Video: TouchKeys + Yarman-24c maqam tuning

Hi everyone,

A while back I posted about an instrument I've been working on called TouchKeys, which adds touch sensing to the surface of the keyboard. Microtonal music was one of the applications I was interested to pursue, since you can configure the key sensors to play different tunings depending on where you strike the key (so 24, 36 or more tones per octave become possible on a traditional keyboard).

Through this group I met Ozan Yarman (Dr. Oz.) who has developed some really interesting tuning systems for Turkish maqam music. The video below uses the Yarman-24c tuning system mapped onto the touch sensors to play different maqams in quick succession:

http://www.youtube.com/watch?v=-QcYgslHq9k

Just thought I would share it here since it's where the ideas some of the ideas originated.

Andrew

:)

Many thanks to my dear colleague Andrew McPherson for his excellent collaboration leading to this charming video. The mapping of the Yarman-24 pitches to TouchKeys was done like this:

LAYER 1 (lower tactile area from key C to key c)
===== ratios given are approximates only =====

1/1 or 0 cents C Dbb unison, perfect prime RAST ♥
21/20 or 83.059 cents C# Db nim zengule
9/8 or 203.910 cents D Ebb major whole tone DÜGAH ♥
58/49 or 292.413 cents D# Eb kürdi
156/125 or 383.542 cents E SEGAH ♥
4/3 or 498.045 cents F Gbb perfect fourth ÇARGAH ♥
7/5 or 581.382 cents F# Gb nim hicaz
187/125 or 697.332 cents G Abb perfect fifth NEVA ♥
41/26 or 788.736 cents G# Ab nim hisar
27/16 or 905.865 cents A Bbb Pyth. major sixth HÜSEYNİ ♥ 440Hz
16/9 or 996.090 cents A# Bb Pyth. minor seventh acem
234/125 or 1085.497 cents B EVİÇ ♥
2/1 or 1200.000 cents c Dbb octave GERDANİYE ♥

MIDI pitch bends of LAYER 1

key
12-tET deg.
cent offset
MIDI pitch bend
C Dbb
0
-5.865
-240
C# Db
100
-20.80607
-852
D Ebb
200
-1.955
-80
D# Eb
300
-13.45203
-551
E Fb
400
-22.32348
-914
F Gbb
500
-7.82
-320
F# Gb
600
-24.4831
-1003
G Abb
700
-8.53279
-350
G# Ab
800
-17.12905
-702
A Bbb
900
0
0
A# Bb
1000
-9.775
-400
B Cb
1100
-20.36848
-834
C Dbb
1200
-5.865
-240

LAYER 2 (upper tactile area from key C> to key c>)
===== ratios given are approximates only =====

67/70 or -75.256 cents B gevasht
88/81 or 143.623 cents Dƀ zengule
19/17 or 191.771 cents Dd dik zengule
11/9 or 348.343 cents Eƀ dik kürdi
69/56 or 362.503 cents Ed nerm segah
75/59 or 415.305 cents E‡ buselik
75/52 or 634.184 cents Gƀ hicaz
16/11 or 648.682 cents Gd bestenigar
18/11 or 853.063 cents Aƀ hisar
117/70 or 887.656 cents Ad dik hisar
42/23 or 1043.623 cents Bƀ dik acem
13/7 or 1071.942 cents Bd nerm eviç
67/35 or 1124.744 cents B‡ mahur

MIDI pitch bends of LAYER 2

key
12-tET deg.
cent offset
MIDI pitch bend
C
0
-81.12077
-3323
C# Db
100
37.75845
1547
D Ebb
200
-14.09424
-577
D# Eb
300
42.47826
1740
E Fb
400
-43.36232
-1776
F
500
-90.56038
-3709
F# Gb
600
28.31884
1160
G
700
-57.18294
-2342
G# Ab
800
47.19806
1933
A Bbb
900
-18.20886
-746
A# Bb
1000
37.75845
1547
B Cb
1100
-33.92271
-1389
C
1200
-81.12077
-3323

