Yahoo Tuning Groups Ultimate Backup tuning Suggestions wanted for wise choice of pitch

Hi guys
I have a scale, or something, and I am wondering if you guys can make
it wise. It is in use, but the exactness of the pitch is lacking, due
to influence of western 12tone ET on the one hand (on players and
instrument makers), and lack of control/perception (of players mainly)
on the other.

It goes like this:
(x = semitone not used
CAPITAL LETTERS show main note
small letters show secondary note
"meri" means dark tone-colour )

x
ri
x
RI MERI
CHI
x
RE
x
tsu
x
TSU MERI
RO

Now, I'll show you the cent interval we generally use between each note:

100c
x
100c
ri
100c
x
125c
RI MERI
75c
CHI
125c
x
75c
RE
100c
x
100c
tsu
100c
x
125c
TSU MERI
75c
RO

I have included pitch intervals even between the pitches I said we
don't use, because they are used when we ... what do you call it ...
move this scale up in pitch?

Linear typing is not so appropriate. Easier to draw it in a circle.
but as I can't type in a circle, I'll give you one example, set out
next to the above one:

("chi kari" is starred so you notice it is 25c different from it's
equivalent on the other set)

100c......100c
x.........x
100c......100c
ri........RI
100c......100c
x.........x
125c......100c
RI MERI...*chi kari*
75c.......100c
CHI.......x
125c......125c
x.........U
75c.......75c
RE........RE
100c......100c
x.........x
100c......100c
tsu.......tsu
100c......100c
x.........x
125c......120c
TSU MERI..TSU MERI
75c.......75c
RO........RO

So that is 2 sets, but we actually use 4 such sets (transpositions?),
or even rarely a 5th one. If you need I can write them too. But I
think you get the idea?

So, the important pitch interval is the ones which are 75cents.
Everything else, however, has been arbitrarily set around the 12 tone
ET temperament. Thus the 125c interval, and all the 100c intervals.
However, I think you guys must know what is better. For example, ro
and chi have a definite relationship, as do ro and re. I am sure that
for example the just intonation answer for the interval relationship
connecting ro, re and chi would be better, or, anyway you guys must
have good suggestions better than 12 tone ET.
Firstly just for the 1st set what would be your suggestions?
Then perhaps after that we could look into some kind of temperament
which would be a "best fit" to cover all 4 common sets? (I can post
more later).

Hope this can stimulate your interest! This is all totally practical.
Thanks!
Justin

🔗justinasia <justinasia@yahoo.com>

🔗Herman Miller <hmiller@IO.COM>

🔗justinasia <justinasia@yahoo.com>

--- In tuning@yahoogroups.com, Klaus Schmirler <KSchmir@...> wrote:

> Actually I was only going to ask what actual scales you use from the
> tuning in the other thread

Hi Klaus. I am not sure if there is a question there? Do you mean to
ask me what scale I use? Apart from pointing to the scale as I
described it in my first post, I would not know what to call it. As
for whether is is pentatonic or not I don't know. I play it and study
traditionally, which does not include any theory. We use 13 notes,
which if you included 2 semitones we don't use, would make 15 notes to
the octave. I have never seen them set out in sets like I did, but
from my intuitive understanding of the music, it seems to me there is
the basic set of 7 notes, 5 main notes (I guess that is pentatonic
then?) with 2 (what I am calling) "secondary" notes, which play a
lesser role. Then that set is transposed 4 or very rarely 5 times,
thus we use altogether about 13 notes.

(My hunch being pentatonic because the note
> names sound Japanese, but the word that's supposed to mean "dark" is
> not in my [tiny] dictionary). Please answer in that other thread.

Ha ha. You got it! Actually I didn't want to mention where it was from
because I didn't want to distract people away from an unbiased
mind-view which would hopefully keep people more open to just logic
and sound. Meri refers actually to a physical manuvre used to create
those notes. It doesn't mean dark. But those notes must be dark. For
this music pitch and tone-colour are at least equally important.

It's sad that nowadays people are using western electronic tuners. We
all know that the meri notes should be "flat", but no-one even seems
to think about all the other notes. Just blindly and unthinnkingly
following 12toneET. So I thought I should try something with the help
of you guys.

Justin

🔗justinasia <justinasia@yahoo.com>

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> It looks like you have two chains of fifths (or fourths). One is a
short
> chain with RI MERI - TSU MERI - and the unnamed pitch between CHI and
> RE. The rest of the notes are in the other chain. One possibility would
> be to use 25/24 (70.672 cents) for the 75 cent interval, and 3/2 for
the
> fifths:
>
> ri = 1/1
> RI MERI = 256/225
> CHI = 32/27
> RE = 4/3
> tsu = 3/2
> TSU MERI = 128/75
> RO = 16/9

Hi Herman
Like that, would RO and RE sound good together? And RO and CHI together?

> The closest scale in the Scala archive is ptolemy_diat4.scl, which is
> described as a "permuted Ptolemy's diatonic" scale.

Can you give me any cultural/historical background on the usage of
that scale? Sounds interesting.

The only difference
> is that it has 8/7 and 12/7 instead of 256/225 and 128/75. The small
> step is only 62.961 cents (28/27) in that version.
>
> Another possibility if you want something closer to 75 cents for the
> small step is to use 25/22 for RI MERI and 75/44 for TSU MERI (the
small
> step works out to be 72.826 cents).

Actually the important steps for me to try to work out are the ones
which have been so far using the 12 tone ET notes. The 75c intervals
sound fine, and that is close enough. Also it is a bit of a personal
taste thing here, different players using different intervals, or even
different for different pieces, or simply just how you feel in that
moment. But the other intervals, they are just set at 100c out of, I
could say ignorance, or, convenience perhaps (use of western electric
tuners).

I am open to all your suggestions. Also if someone would suggest what
it would be in just intonation, I have a feeling that that could be
interesting.

Also, as you have given your answers in fractions, how may I
understand these as cent intervals? For example, interval of "ro" to
"tsu", "ro" to "re", "ro" to "chi", "ro" to "ri"?

Thank you very much!
Justin

🔗Mark Rankin <markrankin95511@yahoo.com>

Folks,

I can't look at your CHI's and RO's without seeing

the greek letters CHI and RHO standing for Christos,

i.e., Christ.

I doubt if your table is arbitrary - what
made you choose the syllables/words

ri = 1/1
RI MERI = 256/225
CHI = 32/27
TSU MERI = 128/75
and RO = 16/9

for your various J.I. intervals?

Mark Rankin

--- justinasia <justinasia@yahoo.com> wrote:

> --- In tuning@yahoogroups.com, Herman Miller
> <hmiller@...> wrote:
>
> > It looks like you have two chains of fifths (or
> fourths). One is a
> short
> > chain with RI MERI - TSU MERI - and the unnamed
> pitch between CHI and
> > RE. The rest of the notes are in the other chain.
> One possibility would
> > be to use 25/24 (70.672 cents) for the 75 cent
> interval, and 3/2 for
> the
> > fifths:
> >
> > ri = 1/1
> > RI MERI = 256/225
> > CHI = 32/27
> > RE = 4/3
> > tsu = 3/2
> > TSU MERI = 128/75
> > RO = 16/9
>
>
> Hi Herman
> Like that, would RO and RE sound good together? And
> RO and CHI together?
>
>
>
>
> > The closest scale in the Scala archive is
> ptolemy_diat4.scl, which is
> > described as a "permuted Ptolemy's diatonic"
> scale.
>
>
>
> Can you give me any cultural/historical background
> on the usage of
> that scale? Sounds interesting.
>
>
>
>
>
>
>
> The only difference
> > is that it has 8/7 and 12/7 instead of 256/225 and
> 128/75. The small
> > step is only 62.961 cents (28/27) in that version.
> >
> > Another possibility if you want something closer
> to 75 cents for the
> > small step is to use 25/22 for RI MERI and 75/44
> for TSU MERI (the
> small
> > step works out to be 72.826 cents).
>
>
> Actually the important steps for me to try to work
> out are the ones
> which have been so far using the 12 tone ET notes.
> The 75c intervals
> sound fine, and that is close enough. Also it is a
> bit of a personal
> taste thing here, different players using different
> intervals, or even
> different for different pieces, or simply just how
> you feel in that
> moment. But the other intervals, they are just set
> at 100c out of, I
> could say ignorance, or, convenience perhaps (use of
> western electric
> tuners).
>
> I am open to all your suggestions. Also if someone
> would suggest what
> it would be in just intonation, I have a feeling
> that that could be
> interesting.
>
> Also, as you have given your answers in fractions,
> how may I
> understand these as cent intervals? For example,
> interval of "ro" to
> "tsu", "ro" to "re", "ro" to "chi", "ro" to "ri"?
>
> Thank you very much!
> Justin
>
>
>
>
>

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🔗justinasia <justinasia@yahoo.com>

🔗Herman Miller <hmiller@IO.COM>

justinasia wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> >> It looks like you have two chains of fifths (or fourths). One is a
> short >> chain with RI MERI - TSU MERI - and the unnamed pitch between CHI and >> RE. The rest of the notes are in the other chain. One possibility would >> be to use 25/24 (70.672 cents) for the 75 cent interval, and 3/2 for
> the >> fifths:
>>
>> ri = 1/1
>> RI MERI = 256/225
>> CHI = 32/27
>> RE = 4/3
>> tsu = 3/2
>> TSU MERI = 128/75
>> RO = 16/9
> > > Hi Herman
> Like that, would RO and RE sound good together? And RO and CHI together?

Yes, the interval between RE and RO is 4/3, and the interval between CHI and RO is 3/2. Any two adjacent notes in this chain will sound good together: tsu - ri - RE - RO - CHI.

>> The closest scale in the Scala archive is ptolemy_diat4.scl, which is >> described as a "permuted Ptolemy's diatonic" scale.
> > > > Can you give me any cultural/historical background on the usage of
> that scale? Sounds interesting.

I'm not familiar with Ptolemy's work in music theory, but probably someone else here is.

> The only difference >> is that it has 8/7 and 12/7 instead of 256/225 and 128/75. The small >> step is only 62.961 cents (28/27) in that version.
>>
>> Another possibility if you want something closer to 75 cents for the >> small step is to use 25/22 for RI MERI and 75/44 for TSU MERI (the
> small >> step works out to be 72.826 cents).
> > > Actually the important steps for me to try to work out are the ones
> which have been so far using the 12 tone ET notes. The 75c intervals
> sound fine, and that is close enough. Also it is a bit of a personal
> taste thing here, different players using different intervals, or even
> different for different pieces, or simply just how you feel in that
> moment. But the other intervals, they are just set at 100c out of, I
> could say ignorance, or, convenience perhaps (use of western electric
> tuners).
> > I am open to all your suggestions. Also if someone would suggest what
> it would be in just intonation, I have a feeling that that could be
> interesting.
> > Also, as you have given your answers in fractions, how may I
> understand these as cent intervals? For example, interval of "ro" to
> "tsu", "ro" to "re", "ro" to "chi", "ro" to "ri"?

