Gunnar Due Tungland
And finally a piece for digital church organ with comparisons between 3 variants of "In Tuningland" + 1/4 and 1/6 comma meantone and 12-ET (Equal temperament)
Click HERE !
If you should happen to experience alternative tunings as strange, it might be due to a combination of two things:
1) the 12-ET is ubiquitous in our world and therefore feels unaccustomed, and
2) the syntonic comma is a problem that still may be present in diverse subtle ways when working with pure intervals.
In addition, this website includes many comparisons with traditional temperaments (Meantones (1/4&1/6),Equal T.) where you can judge for yourself and train your ear at the same time.
.......
1. Arranging of the keyboard
2. Supplementary and overlapping setup
3. Halving the comma shift
4. Economizing amount of pitches
5. Small adjustments (tempering)
6. Expansions
7. Comprehensive setups
And here are the pluses and minuses with IT (click)
......................................................................................................................
In this guide to "In Tuningland", I use completely pure intervals and chords—then what is right and what is wrong will be very clear.
Due to an extensive use of audio files combined with lattices, I can postpone the use of cent values and the calculations until the end of this introduction.
The
work in connection with my website TU
you – a change to TU ,
and living with the imperfections of these tunings, made it natural
for me to start experimenting with tunings of more than 12 pitches
per octave. "In Tuningland" is a result of these efforts.
In Tuningland (IT) represents a new idea (presumably) to tune and arrange ordinary keyboards etc. IT can be employed in the fields of "Just Intonation" with pure or almost pure chords, and has the advantage of hiding the problem of the comma to quite a large extent. And my main goal is that IT should become useful in some way with respect to acoustic instruments..
In Tuningland (IT) represents a new idea (presumably) to tune and arrange ordinary keyboards etc. IT can be employed in the fields of "Just Intonation" with pure or almost pure chords, and has the advantage of hiding the problem of the comma to quite a large extent. And my main goal is that IT should become useful in some way with respect to acoustic instruments..
During
the process of developing IT my assessment has shifted between seeing
the application as just a funny curiosity to thinking that it may
actually have a musical significance.
The
last part of this long process resulted in recordings involving 2
acoustic harpsichords and two musicians.
After
this experiment IT was in my mind upgraded and confirmed to be at
least "social and musical fun in the rehearsal room"!
Since
it is easier to play this tuning with 2 or more musicians, I chose to
call it a social tuning. :)
After
the acoustic tests and recordings, I also found that I would give
harpsichord players an opportunity to test out IT without having to
read the theory on this page.
So this shortcut is for your convenience: first an untempered (not my favourite) version of IT with easy tunings instructions and audio files from real harpsichords.
So this shortcut is for your convenience: first an untempered (not my favourite) version of IT with easy tunings instructions and audio files from real harpsichords.
On
the bottom of that page you will find a link to tuning instructions
for "In Tuningland" in tempered versions.
If you've ever longed to play pure chords on your harpsichord , you'll get exclusively pure chords from Ab inclusive E (seen from the circle of fifths).
If you've ever longed to play pure chords on your harpsichord , you'll get exclusively pure chords from Ab inclusive E (seen from the circle of fifths).
Click
HERE
Another acoustic instrument I've had in mind is the accordion
This instrument is like the harpsichord rich in overtones and the difference between tunings becomes significant. Unfortunately, the accordion is not as easy to tune as a harpsichord.....
If you want to anticipate hearing my digital recordings you can find them by scrolling down HERE.
Another acoustic instrument I've had in mind is the accordion
This instrument is like the harpsichord rich in overtones and the difference between tunings becomes significant. Unfortunately, the accordion is not as easy to tune as a harpsichord.....
If you want to anticipate hearing my digital recordings you can find them by scrolling down HERE.
And finally a piece for digital church organ with comparisons between 3 variants of "In Tuningland" + 1/4 and 1/6 comma meantone and 12-ET (Equal temperament)
Click HERE !
If you should happen to experience alternative tunings as strange, it might be due to a combination of two things:
1) the 12-ET is ubiquitous in our world and therefore feels unaccustomed, and
2) the syntonic comma is a problem that still may be present in diverse subtle ways when working with pure intervals.
I
recommend this introduction to "In Tuningland" also
to those who are more interested in the problem of the syntonic
comma than in this specific tuning. This comma is present in
all traditional Western music, and not only concern the keyboard
players. This website has a lot of audio files combined with
understandable lattices that provide insight into these issues.