>
> We have prudently decided not to use the "MIDI pitch bends of LAYER 2, alternative mapping from closest 12-EDO degree" below, since it would have required haphazard re-assignment of MIDI note numbers over to conventionally existing note numbers at the same keys at several places:
>
> key
> 12-tET deg.
> cent offset
> MIDI pitch bend
> B Cb
> -100
> 18.87923
> 773
> C# Db
> 100
> 37.75845
> 1547
> D Ebb
> 200
> -14.09424
> -577
> D# Eb
> 300
> 42.47826
> 1740
> E Fb
> 400
> -43.36232
> -1776
> E Fb
> 400
> 9.43962
> 387
> F# Gb
> 600
> 28.31884
> 1160
> F# Gb
> 600
> 42.81706
> 1754
> G# Ab
> 800
> 47.19806
> 1933
> A Bbb
> 900
> -18.20886
> -746
> A# Bb
> 1000
> 37.75845
> 1547
> B Cb
> 1100
> -33.92271
> -1389
> B Cb
> 1100
> 18.87923
> 773
>

Therefore, the following was the result:

LOWER UPPER LAYER1 PB value LAYER2 PB value

C C -240 -3323
C# C# -852 1547
D D -80 -577
D# D# -551 1740
E E -914 -1776
F F -320 -3709
F# F# -1003 1160
G G -350 -2342
G# G# -702 1933
A A 0 -746 ===440Hz===
A# Bb -400 1547
B B -834 -1389
c c -240 -3323 OCTAVE

Cordially,
Dr. Oz.

✩ ✩ ✩
www.ozanyarman.com

On Nov 2, 2013, at 2:20 AM, <andrewpmcpherson@yahoo.com> wrote:

>
>
> Hi everyone,
>
>
> A while back I posted about an instrument I've been working on called TouchKeys, which adds touch sensing to the surface of the keyboard. Microtonal music was one of the applications I was interested to pursue, since you can configure the key sensors to play different tunings depending on where you strike the key (so 24, 36 or more tones per octave become possible on a traditional keyboard).
>
> Through this group I met Ozan Yarman (Dr. Oz.) who has developed some really interesting tuning systems for Turkish maqam music. The video below uses the Yarman-24c tuning system mapped onto the touch sensors to play different maqams in quick succession:
>
> http://www.youtube.com/watch?v=-QcYgslHq9k
>
> Just thought I would share it here since it's where the ideas some of the ideas originated.
>
> Andrew
>
>
>

Interesting.

Just few pragmatic questions:
Why so many decimal points (3 or even 5) for cent deviations? Which
instrument can perform it? Which human being can recognize it?
Anyway I suppose it's lost when converted to MIDI PB resolution...

Concerning this, so high numbers looks like you count with 14 bit
resolution for PB, but not every instrument use full PB resolution,
most of them only 7 bit, some 8 or 9 bits. Why not to use retuned notes on instruments equipped with microtonality?

Also different PB data means that it's necessary to use different MIDI
channels for those two layers. But this shouldn't be a big problem, we
can assign the same sound to them.

Daniel Forro

On 2 Nov, 2013, at 10:15 AM, Ozan Yarman wrote:

