Re: [tuning] Re: Piano Tuning Schools [JI/JT scales]

In a message dated 10/6/02 8:08:23 PM Central Daylight Time, clumma@yahoo.com
writes:

> The real problem was, no one had invented
> >a practical all-key scale that would faithfully play music written
> >for tempered scales based on the 12-note octave. But I did invent
> >such a scale, and posted its C scale here.
>
> What's the message # of that post? Or could you reproduce the
> scale in this thread?
>
> -Carl
>
Here's the manual scale in just-temperament cents:

7 7
7
C 0 C# 84 D 200 D#/Eb 268 E 384 F 468 F# 584 G 700 G#/Ab 768 A 900
A#/Bb 968
Split-digitals: 7
7 7
+/-155 400 500 668
+/-855
or 168*
or 868*
B 1084 C2 1200
7
1100 1168

*Requires less tone generators. This C scale has 6 harmonic-minor 7th chords
and 7 harmonic 9th chords--C through B. The F harmonic 7th or 9th chord is
minus its A note.

Since the F chord begining on 500 is also needed to play most music, the F
scale 500 cents higher is also needed. And sometimes the G scale 700 cents
higher. Occassionaly a b scale is needed, as ii, iii, vi, and possibly vii
are sometimes flatted as major chords. Thus my organ has three maanuals, each
tuned to a different scale.
It's tonally split at Middle C for maximum stop use.

Twelve key-signature stops determine which manual has which scale at any
given time. Manual 1 has 5b and 1#. Manual 2 has 6b, 4b, 2b, c, d, e. Manual
three has Eb, F and A The B manual scale hasn't been assigned nor installed
yet, as it's rarely used..

The split-digital scales notes are:
For manual 1 Db/G. Manual 2 Gb/C, Af/D, Bb/E. Manual 3: F/B, Eb/A. Scales an
augmented 4th apart have two notes identical. So two split-digital scales
notes will fit onto 12 split digitals per octave.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

> Here's the manual scale in just-temperament cents:

Here it is as a Scala file:

!
Scale description goes here.
12
!
84.0 ! 5
200.0 ! 12
268.0 ! 16
384.0 ! 23
468.0 ! 28
584.0 ! 35
700.0 ! 42
768.0 ! 46
900.0 ! 54
968.0 ! 58
2/1
!

You are probably aware that this is a subset of 72-tone equal
temperament (approx. degrees shown on right)?

-Carl

I wrote...

> !
> Scale description goes here.
> 12

Whoops -- left out B. The number there (12) must match the
number of tones in the scale. Because of the way your message
was formatted / displayed by Yahoo!, I wasn't able to get
exactly where the split keys happen, but all the numbers I saw
were members of 72-equal. I'd be interested (as would many
others here, I'm sure) to here how you arrived at this scale.

In the meantime, I must disagree that the lack of a scale that
worked in all keys kept microtonal music from happening. One
only need consult Monz's et page for proof of that. [Which
appears to be down right now -- Monz?] Anyway, with the advent
of digital keyboards and the flurry of tuning theory out there
these days, show that these two factors alone cannot explain
the lack of microtonal keyboard music we still suffer from.

-Carl

In a message dated 10/6/02 11:21:09 PM Central Daylight Time,
clumma@yahoo.com writes:

> all the numbers I saw
> were members of 72-equal.

The scale I gave can work with the major 3rds being one cent larger, and the
harmonic minor 7ths 2 cents larger. I chose the E 384 cent value so the large
minor 7th used with it would be 984 cents, one cent larger than 30/17. As
providing a harmonic minor 7th for it, which is rarely used, would require
more tone generators. So whatever name you call it, it's still just
tempermanet, and sounds so.

However, it's true the tone generators are tuned to the 12-ET scale frequency
divided. The difference is, one is used for the root and 5ths, another for
the major 3rds, and anoter for the harmonic minor 7ths. All interlaced so the
right pitches go to the right notes--very complicated wiring to say the
least.

I'd be interested (as would many > others here, I'm sure) to here how you
> arrived at this scale.
>
It appears most devise a scale, then compose music to fit it. I used the
opposite approach. As I wanted a scale that would play music already composed
very long since for tempered scales based on 12 notes per octave.

So I used four-part harmony compositions, mainly hymns, to see what just
pitches were actually used, how, where, and how often. It took years of
experimentation to figure it all out for hundreds of such pieces in several
hymnbooks. I did very much calculation with several hand calculators that
wore out in the process. I finally settled on the scale I posted here as the
best and practical solution.

Part of that solution was the revelation that music isn't composed via just
one just scale for the whole piece, but several scales being used from phrase
to phrase! Thus one phrase in a C piece might use the F scale when the IV
chord is needed, the next phrsee might use the C scale for the V7, and the
next phrse the G scale for the II7, and the next a flated-chord scale, and
so forth.

So I added the split digitals to minimize the complexity of playing different
scales, and reducing the need to change manuals while playing.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

>So I added the split digitals to minimize the complexity of
>playing different scales, and reducing the need to change manuals
>while playing.

Cool. So sorry to just jump in, but did you say you have a
working prototype? What's the status? Do you play it
professionally? Etc.

