(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.

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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.

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.

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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.

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.

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

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: 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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