>
>
> :)
>
> Many thanks to my dear colleague Andrew McPherson for his excellent
> collaboration leading to this charming video. The mapping of the
> Yarman-24 pitches to TouchKeys was done like this:
>
>
>
> LAYER 1 (lower tactile area from key C to key c)
> ===== ratios given are approximates only =====
>
> 1/1 or 0 cents C Dbb unison, perfect prime RAST ♥
> 21/20 or 83.059 cents C# Db nim zengule
> 9/8 or 203.910 cents D Ebb major whole tone DÜGAH ♥
> 58/49 or 292.413 cents D# Eb kürdi
> 156/125 or 383.542 cents E SEGAH ♥
> 4/3 or 498.045 cents F Gbb perfect fourth ÇARGAH ♥
> 7/5 or 581.382 cents F# Gb nim hicaz
> 187/125 or 697.332 cents G Abb perfect fifth NEVA ♥
> 41/26 or 788.736 cents G# Ab nim hisar
> 27/16 or 905.865 cents A Bbb Pyth. major sixth HÜSEYNİ
> ♥ 440Hz
> 16/9 or 996.090 cents A# Bb Pyth. minor seventh acem
> 234/125 or 1085.497 cents B EVİÇ ♥
> 2/1 or 1200.000 cents c Dbb octave GERDANİYE ♥
>
>
> MIDI pitch bends of LAYER 1
>
> key
> 12-tET deg.
> cent offset
> MIDI pitch bend
> C Dbb
> 0
> -5.865
> -240
> C# Db
> 100
> -20.80607
> -852
> D Ebb
> 200
> -1.955
> -80
> D# Eb
> 300
> -13.45203
> -551
> E Fb
> 400
> -22.32348
> -914
> F Gbb
> 500
> -7.82
> -320
> F# Gb
> 600
> -24.4831
> -1003
> G Abb
> 700
> -8.53279
> -350
> G# Ab
> 800
> -17.12905
> -702
> A Bbb
> 900
> 0
> 0
> A# Bb
> 1000
> -9.775
> -400
> B Cb
> 1100
> -20.36848
> -834
> C Dbb
> 1200
> -5.865
> -240
>
>
>
>
>
>
> LAYER 2 (upper tactile area from key C> to key c>)
> ===== ratios given are approximates only =====
>
> 67/70 or -75.256 cents B gevasht
> 88/81 or 143.623 cents Dƀ zengule
> 19/17 or 191.771 cents Dd dik zengule
> 11/9 or 348.343 cents Eƀ dik kürdi
> 69/56 or 362.503 cents Ed nerm segah
> 75/59 or 415.305 cents E‡ buselik
> 75/52 or 634.184 cents Gƀ hicaz
> 16/11 or 648.682 cents Gd bestenigar
> 18/11 or 853.063 cents Aƀ hisar
> 117/70 or 887.656 cents Ad dik hisar
> 42/23 or 1043.623 cents Bƀ dik acem
> 13/7 or 1071.942 cents Bd nerm eviç
> 67/35 or 1124.744 cents B‡ mahur
>
>
> MIDI pitch bends of LAYER 2
>
> key
> 12-tET deg.
> cent offset
> MIDI pitch bend
> C
> 0
> -81.12077
> -3323
> C# Db
> 100
> 37.75845
> 1547
> D Ebb
> 200
> -14.09424
> -577
> D# Eb
> 300
> 42.47826
> 1740
> E Fb
> 400
> -43.36232
> -1776
> F
> 500
> -90.56038
> -3709
> F# Gb
> 600
> 28.31884
> 1160
> G
> 700
> -57.18294
> -2342
> G# Ab
