Chords in eq temps

Hey Robert...nice to see you looking into 19 and other temps. In my piece "Mysteries," from my 1997 CD "Acoustic Stick," there are something close to 54 different chords. There are also a couple of 19 tunes on "Mysterious Female" that have a lot of chords. I tend to use my ear more when composing than any theoretical ideas...sure, I have studied the interval structures of different systems, and know that certain intervals are supposed to better "in tune" than others...but, I've also found that the way things SOUND in reality may be different than what a theory says. I'm gonna try and post the music to "Mysteries" on my site soon, then you could take a look and maybe play through it (if you have a 19 tone instrument). Of course, I believe it is a big big deal to actually compose/play in different systems...music is sound, and the expression of feelings and ideas.

And 34 has a great neutral 3rd as well, plus 2 minor 3rds, and a bunch of other cool stuff...best...Hstick

microstick.net myspace.com/microstick

If you were to explore 88edo, you will find that there are literally thousands of chords which you can voice, using its similarity to LucyTuning, as the basis for its harmonic structure, and scalecoding as the "logic" behind the system's musical structure

The reference pitch is A=440Hz, so it will play "in tune" with all other LucyTuned instruments.

see:

http://www.lucytune.com/midi_and_keyboard/pitch_bend.html
http://www.lucytune.com/midi_and_keyboard/midi_chords.html
http://www.lucytune.com/new_to_lt/chords.html
http://www.lucytune.com/new_to_lt/pitch_05.html
http://www.lucytune.com/scales/

I appreciate that the LucyTune paradigm is heresy for the JI advocates, yet it does actually work as an entire musical system to extend the limitations of Western 12edo harmony, and may be considered as either an edo approximation (using 88edo) or as an unlimited meantone-type structure derived from pi.

On 10 May 2008, at 15:55, <microstick@...> <microstick@...> wrote:

>
> Hey Robert...nice to see you looking into 19 and other temps. In > my piece "Mysteries," from my 1997 CD "Acoustic Stick," there are > something close to 54 different chords. There are also a couple of > 19 tunes on "Mysterious Female" that have a lot of chords. I tend to > use my ear more when composing than any theoretical ideas...sure, I > have studied the interval structures of different systems, and know > that certain intervals are supposed to better "in tune" than > others...but, I've also found that the way things SOUND in reality > may be different than what a theory says. I'm gonna try and post the > music to "Mysteries" on my site soon, then you could take a look > and maybe play through it (if you have a 19 tone instrument). Of > course, I believe it is a big big deal to actually compose/play in > different systems...music is sound, and the expression of feelings > and ideas.
>
> And 34 has a great neutral 3rd as well, plus 2 minor 3rds, and a > bunch of other cool stuff...best...Hstick
>
> microstick.net myspace.com/microstick
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> If you were to explore 88edo, you will find that there are
literally
> thousands of chords which you can voice, using its similarity to
> LucyTuning, as the basis for its harmonic structure, and
scalecoding
> as the "logic" behind the system's musical structure
>
> The reference pitch is A=440Hz, so it will play "in tune" with all
> other LucyTuned instruments.
>
> see:
>
> http://www.lucytune.com/midi_and_keyboard/pitch_bend.html
> http://www.lucytune.com/midi_and_keyboard/midi_chords.html
> http://www.lucytune.com/new_to_lt/chords.html
> http://www.lucytune.com/new_to_lt/pitch_05.html
> http://www.lucytune.com/scales/
>
> I appreciate that the LucyTune paradigm is heresy for the JI
> advocates, yet it does actually work as an entire musical system
to
> extend the limitations of Western 12edo harmony, and may be
considered
> as either an edo approximation (using 88edo) or as an unlimited
> meantone-type structure derived from pi.
>
>
>
> On 10 May 2008, at 15:55, <microstick@...> <microstick@...>
> wrote:
>
> >
> > Hey Robert...nice to see you looking into 19 and other temps.
In
> > my piece "Mysteries," from my 1997 CD "Acoustic Stick," there
are
> > something close to 54 different chords. There are also a couple
of
> > 19 tunes on "Mysterious Female" that have a lot of chords. I tend
to
> > use my ear more when composing than any theoretical ideas...sure,
I
> > have studied the interval structures of different systems, and
know
> > that certain intervals are supposed to better "in tune" than
> > others...but, I've also found that the way things SOUND in
reality
> > may be different than what a theory says. I'm gonna try and post
the
> > music to "Mysteries" on my site soon, then you could take a
look
> > and maybe play through it (if you have a 19 tone instrument). Of
> > course, I believe it is a big big deal to actually compose/play
in
> > different systems...music is sound, and the expression of
feelings
> > and ideas.
> >
> > And 34 has a great neutral 3rd as well, plus 2 minor 3rds, and
a
> > bunch of other cool stuff...best...Hstick
> >
> > microstick.net myspace.com/microstick
> >
> >
>
> Charles Lucy
> lucy@...
>
> - Promoting global harmony through LucyTuning -
>
> for information on LucyTuning go to:
> http://www.lucytune.com
>
> For LucyTuned Lullabies go to:
> http://www.lullabies.co.uk
>
I have studied 44tet and even made 4hours of demo tapes which I
passed on to Warren Burt. But the idea of 88tet seems too mind
boggling to even consider as a common practice for all the musicians
around the
world.
Robert.

