Diatonic Semitones (once more)

Hello, all and FWIW I've done a little further mathematical
experimentation. Using an ancient Greek method of obtaining a
diatonic scale I assigned the following pitch ratios to a Dorian
E-F-G-A diatonic genus tetrachord and also show Archytas' and
Ptolemy's (syntonon) tunings of the same:

E F G A

Archytas 1 28/27 32/27 4/3

Ptolemy 1 16/15 6/5 4/3

Mine 1 15/14 25/21 4/3

My diatonic genus has a 15/14 semitone and 10/9 and 28/25 (whole)
tones. Putting together the E-F-G-A and B-C-D-E tetrachords using my
tuning results in the following diatonic scale:

E F G A B C D E'

1 15/14 25/21 4/3 3/2 45/28 25/14 2

Note the (expected) addition of a 9/8 whole tone between notes A and
B. Other intervals of interest are the 25/21 (quasi-tempered m3) and
25/14 (middle m7). I've endeavored to adhere to the JI idea of
obtaining to the greatest extent intervals as ratios of small integers
given that I wanted to start with a semitone of 15/14 rather than more
common 16/15. It now appears plausible to distinguish 15/14 (`119
cents) and 16/15 (~112 cents) as major and minor diatonic semitones,
respectively. Sincerely,

--- In tuning@yahoogroups.com, "ham_45242" <arl_123@...> wrote:
>
> Hello, all and FWIW I've done a little further mathematical
> experimentation. Using an ancient Greek method of obtaining a
> diatonic scale I assigned the following pitch ratios to a Dorian
> E-F-G-A diatonic genus tetrachord and also show Archytas' and
> Ptolemy's (syntonon) tunings of the same:
>
> E F G A
>
> Archytas 1 28/27 32/27 4/3
>
> Ptolemy 1 16/15 6/5 4/3
>
> Mine 1 15/14 25/21 4/3
>
> My diatonic genus has a 15/14 semitone and 10/9 and 28/25 (whole)
> tones. Putting together the E-F-G-A and B-C-D-E tetrachords using
my
> tuning results in the following diatonic scale:
>
> E F G A B C D E'
>
> 1 15/14 25/21 4/3 3/2 45/28 25/14 2
>
> Note the (expected) addition of a 9/8 whole tone between notes A and
> B. Other intervals of interest are the 25/21 (quasi-tempered m3)
and
> 25/14 (middle m7). I've endeavored to adhere to the JI idea of
> obtaining to the greatest extent intervals as ratios of small
integers
> given that I wanted to start with a semitone of 15/14 rather than
more
> common 16/15. It now appears plausible to distinguish 15/14 (`119
> cents) and 16/15 (~112 cents) as major and minor diatonic semitones,
> respectively. Sincerely,
>

It sounds good, the triad on your D is nice, well flat of Just in a
really pleasant way, and the uneveness is good. The size of the
semitone didn't matter so much as far as creating the diatonic genus,
it was the interval created by the first two intervals- basically if
it was larger than half the tetrachord, you had the diatonic (which
means "stretched"). Notice the quite small Archytus semitone.

Do you have John Chalmer's book, which I've linked a couple of times?
It's the most packed with practical information, but I've enjoyed a
number of different texts because the characters involved (the
ancient Greeks) were very entertaining and "full of beans" as my mom
would say.

-Cameron Bobro

I like the 15/14
here are some like uses of it in this scale
http://anaphoria.com/centaur.html

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

ham_45242 wrote:
>
> Hello, all and FWIW I've done a little further mathematical
> experimentation. Using an ancient Greek method of obtaining a
> diatonic scale I assigned the following pitch ratios to a Dorian
> E-F-G-A diatonic genus tetrachord and also show Archytas' and
> Ptolemy's (syntonon) tunings of the same:
>
> E F G A
>
> Archytas 1 28/27 32/27 4/3
>
> Ptolemy 1 16/15 6/5 4/3
>
> Mine 1 15/14 25/21 4/3
>
> My diatonic genus has a 15/14 semitone and 10/9 and 28/25 (whole)
> tones. Putting together the E-F-G-A and B-C-D-E tetrachords using my
> tuning results in the following diatonic scale:
>
> E F G A B C D E'
>
> 1 15/14 25/21 4/3 3/2 45/28 25/14 2
>
> Note the (expected) addition of a 9/8 whole tone between notes A and
> B. Other intervals of interest are the 25/21 (quasi-tempered m3) and
> 25/14 (middle m7). I've endeavored to adhere to the JI idea of
> obtaining to the greatest extent intervals as ratios of small integers
> given that I wanted to start with a semitone of 15/14 rather than more
> common 16/15. It now appears plausible to distinguish 15/14 (`119
> cents) and 16/15 (~112 cents) as major and minor diatonic semitones,
> respectively. Sincerely,
>
>