> 800
> 47.19806
> 1933
> A Bbb
> 900
> -18.20886
> -746
> A# Bb
> 1000
> 37.75845
> 1547
> B Cb
> 1100
> -33.92271
> -1389
> C
> 1200
> -81.12077
> -3323
>
>
>>
>> We have prudently decided not to use the "MIDI pitch bends of LAYER
>> 2, alternative mapping from closest 12-EDO degree" below, since it
>> would have required haphazard re-assignment of MIDI note numbers
>> over to conventionally existing note numbers at the same keys at
>> several places:
>>
>> key
>> 12-tET deg.
>> cent offset
>> MIDI pitch bend
>> B Cb
>> -100
>> 18.87923
>> 773
>> C# Db
>> 100
>> 37.75845
>> 1547
>> D Ebb
>> 200
>> -14.09424
>> -577
>> D# Eb
>> 300
>> 42.47826
>> 1740
>> E Fb
>> 400
>> -43.36232
>> -1776
>> E Fb
>> 400
>> 9.43962
>> 387
>> F# Gb
>> 600
>> 28.31884
>> 1160
>> F# Gb
>> 600
>> 42.81706
>> 1754
>> G# Ab
>> 800
>> 47.19806
>> 1933
>> A Bbb
>> 900
>> -18.20886
>> -746
>> A# Bb
>> 1000
>> 37.75845
>> 1547
>> B Cb
>> 1100
>> -33.92271
>> -1389
>> B Cb
>> 1100
>> 18.87923
>> 773
>>
>
>
>
> Therefore, the following was the result:
>
>
>
> LOWER UPPER LAYER1 PB value LAYER2 PB value
>
> C C -240 -3323
> C# C# -852 1547
> D D -80 -577
> D# D# -551 1740
> E E -914 -1776
> F F -320 -3709
> F# F# -1003 1160
> G G -350 -2342
> G# G# -702 1933
> A A 0 -746 ===440Hz===
> A# Bb -400 1547
> B B -834 -1389
> c c -240 -3323 OCTAVE
>
>
>
> Cordially,
> Dr. Oz.
>
>
> ✩ ✩ ✩
> www.ozanyarman.com
>
> On Nov 2, 2013, at 2:20 AM, <andrewpmcpherson@yahoo.com> wrote:
>
>>
>>
>> Hi everyone,
>>
>>
>> A while back I posted about an instrument I've been working on
>> called TouchKeys, which adds touch sensing to the surface of the
>> keyboard. Microtonal music was one of the applications I was
>> interested to pursue, since you can configure the key sensors to
>> play different tunings depending on where you strike the key (so
>> 24, 36 or more tones per octave become possible on a traditional
>> keyboard).
>>
>> Through this group I met Ozan Yarman (Dr. Oz.) who has developed
>> some really interesting tuning systems for Turkish maqam music. The
>> video below uses the Yarman-24c tuning system mapped onto the touch
>> sensors to play different maqams in quick succession:
>>
>> http://www.youtube.com/watch?v=-QcYgslHq9k
>>
>> Just thought I would share it here since it's where the ideas some
>> of the ideas originated.
>>
>> Andrew
>>
>>
>
>
>
>