Yes Robert;

I appreciate that you may find it confusing if you only consider the the intervals as steps of 22, 44, or 88edo. The way to think about the intervals is as an educated Western musician does:

i.e. by note names, positions and harmonic relationships.

Although you are working from 88edo, doesn't mean that you have to use all the notes in every composition.

In practice you usually will only use up to 12 different notes in any one section of a piece of music, so select which notes you wish to use, which will also determine the possible scales dependent upon which note you consider to be the "tonic".

If you consider the tunings in note names terms, you will appreciate how what you are composing in 22edo, 44edo, or 88edo and how it works in "harmonic" and musical context.

On 10 May 2008, at 19:40, robert thomas martin wrote:

> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > If you were to explore 88edo, you will find that there are
> literally
> > thousands of chords which you can voice, using its similarity to
> > LucyTuning, as the basis for its harmonic structure, and
> scalecoding
> > as the "logic" behind the system's musical structure
> >
> > The reference pitch is A=440Hz, so it will play "in tune" with all
> > other LucyTuned instruments.
> >
> > see:
> >
> > http://www.lucytune.com/midi_and_keyboard/pitch_bend.html
> > http://www.lucytune.com/midi_and_keyboard/midi_chords.html
> > http://www.lucytune.com/new_to_lt/chords.html
> > http://www.lucytune.com/new_to_lt/pitch_05.html
> > http://www.lucytune.com/scales/
> >
> > I appreciate that the LucyTune paradigm is heresy for the JI
> > advocates, yet it does actually work as an entire musical system
> to
> > extend the limitations of Western 12edo harmony, and may be
> considered
> > as either an edo approximation (using 88edo) or as an unlimited
> > meantone-type structure derived from pi.
> >
> >
> >
> > On 10 May 2008, at 15:55, <microstick@...> <microstick@...>
> > wrote:
> >
> > >
> > > Hey Robert...nice to see you looking into 19 and other temps.
> In
> > > my piece "Mysteries," from my 1997 CD "Acoustic Stick," there
> are
> > > something close to 54 different chords. There are also a couple
> of
> > > 19 tunes on "Mysterious Female" that have a lot of chords. I tend
> to
> > > use my ear more when composing than any theoretical ideas...sure,
> I
> > > have studied the interval structures of different systems, and
> know
> > > that certain intervals are supposed to better "in tune" than
> > > others...but, I've also found that the way things SOUND in
> reality
> > > may be different than what a theory says. I'm gonna try and post
> the
> > > music to "Mysteries" on my site soon, then you could take a
> look
> > > and maybe play through it (if you have a 19 tone instrument). Of
> > > course, I believe it is a big big deal to actually compose/play
> in
> > > different systems...music is sound, and the expression of
> feelings
> > > and ideas.
> > >
> > > And 34 has a great neutral 3rd as well, plus 2 minor 3rds, and
> a
> > > bunch of other cool stuff...best...Hstick
> > >
> > > microstick.net myspace.com/microstick
> > >
> > >
> >
> > Charles Lucy
> > lucy@...
> >
> > - Promoting global harmony through LucyTuning -
> >
> > for information on LucyTuning go to:
> > http://www.lucytune.com
> >
> > For LucyTuned Lullabies go to:
> > http://www.lullabies.co.uk
> >
> I have studied 44tet and even made 4hours of demo tapes which I
> passed on to Warren Burt. But the idea of 88tet seems too mind
> boggling to even consider as a common practice for all the musicians
> around the
> world.
> Robert.
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Yes Robert;
>
> I appreciate that you may find it confusing if you only consider
the
> the intervals as steps of 22, 44, or 88edo. The way to think about
the
> intervals is as an educated Western musician does:
>
> i.e. by note names, positions and harmonic relationships.
>