The fractions are a convention for representing pitches in just intonation. One of these pitches is designated as a reference pitch, 1/1, and the others are frequency ratios relative to that pitch. Using Scala (http://www.xs4all.nl/~huygensf/scala/), I can make a scale with these notes, and show the pitch in cents of each note.

0: 1/1 0.000 unison, perfect prime
1: 256/225 223.463 diminished third
2: 32/27 294.135 Pythagorean minor third
3: 4/3 498.045 perfect fourth
4: 3/2 701.955 perfect fifth
5: 128/75 925.418 diminished seventh
6: 16/9 996.090 Pythagorean minor seventh
7: 2/1 1200.000 octave

With another Scala command (SHOW /INTERVAL), I can see the size of each of the steps in the scale.

0: 9/8 203.910 major whole tone
1: 256/225 223.463 diminished third
2: 25/24 70.672 classic chromatic semitone, minor chroma
3: 9/8 203.910 major whole tone
4: 9/8 203.910 major whole tone
5: 256/225 223.463 diminished third
6: 25/24 70.672 classic chromatic semitone, minor chroma
7: 9/8 203.910 major whole tone

Or if I substitute 25/22 for 256/225 and 75/44 for 128/75, the result is like this:

0: 1/1 0.000 unison, perfect prime
1: 25/22 221.309 undecimal acute whole tone
2: 32/27 294.135 Pythagorean minor third
3: 4/3 498.045 perfect fourth
4: 3/2 701.955 perfect fifth
5: 75/44 923.264
6: 16/9 996.090 Pythagorean minor seventh
7: 2/1 1200.000 octave

0: 9/8 203.910 major whole tone
1: 25/22 221.309 undecimal acute whole tone
2: 704/675 72.826
3: 9/8 203.910 major whole tone
4: 9/8 203.910 major whole tone
5: 25/22 221.309 undecimal acute whole tone
6: 704/675 72.826
7: 9/8 203.910 major whole tone

Another useful thing about Scala is that if you have a MIDI output (which most Windows PC's have in one form or another), you can open up a window with a keyboard-like representation of the scale, click on a key like a musical keyboard, and hear the notes in the scale.

🔗justinasia <justinasia@yahoo.com>

Oh dear
I just realised I may have created unnecessary confusion - in my list
of notes, the one at the bottom was the bottom pitch. The one at the
top was the top pitch. From your mail Herman, it appears I could have
gone counter to convention (wouldn't be the first time!)

Does this mess up all the information you just explained to me? Very
sorry if it does! And, so others are not confused, ought I edit the
first post? Or hopefully everyone interested will be reading this post
too?

I shall try to post some western note name equivalents in just a minute.
Justin

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> justinasia wrote:
> > --- In tuning@yahoogroups.com, Herman Miller <hmiller@> wrote:
> >
> >> It looks like you have two chains of fifths (or fourths). One is a
> > short
> >> chain with RI MERI - TSU MERI - and the unnamed pitch between CHI
and
> >> RE. The rest of the notes are in the other chain. One possibility
would
> >> be to use 25/24 (70.672 cents) for the 75 cent interval, and 3/2 for
> > the
> >> fifths:
> >>
> >> ri = 1/1
> >> RI MERI = 256/225
> >> CHI = 32/27
> >> RE = 4/3
> >> tsu = 3/2
> >> TSU MERI = 128/75
> >> RO = 16/9
> >
> >
> > Hi Herman
> > Like that, would RO and RE sound good together? And RO and CHI
together?
>
> Yes, the interval between RE and RO is 4/3, and the interval between
CHI
> and RO is 3/2. Any two adjacent notes in this chain will sound good
> together: tsu - ri - RE - RO - CHI.
>
> >> The closest scale in the Scala archive is ptolemy_diat4.scl,
which is
> >> described as a "permuted Ptolemy's diatonic" scale.
> >
> >
> >
> > Can you give me any cultural/historical background on the usage of
> > that scale? Sounds interesting.
>
> I'm not familiar with Ptolemy's work in music theory, but probably
> someone else here is.
>
> > The only difference
> >> is that it has 8/7 and 12/7 instead of 256/225 and 128/75. The small
> >> step is only 62.961 cents (28/27) in that version.
> >>
> >> Another possibility if you want something closer to 75 cents for the
> >> small step is to use 25/22 for RI MERI and 75/44 for TSU MERI (the
> > small
> >> step works out to be 72.826 cents).
> >
> >
> > Actually the important steps for me to try to work out are the ones
> > which have been so far using the 12 tone ET notes. The 75c intervals
> > sound fine, and that is close enough. Also it is a bit of a personal
> > taste thing here, different players using different intervals, or even
> > different for different pieces, or simply just how you feel in that
> > moment. But the other intervals, they are just set at 100c out of, I
> > could say ignorance, or, convenience perhaps (use of western electric
> > tuners).
> >
> > I am open to all your suggestions. Also if someone would suggest what
> > it would be in just intonation, I have a feeling that that could be
> > interesting.
> >
> > Also, as you have given your answers in fractions, how may I
> > understand these as cent intervals? For example, interval of "ro" to
> > "tsu", "ro" to "re", "ro" to "chi", "ro" to "ri"?
>
> The fractions are a convention for representing pitches in just
> intonation. One of these pitches is designated as a reference pitch,
> 1/1, and the others are frequency ratios relative to that pitch. Using
> Scala (http://www.xs4all.nl/~huygensf/scala/), I can make a scale with
> these notes, and show the pitch in cents of each note.
>
> 0: 1/1 0.000 unison, perfect prime
> 1: 256/225 223.463 diminished third
> 2: 32/27 294.135 Pythagorean minor third
> 3: 4/3 498.045 perfect fourth
> 4: 3/2 701.955 perfect fifth
> 5: 128/75 925.418 diminished seventh
> 6: 16/9 996.090 Pythagorean minor seventh
> 7: 2/1 1200.000 octave
>
> With another Scala command (SHOW /INTERVAL), I can see the size of each
> of the steps in the scale.
>
> 0: 9/8 203.910 major whole tone
> 1: 256/225 223.463 diminished third
> 2: 25/24 70.672 classic chromatic semitone,
minor
> chroma
> 3: 9/8 203.910 major whole tone
> 4: 9/8 203.910 major whole tone
> 5: 256/225 223.463 diminished third
> 6: 25/24 70.672 classic chromatic semitone,
minor
> chroma
> 7: 9/8 203.910 major whole tone
>
> Or if I substitute 25/22 for 256/225 and 75/44 for 128/75, the
result is
> like this:
>
> 0: 1/1 0.000 unison, perfect prime
> 1: 25/22 221.309 undecimal acute whole tone
> 2: 32/27 294.135 Pythagorean minor third
> 3: 4/3 498.045 perfect fourth
> 4: 3/2 701.955 perfect fifth
> 5: 75/44 923.264
> 6: 16/9 996.090 Pythagorean minor seventh
> 7: 2/1 1200.000 octave
>
> 0: 9/8 203.910 major whole tone
> 1: 25/22 221.309 undecimal acute whole tone
> 2: 704/675 72.826
> 3: 9/8 203.910 major whole tone
> 4: 9/8 203.910 major whole tone
> 5: 25/22 221.309 undecimal acute whole tone
> 6: 704/675 72.826
> 7: 9/8 203.910 major whole tone
>
> Another useful thing about Scala is that if you have a MIDI output
> (which most Windows PC's have in one form or another), you can open
up a
> window with a keyboard-like representation of the scale, click on a key
> like a musical keyboard, and hear the notes in the scale.
>

🔗justinasia <justinasia@yahoo.com>

Hello everyone
I'm sorry, I may have written the scale in the opposite fashion to
your convention. To clarify, I will asign an equivalent western pitch
name to the notes, starting arbitrarily by asigning "D" to "ro":

100c......
x.........C#
100c......
ri........C
100c......
x.........B
125c......
RI MERI...Bb -25c
75c.......
CHI.......A
125c......
x.........Ab -25c
75c.......
RE........G
100c......
x.........F#
100c......
tsu.......F
100c......
x.........E
125c......
TSU MERI..Eb -25c
75c.......
RO........D

So the notes we are using here are:
(C)
Bb -25c
A
G
(F)
Eb -25c
D

To me it seems A is some kind of harmonic of D, so I am expecting
there to be a very obvious "correct" interval between them. Do you
know how many cents that should be? Then D and G seem to have a very
natural relationship, though is this one so straightforward? Is there
a variety of choices for interval for the "correct" relationship
between D and G? (If so, please feel free to elaborate.)

Then, I do not have an idea how to understand F and C, though, I have
a suspicion that the interval of C to D, could be the same as the
interval of G to A. Do you have any feeling to support or counter this
proposition? If it is so, the once we know G and A, we also know F and
C, and therefore the whole scale.

Looking forward to your responses!
Justin

🔗Herman Miller <hmiller@IO.COM>

justinasia wrote:
> Oh dear
> I just realised I may have created unnecessary confusion - in my list
> of notes, the one at the bottom was the bottom pitch. The one at the
> top was the top pitch. From your mail Herman, it appears I could have
> gone counter to convention (wouldn't be the first time!)
> > Does this mess up all the information you just explained to me? Very
> sorry if it does! And, so others are not confused, ought I edit the
> first post? Or hopefully everyone interested will be reading this post
> too?
> > I shall try to post some western note name equivalents in just a minute.
> Justin

I was wondering when you mentioned that the scale is Japanese. It does sound more like a Japanese scale if you invert and transpose it.

0: 1/1 0.000 unison, perfect prime
1: 25/24 70.672 classic chromatic semitone, minor chroma
2: 32/27 294.135 Pythagorean minor third
3: 4/3 498.045 perfect fourth
4: 3/2 701.955 perfect fifth
5: 25/16 772.627 classic augmented fifth
6: 16/9 996.090 Pythagorean minor seventh
7: 2/1 1200.000 octave

Here are the step sizes:

0: 9/8 203.910 major whole tone
1: 25/24 70.672 classic chromatic semitone, minor chroma
2: 256/225 223.463 diminished third
3: 9/8 203.910 major whole tone
4: 9/8 203.910 major whole tone
5: 25/24 70.672 classic chromatic semitone, minor chroma
6: 256/225 223.463 diminished third
7: 9/8 203.910 major whole tone

Here's another possibility, with the size of the fifth set to 705.0 cents; a single chain of fifths includes all the notes in the scale.