The following terms will be explained, visualized and "audiolized" :
The following terms will be explained, visualized and "audiolized" :
1.
Comma shift
2.
Comma drift
3.
Wolf intervals
These
phenomena are problems but are actually also solutions.In addition, this website includes many comparisons with traditional temperaments (Meantones (1/4&1/6),Equal T.) where you can judge for yourself and train your ear at the same time.
For those familiar with the terminology you can click below on the table of contents for a quick survey :
1. Arranging of the keyboard
2. Supplementary and overlapping setup
3. Halving the comma shift
4. Economizing amount of pitches
5. Small adjustments (tempering)
6. Expansions
7. Comprehensive setups
And here are the pluses and minuses with IT (click)
......................................................................................................................
In this guide to "In Tuningland", I use completely pure intervals and chords—then what is right and what is wrong will be very clear.
Due to an extensive use of audio files combined with lattices, I can postpone the use of cent values and the calculations until the end of this introduction.
The
fascination of tuning and the frustration that the world of fifths
and world of thirds doesn`t fit together have haunted musicians for
centuries. Common to all endeavours lies in dealing with commas, not
least the syntonic comma.
The
syntonic comma is the most important comma, at least in traditional
western music.
This comma is markedly present when string players intonate. (The Pythagorean comma, which is maybe more often mentioned, refers to tuning of keyboard instruments and to solo instruments more indirectly)
This comma is markedly present when string players intonate. (The Pythagorean comma, which is maybe more often mentioned, refers to tuning of keyboard instruments and to solo instruments more indirectly)
................................................................
The
fact is: if we tune 4 pure fifths one after another, such as
Bb-F-C-G-D, then this D, named by me as "D 0", is
annoyingly higher than the one we get when tuning a pure major third
from the same starting point, Bb-D (named "D -2").
The difference between "D 0" and "D-2" is exactly one syntonic comma (in this untempered version)
The difference between "D 0" and "D-2" is exactly one syntonic comma (in this untempered version)
The
reason why I define the difference as two units (D 0 and D -2) is
that I want to be completely consistent in my explanations to avoid
confusions.
Later
we want to use 1 unit, a half of a comma.1. Arranging of the keyboard
My
starting point is pure thirds and fifths on a regular keyboard in C
major.
This
C-setup is marked C
In C, pure
C major, F major, Dm, Am, Em, G major, Bb major, D major, A major, E
major are prioritized.
For
this we need 2 D`s, where the highest is placed on the Eb key !
With
this setup, we get three pure fifth rows :
Before
this gets too confusing, we will hurry to our first listening
example.
Such a tuning contains many chords, but because of the problem with the comma, it also has big limitations (only 12 tones), so it is not usable for that much music.
Such a tuning contains many chords, but because of the problem with the comma, it also has big limitations (only 12 tones), so it is not usable for that much music.
I
will nevertheless demonstrate all the 3-tone major and minor triads
in a small piece where I've steered away from the comma problem, but
the curse of the comma still appears in the end. : (
......................
Video (music piece) : C 0 Passing through all pure 3-tones triads + many more
..............................
..............................
Important:
The
observant listener will see and hear that:
Pure
major thirds are obtained from
the fifth row below (- 2 units).
Pure
minor thirds are obtained from the fifth row above(+ 2 units)..
.........
A
pure sus4 chord is 3 tones (2 fifths) horizontally in a row.
Furthermore, we see that a pure D sus4 in this first example, C, is missing (No G-D-A in a horizontal line).
Furthermore, we see that a pure D sus4 in this first example, C, is missing (No G-D-A in a horizontal line).
Around
G-D-A there are major problems, we have a pure G-(high)D
and a pure (low)D-A
, but with 2 different D, not successive.
Pure intervals easily make some other wolf intervals.
The intervals between the red tones below are wolfs, they are not neighbors on a row in the diagram.
But if we avoid them we have actually 3 similar diatonic scales
First C major
C-D(on Eb key)- E- F- G- A-B- C
If we only use one of the red tones at a time (avoid the wolf fifth (high)D-A) , we will get a very pure feeling with cluster possibilities.
The tritonus is as pure as possible.
Notice that the minor third D-F is not pure , but can be used.
Then we have F major.
F-G-A-Bb-C-D(the lower one)E-F
Only use one red tone at a time (avoid the wolf G-(low)D). G-Bb is not pure.
The nice thing is that on the other side of the Dsus4 division (from the view of circle of fifths) we will find exactly the same tuned scale and possibilities in A major as C major. (do not play B and F# at the same time).