> Although you are working from 88edo, doesn't mean that you have to
use
> all the notes in every composition.
>
> In practice you usually will only use up to 12 different notes in
any
> one section of a piece of music, so select which notes you wish to
> use, which will also determine the possible scales dependent upon
> which note you consider to be the "tonic".
>
> If you consider the tunings in note names terms, you will
appreciate
> how what you are composing in 22edo, 44edo, or 88edo and how it
works
> in "harmonic" and musical context.
>
>
>
>
>
>
>
>
> On 10 May 2008, at 19:40, robert thomas martin wrote:
>
> > --- In tuning@yahoogroups.com, Charles Lucy <lucy@> wrote:
> > >
> > > If you were to explore 88edo, you will find that there are
> > literally
> > > thousands of chords which you can voice, using its similarity to
> > > LucyTuning, as the basis for its harmonic structure, and
> > scalecoding
> > > as the "logic" behind the system's musical structure
> > >
> > > The reference pitch is A=440Hz, so it will play "in tune" with
all
> > > other LucyTuned instruments.
> > >
> > > see:
> > >
> > > http://www.lucytune.com/midi_and_keyboard/pitch_bend.html
> > > http://www.lucytune.com/midi_and_keyboard/midi_chords.html
> > > http://www.lucytune.com/new_to_lt/chords.html
> > > http://www.lucytune.com/new_to_lt/pitch_05.html
> > > http://www.lucytune.com/scales/
> > >
> > > I appreciate that the LucyTune paradigm is heresy for the JI
> > > advocates, yet it does actually work as an entire musical system
> > to
> > > extend the limitations of Western 12edo harmony, and may be
> > considered
> > > as either an edo approximation (using 88edo) or as an unlimited
> > > meantone-type structure derived from pi.
> > >
> > >
> > >
> > > On 10 May 2008, at 15:55, <microstick@> <microstick@>
> > > wrote:
> > >
> > > >
> > > > Hey Robert...nice to see you looking into 19 and other temps.
> > In
> > > > my piece "Mysteries," from my 1997 CD "Acoustic Stick," there
> > are
> > > > something close to 54 different chords. There are also a
couple
> > of
> > > > 19 tunes on "Mysterious Female" that have a lot of chords. I
tend
> > to
> > > > use my ear more when composing than any theoretical
ideas...sure,
> > I
> > > > have studied the interval structures of different systems, and
> > know
> > > > that certain intervals are supposed to better "in tune" than
> > > > others...but, I've also found that the way things SOUND in
> > reality
> > > > may be different than what a theory says. I'm gonna try and
post
> > the
> > > > music to "Mysteries" on my site soon, then you could take a
> > look
> > > > and maybe play through it (if you have a 19 tone instrument).
Of
> > > > course, I believe it is a big big deal to actually
compose/play
> > in
> > > > different systems...music is sound, and the expression of
> > feelings
> > > > and ideas.
> > > >
> > > > And 34 has a great neutral 3rd as well, plus 2 minor 3rds, and
> > a
> > > > bunch of other cool stuff...best...Hstick
> > > >
> > > > microstick.net myspace.com/microstick
> > > >
> > > >
> > >
> > > Charles Lucy
> > > lucy@
> > >
> > > - Promoting global harmony through LucyTuning -
> > >
> > > for information on LucyTuning go to:
> > > http://www.lucytune.com
> > >
> > > For LucyTuned Lullabies go to:
> > > http://www.lullabies.co.uk
> > >
> > I have studied 44tet and even made 4hours of demo tapes which I
> > passed on to Warren Burt. But the idea of 88tet seems too mind
> > boggling to even consider as a common practice for all the
musicians
> > around the
> > world.
> > Robert.
> >
> >
> >
>
> Charles Lucy
> lucy@...
>
> - Promoting global harmony through LucyTuning -
>
> for information on LucyTuning go to:
> http://www.lucytune.com
>
> For LucyTuned Lullabies go to:
> http://www.lullabies.co.uk
>
From Robert. If that is so then I think that I would rather choose
12-note groupings from the 128 partials of the 8th octave of the
harmonic series as a working syatem. Robert.