0: 1/1 0.000 unison, perfect prime
1: 75.000 cents 75.000
2: 285.000 cents 285.000
3: 495.000 cents 495.000
4: 705.000 cents 705.000
5: 780.000 cents 780.000
6: 990.000 cents 990.000
7: 2/1 1200.000 octave

And the step sizes:

0: 210.000 cents 210.000
1: 75.000 cents 75.000
2: 210.000 cents 210.000
3: 210.000 cents 210.000
4: 210.000 cents 210.000
5: 75.000 cents 75.000
6: 210.000 cents 210.000
7: 210.000 cents 210.000

🔗justinasia <justinasia@yahoo.com>

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> justinasia wrote:
> > Oh dear
> > I just realised I may have created unnecessary confusion - in my list
Hi Herman
Have you inverted it again? You have numbered yours, from 0 to 7,
making 8 notes. What are they in relation to mine? Is your bottom one
my bottom one or my top one? Also, I have 7 notes, not 8 (or also 12,
or 13, or 15, but the basic scale has 7 (5 main and 2 secondary notes).
Perhaps could we call the notes by the western nearest-note names,
like I did in my last post? So we don't get confused by either my
Japanese names or your number names?

Thank you!
Justin

> > of notes, the one at the bottom was the bottom pitch. The one at the
> > top was the top pitch. From your mail Herman, it appears I could have
> > gone counter to convention (wouldn't be the first time!)
> >
> > Does this mess up all the information you just explained to me? Very
> > sorry if it does! And, so others are not confused, ought I edit the
> > first post? Or hopefully everyone interested will be reading this post
> > too?
> >
> > I shall try to post some western note name equivalents in just a
minute.
> > Justin
>
> I was wondering when you mentioned that the scale is Japanese. It does
> sound more like a Japanese scale if you invert and transpose it.
>
> 0: 1/1 0.000 unison, perfect prime
> 1: 25/24 70.672 classic chromatic semitone,
minor
> chroma
> 2: 32/27 294.135 Pythagorean minor third
> 3: 4/3 498.045 perfect fourth
> 4: 3/2 701.955 perfect fifth
> 5: 25/16 772.627 classic augmented fifth
> 6: 16/9 996.090 Pythagorean minor seventh
> 7: 2/1 1200.000 octave
>
> Here are the step sizes:
>
> 0: 9/8 203.910 major whole tone
> 1: 25/24 70.672 classic chromatic semitone,
minor
> chroma
> 2: 256/225 223.463 diminished third
> 3: 9/8 203.910 major whole tone
> 4: 9/8 203.910 major whole tone
> 5: 25/24 70.672 classic chromatic semitone,
minor
> chroma
> 6: 256/225 223.463 diminished third
> 7: 9/8 203.910 major whole tone
>
> Here's another possibility, with the size of the fifth set to 705.0
> cents; a single chain of fifths includes all the notes in the scale.
>
> 0: 1/1 0.000 unison, perfect prime
> 1: 75.000 cents 75.000
> 2: 285.000 cents 285.000
> 3: 495.000 cents 495.000
> 4: 705.000 cents 705.000
> 5: 780.000 cents 780.000
> 6: 990.000 cents 990.000
> 7: 2/1 1200.000 octave
>
> And the step sizes:
>
> 0: 210.000 cents 210.000
> 1: 75.000 cents 75.000
> 2: 210.000 cents 210.000
> 3: 210.000 cents 210.000
> 4: 210.000 cents 210.000
> 5: 75.000 cents 75.000
> 6: 210.000 cents 210.000
> 7: 210.000 cents 210.000
>

🔗banaphshu <kraiggrady@anaphoria.com>

🔗justinasia <justinasia@yahoo.com>

--- In tuning@yahoogroups.com, "banaphshu" <kraiggrady@...> wrote:
>
> hello justin:
> just recently i was looking at a paper showing the actual tuning used
> on the koto by a variety of prominent players which had intervals
> around the 75 cent size. looking at the fluctuation i tended to hear.
> this as possibly being close to a 24/23 which might seem unusual but
> would put the difference tone a "fifth" (plus octaves)below the top
> string.
> >
>

Do you have the other intervals?
It makes sense they would use the 75cent interval. But it is the other
intervals I want to establish. We agree on the 75cent interval. Even
it doesn't need to be so exact. We can hear what it sounds good at.
However, as for the other intervals, since they are not so
outstandingly unique, all the koto players I know simply use electric
tuners to tune their kotos. Doing that long enough, even if you tune
it by ear your ear will be tuned to 12 tone ET, except of course for
our specific 75cent intervals.

However I think there should be a better, more musical way. That's why
I am posting here.

If you do have the intervals those koto players used, and the notes
(except the 75 cent one) are not on 12 tone ET, that would be
interesting, if there is some consistency. Still, I think it must be
quite a simple matter to one who knows about pitch, harmonics, and
what notes sound good together. That's why I'm posting on this list
here. C'mon you guys, don't be shy!

Justin

🔗Charles Lucy <lucy@harmonics.com>

I am attempting to make sense out of Justin's request for a tuning spec. or scale definition, but there seems to have become so much "noise" and esoteric terminology in the dozen or so postings on the subject that the original purpose, values, and intent seem to have become obscured.

I see a list of intervals in cents with "odd" names by them e.g. MERU, WNR's etc.

As the reader follows the sequence of intervals down the page, is this a list of intervals in ascending or descending pitch order?

If Justin really wants to do this the best way, I suggest making a recording of the pitches that he/she wishes to match, and attaching it to a private email or putting it somewhere as a url.

It would then be very easy to hear what he/she is attempting to achieve; either by ear or software analysis e.g. pitchtracking, Spear, or one of the more sophisticated applications which many of us use.

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

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

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 10 Nov 2007, at 12:29, justinasia wrote:

> --- In tuning@yahoogroups.com, "banaphshu" <kraiggrady@...> wrote:
> >
> > hello justin:
> > just recently i was looking at a paper showing the actual tuning > used
> > on the koto by a variety of prominent players which had intervals
> > around the 75 cent size. looking at the fluctuation i tended to > hear.
> > this as possibly being close to a 24/23 which might seem unusual but
> > would put the difference tone a "fifth" (plus octaves)below the top
> > string.
> > >
> >
>
> Do you have the other intervals?
> It makes sense they would use the 75cent interval. But it is the other
> intervals I want to establish. We agree on the 75cent interval. Even
> it doesn't need to be so exact. We can hear what it sounds good at.
> However, as for the other intervals, since they are not so
> outstandingly unique, all the koto players I know simply use electric
> tuners to tune their kotos. Doing that long enough, even if you tune
> it by ear your ear will be tuned to 12 tone ET, except of course for
> our specific 75cent intervals.
>
> However I think there should be a better, more musical way. That's why
> I am posting here.
>
> If you do have the intervals those koto players used, and the notes
> (except the 75 cent one) are not on 12 tone ET, that would be
> interesting, if there is some consistency. Still, I think it must be
> quite a simple matter to one who knows about pitch, harmonics, and
> what notes sound good together. That's why I'm posting on this list
> here. C'mon you guys, don't be shy!
>
> Justin
>
>
>

🔗justinasia <justinasia@yahoo.com>

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> I am attempting to make sense out of Justin's request for a tuning
> spec. or scale definition, but there seems to have become so much
> "noise" and esoteric terminology in the dozen or so postings on the
> subject that the original purpose, values, and intent seem to have
> become obscured.
>
> I see a list of intervals in cents with "odd" names by them e.g.
> MERU, WNR's etc.

Dear Charles
Thank you for your consideration. I am not sure why my culture's names
of "ro" "tsu" "re" should be any more esoteric than your culture's
names "D" "F" "G". Besides, ro tsu re actually describes what I am
refering to, whereas D F G is a clumsy approximation.
Also I wrote it in cent values as I thought that was an appropriate
way to write temperament. If that was wrong, sorry, I'm afraid I don't
know about writing it in fractions, as my tools deal with cents.

Sorry for the confusion of which direction my scale was going as I
didn't know the convention here, and I did already refer to you, in
our private communication, to the mail which totally explains that and
uses your names for the pitches also:
/tuning/topicId_74247.html#74273

>
> As the reader follows the sequence of intervals down the page, is
> this a list of intervals in ascending or descending pitch order?

Please see link above

> If Justin really wants to do this the best way, I suggest making a
> recording of the pitches that he/she wishes to match, and attaching
> it to a private email or putting it somewhere as a url.
>
> It would then be very easy to hear what he/she is attempting to
> achieve; either by ear or software analysis e.g. pitchtracking,
> Spear, or one of the more sophisticated applications which many of us
> use.

If you follow the example given in the link above, and read the text,
I think you will understand. I have all the equipment needed to
measure pitch. That is not necessary. I am actually trying to find out
what better pitches we could be using, as musicians. If it is not
quite clear alreasy, please ask and I shall try to explain everything
in one more concise and easily understandable mail.

Again just I shall mention, it is not the pitch of the "western note
-25cent" notes which I require help with. It is the notes which are
currently at 12toneET values which I need help with. Because I know
12toneET is always out of tune, so surely can never be the correct
choice for our music, and is only being used because it is "close
enough" and people don't even question it, seeing as they don't even
know it is out of tune. It is only the "western note -25" that we can
hear so obviously is out of tune if set to the western value. The
other notes are too subtle for these now western-music-saturated ears,
so that is why I am turning to you guys, experts about pitch, for your
knowledge.

Thank you all very much
Justin

>
>
>
>
> Charles Lucy lucy@...
>
> ----- Promoting global harmony through LucyTuning -----
>
> For information on LucyTuning go to: http://www.lucytune.com
>
> LucyTuned Lullabies (from around the world):
> http://www.lullabies.co.uk
>
> Skype user = lucytune
>
> http://www.myspace.com/lucytuning
>
>
> On 10 Nov 2007, at 12:29, justinasia wrote:
>
> > --- In tuning@yahoogroups.com, "banaphshu" <kraiggrady@> wrote:
> > >
> > > hello justin:
> > > just recently i was looking at a paper showing the actual tuning
> > used
> > > on the koto by a variety of prominent players which had intervals
> > > around the 75 cent size. looking at the fluctuation i tended to
> > hear.
> > > this as possibly being close to a 24/23 which might seem unusual but
> > > would put the difference tone a "fifth" (plus octaves)below the top
> > > string.
> > > >
> > >
> >
> > Do you have the other intervals?
> > It makes sense they would use the 75cent interval. But it is the other
> > intervals I want to establish. We agree on the 75cent interval. Even
> > it doesn't need to be so exact. We can hear what it sounds good at.
> > However, as for the other intervals, since they are not so
> > outstandingly unique, all the koto players I know simply use electric
> > tuners to tune their kotos. Doing that long enough, even if you tune
> > it by ear your ear will be tuned to 12 tone ET, except of course for
> > our specific 75cent intervals.
> >
> > However I think there should be a better, more musical way. That's why
> > I am posting here.
> >
> > If you do have the intervals those koto players used, and the notes
> > (except the 75 cent one) are not on 12 tone ET, that would be
> > interesting, if there is some consistency. Still, I think it must be
> > quite a simple matter to one who knows about pitch, harmonics, and
> > what notes sound good together. That's why I'm posting on this list
> > here. C'mon you guys, don't be shy!
> >
> > Justin
> >
> >
> >
>

🔗Herman Miller <hmiller@IO.COM>

justinasia wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>> justinasia wrote:
>>> Oh dear
>>> I just realised I may have created unnecessary confusion - in my list
> Hi Herman
> Have you inverted it again? You have numbered yours, from 0 to 7,
> making 8 notes. What are they in relation to mine? Is your bottom one
> my bottom one or my top one? Also, I have 7 notes, not 8 (or also 12,
> or 13, or 15, but the basic scale has 7 (5 main and 2 secondary notes).
> Perhaps could we call the notes by the western nearest-note names,
> like I did in my last post? So we don't get confused by either my
> Japanese names or your number names?

