Melody-Centric Just Intonation 5-Tone Tuning #1:

Intervals in melodic sequence:

1. Pitch class #1: descend 4/3 (498.0 cents) to...

2. Pitch class #2: ascend 5/4 (386.3 cents) to..

3. Pitch class #3: ascend 6/5 (315.6 cents) to...

4. Pitch class #4: descend 8/7 (231.2 cents) to...

5 Pitch class #5

Adjacent intervals in linear sequence ascending from 1/1:

1. 5/4 (386.3 cents)

2. ?/? (84.4 cents)

3. ?/? (27.3 cents)

4. ?/? (203.9 cents)

5. 4/3 + .1 cent (498.1 cents)

#2 + #3 + #4= 6/5 (315.6 cents)

Pitch class numberings ascending from 1/1:

1. Pitch class #2 (1/1)

2. Pitch class #3

3. Pitch class #5

4. Pitch class #1

5. Pitch class #4

6. Pitch class #2 one octave higher (2/1)

I hope this is understandable. I can't think of any
other way to diagram it in text, and don't have access
to any drawing programs.

Bill Flavell

Hiya Bill,

> Intervals in melodic sequence:
> 1. Pitch class #1: descend 4/3 (498.0 cents) to...
> 2. Pitch class #2: ascend 5/4 (386.3 cents) to..
> 3. Pitch class #3: ascend 6/5 (315.6 cents) to...
> 4. Pitch class #4: descend 8/7 (231.2 cents) to...
> 5. Pitch class #5
>
>I hope this is understandable. I can't think of any
>other way to diagram it in text, and don't have access
>to any drawing programs.

It's understandable to me. The precise details of why
this algorithm is your favorite aren't clear yet -- hoping
you'll take the time to explain that.

But the best thing for you to do would be to post Scala
files. They can be written by hand, and read by Scala.
Here is equal temperament...

!
The standard affair.
12
!
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
900.0
1000.0
1100.0
2/1
!

...The 2nd line is a comment, and the 3rd is the number of
tones. Scala just "tiles" (repeats) this pattern over and
over again onto your keyboard, or its on-screen keyboard.
The last note doesn't have to be an octave, and the notes
don't have to be pitch-ascending. Each line with a decimal
point is read in cents, and lines with a slash are read as
ratios. Even though you can't run Scala, by posting a
Scala file, everyone knows what you're talking about, and
Scala users can play your scale and hear it. If you don't
understand something I've said here, check the Scala web
site for more info.

I'm not sure how you would like to render your scales
in Scala format, but here is a guess for the above scale...

!
Melody-Centric Just Intonation 5-Tone Tuning #1.
5
!
1/1
3/4
15/16
9/8
63/64
!
! Bill Flavell, Tuning 60136.

Is that right? Maybe you don't know that to add two musical
ratios, one multiplies them. And to subtract ratio A from
ratio B, one multiplies B and the reciprocal of A.

Here's a question for you: do you intend this scale to be
used only on instruments with 5 tones? If not, how is the
scale extended to more tones? Would you tile this scale
across a keyboard, or would you continue applying the
algorithm to cover the keyboard? I don't if there's a way
to automate your algorithm like this in Scala (maybe Manuel,
Scala's author, can tell us), but you can always make a
Scala file with 88 entries, one for each keyboard key, or
whatever. That's harder to make by hand, I admit.

-Carl

Thank you very much for the nice response, Carl! :)

I had to leave UCLA for the weekend, and won't be back until Tuesday
morning. I'll try and give a detailed response then. The scala format
looks very straightforward and interesting.

I made a mistake in my tuning, though, not using the smaller forms of
the 4 simplest just intervals. The last one is wrong. I'll try and
correct that, too.