How about this brand new 24-tone maqam scale?

20/19
38/35
125/112
9/8
32/27
6/5
16/13
5/4
19/15
4/3
7/5
36/25
121/81
3/2
19/12
18/11
5/3
27/16
16/9
9/5
13/7
15/8
21/11
2/1

Here are the specs:

24-tone maqam music scale
|
0: 1/1 0.000 unison, perfect prime
1: 20/19 88.801 small undevicesimal semitone
2: 38/35 142.373
3: 125/112 190.115 classic augmented semitone
4: 9/8 203.910 major whole tone
5: 32/27 294.135 Pythagorean minor third
6: 6/5 315.641 minor third *
7: 16/13 359.472 tridecimal neutral third
8: 5/4 386.314 major third
9: 19/15 409.244 undevicesimal ditone
10: 4/3 498.045 perfect fourth
11: 7/5 582.512 septimal or Huygens' tritone, BP fourth
12: 36/25 631.283 classic diminished fifth
13: 121/81 694.816 two (undecimal neutral third)
14: 3/2 701.955 perfect fifth
15: 19/12 795.558 undevicesimal minor sixth
16: 18/11 852.592 undecimal neutral sixth
17: 5/3 884.359 major sixth, BP sixth
18: 27/16 905.865 Pythagorean major sixth
19: 16/9 996.090 Pythagorean minor seventh
20: 9/5 1017.596 just minor seventh, BP seventh *
21: 13/7 1071.702 16/3-tone
22: 15/8 1088.269 classic major seventh
23: 21/11 1119.463 undecimal major seventh
24: 2/1 1200.000 octave

Maqam music perdes with cent values in an octave:

0 RAST
89 Nim Zengule (Shuri)
142 Zengule
190 Nerm DUGAH
204 DUGAH
294 Kurdi
316 Dik Kurdi *
359 Nerm Segah (Ushshaq)
386 SEGAH
409 Buselik
498 TCHARGAH
583 Hijaz
631 Dik Hijaz (Saba)
695 Nerm NEVA
702 NEVA
796 Nim Hisar (Beyati)
853 Hisar
884 Hisarek
906 HUSEYNI
996 Ajem
1018 Dik Ajem *
1072 Nerm EVDJ
1088 EVDJ
1119 Mahur
1200 GERDANIYE

Tones marked with asterisks are independent of cycle of fifths.