Only use one red tone at a time.
A-B-C#-D(the lower one)-E-F#-G#-A
Pure intervals easily make some other wolf intervals.
The intervals between the red tones below are wolfs, they are not neighbors on a row in the diagram.
But if we avoid them we have actually 3 similar diatonic scales
First C major
C-D(on Eb key)- E- F- G- A-B- C
If we only use one of the red tones at a time (avoid the wolf fifth (high)D-A) , we will get a very pure feeling with cluster possibilities.
The tritonus is as pure as possible.
Notice that the minor third D-F is not pure , but can be used.
Then we have F major.
F-G-A-Bb-C-D(the lower one)E-F
Only use one red tone at a time (avoid the wolf G-(low)D). G-Bb is not pure.
The nice thing is that on the other side of the Dsus4 division (from the view of circle of fifths) we will find exactly the same tuned scale and possibilities in A major as C major. (do not play B and F# at the same time).
Only use one red tone at a time.
A-B-C#-D(the lower one)-E-F#-G#-A
To
become familiar with this setup in C, it is very useful to play these
scales and chords.
Also highly recommended is to play 2 melodic minor scales with their associated chords.
First in A minor.
Don`t use B and F# at the same time Avoid ii -chord
A-B-C-D-E-F#-G#-A
So D minor, avoid G-D at the same time .
Avoid IV -chord
Here we can play I-ii-V-I (D(m)-Em-A-D(m))
D-E-F-G-A-B-C#-D
If you have tried some scales and chords in this setup (in your mind:), You are now ready for a transposing to Bb !
............................................
2. Supplementary and overlapping setup
Also highly recommended is to play 2 melodic minor scales with their associated chords.
First in A minor.
Don`t use B and F# at the same time Avoid ii -chord
A-B-C-D-E-F#-G#-A
So D minor, avoid G-D at the same time .
Avoid IV -chord
Here we can play I-ii-V-I (D(m)-Em-A-D(m))
D-E-F-G-A-B-C#-D
If you have tried some scales and chords in this setup (in your mind:), You are now ready for a transposing to Bb !
............................................
2. Supplementary and overlapping setup
If
we transpose this tuning to Bb we get 2 pitches of C (instead of 2 of D), the
highest of them is placed on the C# key. .
Now
we see that we have both a pure Dsus4 (G-D-A) and the opportunity to
play a pure Dm-G-C progression. The problem has been moved to Csus4.
F-C-G
The text about scales and chords from C above , are transposed to Bb HERE !
The text about scales and chords from C above , are transposed to Bb HERE !
But couldn`t
we just let Bb take
over when we meet problems in C ??
Here I have merged them with a common area in grey.
Here I have merged them with a common area in grey.
Like
this:
But
then we get a new big problem. We end up somewhere else than
where we started, a phenomenon called comma drift.
Hear and see this in extreme, only pure chords, and the common tones between the chords have the same pitch.
This is the syntonic comma at its worst and funniest :)
Video: RISING !
Video: FALLING !
Hear and see this in extreme, only pure chords, and the common tones between the chords have the same pitch.
This is the syntonic comma at its worst and funniest :)
Video: RISING !
Video: FALLING !
Bb,
is resolving something by giving other chords and scales, but we still have the urgent comma problem.
.....................................
3. Halving the comma shift
3. Halving the comma shift
Here
we are in the core of "In Tuningland".
We
now raise Bb by
half of a comma, to a Bb +1.
Like this :
Like this :
The same displayed in another way :
Then we will get a D in Bb +1, now denoted as D -1 that will end in the middle of D 0 and D-2 in C 0.
The comma shift is halved while these two manuals complement each other regarding chords.
And if we go to the problem with the two pitches of C in Bb+1 which after the rising gives them the names C +1 and C -1, then we see that C 0 from C 0 is lying in the middle of these two tones in the same way.
If we are to sum up this IT variant with the lowest amount of pitches (24), which can be tuned on a two-manual harpsichord, then we now can see that these manuals are overlapping and complementing each other in a nice way.
1. Some chords are available on just one manual.
Some chords are to be found on both manuals.
2. Some chords are pure on just one manual.
Some chords are pure on both manuals.
3. You can change the manual when the curse of the comma looms.
In
a way, we have a comma shift and a comma drift at the same time, but only the half of it.
Now
we have complementary setups with a halved comma shift.
A
nice thing : We have Dm, Am, Em,......, F#m , C#m , but miss Bm in C 0
But
we do have Bm in Bb+1 (which is a more distant key) !
