Archytas enharmonic and diatonic

Hi all,
I have som problems with understanding Archytas enharmonic and diatonic scales
Im what you would call a newbie in this field of tuning, so you have to bare with me on
this. Since the Tonalsoft site seemes to be down at the moment
I hope that somone on this list can help me.
What i know is that the Archytas enharmonic tetrachord consist of 5/4 36/35 and 28/27
and the diatonic consist of 9/8 8/7 and 28/27.
Now if i combine two enharmonic tetrachords separeted with a 9:8
the upper being 3:2 6:5 7:6 9:8 and the lower 1:1 8:5 14:9 3:2

I got this scale: 1:1, 9:8, 7:6, 6:5, 3:2, 14:9, 8:5 2:1
but surely this is not correct? I had look in Partch Genesis of a music,where it is listed as
1:1, 28:27, 16:15, 4:3, 3:2, 14:9 8:5, 2:1
What am I missing here ? or in what way are im thinking wrong
this a humble request for somone to explain this to me.
Also how would one express the Archytas diatonic on a scale?
sorry for any obvious mistake I might have done

regards

Anders

Maybe I'm missing your question, but wouldn't that be 2:1...3:2 for
the upper tetrachord and 4:3...1:1 for the lower, ie, 1:1 to 4:3,
then 3:2 to 2:1, there being 9:8 between 4:3 and 3:2.

-Cameron Bobro

--- In tuning@yahoogroups.com, "gradientmusic" <gradientmusic@...>
wrote:
>
> Hi all,
> I have som problems with understanding Archytas enharmonic and
diatonic scales
> Im what you would call a newbie in this field of tuning, so you
have to bare with me on
> this. Since the Tonalsoft site seemes to be down at the moment
> I hope that somone on this list can help me.
> What i know is that the Archytas enharmonic tetrachord consist of
5/4 36/35 and 28/27
> and the diatonic consist of 9/8 8/7 and 28/27.
> Now if i combine two enharmonic tetrachords separeted with a 9:8
> the upper being 3:2 6:5 7:6 9:8 and the lower 1:1 8:5 14:9 3:2
>
> I got this scale: 1:1, 9:8, 7:6, 6:5, 3:2, 14:9, 8:5 2:1
> but surely this is not correct? I had look in Partch Genesis of a
music,where it is listed as
> 1:1, 28:27, 16:15, 4:3, 3:2, 14:9 8:5, 2:1
> What am I missing here ? or in what way are im thinking wrong
> this a humble request for somone to explain this to me.
> Also how would one express the Archytas diatonic on a scale?
> sorry for any obvious mistake I might have done
>
> regards
>
> Anders
>

Hi Anders,

--- In tuning@yahoogroups.com, "gradientmusic" wrote:
>
> Hi all,
> I have som problems with understanding Archytas enharmonic and
diatonic scales. Im what you would call a newbie in this field of
tuning, so you have to bare with me on this. Since the Tonalsoft site
seemes to be down at the moment I hope that somone on this list can
help me.
> What i know is that the Archytas enharmonic tetrachord consist of
5/4 36/35 and 28/27 and the diatonic consist of 9/8 8/7 and 28/27.
Now if i combine two enharmonic tetrachords separeted with a 9:8 the
upper being 3:2 6:5 7:6 9:8 and the lower 1:1 8:5 14:9 3:2
>
> I got this scale: 1:1, 9:8, 7:6, 6:5, 3:2, 14:9, 8:5 2:1 but
surely this is not correct? I had look in Partch Genesis of a music,
where it is listed as 1:1, 28:27, 16:15, 4:3, 3:2, 14:9 8:5, 2:1
> What am I missing here ? or in what way are im thinking wrong
this a humble request for somone to explain this to me.

> Also how would one express the Archytas diatonic on a scale? sorry
for any obvious mistake I might have done
> regards
> Anders

It may help you to know that the ancient Greeks
reckoned all their scales, including tetrachords,
*downwards*, rather than upwards as is now the
standard practice in Western music.