The 12-tone mode and cycle:

|
0: 1/1 0.000 unison, perfect prime
1: 20/19 88.801 small undevicesimal semitone
2: 125/112 190.115 classic augmented semitone
3: 32/27 294.135 Pythagorean minor third
4: 5/4 386.314 major third
5: 4/3 498.045 perfect fourth
6: 7/5 582.512 septimal or Huygens' tritone, BP fourth
7: 121/81 694.816 two (undecimal neutral third)
8: 19/12 795.558 undevicesimal minor sixth
9: 5/3 884.359 major sixth, BP sixth
10: 16/9 996.090 Pythagorean minor seventh
11: 15/8 1088.269 classic major seventh
12: 2/1 1200.000 octave

|
0: 0.000 cents 0.000 0 0 commas
7: 694.816 cents -7.139 -219 -neutral third comma
2: 695.299 cents -13.795 -423 -small septimal comma
9: 694.243 cents -21.506 -660 -syntonic comma, Didymus comma
4: 701.955 cents -21.506 -660 -syntonic comma, Didymus comma
11: 701.955 cents -21.506 -660 -syntonic comma, Didymus comma
6: 694.243 cents -29.218 -897
1: 706.289 cents -24.884 -764
8: 706.757 cents -20.082 -616
3: 698.577 cents -23.460 -720 -Pythagorean comma, ditonic comma
10: 701.955 cents -23.460 -720 -Pythagorean comma, ditonic comma
5: 701.955 cents -23.460 -720 -Pythagorean comma, ditonic comma
12: 701.955 cents -23.460 -720 -Pythagorean comma, ditonic comma
Average absolute difference: 21.1231 cents
Root mean square difference: 22.7766 cents
Maximum absolute difference: 29.2178 cents
Maximum formal fifth difference: 7.7115 cents
|

The 17-tone mode and cycle:

|
0: 1/1 unison, perfect prime
1: 20/19 small undevicesimal semitone
2: 38/35
3: 9/8 major whole tone
4: 32/27 Pythagorean minor third
5: 16/13 tridecimal neutral third
6: 19/15 undevicesimal ditone
7: 4/3 perfect fourth
8: 7/5 septimal or Huygens' tritone, BP fourth
9: 36/25 classic diminished fifth
10: 3/2 perfect fifth
11: 19/12 undevicesimal minor sixth
12: 18/11 undecimal neutral sixth
13: 27/16 Pythagorean major sixth
14: 16/9 Pythagorean minor seventh
15: 13/7 16/3-tone
16: 21/11 undecimal major seventh
17: 2/1 octave

|
0: 0.000 cents 0.000 0 0 commas
10: 701.955 cents 0.000 0 0 commas
3: 701.955 cents 0.000 0 0 commas
13: 701.955 cents 0.000 0 0 commas
6: 703.379 cents 1.424 44 Eratosthenes' comma
16: 710.219 cents 9.688 297 undecimal semicomma
9: 711.820 cents 19.553 600 diaschisma
2: 711.091 cents 28.688 880
12: 710.219 cents 36.952 1134 undecimal minor diesis
5: 706.880 cents 41.877 1285
15: 712.229 cents 52.152 1601
8: 710.810 cents 61.007 1872
1: 706.289 cents 65.341 2005
11: 706.757 cents 70.143 2153
4: 698.577 cents 66.765 2049 Pythagorean double diminished
14: 701.955 cents 66.765 2049 Pythagorean double diminished
7: 701.955 cents 66.765 2049 Pythagorean double diminished
17: 701.955 cents 66.765 2049 Pythagorean double diminished
Average absolute difference: 38.4638 cents
Root mean square difference: 48.6581 cents
Maximum absolute difference: 70.1430 cents
Maximum formal fifth difference: 10.2744 cents

Oz.