-Carl

In-Reply-To: <anr205+jasj@eGroups.com>
Carl Lumma wrote:

> Whoops -- left out B. The number there (12) must match the
> number of tones in the scale. Because of the way your message
> was formatted / displayed by Yahoo!, I wasn't able to get
> exactly where the split keys happen, but all the numbers I saw
> were members of 72-equal. I'd be interested (as would many
> others here, I'm sure) to here how you arrived at this scale.

I don't see that it even works for the numbers you originally gave.
Here's a table:

84.0 5.0 5 83.3
200.0 12.0 12 200.0
268.0 16.1 16 266.7
384.0 23.0 23 383.3
468.0 28.1 28 466.7
584.0 35.0 35 583.3
700.0 42.0 42 700.0
768.0 46.1 46 766.7
900.0 54.0 54 900.0
968.0 58.1 58 966.7

The left hand column is the size in cents, then the corresponding size in
steps of 72-equal, then that number rounded to an integer, and then the
cents value you get by converting back the other way. It can be more than
a cent out, for example 286.0 as against 266.7. The two are close, but
that follows from them both being close to just intonation.

Here's another table showing all the numbers I could find in Pauline's
message, converting them to 72 and then the rounded value converted to
cents:

0 0.0 0.0
84 5.0 83.3
200 12.0 200.0
268 16.1 266.7
384 23.0 383.3
468 28.1 466.7
584 35.0 583.3
700 42.0 700.0
768 46.1 766.7
900 54.0 900.0
968 58.1 966.7
155 9.3 150.0
855 51.3 850.0
168 10.1 166.7
400 24.0 400.0
500 30.0 500.0
668 40.1 666.7
868 52.1 866.7
1084 65.0 1083.3
1200 72.0 1200.0

155 and 855 cents are nowhere near 72th divisions of the octave.

Graham

In a message dated 10/7/02 10:06:34 AM Central Daylight Time,
clumma@yahoo.com writes:

> but did you say you have a
> working prototype? What's the status? Do you play it
> professionally? Etc.
>
> -Carl
>
The working prototype isn't finished. Today I worked on getting the bugs
(dead ntoes, wrong notes) out of the manual one splitt digitals for the
treble side. It's a lot of work troubleshooting what one has created! No matt
howhard I try to be perfect, there's always something not just right that has
to be fixed after major wiring.

I'm a trained organist, but I haven't played my instrument publicly. The
console is a butcher-block bench openon all sides for working on it!

Pauline

In a message dated 10/7/02 10:28:52 AM Central Daylight Time,
graham@microtonal.co.uk writes:

> 155 and 855 cents are nowhere near 72th divisions of the octave.
>
>
> Graham

155 cents 35/32 is the harmonic minor 7th for Tenor E. 855 cents is the
tempered harmonic minor 7th for Tenor B. The theoretical value is 857 cents
105/64.

Pauline

> I don't see that it even works for the numbers you originally
> gave. Here's a table:
>
> 84.0 5.0 5 83.3
> 200.0 12.0 12 200.0
> 268.0 16.1 16 266.7
> 384.0 23.0 23 383.3
> 468.0 28.1 28 466.7
> 584.0 35.0 35 583.3
> 700.0 42.0 42 700.0
> 768.0 46.1 46 766.7
> 900.0 54.0 54 900.0
> 968.0 58.1 58 966.7
>
> The left hand column is the size in cents, then the corresponding
> size in steps of 72-equal, then that number rounded to an integer,
> and then the cents value you get by converting back the other way.
> It can be more than a cent out, for example 286.0 as against
> 266.7. The two are close, but that follows from them both being
> close to just intonation.

I'd say it follows from them both being close to 225:224
temperament. Would you say that these small differences
make an application of the periodicity block model invalid?

> Here's another table showing all the numbers I could find in
> Pauline's message, converting them to 72 and then the rounded
> value converted to cents:
>
> 0 0.0 0.0
> 84 5.0 83.3
> 200 12.0 200.0
> 268 16.1 266.7
> 384 23.0 383.3
> 468 28.1 466.7
> 584 35.0 583.3
> 700 42.0 700.0
> 768 46.1 766.7
> 900 54.0 900.0
> 968 58.1 966.7
> 155 9.3 150.0
> 855 51.3 850.0
> 168 10.1 166.7
> 400 24.0 400.0
> 500 30.0 500.0
> 668 40.1 666.7
> 868 52.1 866.7
> 1084 65.0 1083.3
> 1200 72.0 1200.0
>
> 155 and 855 cents are nowhere near 72th divisions of the octave.

Okay, it looks like I should have been more careful. I cut and
pasted her post into my text editor and tried to figure out the
formatting, and where the 7's were coming from, and I must have
missed those two.

-Carl

>The working prototype isn't finished. Today I worked on getting
>the bugs (dead ntoes, wrong notes) out of the manual one split
>digitals for the treble side. It's a lot of work troubleshooting
>what one has created!

For sure. Good luck! I'm sure we'd all be interested in whatever
sights/sounds you care to share along the way.

>No matt howhard I try to be perfect, there's always something not
>just right that has to be fixed after major wiring.

Welcome to the human condition.

-Carl