Yes Daniel, those cent decimals only serve as screen clutter here, but I'm so very fond of the representation of numeric detail. Anyway, as you noticed, they are rounded off to whole integers in PB resolution.

Unfortunately, TouchKeys only works through a computer interface using a special software for now. That's why the 14-bit PB resolution is not only a good idea, it is necessary. Until Andrew can figure out a way to re-direct the stream of PB data into the synthesizer's chip, we are condemned to use a computer router to hear Touchkeys in action.

Herein comes Robert Walker with his excellent implementation of my "keyswitch retuning" suggestion to use the topmost MIDI notes' velocities for single-channel tuning of all pitches:

http://robertinventor.com/ftswiki/Velocity_keyswitches_retuning

These two technologies combined can help us modify or create keyboards that can singlehandedly perform the Yarman-24c layout or any other layout one might like to have without need to connect to a computer setup.

Cordially,
Dr. Oz.

✩ ✩ ✩
www.ozanyarman.com

On Nov 2, 2013, at 3:43 AM, Daniel Forró wrote:

>
>
> Interesting.
>
> Just few pragmatic questions:
> Why so many decimal points (3 or even 5) for cent deviations? Which instrument can perform it? Which human being can recognize it?
> Anyway I suppose it's lost when converted to MIDI PB resolution...
>
> Concerning this, so high numbers looks like you count with 14 bit resolution for PB, but not every instrument use full PB resolution, most of them only 7 bit, some 8 or 9 bits. Why not to use retuned notes on instruments equipped with microtonality?
>
> Also different PB data means that it's necessary to use different MIDI channels for those two layers. But this shouldn't be a big problem, we can assign the same sound to them.
>
> Daniel Forro
>
>
> On 2 Nov, 2013, at 10:15 AM, Ozan Yarman wrote:
>
>>
>>
>> :)
>>
>> Many thanks to my dear colleague Andrew McPherson for his excellent collaboration leading to this charming video. The mapping of the Yarman-24 pitches to TouchKeys was done like this:
>>
>>
>>
>> LAYER 1 (lower tactile area from key C to key c)
>> ===== ratios given are approximates only =====
>>
>> 1/1 or 0 cents C Dbb unison, perfect prime RAST ♥
>> 21/20 or 83.059 cents C# Db nim zengule
>> 9/8 or 203.910 cents D Ebb major whole tone DÜGAH ♥
>> 58/49 or 292.413 cents D# Eb kürdi
>> 156/125 or 383.542 cents E SEGAH ♥
>> 4/3 or 498.045 cents F Gbb perfect fourth ÇARGAH ♥
>> 7/5 or 581.382 cents F# Gb nim hicaz
>> 187/125 or 697.332 cents G Abb perfect fifth NEVA ♥
>> 41/26 or 788.736 cents G# Ab nim hisar
>> 27/16 or 905.865 cents A Bbb Pyth. major sixth HÜSEYNİ ♥ 440Hz
>> 16/9 or 996.090 cents A# Bb Pyth. minor seventh acem
>> 234/125 or 1085.497 cents B EVİÇ ♥
>> 2/1 or 1200.000 cents c Dbb octave GERDANİYE ♥
>>
>>
>> MIDI pitch bends of LAYER 1
>>
>> key
>> 12-tET deg.
>> cent offset
>> MIDI pitch bend
>> C Dbb
>> 0
>> -5.865
>> -240
>> C# Db
>> 100
>> -20.80607
>> -852
>> D Ebb
>> 200
>> -1.955
>> -80
>> D# Eb
>> 300
>> -13.45203
>> -551
>> E Fb
>> 400
>> -22.32348
>> -914
>> F Gbb
>> 500
>> -7.82
>> -320
>> F# Gb
>> 600
>> -24.4831
>> -1003
>> G Abb
>> 700
>> -8.53279
>> -350
>> G# Ab
>> 800
>> -17.12905
>> -702
>> A Bbb
>> 900
>> 0
>> 0
>> A# Bb
>> 1000
>> -9.775
>> -400
>> B Cb
>> 1100
>> -20.36848
>> -834
>> C Dbb
>> 1200
>> -5.865
>> -240
>>
>>
>>
>>
>>
>>