On May 10, 2008, at 9:40 PM, robert thomas martin wrote:
>> SNIP
> I have studied 44tet and even made 4hours of demo tapes which I
> passed on to Warren Burt. But the idea of 88tet seems too mind
> boggling to even consider as a common practice for all the musicians
> around the
> world.
> Robert.
>
>

--- In tuning@yahoogroups.com, "ozanyarman@..." <ozanyarman@...>
wrote:
>
> How about this brand new 24-tone maqam scale?
>
> 20/19
> 38/35
> 125/112
> 9/8
> 32/27
> 6/5
> 16/13
> 5/4
> 19/15
> 4/3
> 7/5
> 36/25
> 121/81
> 3/2
> 19/12
> 18/11
> 5/3
> 27/16
> 16/9
> 9/5
> 13/7
> 15/8
> 21/11
> 2/1
>
> Here are the specs:
>
> 24-tone maqam music scale
> |
> 0: 1/1 0.000 unison, perfect prime
> 1: 20/19 88.801 small undevicesimal semitone
> 2: 38/35 142.373
> 3: 125/112 190.115 classic augmented semitone
> 4: 9/8 203.910 major whole tone
> 5: 32/27 294.135 Pythagorean minor third
> 6: 6/5 315.641 minor third *
> 7: 16/13 359.472 tridecimal neutral third
> 8: 5/4 386.314 major third
> 9: 19/15 409.244 undevicesimal ditone
> 10: 4/3 498.045 perfect fourth
> 11: 7/5 582.512 septimal or Huygens' tritone,
BP
> fourth
> 12: 36/25 631.283 classic diminished fifth
> 13: 121/81 694.816 two (undecimal neutral third)
> 14: 3/2 701.955 perfect fifth
> 15: 19/12 795.558 undevicesimal minor sixth
> 16: 18/11 852.592 undecimal neutral sixth
> 17: 5/3 884.359 major sixth, BP sixth
> 18: 27/16 905.865 Pythagorean major sixth
> 19: 16/9 996.090 Pythagorean minor seventh
> 20: 9/5 1017.596 just minor seventh, BP seventh
*
> 21: 13/7 1071.702 16/3-tone
> 22: 15/8 1088.269 classic major seventh
> 23: 21/11 1119.463 undecimal major seventh
> 24: 2/1 1200.000 octave
>
>
> Maqam music perdes with cent values in an octave:
>
> 0 RAST
> 89 Nim Zengule (Shuri)
> 142 Zengule
> 190 Nerm DUGAH
> 204 DUGAH
> 294 Kurdi
> 316 Dik Kurdi *
> 359 Nerm Segah (Ushshaq)
> 386 SEGAH
> 409 Buselik
> 498 TCHARGAH
> 583 Hijaz
> 631 Dik Hijaz (Saba)
> 695 Nerm NEVA
> 702 NEVA
> 796 Nim Hisar (Beyati)
> 853 Hisar
> 884 Hisarek
> 906 HUSEYNI
> 996 Ajem
> 1018 Dik Ajem *
> 1072 Nerm EVDJ
> 1088 EVDJ
> 1119 Mahur
> 1200 GERDANIYE
>
> Tones marked with asterisks are independent of cycle of fifths.
>
> The 12-tone mode and cycle:
>
> |
> 0: 1/1 0.000 unison, perfect prime
> 1: 20/19 88.801 small undevicesimal semitone
> 2: 125/112 190.115 classic augmented semitone
> 3: 32/27 294.135 Pythagorean minor third
> 4: 5/4 386.314 major third
> 5: 4/3 498.045 perfect fourth
> 6: 7/5 582.512 septimal or Huygens' tritone,
BP
> fourth
> 7: 121/81 694.816 two (undecimal neutral third)
> 8: 19/12 795.558 undevicesimal minor sixth
> 9: 5/3 884.359 major sixth, BP sixth
> 10: 16/9 996.090 Pythagorean minor seventh
> 11: 15/8 1088.269 classic major seventh
> 12: 2/1 1200.000 octave
>
> |
> 0: 0.000 cents 0.000 0 0 commas
> 7: 694.816 cents -7.139 -219 -neutral third comma
> 2: 695.299 cents -13.795 -423 -small septimal comma