That means an enharmonic tetrachord of Archytas,
consisting of the three intervals 5/4, 36/35 and
28/27 downwards from the octave 2/1, gives the
four notes 2/1, 8/5, 14/9, 3/2. Stepping down a
whole tone of 9/8 gives 4/3. A second enharmonic
tetrachord downwards gives 4/3, 16/15, 28/27, 1/1.
So the scale, descending, is:
2/1, 8/5, 14/9, 3/2, 4/3, 16/15, 28/27, 1/1
and ascending is:
1/1, 28/27, 16/15, 4/3, 3/2, 14/9, 8/5, 2/1.

I hope this helps you.

Regards,
Yahya

Hi Anders,
>
> --- In tuning@yahoogroups.com, "gradientmusic" wrote:
>
> > Also how would one express the Archytas diatonic on a scale?

Further to my previous message, I experimented
and found I could retune my (Roland E-28) keyboard
to play the Archytas enharmonic scale you described,
as in the table below. (This is NOT the diatonic.)

For ease of reading, click on "Reply" on the
Yahoo!groups website; this will align the vertical
rule or "pipe" characters "|". Or you may import
the table into a spreadsheet such as Excel, which
is how I created it.

The table shows the nearest semitone (t/2),
quartertone (t/4), sixthtone (t/6) and eighthtone
(t/8) to the exact ratios.

It also shows the cents for each ratio, which note
on the keyboard to use, and the cents tuning adjust-
ment for that note.

I have found the scale quite pleasant to use, using
the higher notes D and A when ascending and using
the lower notes C# and G# when descending.

Please feel free to ask if anything is not clear.

Regards,
Yahya

Scale of two stacked Archytas' enharmonic tetrachords:
.-----------------------------------------------------------.
| | | | nearest| |near|use|k/b| use|
|note |ratio| cents|t/2|t/4|t/6|t/8| step| t/2|t/2|adj|note|
|-----|-----|-------|---|---|---|---|-----|----|---|---|----|
| C | 1/1 | 0.00| 0| 0| 0| 0| | 0| 0| 43| C|
| | | | | | | |28/27| | | | |
| |C# |28/27| 62.96| 1| 1| 4| 5| | 1| 1| 6| C#|
| | | | | | | |36/35| | | | |
| |Db |16/15| 111.73| 1| 2| 7| 9| | 2| 2|-45| D|
| | | | | | | | 5/4| | | | |
| F | 4/3| 498.04| 5| 10| 30| 40| | 5| 6|-59| F#|
| | | | | | | | 9/8| | | | |
| G | 3/2| 701.96| 7| 14| 42| 56| | 7| 7| 45| G|
| | | | | | | |28/27| | | | |
| |G# | 14/9| 764.92| 8| 15| 46| 61| | 8| 8| 8| G#|
| | | | | | | |36/35| | | | |
| |Ab | 8/5| 813.69| 8| 16| 49| 65| | 9| 9|-43| A|
| | | | | | | | 5/4| | | | |
| C'| 2/1 |1200.00| 12| 24| 72| 96| | 12| 12| 43| C'|
'-----------------------------------------------------------'

Hi Anders,

Sorry that the Tonalsoft site was down for a day or so ... it
wasn't our fault -- something happened to the server. Anyway,
it's back up now.

You should look at my pages on the PIS and its related
subset systems for a full understanding of how the Greeks
constructed their scales from tetrachords:

http://tonalsoft.com/enc/p/pis.aspx

http://tonalsoft.com/enc/g/gps.aspx

http://tonalsoft.com/enc/l/lps.aspx

The actual ratios of Archytas's three tetrachords, along
with those of all the other ancient Greek and Roman writers,
are here:

http://tonalsoft.com/enc/d/diatonic-genus.aspx

http://tonalsoft.com/enc/c/chromatic-genus.aspx

http://tonalsoft.com/enc/e/enharmonic-genus.aspx

You would have to calculate the other tetrachords according
to the scheme outline in the PIS webpage.

And if you are having trouble understanding how tetrachord
theory works, you can read my tutorial here:

http://tonalsoft.com/monzo/aristoxenus/tutorial.htm

(a greatly expanded version of that was just published in
_Xenharmonikon 18_.)

We are working on making what we have of Tonescape so far
available as a free demo ... when it comes out, you will
have Archytas's scale available as Tonescape tuning files,
and you will be able to use them to compose in Tonescape.