In a way, we have a comma shift and a comma drift at the same time, but only the half of it.
Now we have complementary setups with a halved comma shift. A nice thing : We have Dm, Am, Em,......, F#m , C#m , but miss Bm in C 0.
But we do have Bm in Bb+1 (which is a more distant key) !
In the two first examples I am dancing with the wolves :) : and that is NOT so nice.
A survey for the chords is available HERE.
4. Economizing amount of pitches
But it is much more difficult to find a tuning that is economizing regarding amount of pitches and therefore can be used in a acoustic way.
In a way, we have a comma shift and a comma drift at the same time, but only the half of it.
Now we have complementary setups with a halved comma shift. A nice thing : We have Dm, Am, Em,......, F#m , C#m , but miss Bm in C 0.
But we do have Bm in Bb+1 (which is a more distant key) !
In the two first examples I am dancing with the wolves :) : and that is NOT so nice.
C 0 with the comma problem :
Video: HERE
Bb+1 with the comma problem :
Video HERE
And now at last we can hear and see the results of the efforts C0 and Bb+1 combined, and the comma problem reduced:
Video: HERE
The chords from C 0 and Bb +1 are interlaced into each other.
Video: HERE
Bb+1 with the comma problem :
Video HERE
And now at last we can hear and see the results of the efforts C0 and Bb+1 combined, and the comma problem reduced:
Video: HERE
The chords from C 0 and Bb +1 are interlaced into each other.
Some
chords have a bit higher pitch in Bb +1 than
in C 0 and
vice verca.
A survey for the chords is available HERE.
I started with C 0 because it is easiest to understand thus I have used this as a starting point. However, if we look at the range in scales and chords, it would perhaps be more natural selecting F 0 and G-1 to get C major as the centre.
Here is a view of the scales (not chords):
| Bb +1 C 0 | F 0 G -1 |
| Eb major | Bb major |
| Bb major | F major |
| F major | C major |
| C major | G major |
| G major | D major |
| A major | E major |
| C minor | G minor |
| G minor | D minor |
| D minor | A minor |
| A minor | E minor |
4. Economizing amount of pitches
This
is an economizing model and can not be compared with the digital
world's approach to infinite pitch adjustments.
Working
with Just Intonation on digital instruments:
you
can take a look on this APP,
and
this SOFTWARE.
But it is much more difficult to find a tuning that is economizing regarding amount of pitches and therefore can be used in a acoustic way.
Because
of the relative few pitches IT can be used on one or several double
manual harpsichords. Just Intonation is really something different
playing it acoustically.
"Yes, many find the purity of computer-generated sounds utterly unnatural. The reason is that there will be a fixed pattern of phase cancellation among some of the coinciding partials depending on your onset times. This frozen pattern of phase cancellation does not occur in real music, where phase relationships among coinciding partials will cycle between constructive and destructive. Without this effect, the dyad or chord will sound like a single timbre rather than a harmony." Paul Erlich
Of course you can (like me) use In Tuningland in a digital way, if your keyboard/software allows for IT.
5. Small adjustments (tempering)
Until now we have operated exclusively with pure intervals.
Those who will try to tune their double-manual harpsichord can use this table. Or you can tune by ear using TUNING INSTRUCTIONS
You can do it on a digital keyboard too, but if the two pitches of D in C 0 and two of C in Bb+1 make troubles then it will be better using the spreadsheets. Explanation below.
Those who will try to tune their double-manual harpsichord can use this table. Or you can tune by ear using TUNING INSTRUCTIONS
You can do it on a digital keyboard too, but if the two pitches of D in C 0 and two of C in Bb+1 make troubles then it will be better using the spreadsheets. Explanation below.
If the comma shift still is perceived
as annoying then my solution and maybe my favourite version is to narrow/temper all fifths with 1 cent. Then the comma shift will decrease from 10,8 to 8,8 cent.
Here is the table for this.
Here is the table for this.
You can use the
spreadsheet to find your own solution. See further down.
The tempered version (-1 cent) is used both in
15 HYMNS,
the acoustic harpsichord recordings and
2 simple improvisations.
My (digital) accordion recordings with comparing possibilities
can be heard HERE. (Read or scroll down)
There are pluses and minuses when choosing the quality of the fifths.
Take a look : HERE
The tempered version (-1 cent) is used both in
15 HYMNS,
the acoustic harpsichord recordings and
2 simple improvisations.