> 9: 694.243 cents -21.506 -660 -syntonic comma, Didymus
comma
> 4: 701.955 cents -21.506 -660 -syntonic comma, Didymus
comma
> 11: 701.955 cents -21.506 -660 -syntonic comma, Didymus
comma
> 6: 694.243 cents -29.218 -897
> 1: 706.289 cents -24.884 -764
> 8: 706.757 cents -20.082 -616
> 3: 698.577 cents -23.460 -720 -Pythagorean comma, ditonic
comma
> 10: 701.955 cents -23.460 -720 -Pythagorean comma,
ditonic
> comma
> 5: 701.955 cents -23.460 -720 -Pythagorean comma, ditonic
comma
> 12: 701.955 cents -23.460 -720 -Pythagorean comma,
ditonic
> comma
> Average absolute difference: 21.1231 cents
> Root mean square difference: 22.7766 cents
> Maximum absolute difference: 29.2178 cents
> Maximum formal fifth difference: 7.7115 cents
> |
>
> The 17-tone mode and cycle:
>
> |
> 0: 1/1 unison, perfect prime
> 1: 20/19 small undevicesimal semitone
> 2: 38/35
> 3: 9/8 major whole tone
> 4: 32/27 Pythagorean minor third
> 5: 16/13 tridecimal neutral third
> 6: 19/15 undevicesimal ditone
> 7: 4/3 perfect fourth
> 8: 7/5 septimal or Huygens' tritone, BP fourth
> 9: 36/25 classic diminished fifth
> 10: 3/2 perfect fifth
> 11: 19/12 undevicesimal minor sixth
> 12: 18/11 undecimal neutral sixth
> 13: 27/16 Pythagorean major sixth
> 14: 16/9 Pythagorean minor seventh
> 15: 13/7 16/3-tone
> 16: 21/11 undecimal major seventh
> 17: 2/1 octave
>
> |
> 0: 0.000 cents 0.000 0 0 commas
> 10: 701.955 cents 0.000 0 0 commas
> 3: 701.955 cents 0.000 0 0 commas
> 13: 701.955 cents 0.000 0 0 commas
> 6: 703.379 cents 1.424 44 Eratosthenes' comma
> 16: 710.219 cents 9.688 297 undecimal semicomma
> 9: 711.820 cents 19.553 600 diaschisma
> 2: 711.091 cents 28.688 880
> 12: 710.219 cents 36.952 1134 undecimal minor diesis
> 5: 706.880 cents 41.877 1285
> 15: 712.229 cents 52.152 1601
> 8: 710.810 cents 61.007 1872
> 1: 706.289 cents 65.341 2005
> 11: 706.757 cents 70.143 2153
> 4: 698.577 cents 66.765 2049 Pythagorean double
diminished
> 14: 701.955 cents 66.765 2049 Pythagorean double
diminished
> 7: 701.955 cents 66.765 2049 Pythagorean double
diminished
> 17: 701.955 cents 66.765 2049 Pythagorean double
diminished
> Average absolute difference: 38.4638 cents
> Root mean square difference: 48.6581 cents
> Maximum absolute difference: 70.1430 cents
> Maximum formal fifth difference: 10.2744 cents
>
> Oz.
>
> On May 10, 2008, at 9:40 PM, robert thomas martin wrote:
> >> SNIP
> > I have studied 44tet and even made 4hours of demo tapes which I
> > passed on to Warren Burt. But the idea of 88tet seems too mind
> > boggling to even consider as a common practice for all the
musicians
> > around the
> > world.
> > Robert.
> >
> > From Robert. This is not a criticism. Just an observation. When I
carried out experiments with the neutral third I always used 351cents.
> The only reason I did this was because 351 is the middle point
between 316 and 386 cents. Values in the literature seem to vary from
351 +/-10cents.