If you take RO = D as the first note of the scale, that's the one I've got as 1/1 or 0.000 cents. The other notes of the scale are relative to that pitch. So here are two different options for each pitch:

RO = D
>> 0: 1/1 0.000 unison, perfect prime

TSU MERI = Eb -25c
>> 1: 25/24 70.672 classic chromatic semitone,
>> 1: 75.000 cents 75.000

tsu = F
>> 2: 32/27 294.135 Pythagorean minor third
>> 2: 285.000 cents 285.000

RE = G
>> 3: 4/3 498.045 perfect fourth
>> 3: 495.000 cents 495.000

CHI = A
>> 4: 3/2 701.955 perfect fifth
>> 4: 705.000 cents 705.000

RI MERI = Bb - 25c
>> 5: 25/16 772.627 classic augmented fifth
>> 5: 780.000 cents 780.000

ri = C
>> 6: 16/9 996.090 Pythagorean minor seventh
>> 6: 990.000 cents 990.000

and it's customary in Scala to include the octave above.
RO = D
>> 7: 2/1 1200.000 octave

This is the first scale, the one with the just ratios. Note the lack of beating when two notes are played together, with the exception of the fourth (F : Bb) at 0:25.
http://home.comcast.net/~teamouse/scale1.mp3

This is the alternative scale, with slightly wide fifths of 705.0 cents. This improves the F:Bb interval at the expense of slight beating in the other intervals.
http://home.comcast.net/~teamouse/scale2.mp3

For comparison, this is a scale with a single chain of just (701.955 cent) fifths (note the wider 90.225 cent steps).
http://home.comcast.net/~teamouse/scale3.mp3

🔗Charles Lucy <lucy@harmonics.com>

I believe that I have figured out approximately what you are attempting to create.
In LucyTuning terms the ascending notes are D D# F G A A# C

So that you can check this and compare with what you are hearing I have made an mp3 of these notes and put it at:

http://www.lucytune.com/justin/JustinFlute.mp3

Do you want the values in Hertz, cents or what?

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

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

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 11 Nov 2007, at 00:05, justinasia wrote:

> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > I am attempting to make sense out of Justin's request for a tuning
> > spec. or scale definition, but there seems to have become so much
> > "noise" and esoteric terminology in the dozen or so postings on the
> > subject that the original purpose, values, and intent seem to have
> > become obscured.
> >
> > I see a list of intervals in cents with "odd" names by them e.g.
> > MERU, WNR's etc.
>
> Dear Charles
> Thank you for your consideration. I am not sure why my culture's names
> of "ro" "tsu" "re" should be any more esoteric than your culture's
> names "D" "F" "G". Besides, ro tsu re actually describes what I am
> refering to, whereas D F G is a clumsy approximation.
> Also I wrote it in cent values as I thought that was an appropriate
> way to write temperament. If that was wrong, sorry, I'm afraid I don't
> know about writing it in fractions, as my tools deal with cents.
>
> Sorry for the confusion of which direction my scale was going as I
> didn't know the convention here, and I did already refer to you, in
> our private communication, to the mail which totally explains that and
> uses your names for the pitches also:
> /tuning/topicId_74247.html#74273
>
> >
> > As the reader follows the sequence of intervals down the page, is
> > this a list of intervals in ascending or descending pitch order?
>
> Please see link above
>
> > If Justin really wants to do this the best way, I suggest making a
> > recording of the pitches that he/she wishes to match, and attaching
> > it to a private email or putting it somewhere as a url.
> >
> > It would then be very easy to hear what he/she is attempting to
> > achieve; either by ear or software analysis e.g. pitchtracking,
> > Spear, or one of the more sophisticated applications which many > of us
> > use.
>
> If you follow the example given in the link above, and read the text,
> I think you will understand. I have all the equipment needed to
> measure pitch. That is not necessary. I am actually trying to find out
> what better pitches we could be using, as musicians. If it is not
> quite clear alreasy, please ask and I shall try to explain everything
> in one more concise and easily understandable mail.
>
> Again just I shall mention, it is not the pitch of the "western note
> -25cent" notes which I require help with. It is the notes which are
> currently at 12toneET values which I need help with. Because I know
> 12toneET is always out of tune, so surely can never be the correct
> choice for our music, and is only being used because it is "close
> enough" and people don't even question it, seeing as they don't even
> know it is out of tune. It is only the "western note -25" that we can
> hear so obviously is out of tune if set to the western value. The
> other notes are too subtle for these now western-music-saturated ears,
> so that is why I am turning to you guys, experts about pitch, for your
> knowledge.
>
> Thank you all very much
> Justin
>
> >
> >
> >
> >
> > Charles Lucy lucy@...
> >
> > ----- Promoting global harmony through LucyTuning -----
> >
> > For information on LucyTuning go to: http://www.lucytune.com
> >
> > LucyTuned Lullabies (from around the world):
> > http://www.lullabies.co.uk
> >
> > Skype user = lucytune
> >
> > http://www.myspace.com/lucytuning
> >
> >
> > On 10 Nov 2007, at 12:29, justinasia wrote:
> >
> > > --- In tuning@yahoogroups.com, "banaphshu" <kraiggrady@> wrote:
> > > >
> > > > hello justin:
> > > > just recently i was looking at a paper showing the actual tuning
> > > used
> > > > on the koto by a variety of prominent players which had > intervals
> > > > around the 75 cent size. looking at the fluctuation i tended to
> > > hear.
> > > > this as possibly being close to a 24/23 which might seem > unusual but
> > > > would put the difference tone a "fifth" (plus octaves)below > the top
> > > > string.
> > > > >
> > > >
> > >
> > > Do you have the other intervals?
> > > It makes sense they would use the 75cent interval. But it is > the other
> > > intervals I want to establish. We agree on the 75cent interval. > Even
> > > it doesn't need to be so exact. We can hear what it sounds good > at.
> > > However, as for the other intervals, since they are not so
> > > outstandingly unique, all the koto players I know simply use > electric
> > > tuners to tune their kotos. Doing that long enough, even if you > tune
> > > it by ear your ear will be tuned to 12 tone ET, except of > course for
> > > our specific 75cent intervals.
> > >
> > > However I think there should be a better, more musical way. > That's why
> > > I am posting here.
> > >
> > > If you do have the intervals those koto players used, and the > notes
> > > (except the 75 cent one) are not on 12 tone ET, that would be
> > > interesting, if there is some consistency. Still, I think it > must be
> > > quite a simple matter to one who knows about pitch, harmonics, and
> > > what notes sound good together. That's why I'm posting on this > list
> > > here. C'mon you guys, don't be shy!
> > >
> > > Justin
> > >
> > >
> > >
> >
>
>
>

🔗Graham Breed <gbreed@gmail.com>

🔗justinasia <justinasia@yahoo.com>

Dear Herman
Thank you very much!
The perfoct fourth and fifth sound, well, perfect - just what I was
looking for! (Full of puns all unintended).

As for the "classic chromatic semitone" (occurs twice), could you tell
me a little more about that? (Imagine I have a good brain, play music,
and have no schooling). For example, it is a note which occurs as an
harmonic within the natural sound of any of the other notes of the
scale? (I mean, if there seems a good reason to think this should be
the natural value of this note, I will back it. Otherwise perhaps
there is no particular reason to favour it over 75 cents? I mean, if
it is not a harmonic choice or something).

Then the Pythagorean minor third and seventh - are they the only
choices you see viable here? Are they contained in the harmonic makeup
of any of the other notes in the scale? Is there any specific reason
why to choose them? If there are other choices which also have some
viability, what would they be? (somehow sounds to me less
straightforward than those "perfect" ones, is it?)

If I may I'd love to follow this up with more details about the other
3 sets (do we call them transpositions?) a little later.

Thank you very much
Justin

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> justinasia wrote:
> > --- In tuning@yahoogroups.com, Herman Miller <hmiller@> wrote:
> >> justinasia wrote:
> >>> Oh dear
> >>> I just realised I may have created unnecessary confusion - in my
list
> > Hi Herman
> > Have you inverted it again? You have numbered yours, from 0 to 7,
> > making 8 notes. What are they in relation to mine? Is your bottom one
> > my bottom one or my top one? Also, I have 7 notes, not 8 (or also 12,
> > or 13, or 15, but the basic scale has 7 (5 main and 2 secondary
notes).
> > Perhaps could we call the notes by the western nearest-note names,
> > like I did in my last post? So we don't get confused by either my
> > Japanese names or your number names?
>
> If you take RO = D as the first note of the scale, that's the one I've
> got as 1/1 or 0.000 cents. The other notes of the scale are relative to
> that pitch. So here are two different options for each pitch:
>
> RO = D
> >> 0: 1/1 0.000 unison, perfect prime
>
> TSU MERI = Eb -25c
> >> 1: 25/24 70.672 classic chromatic semitone,
> >> 1: 75.000 cents 75.000
>
> tsu = F
> >> 2: 32/27 294.135 Pythagorean minor third
> >> 2: 285.000 cents 285.000
>
> RE = G
> >> 3: 4/3 498.045 perfect fourth
> >> 3: 495.000 cents 495.000
>
> CHI = A
> >> 4: 3/2 701.955 perfect fifth
> >> 4: 705.000 cents 705.000
>
> RI MERI = Bb - 25c
> >> 5: 25/16 772.627 classic augmented fifth
> >> 5: 780.000 cents 780.000
>
> ri = C
> >> 6: 16/9 996.090 Pythagorean minor seventh
> >> 6: 990.000 cents 990.000
>
> and it's customary in Scala to include the octave above.
> RO = D
> >> 7: 2/1 1200.000 octave
>
> This is the first scale, the one with the just ratios. Note the lack of
> beating when two notes are played together, with the exception of the
> fourth (F : Bb) at 0:25.
> http://home.comcast.net/~teamouse/scale1.mp3
>
> This is the alternative scale, with slightly wide fifths of 705.0
cents.
> This improves the F:Bb interval at the expense of slight beating in the
> other intervals.
> http://home.comcast.net/~teamouse/scale2.mp3
>
> For comparison, this is a scale with a single chain of just (701.955
> cent) fifths (note the wider 90.225 cent steps).
> http://home.comcast.net/~teamouse/scale3.mp3
>

🔗Charles Lucy <lucy@harmonics.com>

Here are the cent values from A = 0 (in LucyTuning = 440 Hz - Octave ratio = 2.0 = 1200 cents).