My (digital) accordion recordings with comparing possibilities
can be heard HERE. (Read or scroll down)
There are pluses and minuses when choosing the quality of the fifths.
Take a look : HERE
Here is a collection to get familiar with In Tuningland in the smallest version (24 pitches). It is 15 hymns with lattices and I have also lowered the speed (1/3). In slow tempo you get an opportunity to follow the idea with much time to think and understand.
You can also choose to compare IT with 1/4 comma meantone and Equal temperament.
VIDEOS, 15 Hymns : HERE
6. Expansions
The principle of "In Tuningland" can be expanded.
By
replacing only 5 tones in C
0 we get exactly the corresponding setup transposed
to Ab,
marked
as Ab +2.
In the same way as in C 0 and Bb +1 we have two pitches of a tone, in Ab +2 we have Bb:
Bb 0 and a Bb +2, the latter on the B key.
In the same way as in C 0 and Bb +1 we have two pitches of a tone, in Ab +2 we have Bb:
Bb 0 and a Bb +2, the latter on the B key.
And
if we replace 5 tones in Bb
+ 1 we can get D
-1.
Here we have two pitches of E :
E-3 and E-1, the last placed on the F key.
Here we have two pitches of E :
E-3 and E-1, the last placed on the F key.
Tables
of the chords available , where to find and which is highest in
pitch: HERE
Below you will find the notes interlaced.
The darkest red is common for Ab+2 and C 0
The darkest green is common for Bb+1 and D-1.
The five tones in lilac on the top belongs to Ab+2.
The five light red to the right (and second bottom row) belongs to C 0.
The five lighter green notes in 2nd row belongs to Bb+1.
The five light green notes to the right (and bottom) belongs to D-1.
IT provides here a wide range of chords using 34 pitches.
In this piece I will show some of the possibilities. Everytime I shift keyboard/setup there will come a sign up to the left.
And you can compare it with common temperaments.
In meantone (1/4&1/6) only 8 major thirds are useful.
In my comparisons I use extended meantone, that means
more than 12 pitches pr.octave, similar to keyboards with split keys . Here my focus is on the qualities of the sound and not the practical solutions for the meantones.
This is also the right time for you to judge by yourself and train your ears using my little organ piece
"A PURE MIX"
..............................
Of course, economic use of the number of pitches is not so important in the advanced part of the digital tuning world, and even with two acoustic harpsichords we are still using 48 keys on these 34 pitches.
But used on an archicembalo this will be of utmost importance.
(See spreadsheet link to archicembalo down below.)
It would have been nice to test In Tuningland on a harpsichord or organ with Vicentino`s keyboard idea !
https://en.wikipedia.org/wiki/Archicembalo
And if IT is used on an organ (like the Groven organ) where the right pitch is chosen automatic, the advantage of few pitches is obvious.
7. Comprehensive setups
In the beginning of this introduction I was promoting a nice version for 2 harpsichords .
HERE you can check how many tones that is common in a couple of setups with same color.
The same, but shifted.
......................................................................................................
Then
to the :
SPREADSHEETS
They are made in LibreOffice (It is free to download)
But you can open them in Excel too.
Below you will find the notes interlaced.
The darkest red is common for Ab+2 and C 0
The darkest green is common for Bb+1 and D-1.
The five tones in lilac on the top belongs to Ab+2.
The five light red to the right (and second bottom row) belongs to C 0.
The five lighter green notes in 2nd row belongs to Bb+1.
The five light green notes to the right (and bottom) belongs to D-1.
IT provides here a wide range of chords using 34 pitches.
In this piece I will show some of the possibilities. Everytime I shift keyboard/setup there will come a sign up to the left.
And you can compare it with common temperaments.
In meantone (1/4&1/6) only 8 major thirds are useful.
In my comparisons I use extended meantone, that means
more than 12 pitches pr.octave, similar to keyboards with split keys . Here my focus is on the qualities of the sound and not the practical solutions for the meantones.
Full tempo |
1/2 tempo |
1/3 tempo |
|
IT Pure fifths |
VIDEO |
VIDEO |
VIDEO |
IT -1 cent fifths |
VIDEO |
VIDEO |
|
IT -2 cent fifths |
VIDEO |
VIDEO |
|
1/4 c meantone |
VIDEO |
VIDEO |
|
1/6 c meantone |
VIDEO |
VIDEO |
|
Equal temperament |
VIDEO |
VIDEO |
This is also the right time for you to judge by yourself and train your ears using my little organ piece
"A PURE MIX"
..............................
