Synclavier Special Tuning Options

(NB: This document is taken from the original Synclavier II manual and should apply to ALL models of Synclavier)

 

Western Scale
Overall Tuning

Octave Ratio

Special Scales and Examples

More On Tuning

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The Western Scale

The standard Western scale divides the octave into twelve pitches with an equal interval, the semitone, between each pitch.  The six octaves of the Synclavier keyboard are based on the equal-tempered scale.  The A above middle C on the keyboard is assigned the frequency of 440.0 Hertz and the frequency of notes above and below middle A are computed by using the mathmatical ratio 1.059462.

Whenever you load the Synlcavier operating system, the keyboard will be perfectly tuned in this way, regardless of changes in temperature or humidity.  But you can quickly change the tuning of the Synclavier to play along with analog or acoustic instruments.

You can also change the intervals between the notes and establish special tunings.

As a quick reference, press the overall tuning button and use the control knob to change from standard pitch (440Hz) to concert pitch (442Hz) tuning.

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Overall Tuning

 

You can change the overall pitch of the keyboard by pressing the OVERALL TUNING button on the later VPK keyboard or the TUNING BASE button on the original ORK keyboard, and turning the silver control knob. (pressing repeatedly enables octave changes automatically)

Middle A, the tuning base, can be tuned in 0.1 Hertz intervals to any frequency between 00.0 and 1,760 Hertz. All other notes will change tune up or down correspondingly.

This tuning will remain in computer memory and will affect any notes you play in real time and any sequences you recall and play back.

When you alter the OVERALL TUNING of the Synclavier, you change it to an out-of-the-ordinary tuning for a special situation, rather than adjust it to standard pitch as you do with acoustic instruments.  The Synclavier is automatically tuned to standard pitch by default. Therefore changes in OVERALL TUNING are not saved when you store a sequence. When the sequence is later recalled it will play back in the current tuning of the keyboard.


Changing The Tuning

1. Press OVERALL TUNING (or TUNING BASE on early keyboard).

The OVERALL TUNING button will light up. 440.0 HERTZ will appear in the keyboard display panel. This indicates that the overall pitch of the Synclavier is tuned to A = 440 Hertz.

2. Now turn the knob to the left to lower the pitch, or to the right to raise it.

3. Press OVERALL TUNING again (or TUNING BASE on early keyboard).

The number in the keyboard display will change to 880.0 HERTZ

Besides doing precise tuning with the knob you can make instant OCTAVE changes in pitch. Each additional press will step you through octave tuning like so;

110.0 -- 220.0 -- 440.0 -- 880.0 -- 1760.0 -- 110.0 -- 220.0 -- etc. Hertz

4. Be sure to return to A = 440 tuning when you finish experimenting. The last tuning you establish will remain in effect until you restart the system.

 

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Octave Ratio

In the Synclavier the OCTAVE RATIO determines the relationship between the keyboard octave and the actual tonal octave. With the standard octave ratio of 1.000 every keyboard will also produce the perfect tonal octave; a doubling in frequency. By changing this ratio you can expand or contract the frequency range defined by the keyboard octave, and at the same time the interval between any two adjacent keys as well as the overall range of the keyboard. The pivot pitch around which the range will expand or contract is middle A (440.0 Hertz).

To change the octave ratio you press the OCTAVE RATIO button and dial a new ratio between 0.000 and 4.000. If you dial a ratio of 4.000 there will be a frequency range of four octaves for every keyboard octave and the interval between any two adjacent keys will be 1/3rd of an octave, or 4 semitones. If you dial in a ratio of 2.000 there will be a range of 2 octaves for every keyboard octave, the intervals between notes now being 1/6th of an octave or 2 semitones (1 whole tone).

Microtonal scales can be established by dialing octave ratios of less than 1.000. With an octave ratio of 0.000 every key on the keyboard will produce the same pitch.

The table below lists the OCTAVE RATIO settings for various intervals between adjacent keys on the keyboard.