D 504.5

D# 573.0

F 818.0

G 1009.0

A 0.0

A# 68.5

C 313.5

Using these values will enable you to play your instruments "in tune" with all other LucyTuned instruments

For your reference information
Here are the cent values calculated from D = 0

D 0.0

D# 68.5

F 313.5

G 504.5

A 695.5

A# 764.0

C 1009.0

As a matter of interest, the scalecoding for this collection of seven notes (assuming Tonic is D) is:

F-C-G-D-A-x-x-x-x-x-D#-A#

11/678910/4

You can find more examples of scalecoding in this folder:

http://www.lucytune.com/scales/

I shall soon be adding a further 200 scales to give a total of approx. 650 unique scales.

This is the first time that I have come across this scale.

(The F-C-G-D-A group of notes will sound comparatively consonant when played together)

or the A# and D# will sound consonant, although if you use either D# or A# with the others the sound will be much more dissonant.

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

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

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 11 Nov 2007, at 12:18, justinasia wrote:

> Hi Charles
> In cents please. Thank you very much!
> Justin
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > I believe that I have figured out approximately what you are
> > attempting to create.
> > In LucyTuning terms the ascending notes are D D# F G A A# C
> >
> > So that you can check this and compare with what you are hearing I
> > have made an mp3 of these notes and put it at:
> >
> > http://www.lucytune.com/justin/JustinFlute.mp3
> >
> >
> > Do you want the values in Hertz, cents or what?
> >
> >
> >
>
>
>

🔗justinasia <justinasia@yahoo.com>

Hi Charles
Thank you for that.
You may have read Herman's suggestions. His first suggestion includes
G and A being respectively the perfect fourth and fifth. Can you tell
me why you think it is better that they are your suggested values,
instead of the perfect fourth and fifth? So far Herman's suggestion of
the perfect fourth and fifth sounds extremely logical, and natural. I
am happy to hear why you think these other pitches you suggest would
be more musical.

Thank you again
Justin

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Here are the cent values from A = 0 (in LucyTuning = 440 Hz - Octave
> ratio = 2.0 = 1200 cents).
>
> D 504.5
>
> D# 573.0
>
> F 818.0
>
> G 1009.0
>
> A 0.0
>
> A# 68.5
>
> C 313.5
>
> Using these values will enable you to play your instruments "in tune"
> with all other LucyTuned instruments
>
> For your reference information
> Here are the cent values calculated from D = 0
>
> D 0.0
>
> D# 68.5
>
> F 313.5
>
> G 504.5
>
> A 695.5
>
> A# 764.0
>
> C 1009.0
>
>
> As a matter of interest, the scalecoding for this collection of seven
> notes (assuming Tonic is D) is:
>
>
> F-C-G-D-A-x-x-x-x-x-D#-A#
>
> 11/678910/4
>
> You can find more examples of scalecoding in this folder:
>
> http://www.lucytune.com/scales/
>
>
> I shall soon be adding a further 200 scales to give a total of
> approx. 650 unique scales.
>
> This is the first time that I have come across this scale.
>
> (The F-C-G-D-A group of notes will sound comparatively consonant when
> played together)
>
> or the A# and D# will sound consonant, although if you use either D#
> or A# with the others the sound will be much more dissonant.
>
>
> Charles Lucy lucy@...
>
> ----- Promoting global harmony through LucyTuning -----
>
> For information on LucyTuning go to: http://www.lucytune.com
>
> LucyTuned Lullabies (from around the world):
> http://www.lullabies.co.uk
>
> Skype user = lucytune
>
> http://www.myspace.com/lucytuning
>
>
> On 11 Nov 2007, at 12:18, justinasia wrote:
>
> > Hi Charles
> > In cents please. Thank you very much!
> > Justin
> >
> > --- In tuning@yahoogroups.com, Charles Lucy <lucy@> wrote:
> > >
> > > I believe that I have figured out approximately what you are
> > > attempting to create.
> > > In LucyTuning terms the ascending notes are D D# F G A A# C
> > >
> > > So that you can check this and compare with what you are hearing I
> > > have made an mp3 of these notes and put it at:
> > >
> > > http://www.lucytune.com/justin/JustinFlute.mp3
> > >
> > >
> > > Do you want the values in Hertz, cents or what?
> > >
> > >
> > >
> >
> >
> >
>

🔗Charles Lucy <lucy@harmonics.com>

Using perfect fourths and fifths are what you would want to do if you are aiming for zero beating, as is intended by users of integer frequency ratios as in Just Intonation.

If you choose this type of tuning, you will have intervals of inconsistent sizes, and "problems" with transposition and modulation.

The shortcomings of JI are well documented elsewhere, so I won't labour the point again.

My thinking on this is still controversial, for I maintain that musical "harmonics" should beat.

(It may take a few generations until a "critical mass" understand and appreciate this concept.)

Musicians are generally very conservative in their musical "thinking", for they often have years of study invested in a particular system.

e.g. Just Intonation, 12edo, meantone, or even LucyTuning;-)

Many 20th century trained musicians still find any type of microtuning threatening.

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

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

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 11 Nov 2007, at 13:12, justinasia wrote:

> Hi Charles
> Thank you for that.
> You may have read Herman's suggestions. His first suggestion includes
> G and A being respectively the perfect fourth and fifth. Can you tell
> me why you think it is better that they are your suggested values,
> instead of the perfect fourth and fifth? So far Herman's suggestion of
> the perfect fourth and fifth sounds extremely logical, and natural. I
> am happy to hear why you think these other pitches you suggest would
> be more musical.
>
> Thank you again
> Justin
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > Here are the cent values from A = 0 (in LucyTuning = 440 Hz - Octave
> > ratio = 2.0 = 1200 cents).
> >
> > D 504.5
> >
> > D# 573.0
> >
> > F 818.0
> >
> > G 1009.0
> >
> > A 0.0
> >
> > A# 68.5
> >
> > C 313.5
> >
> > Using these values will enable you to play your instruments "in > tune"
> > with all other LucyTuned instruments
> >
> > For your reference information
> > Here are the cent values calculated from D = 0
> >
> > D 0.0
> >
> > D# 68.5
> >
> > F 313.5
> >
> > G 504.5
> >
> > A 695.5
> >
> > A# 764.0
> >
> > C 1009.0
> >
> >
> > As a matter of interest, the scalecoding for this collection of > seven
> > notes (assuming Tonic is D) is:
> >
> >
> > F-C-G-D-A-x-x-x-x-x-D#-A#
> >
> > 11/678910/4
> >
> > You can find more examples of scalecoding in this folder:
> >
> > http://www.lucytune.com/scales/
> >
> >
> > I shall soon be adding a further 200 scales to give a total of
> > approx. 650 unique scales.
> >
> > This is the first time that I have come across this scale.
> >
> > (The F-C-G-D-A group of notes will sound comparatively consonant > when
> > played together)
> >
> > or the A# and D# will sound consonant, although if you use either D#
> > or A# with the others the sound will be much more dissonant.
> >
> >
> > Charles Lucy lucy@...
> >
> > ----- Promoting global harmony through LucyTuning -----
> >
> > For information on LucyTuning go to: http://www.lucytune.com
> >
> > LucyTuned Lullabies (from around the world):
> > http://www.lullabies.co.uk
> >
> > Skype user = lucytune
> >
> > http://www.myspace.com/lucytuning
> >
> >
> > On 11 Nov 2007, at 12:18, justinasia wrote:
> >
> > > Hi Charles
> > > In cents please. Thank you very much!
> > > Justin
> > >
> > > --- In tuning@yahoogroups.com, Charles Lucy <lucy@> wrote:
> > > >
> > > > I believe that I have figured out approximately what you are
> > > > attempting to create.
> > > > In LucyTuning terms the ascending notes are D D# F G A A# C
> > > >
> > > > So that you can check this and compare with what you are > hearing I
> > > > have made an mp3 of these notes and put it at:
> > > >
> > > > http://www.lucytune.com/justin/JustinFlute.mp3
> > > >
> > > >
> > > > Do you want the values in Hertz, cents or what?
> > > >
> > > >
> > > >
> > >
> > >
> > >
> >
>
>
>

🔗justinasia <justinasia@yahoo.com>

Hi Charles

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Using perfect fourths and fifths are what you would want to do if you
> are aiming for zero beating, as is intended by users of integer
> frequency ratios as in Just Intonation.
>
> If you choose this type of tuning, you will have intervals of
> inconsistent sizes, and "problems" with transposition and modulation.

So just for the scale I mentioned, there are no problems. A little
later (when I have time, soon I hope) I will write exactly the
transpositions we use and we I hope can look at this point more
specifically. First I was trying to get the ideal without any
transpositioning.

>
> The shortcomings of JI are well documented elsewhere, so I won't
> labour the point again.

Presumably there are no problems if you just play in that one scale -
presumably then JI would be the best?

>
> My thinking on this is still controversial, for I maintain that
> musical "harmonics" should beat.

Can you explain why?
For example, do the natural harmonics produced by the natural strings,
air etc, beat? Are your pitches taken from nature? More so than JI?

> (It may take a few generations until a "critical mass" understand and
> appreciate this concept.)

If you can explain briefly, I have time and interest to listen.

> Many 20th century trained musicians still find any type of
> microtuning threatening.

I guess that means anything other than 12toneET right? Don't worry, I
don't feel threatened. I'm just interested in music.

Thanks
Justin

🔗Charles Lucy <lucy@harmonics.com>

Hi Justin;

It should work fine using the LucyTuned values, and be already set up to modulate or transpose easily with consistent intervals sizes, and match other instruments.

If you tune it to JI intervals, you are locking yourself into a "box" with that instrument, hence I would recommend that you avoid JI and integer frequency ratios.

If you tune it to the Just Intonation or whole number ratios, you will find that it will "work" as a single isolated piece in only one or two keys, yet you will have future problems if you should wish

to use it with other instruments, transpose, or modulate, at a later time, for the reasons that I stated earlier.