>> LAYER 2 (upper tactile area from key C> to key c>)
>> ===== ratios given are approximates only =====
>>
>> 67/70 or -75.256 cents B gevasht
>> 88/81 or 143.623 cents Dƀ zengule
>> 19/17 or 191.771 cents Dd dik zengule
>> 11/9 or 348.343 cents Eƀ dik kürdi
>> 69/56 or 362.503 cents Ed nerm segah
>> 75/59 or 415.305 cents E‡ buselik
>> 75/52 or 634.184 cents Gƀ hicaz
>> 16/11 or 648.682 cents Gd bestenigar
>> 18/11 or 853.063 cents Aƀ hisar
>> 117/70 or 887.656 cents Ad dik hisar
>> 42/23 or 1043.623 cents Bƀ dik acem
>> 13/7 or 1071.942 cents Bd nerm eviç
>> 67/35 or 1124.744 cents B‡ mahur
>>
>>
>> MIDI pitch bends of LAYER 2
>>
>> key
>> 12-tET deg.
>> cent offset
>> MIDI pitch bend
>> C
>> 0
>> -81.12077
>> -3323
>> C# Db
>> 100
>> 37.75845
>> 1547
>> D Ebb
>> 200
>> -14.09424
>> -577
>> D# Eb
>> 300
>> 42.47826
>> 1740
>> E Fb
>> 400
>> -43.36232
>> -1776
>> F
>> 500
>> -90.56038
>> -3709
>> F# Gb
>> 600
>> 28.31884
>> 1160
>> G
>> 700
>> -57.18294
>> -2342
>> G# Ab
>> 800
>> 47.19806
>> 1933
>> A Bbb
>> 900
>> -18.20886
>> -746
>> A# Bb
>> 1000
>> 37.75845
>> 1547
>> B Cb
>> 1100
>> -33.92271
>> -1389
>> C
>> 1200
>> -81.12077
>> -3323
>>
>>
>>>
>>> We have prudently decided not to use the "MIDI pitch bends of LAYER 2, alternative mapping from closest 12-EDO degree" below, since it would have required haphazard re-assignment of MIDI note numbers over to conventionally existing note numbers at the same keys at several places:
>>>
>>> key
>>> 12-tET deg.
>>> cent offset
>>> MIDI pitch bend
>>> B Cb
>>> -100
>>> 18.87923
>>> 773
>>> C# Db
>>> 100
>>> 37.75845
>>> 1547
>>> D Ebb
>>> 200
>>> -14.09424
>>> -577
>>> D# Eb
>>> 300
>>> 42.47826
>>> 1740
>>> E Fb
>>> 400
>>> -43.36232
>>> -1776
>>> E Fb
>>> 400
>>> 9.43962
>>> 387
>>> F# Gb
>>> 600
>>> 28.31884
>>> 1160
>>> F# Gb
>>> 600
>>> 42.81706
>>> 1754
>>> G# Ab
>>> 800
>>> 47.19806
>>> 1933
>>> A Bbb
>>> 900
>>> -18.20886
>>> -746
>>> A# Bb
>>> 1000
>>> 37.75845
>>> 1547
>>> B Cb
>>> 1100
>>> -33.92271
>>> -1389
>>> B Cb
>>> 1100
>>> 18.87923
>>> 773
>>>
>>
>>
>>
>> Therefore, the following was the result:
>>
>>
>>
>> LOWER UPPER LAYER1 PB value LAYER2 PB value
>>
>> C C -240 -3323
>> C# C# -852 1547
>> D D -80 -577
>> D# D# -551 1740
>> E E -914 -1776
>> F F -320 -3709
>> F# F# -1003 1160
>> G G -350 -2342
>> G# G# -702 1933
>> A A 0 -746 ===440Hz===
>> A# Bb -400 1547
>> B B -834 -1389
>> c c -240 -3323 OCTAVE
>>
>>
>>
>> Cordially,
>> Dr. Oz.
>>
>>
>> ✩ ✩ ✩
>> www.ozanyarman.com
>>
>> On Nov 2, 2013, at 2:20 AM, <andrewpmcpherson@...> wrote:
>>
>>>
>>>
>>> Hi everyone,
>>>
>>>
>>> A while back I posted about an instrument I've been working on called TouchKeys, which adds touch sensing to the surface of the keyboard. Microtonal music was one of the applications I was interested to pursue, since you can configure the key sensors to play different tunings depending on where you strike the key (so 24, 36 or more tones per octave become possible on a traditional keyboard).
>>>
>>> Through this group I met Ozan Yarman (Dr. Oz.) who has developed some really interesting tuning systems for Turkish maqam music. The video below uses the Yarman-24c tuning system mapped onto the touch sensors to play different maqams in quick succession:
>>>
>>> http://www.youtube.com/watch?v=-QcYgslHq9k
>>>
>>> Just thought I would share it here since it's where the ideas some of the ideas originated.
>>>
>>> Andrew
>>>
>>>
>>
>>
>>
>
>
>
>