INTERVAL SETTING
Semitone 1.000
Whole-tone 2.000
Quarter-tone 0.500
Microtones 0.001 to 0.999

 

The OCTAVE RATIO setting will remain in computer memory until you change it, recall a sequence or turn off the system. You can re-establish the equal-tempered scale at any time by pressing the OCTAVE RATION button twice or the SCALE RESET button twice. When you store a sequence the current OCTAVE RATIO will be saved along with it.


Establishing Quarter-Tone and Whole-Tone Scales

 1. Recall any timbre to the keyboard.

 2. Press OCTAVE RATIO.

The number 1.000 in the keyboard display indicates the standard octave ratio.

 3. Dial 0.500 with the control knob.

The interval between any two keys on the keyboard is now half a semitone - a quarter tone

 4. Dial 2.000.

Now the interval between any two keys is a whole tone.

 

 


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Special Scales

Besides changing the intervals between all the keys, you can change the relative pitch of any individual notes within the scale. Consider the octave of the keyboard starts with middle C. The fundamental frequencies of the notes produced by each of these 12 keys in the octave can be seen in the table below.

C3
261.6
 C#
277.1
D
293.7
 D#
311.1
E
329.5
F
349.3
 F#
370.1
G
391.9
 G#
415.5
A
440.0
 A#
466.1
B
493.9
C4
523.0

Since the C above middle C has a fundamental frequency of 523.0 hertz we can say the middle octave spans the frequency range of 261.6 to 523.0 Hertz.

Each of these twelve keys can be assigned any frequency in the middle octave range. To dial in a new scale you use the buttons in the HARMONIC CONTROL section of the keyboard (first panel on left). These 12 buttons have multiple functions - three separate harmonics, pitch/frequency control and auto loop control. (not all these functions are available on the Original Keyboard). First you press the PITCH CLASS (SCALE ADJUST on original keyboard) button to assign the pitch control function to the 12 buttons. Next you press a HARMONIC CONTROL button and turn the control knob to change the pitch of the corresponding third octave key. (button 1 = C3, button 2 = C#3 etc.) The frequencies of the same note in all other keyboard octaves will be changed to preserve the octave intervals. However, the other pitches in the scale will remain unaffected.

The adjusted tunings will be stored in computer memory until you turn off the system, change the tunings, recall a sequence or press the SCALE RESET button twice. Pressing SCALE RESET twice restores the tempered tuning up and down the keyboard.

Unlike OVERALL TUNING, you can save PITCH CLASS special scales to disk for a later time. Whenever you store a sequence to disk the current scale is also saved. So you can save the adjusted scale as a sequence even if it has no note events recorded.

There are many systems of tuning and temperament which can be precisely created on the Synclavier. The exercise below shows you how to dial in a just tuning in the key of D.

Establishing a Just Tuning in the key of D

 Recall a timbre to the keyboard.

 1. Press PITCH CLASS (SCALE ADJUST on original keyboard)

The PITCH CLASS/SCALE ADJUST button will light. The HARMONIC CONTROL buttons will now be assigned to the 12 pitches of the middle octave (C3 - B3), rather than the harmonic coefficients of an FM partial timbre.

 2. Select the pitch 'A' corresponding to the button as shown in the listing below;

HARMONIC CONTROL button
1 = C
2 = C#
3 = D
4 = D#
5 = E
6 = F
7 = F#
8 = G
9 = G#
10 = A
11 = A#
12 = B

You press HARMONIC CONTROL 10 to select A. The keyboard display will show '440.0 HERTZ A' referring to A3 on the keyboard indicating that A3 is tuned to 440.0 Hertz.

The programmable frequency range for this key (and all others in the third octave) is from 261.6 to 523.0 Hertz (see previous table).

The frequencies of the other 11 keys in the 3rd octave will remain unchanged as you tune A3.

 3. While holding the D and the A keys on the keyboard slowly dial 440.5 Hertz

You will be able to hear the interval transform from the equal tempered tuning into the acoustically pure 5th. (For a scale other than D chose the corresponding key).

 4. Play the other A's above and below on the keyboard.

You will notice that all the A keys track middle A as you change it's frequency. Their frequencies will remain a perfect octave apart.