Taken from nature? That depends what you mean by nature. If you consider that pi exists in nature; then yes, I suppose you could say that.

In the natural world (e.g. bird song) you will find that the intervals are not consistent as you might get with a signal generator for the voices change pitch from vibrato.

So using pi could give you a "central pitch" about which that vibrato moves.

Why not try making and tuning two instruments using both ways and experiment for yourself to find what works for you?

I will attempt to answer your other questions in a simple form:

The traditional model of musical "harmonics" was that the harmonics occurred only and always at intervals whose frequencies were at whole number frequency ratios e.g. if A=440 Hz; E = 440 *(3/2) = 660 Hz.

You could set up these frequencies 440 & 660 with a signal generator, computer, or musical instrument (approximately only as physical musical instruments are effected by many factors, temperature changes, pressure etc.)

In the (perfect world) situation when tuned exactly you would hear no beating. This may be what you want. (Yet it sounds very "bland" to my ear).

You could show on an oscilloscope how the peaks of the waveforms coincide.

I suspect that this is a fairly naive two-dimensional, static view of what I believe is a much more complex underlying pattern, which I can only describe by analogy.

If you search on my name and the word "cave" in the tuning list archives you should find various ideas that I have written about on this subject in the past.

I am suggesting that the "traditional model" of a sine wave is only the cross-section of a cylindrical or other multidimensional geometric pattern.

Imagine a coiled spring, or use the coiled cable that you sometimes find on an old phone between the handset and the phone.

If you position that cable between a light source and a wall you will find that it casts a shadow.

There is a particular position at which you can hold the cable so that it makes a shadow that looks like a sinewave.

I suggest that this pattern on the wall is similar to what is seen on an oscilloscope as a sine wave, and only one view of what is actually happening.

You know that the phone cable is three dimensional, yet the static image on the wall could make you believe that the pattern is only in two dimensions.

Using pi enables the mapping of the positions on the cable and their relationships to be "mapped" as a spiral spring.

Take a look at this page, and you may appreciate the way that I am experiencing this and thinking.

There is a Mac animation application on the page if you can run it.

http://www.lucytune.com/new_to_lt/recipe.html

Your questions open a whole truckload of tuning worms; which I have attempted to tame with various postings on the subject over the years, so instead of repeating myself,

I'll leave it at that for now, and get some sleep;-)

Ultimately it is all about perception, and also about your own musical tastes.

(Some people even prefer no beating).

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

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

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 11 Nov 2007, at 16:00, justinasia wrote:

> Hi Charles
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > Using perfect fourths and fifths are what you would want to do if > you
> > are aiming for zero beating, as is intended by users of integer
> > frequency ratios as in Just Intonation.
> >
> > If you choose this type of tuning, you will have intervals of
> > inconsistent sizes, and "problems" with transposition and > modulation.
>
> So just for the scale I mentioned, there are no problems. A little
> later (when I have time, soon I hope) I will write exactly the
> transpositions we use and we I hope can look at this point more
> specifically. First I was trying to get the ideal without any
> transpositioning.
>
> >
> > The shortcomings of JI are well documented elsewhere, so I won't
> > labour the point again.
>
> Presumably there are no problems if you just play in that one scale -
> presumably then JI would be the best?
>

>
>
> >
> > My thinking on this is still controversial, for I maintain that
> > musical "harmonics" should beat.
>
> Can you explain why?
> For example, do the natural harmonics produced by the natural strings,
> air etc, beat? Are your pitches taken from nature? More so than JI?
>
> > (It may take a few generations until a "critical mass" understand > and
> > appreciate this concept.)
>
> If you can explain briefly, I have time and interest to listen.
>
> > Many 20th century trained musicians still find any type of
> > microtuning threatening.
>
> I guess that means anything other than 12toneET right? Don't worry, I
> don't feel threatened. I'm just interested in music.
>
> Thanks
> Justin
>
>
>

🔗justinasia <justinasia@yahoo.com>

Hi Charles

> You could show on an oscilloscope how the peaks of the waveforms
> coincide.
>
> I suspect that this is a fairly naive two-dimensional, static view of
> what I believe is a much more complex underlying pattern, which I can
> only describe by analogy.

Well, surely no-one ever thought that the reality was 2 dimensional!
Since our machines have 2 dimensional displays, we create symbolic
ways to display information in 2 dimensions, for displays, and for
putting on paper, right? I thought everyone knew that what is
represented is actually a 4 dimensional reality, vibrations of air in
the 3 dimensions of space and one of time. No?

> Your questions open a whole truckload of tuning worms; which I have
> attempted to tame with various postings on the subject over the
> years, so instead of repeating myself,

It's a pity you don't want to answer them. Sorry like I mentioned I
don't have time to trawl through tons of words on the internet. Also,
I wasn't talking about sine waves and abstractions, but the natural
harmonics to be experiences in columns of air, and strings. If you
notes are not coming from them, whereas Herman's "perfect fourths and
fifths" seem to be, then it seems as if, at least in a single scale,
they should be more musical. Since you have offered no reason to the
contrary, I'll have to go with Herman's idea.

Still I have to mention about the other 3 sets, so we can see then
which compromise might be best suited. Just I didn't want to start out
with a compromise for just a single scale (which it seems your Lucy
tuning is). I wanted to see what the best would be for just a single
scale. So then when creating a compromise if necessary, for all 4 sets
together, we can see how much it deviates from the ideal.

I'll try to get it soon.
Thank you
Justin

🔗justinasia <justinasia@yahoo.com>

🔗Charles Lucy <lucy@harmonics.com>

I am continuing with my analysis of all possible unique scales, so for those who are following the saga:

I have found 480 unique scales of two or more notes which can be constructed from meantone chains of up to 7 steps,

of these 480, 35 will sound identical to another scale when played in 12 edo.

BTW the scale which Justin is considering if played in 12 edo (starting from C) would be:

C C# Eb F G G# Bb

which would sound identical to

C Db Eb F G Ab Bb

which is the same as all white notes ascending from E to D and known as

Phrygian, or Bhairavi

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

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

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

>
>
>

🔗justinasia <justinasia@yahoo.com>

🔗Herman Miller <hmiller@IO.COM>

justinasia wrote:

> As for the "classic chromatic semitone" (occurs twice), could you tell
> me a little more about that? (Imagine I have a good brain, play music,
> and have no schooling). For example, it is a note which occurs as an
> harmonic within the natural sound of any of the other notes of the
> scale? (I mean, if there seems a good reason to think this should be
> the natural value of this note, I will back it. Otherwise perhaps
> there is no particular reason to favour it over 75 cents? I mean, if
> it is not a harmonic choice or something).

It depends if just major thirds (5:4) are a desired feature -- which in this case it looks like they're not. If you start with the note D and go down a fifth to G, then up two major thirds to B and D#, then the D# will be a ratio of 25/24 above the D. But since the basic scale in this case doesn't have a B, there wouldn't be a particular advantage for 25/24 over anything else in that general size range. It's also a kind of interval that's called "superparticular" -- which just means the numerator of the ratio is one more than the denominator. There are some reasons for preferring superparticular ratios, but Kraig Grady's suggestion of 24/23 is also superparticular, and it's closer to 75 cents (it's 73.681 cents), so that might be a better option for that pitch. In that case, RI MERI could be tuned as 36/23, or 775.636 cents.

> Then the Pythagorean minor third and seventh - are they the only
> choices you see viable here? Are they contained in the harmonic makeup
> of any of the other notes in the scale? Is there any specific reason
> why to choose them? If there are other choices which also have some
> viability, what would they be? (somehow sounds to me less
> straightforward than those "perfect" ones, is it?)

If "RE" (G) and "ri" (C) are played together, the result will be best if "ri" is tuned to a perfect fourth above "RE". But if you play "CHI" (A) and "ri" (C) together, there are other possibilities for the tuning of "ri" (e.g., 9/5). Or you could tune it to something that sounds good with "TSU MERI" (Eb). Similarly, the best tuning of "tsu" (F) depends on which other notes it is used in combination with.

🔗justinasia <justinasia@yahoo.com>

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> down a fifth to G, then up two major thirds to B and D#, then the D#
> will be a ratio of 25/24 above the D. But since the basic scale in this
> case doesn't have a B, there wouldn't be a particular advantage for
> 25/24 over anything else in that general size range.

Hi Herman
Yes, if you see the "4 sets" table I just posted, we don't use B at
all. Sounds that 25/24, or 24/23, would be best then.

It's also a kind of
> interval that's called "superparticular" -- which just means the
> numerator of the ratio is one more than the denominator. There are some
> reasons for preferring superparticular ratios,

What reasons?

but Kraig Grady's
> suggestion of 24/23 is also superparticular, and it's closer to 75
cents
> (it's 73.681 cents), so that might be a better option for that
pitch. In
> that case, RI MERI could be tuned as 36/23, or 775.636 cents.
>
> > Then the Pythagorean minor third and seventh - are they the only
> > choices you see viable here? Are they contained in the harmonic makeup
> > of any of the other notes in the scale? Is there any specific reason
> > why to choose them? If there are other choices which also have some
> > viability, what would they be? (somehow sounds to me less
> > straightforward than those "perfect" ones, is it?)
>
> If "RE" (G) and "ri" (C) are played together, the result will be
best if
> "ri" is tuned to a perfect fourth above "RE". But if you play "CHI" (A)
> and "ri" (C) together, there are other possibilities for the tuning of
> "ri" (e.g., 9/5).

ri (C) together with re (G) are probably more important that chi(A)
with ri (C).

Or you could tune it to something that sounds good
> with "TSU MERI" (Eb).

Such as? Sounds interesting. ri (C) with tsu meri (Eb-25) are more
likely to occur near each other, I think, than ri(C) and chi(A).

Similarly, the best tuning of "tsu" (F) depends on
> which other notes it is used in combination with.
>

Is is possible/permissible to post an mp3 here? To give you an idea
what music this actually is? My don't use "harmony", but we do
sometimes play different notes together (in another post I was trying
to figure out whether this is what is referred to as "polyphony")
Thanks!
Justin

🔗Graham Breed <gbreed@gmail.com>

🔗justinasia <justinasia@yahoo.com>

🔗banaphshu <kraiggrady@anaphoria.com>

🔗justinasia <justinasia@yahoo.com>

🔗Klaus Schmirler <KSchmir@online.de>

justinasia schrieb:

> Is is possible/permissible to post an mp3 here? To give you an idea
> what music this actually is? My don't use "harmony", but we do
> sometimes play different notes together (in another post I was trying
> to figure out whether this is what is referred to as "polyphony")
> Thanks!
> Justin

I wasn't going to guess anything before learning more about the music. Seeing that I can't even find the little written information I must have, I can no more than give you a couple of vague pointers:

I've heard about monks' chants that the music moves inside a fixed fourth; that's 4/3, or 498 cents. But the tone (and here it fails me; maybe they use two tones within the frame interval) are any thing but stable or difficult to define, since it's mostly glides.