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

--- In tuning@yahoogroups.com, "gradientmusic" <gradientmusic@...> wrote:
>
> Hi all,
> I have som problems with understanding Archytas enharmonic and
diatonic scales
> Im what you would call a newbie in this field of tuning, so you have
to bare with me on
> this. Since the Tonalsoft site seemes to be down at the moment
> I hope that somone on this list can help me.
> What i know is that the Archytas enharmonic tetrachord consist of
5/4 36/35 and 28/27
> and the diatonic consist of 9/8 8/7 and 28/27.
> Now if i combine two enharmonic tetrachords separeted with a 9:8
> the upper being 3:2 6:5 7:6 9:8 and the lower 1:1 8:5 14:9 3:2
>
> I got this scale: 1:1, 9:8, 7:6, 6:5, 3:2, 14:9, 8:5 2:1
> but surely this is not correct? I had look in Partch Genesis of a
music,where it is listed as
> 1:1, 28:27, 16:15, 4:3, 3:2, 14:9 8:5, 2:1
> What am I missing here ? or in what way are im thinking wrong
> this a humble request for somone to explain this to me.
> Also how would one express the Archytas diatonic on a scale?
> sorry for any obvious mistake I might have done
>
> regards
>
> Anders
>

Thanks a lot monz!
And to all of you who responded to my question
Looking forward to the release of Tonescape

Anders

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Anders,
>
>
> Sorry that the Tonalsoft site was down for a day or so ... it
> wasn't our fault -- something happened to the server. Anyway,
> it's back up now.
>
> You should look at my pages on the PIS and its related
> subset systems for a full understanding of how the Greeks
> constructed their scales from tetrachords:
>
> http://tonalsoft.com/enc/p/pis.aspx
>
> http://tonalsoft.com/enc/g/gps.aspx
>
> http://tonalsoft.com/enc/l/lps.aspx
>
>
> The actual ratios of Archytas's three tetrachords, along
> with those of all the other ancient Greek and Roman writers,
> are here:
>
> http://tonalsoft.com/enc/d/diatonic-genus.aspx
>
> http://tonalsoft.com/enc/c/chromatic-genus.aspx
>
> http://tonalsoft.com/enc/e/enharmonic-genus.aspx
>
> You would have to calculate the other tetrachords according
> to the scheme outline in the PIS webpage.
>
>
> And if you are having trouble understanding how tetrachord
> theory works, you can read my tutorial here:
>
> http://tonalsoft.com/monzo/aristoxenus/tutorial.htm
>
> (a greatly expanded version of that was just published in
> _Xenharmonikon 18_.)
>
>
> We are working on making what we have of Tonescape so far
> available as a free demo ... when it comes out, you will
> have Archytas's scale available as Tonescape tuning files,
> and you will be able to use them to compose in Tonescape.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
> --- In tuning@yahoogroups.com, "gradientmusic" <gradientmusic@>
wrote:
> >
> > Hi all,
> > I have som problems with understanding Archytas enharmonic and
> diatonic scales
> > Im what you would call a newbie in this field of tuning, so you
have
> to bare with me on
> > this. Since the Tonalsoft site seemes to be down at the moment
> > I hope that somone on this list can help me.
> > What i know is that the Archytas enharmonic tetrachord consist of
> 5/4 36/35 and 28/27
> > and the diatonic consist of 9/8 8/7 and 28/27.
> > Now if i combine two enharmonic tetrachords separeted with a 9:8
> > the upper being 3:2 6:5 7:6 9:8 and the lower 1:1 8:5 14:9 3:2
> >
> > I got this scale: 1:1, 9:8, 7:6, 6:5, 3:2, 14:9, 8:5 2:1
> > but surely this is not correct? I had look in Partch Genesis of a
> music,where it is listed as
> > 1:1, 28:27, 16:15, 4:3, 3:2, 14:9 8:5, 2:1
> > What am I missing here ? or in what way are im thinking wrong
> > this a humble request for somone to explain this to me.
> > Also how would one express the Archytas diatonic on a scale?
> > sorry for any obvious mistake I might have done
> >
> > regards
> >
> > Anders
> >
>