 5. Now press the HARMONIC CONTROL button for A twice. (Button 10).

The A keys will return to tempered tuning.

 6. Now press the F# key (button 7) under HARMONIC CONTROL.

 7. While holding down the D and the F# key, tune the F# to 367.7

The interval between the D and the F# will become an acoustically pure major third.

 8. Now press HARMONIC SELECT. (Harmonic Group Select 1 on ORK keyboard)

The twelve HARMONIC buttons will now revert back to control of the first 12 harmonics in the partial timbre. The adjusted scale will be kept in computer memory and will continue to affect the sound triggered by every F# key on the keyboard.

 9. Press SCALE RESET twice.

The complete equal-tempered scale will be restored.

At any time, perhaps after a particular passage in a composition, you can instantly return to the equal-tempered scale by pressing the SCALE RESET button twice.

For your convenience, we have included a few tables which list specific settings for just intonation in the ky of C and the key of A, as well as Pythagorean and mean-tone tuning for the key of A.

The first table below indicates the Synclavier settings for just intonation for twochromatic scales. The frequencies in each list are all relative to the base frequency - C = 261.6 or A = 440.0.

 

Table of Just Intonation For Two Chromatic Scales

Base of C (Hz)
Ratio

Base of A (Hz)

Result for base A
before dividing by 2
C
 = 261.6
A
 = 440.0
 
C#
 = 272.5
25/24
A#
 = 458.3
 
Db
 = 279.0
16/15
Bb
 = 469.3
 
D
 = 294.3
9/8
B
 = 495.0
 
D#
 = 306.5
75/64
B#
 =515.8
 
Eb
 = 314.1
6/5
C
 = 264.1
528.0
E
 = 328.1
5/4
C#
 = 275.1
550.0
F
 = 348.8
4/3
D
 = 293.3
586.7
F#
 = 368.0
45/32
D#
 = 309.3
618.8
G
 = 392.4
3/2
E
 = 330.0
660.0
G#
 = 409.0
25/16
E#
 = 344.0
687.5
Ab
 = 418.5
8/5
F
 = 351.9
704.0
A
 = 435.9
5/3
F#
 = 366.7
733.3
Bb
 = 470.9
9/5
G
 = 396.1
792.0
B
 = 490.6
15/8
G#
 = 412.6 825.0

Note 1: In the C scale, the A relative to C as a base frequency is 436.0.
Note 2: In the A scale, the frequencies above B# were calculated using the appropriate ratios and then divided by 2 in order to arrive at the settings within the middle octave range. The actual frequencies of those upper tones are listed in the right column.

Note 3: In both scales when enharmonically equivalent tones (such as C sharp and D flat) differ in pitch, you must chose one or the other for tuning.

 

The following table shows Synclavier settings for just, mean-tone, and Pythagorean tuning for diatonic scales in the key of A. The standard equal temperament tuning is listed for comparison.

Four Diatonic Scales in the Key of A

Note

Equal Temperament
Just Intonation
Pythagorean
Mean-Tone
 C#
277.1
275.1
278.5
275.3
D
293.7
293.3
293.3
optional
E
329.5
330.0
330.0
329.1
 F#
370.1
366.7
371.2
368.0
 G#
415.5
412.6
417.7
optional
A
440.0
440.0
440.0
440.0
tuning base
B
493.9
495.0
495.0
492.1

Note: In the mean-tone scale in the key of A, the tuning of D and G# varies according to the taste of the performer.

 

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More On Tuning

You can combine the OCTAVE RATIO and PITCH CLASS functions. If you have changed the range of the middle octave by establishing a different OCTAVE RATIO, the HARMONIC CONTROL buttons will still change the pitch of the keys corresponding to each button. Frequency intervals will be contracted or expanded by the OCTAVE RATIO.

You can also use the OVERALL TUNING button to adjust the overall pitch (tuning) of the keyboard that has been redefined by the OCTAVE RATIO and PITCH CLASS functions. The entire keyboard of frequencies, with any established overall range or scale relationships can be tuned up or down by 0.1 Hertz increments.

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