If you can find a shō builder and ask how they tune their reeds and pipes, you'll get a definition of the fixed intervals in use in authentic Japanese terms. I, and probably others, would be very interested to learn about this, and a conversion to cents won't be a problem if the explanation is technical enough (hopefully).

If you play the koto, it is probably save to say (without any actual knowledge of the instrument) that the tuning proceeds by just fifths and fourths, because these intervals can be derived from the harmonics of the strings - except for the meri pitches. "Pythagorean" in Herman's posts simply means that these thirds and sevenths result from a chain of just fifths; Pythagoras is identified with restricting tuning mathematics to the numbers 2 and 3. The meri pitches may be derived by tempering the fifth (Herman's 705 cent; the problem is that the harmonic fifths can't be used for tuning), by extending the chain of fifths until you reach an approximation of the meri intervals that satisfies you, or by combining the two (a chain of 14 fifths gives you all the 15 notes you need for transpositions; its size is 696.4286 cents to hit the 75 cent meri interval. Since Herman's 705 cent solution is closer to the acoustic fifth, I'd prefer it).

If you play the shakuhachi (which is really what I think you do), bear in mind that the sound of the note is also important. However you define the ideal sound of a meri note, the amount of bending you need probably depends on the instrument, weather, mood, whatever. Be flexible, and damn those pretuned strings and pipes :O).

As for "polyphony", no. The Japanese music I know (i.e., popular traditional) is heterophonic, each instrument adding a little from its own resources, but all sticking to the same melody. In polyphony, they would purposefully keep out of each other's way.

Klaus

🔗Paul Poletti <paul@polettipiano.com>

🔗Herman Miller <hmiller@IO.COM>

justinasia wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> It's also a kind of >> interval that's called "superparticular" -- which just means the >> numerator of the ratio is one more than the denominator. There are some >> reasons for preferring superparticular ratios,
> > > What reasons?

For one thing, the difference tones will be multiples of the same low-pitched frequency. Take A = 440 Hz for example, and a second pitch at 459.13 Hz (a ratio of 24/23 above 440 Hz). All the difference tones are integer multiples of 19.13 Hz. On the other hand, if the second pitch is 459.48 Hz, you get difference tones that don't have any relation to each other. There may be other reasons, but that's the main one that comes to mind.

> Or you could tune it to something that sounds good >> with "TSU MERI" (Eb).
> > > Such as? Sounds interesting. ri (C) with tsu meri (Eb-25) are more
> likely to occur near each other, I think, than ri(C) and chi(A).

An interval of 12/7 above tsu meri is one possibility; if you pick 24/23 (73.681 cents) for tsu meri, then 12/7 above that is 288/161 (1006.810 cents).

> Similarly, the best tuning of "tsu" (F) depends on >> which other notes it is used in combination with.
>>
> > Is is possible/permissible to post an mp3 here? To give you an idea
> what music this actually is? My don't use "harmony", but we do
> sometimes play different notes together (in another post I was trying
> to figure out whether this is what is referred to as "polyphony")
> Thanks!
> Justin

Yahoo has space for files on the web site. At one time the space for this group was full, but it looks like there's room for more files now.

/tuning/files/

🔗Herman Miller <hmiller@IO.COM>

justinasia wrote:
> Hi everyone
> Okay, I will try to find a way to illustrate the 4 sets of the scale
> now (the transpositions):
> > > I am going to use numbers now to identify the notes in the scale, as
> Herman did. Also I will write the western name for the notes we (until
> now) have been using 12toneET for, and write "-25c" for those which we
> play 25 cents lower.
> > D ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 1 ï¿½ 5 ï¿½ 4 ï¿½ï¿½ï¿½
> D#-25 ï¿½ï¿½ï¿½ 2 ï¿½ 6 ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½
> D# ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 3
> E ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 5 ï¿½ï¿½ï¿½
> F-25 ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 6 ï¿½ï¿½ï¿½
> F ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 3 ï¿½ 7 ï¿½ï¿½ï¿½ï¿½ï¿½ 4
> F# ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½
> G ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 4 ï¿½ 1 ï¿½ 7 ï¿½ 5
> Ab-25 ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ 2 ï¿½ï¿½ï¿½ï¿½ï¿½ 6
> A ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 5 ï¿½ï¿½ï¿½ï¿½ï¿½ 1 ï¿½ï¿½ï¿½
> Bb-25 ï¿½ï¿½ï¿½ 6 ï¿½ï¿½ï¿½ï¿½ï¿½ 2 ï¿½ï¿½ï¿½
> Bb ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ 3 ï¿½ï¿½ï¿½ï¿½ï¿½ 7
> B ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½
> C ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 7 ï¿½ 4 ï¿½ 3 ï¿½ 1
> C#-25 ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 2

If in each case you want the pairs 1-4 and 1-5 to be consonant intervals, then you have a chain of E-A-D-G-C-F. Then if you want all the transpositions to sound the same, you can continue the chain with Bb and Eb.

D ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 1 ï¿½ 5 ï¿½ 4 ï¿½ï¿½ï¿½
0: 1/1 0.000 unison, perfect prime

D#-25 ï¿½ï¿½ï¿½ 2 ï¿½ 6 ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½
1: 24/23 73.681

D# ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 3
2: 256/243 90.225 limma, Pythagorean minor second

E ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 5 ï¿½ï¿½ï¿½
3: 9/8 203.910 major whole tone

F-25 ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 6 ï¿½ï¿½ï¿½
4: 27/23 277.591 vicesimotertial minor third

F ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 3 ï¿½ 7 ï¿½ï¿½ï¿½ï¿½ï¿½ 4
5: 32/27 294.135 Pythagorean minor third

G ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 4 ï¿½ 1 ï¿½ 7 ï¿½ 5
6: 4/3 498.045 perfect fourth

Ab-25 ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ 2 ï¿½ï¿½ï¿½ï¿½ï¿½ 6
7: 32/23 571.726 23rd subharmonic

A ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 5 ï¿½ï¿½ï¿½ï¿½ï¿½ 1 ï¿½ï¿½ï¿½
8: 3/2 701.955 perfect fifth

Bb-25 ï¿½ï¿½ï¿½ 6 ï¿½ï¿½ï¿½ï¿½ï¿½ 2 ï¿½ï¿½ï¿½
9: 36/23 775.636

Bb ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ 3 ï¿½ï¿½ï¿½ï¿½ï¿½ 7
10: 128/81 792.180 Pythagorean minor sixth

C ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 7 ï¿½ 4 ï¿½ 3 ï¿½ 1
11: 16/9 996.090 Pythagorean minor seventh

C#-25 ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 2
12: 128/69 1069.771

🔗justinasia <justinasia@yahoo.com>

Hi Herman
My comments below:

> justinasia wrote:
> > --- In tuning@yahoogroups.com, Herman Miller <hmiller@> wrote:
> > It's also a kind of
> >> interval that's called "superparticular" -- which just means the
> >> numerator of the ratio is one more than the denominator. There
are some
> >> reasons for preferring superparticular ratios,
> >
> >
> > What reasons?
>
> For one thing, the difference tones will be multiples of the same
> low-pitched frequency. Take A = 440 Hz for example, and a second pitch
> at 459.13 Hz (a ratio of 24/23 above 440 Hz). All the difference tones
> are integer multiples of 19.13 Hz. On the other hand, if the second
> pitch is 459.48 Hz, you get difference tones that don't have any
> relation to each other. There may be other reasons, but that's the main
> one that comes to mind.

Sorry for my lack of education - it sounds quite abstract to me just
now. Could you suggest what this means in terms of how it sounds?

> > Is is possible/permissible to post an mp3 here? To give you an idea
> > what music this actually is? My don't use "harmony", but we do
> > sometimes play different notes together (in another post I was trying
> > to figure out whether this is what is referred to as "polyphony")
> > Thanks!
> > Justin
>
> Yahoo has space for files on the web site. At one time the space for
> this group was full, but it looks like there's room for more files now.

I posted it now. Just a little excerpt of me and another playing "Haru
no Kyoku". Sorry for the mistakes. I wasn't well practiced when I
played it, but hopefully it gives you an idea of the music at least.

Justin

🔗justinasia <justinasia@yahoo.com>

Here are the 4 sets (transpositions of the scale), layed out
differently, in case my chart was confusing people! (Margo I hope you
can read it better now).

1st set
D, D#-25, F, G, A, Bb-25, C

2nd set
G, Ab-25, Bb, C, D, D#-25, F

3rd set
A, Bb-25, C, D, E, F-25, G

4th set
C, C#-25, D#, F, G, Ab-25, Bb

Herman, in your mail included below, had you understood my chart
right, as above? (Sorry if I had confused you). If you had, I'm glad
it seems the solution has turned out so simple! But before I get
excited, I'll wait to hear if you had understood the chart right.
Also when you say "If in each case you want the pairs 1-4 and 1-5 to
be consonant intervals", do you mean, whether they should be the same
interval in each of the 4 sets? Yes, I am hoping to get all 4 sets
playing equally. I'm sorry I don't understand about the "chain". But
are you saying we can keep D, F, C, A and G the same as your original
idea (first option in this post:
/tuning/topicId_74247.html#74284 ) even for
all 4 sets? That sounds so good!

Thank you
Justin

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> If in each case you want the pairs 1-4 and 1-5 to be consonant
> intervals, then you have a chain of E-A-D-G-C-F. Then if you want all
> the transpositions to sound the same, you can continue the chain
with Bb
> and Eb.
>
> D 1 5 4
> 0: 1/1 0.000 unison, perfect prime
>
> D#-25 2 6
> 1: 24/23 73.681
>
> D# 3
> 2: 256/243 90.225 limma, Pythagorean minor second
>
> E 5
> 3: 9/8 203.910 major whole tone
>
> F-25 6
> 4: 27/23 277.591 vicesimotertial minor third
>
> F 3 7 4
> 5: 32/27 294.135 Pythagorean minor third
>
> G 4 1 7 5
> 6: 4/3 498.045 perfect fourth
>
> Ab-25 2 6
> 7: 32/23 571.726 23rd subharmonic
>
> A 5 1
> 8: 3/2 701.955 perfect fifth
>
> Bb-25 6 2
> 9: 36/23 775.636
>
> Bb 3 7
> 10: 128/81 792.180 Pythagorean minor sixth
>
> C 7 4 3 1
> 11: 16/9 996.090 Pythagorean minor seventh
>
> C#-25 2
> 12: 128/69 1069.771
>

🔗Herman Miller <hmiller@IO.COM>

justinasia wrote:
> Herman, in your mail included below, had you understood my chart
> right, as above? (Sorry if I had confused you). If you had, I'm glad
> it seems the solution has turned out so simple! But before I get
> excited, I'll wait to hear if you had understood the chart right.
> Also when you say "If in each case you want the pairs 1-4 and 1-5 to
> be consonant intervals", do you mean, whether they should be the same
> interval in each of the 4 sets? Yes, I am hoping to get all 4 sets
> playing equally. I'm sorry I don't understand about the "chain". But
> are you saying we can keep D, F, C, A and G the same as your original
> idea (first option in this post:
> /tuning/topicId_74247.html#74284 ) even for
> all 4 sets? That sounds so good!