Bill Flavell

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> Hiya Bill,
>
> > Intervals in melodic sequence:
> > 1. Pitch class #1: descend 4/3 (498.0 cents) to...
> > 2. Pitch class #2: ascend 5/4 (386.3 cents) to..
> > 3. Pitch class #3: ascend 6/5 (315.6 cents) to...
> > 4. Pitch class #4: descend 8/7 (231.2 cents) to...
> > 5. Pitch class #5
> >
> >I hope this is understandable. I can't think of any
> >other way to diagram it in text, and don't have access
> >to any drawing programs.
>
> It's understandable to me. The precise details of why
> this algorithm is your favorite aren't clear yet -- hoping
> you'll take the time to explain that.
>
> But the best thing for you to do would be to post Scala
> files. They can be written by hand, and read by Scala.
> Here is equal temperament...
>
> !
> The standard affair.
> 12
> !
> 100.0
> 200.0
> 300.0
> 400.0
> 500.0
> 600.0
> 700.0
> 800.0
> 900.0
> 1000.0
> 1100.0
> 2/1
> !
>
> ...The 2nd line is a comment, and the 3rd is the number of
> tones. Scala just "tiles" (repeats) this pattern over and
> over again onto your keyboard, or its on-screen keyboard.
> The last note doesn't have to be an octave, and the notes
> don't have to be pitch-ascending. Each line with a decimal
> point is read in cents, and lines with a slash are read as
> ratios. Even though you can't run Scala, by posting a
> Scala file, everyone knows what you're talking about, and
> Scala users can play your scale and hear it. If you don't
> understand something I've said here, check the Scala web
> site for more info.
>
> I'm not sure how you would like to render your scales
> in Scala format, but here is a guess for the above scale...
>
> !
> Melody-Centric Just Intonation 5-Tone Tuning #1.
> 5
> !
> 1/1
> 3/4
> 15/16
> 9/8
> 63/64
> !
> ! Bill Flavell, Tuning 60136.
>
> Is that right? Maybe you don't know that to add two musical
> ratios, one multiplies them. And to subtract ratio A from
> ratio B, one multiplies B and the reciprocal of A.
>
> Here's a question for you: do you intend this scale to be
> used only on instruments with 5 tones? If not, how is the
> scale extended to more tones? Would you tile this scale
> across a keyboard, or would you continue applying the
> algorithm to cover the keyboard? I don't if there's a way
> to automate your algorithm like this in Scala (maybe Manuel,
> Scala's author, can tell us), but you can always make a
> Scala file with 88 entries, one for each keyboard key, or
> whatever. That's harder to make by hand, I admit.
>
> -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> Hiya Bill,
>
> > Intervals in melodic sequence:
> > 1. Pitch class #1: descend 4/3 (498.0 cents) to...
> > 2. Pitch class #2: ascend 5/4 (386.3 cents) to..
> > 3. Pitch class #3: ascend 6/5 (315.6 cents) to...
> > 4. Pitch class #4: descend 8/7 (231.2 cents) to...
> > 5. Pitch class #5
> >
> >I hope this is understandable. I can't think of any
> >other way to diagram it in text, and don't have access
> >to any drawing programs.
>
> It's understandable to me. The precise details of why
> this algorithm is your favorite aren't clear yet -- hoping
> you'll take the time to explain that.

OK, I'll do that under a different subject header.

> But the best thing for you to do would be to post Scala
> files. They can be written by hand, and read by Scala.
> Here is equal temperament...
>
> !
> The standard affair.
> 12
> !
> 100.0
> 200.0
> 300.0
> 400.0
> 500.0
> 600.0
> 700.0
> 800.0
> 900.0
> 1000.0
> 1100.0
> 2/1
> !
>
> ...The 2nd line is a comment, and the 3rd is the number of
> tones. Scala just "tiles" (repeats) this pattern over and
> over again onto your keyboard, or its on-screen keyboard.
> The last note doesn't have to be an octave, and the notes
> don't have to be pitch-ascending. Each line with a decimal
> point is read in cents, and lines with a slash are read as
> ratios. Even though you can't run Scala, by posting a
> Scala file, everyone knows what you're talking about, and
> Scala users can play your scale and hear it. If you don't
> understand something I've said here, check the Scala web
> site for more info.

Thanks very much for that info, Carl! I'll do a Scala format
on my next tuning post.

> I'm not sure how you would like to render your scales
> in Scala format, but here is a guess for the above scale...
>
> !
> Melody-Centric Just Intonation 5-Tone Tuning #1.
> 5
> !
> 1/1
> 3/4
> 15/16
> 9/8
> 63/64
> !
> ! Bill Flavell, Tuning 60136.
>
> Is that right?

Yes, that's great, except I would want to mention
the four intervals used melodically in the comment
line.

> Maybe you don't know that to add two musical
> ratios, one multiplies them. And to subtract ratio A from
> ratio B, one multiplies B and the reciprocal of A.

Right. I was just using the cents values instead of worrying
about multiplying intervals.

> Here's a question for you: do you intend this scale to be
> used only on instruments with 5 tones?

Yes.

> If not, how is the
> scale extended to more tones? Would you tile this scale
> across a keyboard, or would you continue applying the
> algorithm to cover the keyboard?

All I can think of would be to use the first 5 white
keys of each keyboard octave for the scale.

> I don't if there's a way> to automate your algorithm like this
> in Scala (maybe Manuel,
> Scala's author, can tell us),

Yes, that would be nice! :)

Then you would only need to be concerned with which
intervals to use and what order to play them in.

> but you can always make a
> Scala file with 88 entries, one for each keyboard key, or
> whatever. That's harder to make by hand, I admit.

Well, I'll do them in Scala format from now on. I'm not so
interested in the physical actualization end of things. That's why
I'm on this list. I'll do the conceptual work and somebody more
instrumet-oriented can work on that end.

Thanks very much for the great response! :)

Bill Flavell