET or EDL?

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.tripod.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Tom Dent
Sent: Monday, December 04, 2006 7:38 PM
To: tuning@yahoogroups.com
Subject: [tuning] Re: Septenarius webpage up

For reasons explained in my article, I would recommend the use of 175
rather than 176. Look carefully at the EDL marked out on the 1691
monochord illustration...

Looking at the length differences it becomes clear that this note may
be a problem, compared to expected sizes of semitones and tones in
well-temperament.

The successive differences of length with 176 are:

(C) 10, 10 (D) 11, 9 (E) 9 (F) 8, 8 (G) 7, 7 (A) 7, 6 (B) 6 (c)

which would make C-C# and C#-D similarly narrow, but D-Eb much the
widest semitone. Also C-D would be 196:176 which is almost a minor
tone 10:9 = 200:180, whereas D-E would be 176:156 which is wider than
the major tone 180:160! Not much sense in dividing the major third
into two tones if one of them is *wider* than 9:8.

(C) 10, 11 (D) 10, 9 (E) 9 (F) 8, 8 (G) 7, 7 (A) 7, 6 (B) 6 (c)

now the tones C-D and D-E are much more even.

Equal temperament would be

196, 185, 174.6, 164.8, 155.6, 146.8, 138.6, 130.8, 123.5, 116.5, 110,
103.8, 98.

~~~T~~~

--- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> , "Mohajeri Shahin" <shahinm@...> wrote:
>
> Hi all
>
>
> Werckmeister IV (the Septenarius tuning)
<http://en.wikipedia.org/wiki/Werckmeister_temperament#Werckmeister_IV_.28VI.29:_the_Septenarius_tunings <http://en.wikipedia.org/wiki/Werckmeister_temperament#Werckmeister_IV_.28VI.29:_the_Septenarius_tunings> >
is a good reason that EDL systems which are based on length divisions
are used not only by greek musicians like Ptolemy as john Chalmers
mentioned
<http://pages.google.com/draft/240edo/John_chalmers_notes_on_EDL.doc?authtoken=6768b02d432c154f06bea5594bcc8f005d869fa8 <http://pages.google.com/draft/240edo/John_chalmers_notes_on_EDL.doc?authtoken=6768b02d432c154f06bea5594bcc8f005d869fa8> >
, but other music theorists like Andreas Werckmeister
<http://en.wikipedia.org/wiki/Andreas_Werckmeister <http://en.wikipedia.org/wiki/Andreas_Werckmeister> > had a glance at
it.Septenarius is a subset of 196-EDL , which shows usage of EDL
systems to show irregular tunings.
>
> You can see this excel spreadsheet
<http://240edo.googlepages.com/196-EDLandseptenarius.xls <http://240edo.googlepages.com/196-EDLandseptenarius.xls> > for
Septenarius tuning to see :
>
> * Interval matrix
>
> * Deviation of interval matrix with 12-EDO
>
> * Graphical presentation of interval matrix
>
> * Frequency of notes in a range of one octave (from C)
>
> * Frequency of beats
>
> * Circle of fifths and fourths
>
>
>
> Shaahin Mohajeri
>
> Tombak Player & Researcher , Microtonal Composer
>
>