Hi Daniel,

Good points. The PB resolution depends in part on the overall pitch bend range. The trombone instrument I use in the video (Sample Modeling) has a 3-semitone PB range. That's 300 cents for 8192 steps = .04 cents per tick. Clearly this will be well beyond what's audible.

Interestingly, even if only 7 bits are used, that's still 2.3 cents resolution, which is probably just barely audible. Also possibly of interest: Apple appears to use 48-semitone pitch bend resolution on its iPad-Logic interface. Even at that extreme of a range, you can still achieve 0.5 cent precision on the pitch wheel. So probably 14 bits are enough.

It's true that to do this kind of thing polyphonically, you need multiple identically-configured MIDI channels. (Since the trombone examples were mono, I used one channel.) Basically, it's the usual headache for multitimbral instruments.

On the TouchKeys, the benefits of implementing it with pitch wheel rather than with a pre-tuned instrument are (1) you can easily change microtunings on the fly, and (2) you can also add vibrato and pitch bends independently per note. The drawback is that some instruments, especially some wind/string emulations, will also change the timbre on a pitch bend to simulate what happens on a real instrument-- not always the desired effect.

Andrew

---In makemicromusic@yahoogroups.com, <dan.for@...> wrote:

Interesting.

Just few pragmatic questions:
Why so many decimal points (3 or even 5) for cent deviations? Which instrument can perform it? Which human being can recognize it?
Anyway I suppose it's lost when converted to MIDI PB resolution...

Concerning this, so high numbers looks like you count with 14 bit resolution for PB, but not every instrument use full PB resolution, most of them only 7 bit, some 8 or 9 bits. Why not to use retuned notes on instruments equipped with microtonality?

Also different PB data means that it's necessary to use different MIDI channels for those two layers. But this shouldn't be a big problem, we can assign the same sound to them.

Daniel Forro

On 2 Nov, 2013, at 10:15 AM, Ozan Yarman wrote:

:)

Many thanks to my dear colleague Andrew McPherson for his excellent collaboration leading to this charming video. The mapping of the Yarman-24 pitches to TouchKeys was done like this:

LAYER 1 (lower tactile area from key C to key c)
===== ratios given are approximates only =====

1/1 or 0 cents C Dbb unison, perfect prime RAST ♥
21/20 or 83.059 cents C# Db nim zengule
9/8 or 203.910 cents D Ebb major whole tone DÜGAH ♥
58/49 or 292.413 cents D# Eb kürdi
156/125 or 383.542 cents E SEGAH ♥
4/3 or 498.045 cents F Gbb perfect fourth ÇARGAH ♥
7/5 or 581.382 cents F# Gb nim hicaz
187/125 or 697.332 cents G Abb perfect fifth NEVA ♥
41/26 or 788.736 cents G# Ab nim hisar
27/16 or 905.865 cents A Bbb Pyth. major sixth HÜSEYNİ ♥ 440Hz
16/9 or 996.090 cents A# Bb Pyth. minor seventh acem
234/125 or 1085.497 cents B EVİÇ ♥
2/1 or 1200.000 cents c Dbb octave GERDANİYE ♥

MIDI pitch bends of LAYER 1

key
12-tET deg.
cent offset
MIDI pitch bend
C Dbb
0
-5.865
-240
C# Db
100
-20.80607
-852
D Ebb
200
-1.955
-80
D# Eb
300
-13.45203
-551
E Fb
400
-22.32348
-914
F Gbb
500
-7.82
-320
F# Gb
600
-24.4831
-1003
G Abb
700
-8.53279
-350
G# Ab
800
-17.12905
-702
A Bbb
900
0
0
A# Bb
1000
-9.775
-400
B Cb
1100
-20.36848
-834
C Dbb
1200
-5.865
-240

LAYER 2 (upper tactile area from key C> to key c>)
===== ratios given are approximates only =====

67/70 or -75.256 cents B gevasht
88/81 or 143.623 cents Dƀ zengule
19/17 or 191.771 cents Dd dik zengule
11/9 or 348.343 cents Eƀ dik kürdi
69/56 or 362.503 cents Ed nerm segah
75/59 or 415.305 cents E‡ buselik
75/52 or 634.184 cents Gƀ hicaz
16/11 or 648.682 cents Gd bestenigar
18/11 or 853.063 cents Aƀ hisar
117/70 or 887.656 cents Ad dik hisar
42/23 or 1043.623 cents Bƀ dik acem
13/7 or 1071.942 cents Bd nerm eviç
67/35 or 1124.744 cents B‡ mahur

MIDI pitch bends of LAYER 2

key
12-tET deg.
cent offset
MIDI pitch bend
C
0
-81.12077
-3323
C# Db
100
37.75845
1547
D Ebb
200
-14.09424
-577
D# Eb
300
42.47826
1740
E Fb
400
-43.36232
-1776
F