Of course, economic use of the number of pitches is not so important in the advanced part of the digital tuning world, and even with two acoustic harpsichords we are still using 48 keys on these 34 pitches.
But used on an archicembalo this will be of utmost importance.
(See spreadsheet link to archicembalo down below.)
It would have been nice to test In Tuningland on a harpsichord or organ with Vicentino`s keyboard idea !
https://en.wikipedia.org/wiki/Archicembalo
And if IT is used on an organ (like the Groven organ) where the right pitch is chosen automatic, the advantage of few pitches is obvious.
7. Comprehensive setups
Under
point 6. the number of chords was expanded using 4 setups:
Ab +2, Bb +1, C 0 and D -1.
Ab +2, Bb +1, C 0 and D -1.
Apart
from the very nice growth of chords, flexibility does not get so much
better.
In the beginning of this introduction I was promoting a nice version for 2 harpsichords .
We
can use Bb +1, F
0, C 0 and G
-1 (32 pitches per octave).
This
system provides much better handling of passing tones and will allow
access to some material from the renaissance. The advantage of 2
cembalists is that each of them has only 2 tones on the wrong keys
each to keep track of. And with 2 players we will get much more
smooth transitions regarding switching of the manuals. See the
acoustic and practical page to this idea. HERE
!
HERE you can check how many tones that is common in a couple of setups with same color.
This
combination provides 2 additional major triads compared to meantone.
We
can play pure Ab, B and G#m. Actually we can also play a pure Fm with
a combination of 2 manuals (F-C on G-1 and
Ab on Bb +1)
Tables of the chords available , where to find and which is highest in pitch: HERE
Tables of the chords available , where to find and which is highest in pitch: HERE
The
dark red is common for C
0 and F 0,
The
dark green is common for Bb
+1 and G -1
The
lilac to the right is only for C
0,
The
lilac to the left only for F
0
The
light green on the top is only for Bb
+1,
The
yellowish green to the left (and bottom) is only for for G
-1.
The same, but shifted.
......................................................................................................
SPREADSHEETS
They are made in LibreOffice (It is free to download)
But you can open them in Excel too.
The simplest spreadsheet: C 0 and Bb +1 (Click and download)
Under the green INPUT you will find the cells where you can enter a variable.
The green INPUT at the top to the right is just a calculator where you can have comma shift as a variable.
The calculator has no effect on the main tables.
Up to the left you will find:
I always let the major third be pure (0) , but if you want another value you can change it.
The cell for the fifths is important. If you enter -1 (my favourite) in the Fifth cell, you will see a double reduction (-2 cent) of the comma shift from 10,753 to 8,753.
Then you have 3 INPUTs to the left around C0
If the yellow and blue cells are set to 0 and you enter the values for a setup into a synthesizer or a tuning app, than the tones with a square will be a semitone too high.
Therefore set the blue cell to - 100 to lower these tones with a semitone.
But then these values will get very low.
Many synthesizers don`t allow values outside -63/+63.
To fix that enter a positive value into the yellow cell
eg +50. Then all the values will come inside this range.
Another BUT:
But then the cent values will be too high and your desired concert pitch (eg 440 Hz) will be far from right.
So therefore enter eg 440 into the brown cell and just to the right in the light brown cell you will get a Hz value to enter to get the right pitch.
Now everything is fine and you can enter cent numbers for the different setups, in our example C0 with one extra D, and Bb+1 with one extra C, both in squares.
....................................
If you want to delete a setup from the selection in a spreadsheet, then highlight the rows in the margin to the left.
A right click, and delete !
Therefore set the blue cell to - 100 to lower these tones with a semitone.
But then these values will get very low.
Many synthesizers don`t allow values outside -63/+63.
To fix that enter a positive value into the yellow cell
eg +50. Then all the values will come inside this range.
Another BUT:
But then the cent values will be too high and your desired concert pitch (eg 440 Hz) will be far from right.
So therefore enter eg 440 into the brown cell and just to the right in the light brown cell you will get a Hz value to enter to get the right pitch.
Now everything is fine and you can enter cent numbers for the different setups, in our example C0 with one extra D, and Bb+1 with one extra C, both in squares.
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If you want to delete a setup from the selection in a spreadsheet, then highlight the rows in the margin to the left.
A right click, and delete !
You will find the spreadsheets HERE with several combinations of the setups.
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I hope you will like "In Tuningland" , whether it is from
a musical, educational or meditative point of view .
Gunnar Tungland, september 2017