Yes, I think I understood correctly. Let's see if this works out the way you were expecting....

Start with D, G, A in the first set; if you want to tune so that the intervals D-G and D-A are beatless, you'll want to tune G to 498.045 cents above D (G - 1.955 cents), and A to 701.955 cents above D (A + 1.955 cents).

Now in the second set, the corresponding intervals are G-C and G-D. Since G is tuned to G - 1.955 cents, C should be tuned to C - 2.91 cents. Similarly, in the 3rd set, E is tuned to E + 2.91 cents. Then in the 4th set, which starts on C - 2.91 cents, to make the C-F interval beatless you need to tune F to F - 5.865 cents.

That gives you this set of pitches:

D = 1/1 = 0.000
E + 2.910 = 9/8 = 203.910
F - 5.865 = 32/27 = 294.135
G - 1.955 = 4/3 = 498.045
A + 1.955 = 3/2 = 701.955
C - 2.910 = 16/9 = 996.090

So these pitches will sound good with notes 1, 4, and 5 in all 4 sets. How about notes 3 and 7 in the first set? D-F is a very reasonable minor third -- a little smaller than the minor third in equal temperament, but this 32/27 is a commonly used interval and should fit this scale very nicely. 16/9 is fine for D-C. The one interval you might want to watch out for in this tuning is F-A; it's noticeably wider than the major third in equal temperament, which is already wide.

So if these notes are acceptable, the remaining notes in the 1st set are D#-25 and Bb-25. If those are tuned as 24/23 (73.681 cents or D#-26.319) and 36/23 (775.636 cents or Bb-24.394), then the interval between them is beatless.

The other pitches in the list are just the same 7 notes transposed to start on each of the 4 tonics (D, G, A, C).

🔗Dave Keenan <d.keenan@bigpond.net.au>

Hi Justin,

After doing some reading, and considering your question from many
different angles, I conclude that the method of using a 12-equal
electronic tuner and lowering some notes by 25 cents is probably well
within the range of typical historical Koto and Shakuhachi tunings.

Considerations of just intonation, in the sense of beatlessness or
slow beating or difference tones, would seem to be irrelevant since
Koto/Shakuhachi music does not traditionally involve harmony.

If, as you say, the approximately 75 cent melodic interval is the
essential thing here, then it needs no harmonic justification.

The Scala archive contains three files with Koto pentatonic scales,
although they seem to have the wrong note as tonic. What they have as
tonic is really the fourth.

! hirajoshi.scl
!
Observed Japanese pentatonic koto scale. Helmholtz/Ellis p.519, nr.112
5
!
185.00000
337.00000
683.00000
790.00000
2/1

! hirajoshi2.scl
!
Japanese pentatonic koto scale, theoretical. Helmholz/Ellis p.519, nr.110
5
!
9/8
6/5
3/2
8/5
2/1

to the nearest cents that's
204
316
702
814
1200

! hirajoshi3.scl
!
Observed Japanese pentatonic koto scale. Helmholtz/Ellis p.519, nr.111
5
!
193.00000
357.00000
719.00000
801.00000
1199.00000

As you can see, the variation between the three is enormous.

According to this paper's abstract
http://ci.nii.ac.jp/naid/110003105880/en/
The small step arises from a chain of 5 fourths (approximate 3:4
ratios or 498 cent intervals). Or from a chain of 5 fifths
(approximate 2:3 ratios or 702 cent intervals) in reverse.

However, if we assume 1200 cent octaves and 498 cent fourths this
would give the smallest step a size of 90 cents, not 75 cents. To
nearest cents, with same wrong tonic as above, for direct comparison.

204
294
702
792
1200

-- Dave Keenan

🔗Carl Lumma <carl@lumma.org>

🔗justinasia <justinasia@yahoo.com>

Hi Carl
Where did you get that? I wonder if that might have come from me! I
did hundreds of measurements of some honkyoku recordings several years
ago, and out the results on the net.
The thing is, as I am quite inside the shakuhachi world, I know what
made the pitch. It was the player who made all the 75 cent intervals,
and it was the maker who made the 100 cent intervals with his tuner!
If a shakuhachi has the notes spot on 100 cents, it means the maker
was very good at making pitch. (This is extraordinarily rare for any
more than 10 or 20 years old). As I have mentioned, since it is us
makers who are actually determining a large part of the tuning of the
scale, I am trying to give the players a good deal now and quit the
12toneET compromise, for at least those notes which the maker determines.

I will get back to all of you about the specific scales suggested. As
I have said, I am very grateful to all of you. I need a little time to
digest them.

Thank you!
Justin

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> I haven't followed this thread, but if real Shakuhachi
> scales are an issue, this may be of interest.
>
> !
> Honkyoku tuning for Shakuhachi.
> 9
> !
> 75.0 ! Eb
> 400.0 ! F
> 500.0 ! G
> 575.0 ! G#
> 700.0 ! A
> 775.0 ! A#
> 1000.0 ! C
> 1075.0 ! C#
> 2/1 ! D
> !
> ! Measured with Celemony Melodyne, TL 60960.
> !
> ! recording # 1 2 3 4 5
> ! D y y y y y
> ! Eb y y y y
> ! F y y y y
> ! G y y y y y
> ! G# y y y y
> ! A y y y y
> ! A# y y y y
> ! C y y y y
> ! C# y y y
>
> -Carl
>

🔗Carl Lumma <carl@lumma.org>

🔗banaphshu <kraiggrady@anaphoria.com>

Beyond The Windows Perhaps Among The Podcorn

John Clare, reviewer
November 24, 2007

If trumpets could bring down the walls of Jericho, imagine the havoc a
rock band or cathedral organ would wreak. Obviously the trumpets were
mere symbols of God's will.

Still, anyone with the slightest interest in acoustics will know that
certain combinations of frequency and amplitude can have powerful
physical and psychological effects. This composition by instrument
maker and microtonal pitch expert Grady is 55 minutes of sustained
tones which shift, often microtonally, to produce eerie pulsing and
beating, plus extra "difference notes" rising from the interaction of
"real" notes.

Often sounding electronic, the ensemble is cello, bassoon, saxophones,
trumpet and voices. At a first hearing I found it as disorienting as
one of those alarms designed to send burglars running from your house
in delirium. At one point the vibrations loosened the banana clip in
one speaker, producing a static that made me jump out of my skin.
Pushing the clip back, my fingers were full of pulsing.

My mistake was playing it much too loud, due to the ethereal quietness
of the beginning.

Having recovered, I played it quietly. Suddenly the changing moire
patterns were beautiful - initially like pale light gathering on the
sea. It is a composition, of changing resonances, with slow counter
lines often in assonant harmony. Sometimes the ensemble sounds like an
organ, with the "extra-musical" overtones that a large instrument
would produce.

I recount my volume misadventure because some may want to be pushed to
the edge and because it is a dramatic demonstration of how music can
change character when played at different volumes. Played loudly, this
is as weird as Aphex Twin. It is tranquillity distilled when played
quietly.

Of course many people play music too quietly in the belief that it is
cerebral and introspective - which it will be if it is not played loud
enough for the physicality of the sound to be felt.

There is some relation in Grady's piece to minimalism. Also to the
horns, gongs and chanting of Tibetan Buddhism. Sun-Treader by Carl
Ruggles also comes to mind but in many respects this is different.
Technology has expanded this area but much can still be done
acoustically, as here, though feats of breathing and pitch control are
demanded.

If you are interested in Grady's sound world - of which this is just
one aspect - see www.anaphoria.com.

This story was found at:
http://www.smh.com.au/articles/2007/11/23/1195753288142.html

🔗Dave Seidel <dave@superluminal.com>

A very nice review of a beautiful piece.

- Dave

banaphshu wrote:
> Beyond The Windows Perhaps Among The Podcorn
> > John Clare, reviewer
> November 24, 2007
> > > If trumpets could bring down the walls of Jericho, imagine the havoc a
> rock band or cathedral organ would wreak. Obviously the trumpets were
> mere symbols of God's will.
> > Still, anyone with the slightest interest in acoustics will know that
> certain combinations of frequency and amplitude can have powerful
> physical and psychological effects. This composition by instrument
> maker and microtonal pitch expert Grady is 55 minutes of sustained
> tones which shift, often microtonally, to produce eerie pulsing and
> beating, plus extra "difference notes" rising from the interaction of
> "real" notes.
> > Often sounding electronic, the ensemble is cello, bassoon, saxophones,
> trumpet and voices. At a first hearing I found it as disorienting as
> one of those alarms designed to send burglars running from your house
> in delirium. At one point the vibrations loosened the banana clip in
> one speaker, producing a static that made me jump out of my skin.
> Pushing the clip back, my fingers were full of pulsing.
> > My mistake was playing it much too loud, due to the ethereal quietness
> of the beginning.
> > Having recovered, I played it quietly. Suddenly the changing moire
> patterns were beautiful - initially like pale light gathering on the
> sea. It is a composition, of changing resonances, with slow counter
> lines often in assonant harmony. Sometimes the ensemble sounds like an
> organ, with the "extra-musical" overtones that a large instrument
> would produce.
> > I recount my volume misadventure because some may want to be pushed to
> the edge and because it is a dramatic demonstration of how music can
> change character when played at different volumes. Played loudly, this
> is as weird as Aphex Twin. It is tranquillity distilled when played
> quietly.
> > Of course many people play music too quietly in the belief that it is
> cerebral and introspective - which it will be if it is not played loud
> enough for the physicality of the sound to be felt.
> > There is some relation in Grady's piece to minimalism. Also to the
> horns, gongs and chanting of Tibetan Buddhism. Sun-Treader by Carl
> Ruggles also comes to mind but in many respects this is different.
> Technology has expanded this area but much can still be done
> acoustically, as here, though feats of breathing and pitch control are
> demanded.
> > If you are interested in Grady's sound world - of which this is just
> one aspect - see www.anaphoria.com.
> > This story was found at:
> http://www.smh.com.au/articles/2007/11/23/1195753288142.html