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CONCERT PITCH vs TUNING SYSTEM

(A COMMON MISUNDERSTANDING)

A common misunderstanding when it comes to 432-Tuning is that many people do not understand the difference between “concert pitch” and “tuning system”. If you do not know the difference, then please, read this first!

In short:
Concert Pitch 432Hz = using reference tone A4=432Hz to tune to, without Temperamental specifications.
432-Tuning = using the reference tone A4=432Hz in combination with Pythagorean Temperament (or variation).


WHY IS ONLY CHANGING THE CONCERT PITCH NOT ENOUGH?

Well, when a piece was recorded using for example the 12-Tone Equal Temperament (12-TET, the present standard), pitching the whole piece down with -0.3166… cents is not sufficient. The “intervallic” relationship between the tones has not changed, when a change of Concert Pitch is implemented. Even though the A would then be in tune with 432-Tuning, the other 11 tones are still off pitch. The Temperament is still Equal Temperament. 

EXAMPLE: 12-TONE EQUAL TEMPERAMENT (the present standard)

In twelve-tone equal temperament, which divides the octave into 12 equal parts, the width of a semitone, i.e. the frequency ratio of the interval between two adjacent notes, is the twelfth root of two:

\sqrt[12]{2}=2^{\frac{1}{12}}\approx 1.059463

There are many other Musical Temperaments (most more complicated then 12-TET), using various mathematical formulas to create other ratios then 1.059463. The most know Temperaments are the: Pythagorean TuningMeantone TemperamentWell TemperamentJust Intonation and Five-Limit Tuning.

If your intentions are to use the 432-TUNING SYSTEM (not just 432Hz as Concert Pitch) you also need to implement The Pythagorean Temperament.


432 TUNING – USING THE PYTHAGOREAN TEMPERAMENT

PYTHAGOREAN TEMPERAMENT
The Pythagorean temperament is been noted as the only correct temperament when we talk about 432-tuning. The Most Harmonic Numbers concept uses this method.

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2,  a ratio from the harmonic series. This ratio, also known as the “pure” or perfect fifth, is chosen because it is one of the most consonant intervals and easy to tune on by ear.

The Pythagorean Temperament is thus one of the oldest known “Just Intonation” (3-limit) Temperaments.

More information: Wikipedia

IMPORTANTWhen using the Scientific Pitch (C4=256Hz) and you wish A4 to be 432Hz as well, then there are NO alternatives for the Pythagorean Temperament (and variations on it)! Any other temperament used with C4=256Hz, will not result in A4=432Hz but by example with 12-TET in A4=430.5Hz (430.53824925657256Hz).


THE BEST ALTERNATIVE IMPLEMENTATION OF THE PYTHAGOREAN TEMPERAMENT:

TWELVE TRUE FIFTHS TUNING” (BY MARIA RENOLD)
Graham H Jackson explains this tuning system on his web site as follows: 

“For the “twelve true-5ths tuning”: you first set C at 256 Hz. Then you tune the 7 “white keys” by the circle of 5ths, using however natural 5ths. Then you divide the octave at C exactly in half (which can be done handily with a special tuning fork), and tune the 5 “black keys” by natural 5ths to that F#. You end up with two series of natural 5ths–one of 7 notes and one of 5 notes, linked by an “unnatural” interval of an augmented 4th (which is actually the same augmented 4th found in the equal-tempered system).” [ Read More ] ►

OTHER ALTERNATIVES FOR THE PYTHAGOREAN TEMPERAMENT?

Within the “432-Tuning community” there are those who favor other temperaments due to certain “limitations” of the Pythagorean Temperament, or simply because they prefer the usage of other perfect intervals (like a perfect Third) over the Perfect Fifth. If you could still call these methods of tuning “432-Tuning” is questionable (see blog “Concert Pitch” vs “Tuning System“).

Most popular alternative temperaments (not based on Perfect Fifths) used in combination with A4=432Hz are:

JUST INTONATION

In music, just intonation (sometimes abbreviated as JI) or pure intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a pure or just interval. The two notes in any just interval are members of the same harmonic series. Frequency ratios involving large integers such as 1024:927 are not generally said to be justly tuned. Just intonation is the tuning system of the later ancient Greek modes as codified by Ptolemy. More information: Wikipedia | XenHarmonic

FIVE-LIMITED TUNING (diatonic scale)

Five-limit tuning, or 5-limit tuning is a method to obtain a justly tuned musical scale. The frequencies of the notes of such a scale are obtained by multiplying the frequency of a given reference note (the base note) by powers of 2, 3, or 5, or a combination of them. More information: Wikipedia | XenHarmonic

FIBONACCI + CONCERT PITCH A4=432Hz

The clearest demonstration of Fibonacci being represented in music is seen in scales. 13: the Octave is made of 12 chromatic tones plus 1 the octave. A (basic) scale is composed of 8 notes. The 5th and 3rd notes create basic foundation of chords, based off a whole tone that is 2 steps above root tone, which is the 1st note of scale. Ratios found in the first 7 numbers of the Fibonacci series (0, 1, 1, 2, 3, 5, 8) are related to key frequencies of musical notes.
Read More ] ►


POST-PRODUCTION RE-PITCHING

CHANGING THE CONCERT PITCH IN POST PRODUCTION

If you would only like to change the concert pitch, then there are two ways to do so.

1) PREFERED OPTION: CHANGING THE SPEED
When you change the speed of a piece of music, both Tempo and Pitch will change. This method is the equivalent of slowing down a turntable. In order to get a -31.667 cents pitch change, you should reduce the speed with -1.818%.

How to: A “2-step” instruction how to change the Concert Pitch with Software.

2) SECONDARY OPTION: CHANGING THE PITCH
When you change the Concert Pitch from 440Hz to 432Hz, you need to pitch the audio-material down with -31.76665363342977 cents or -0.3176665363342977 semitones. If the software or hardware you use only allows you to use round numbers, you can set it to -31 or -32 cents. For electronic music -31 cents might work better (since that music is generally required to be more “punchy”), for acoustic music -32 cents seems to work out best in most cases.

IMPORTANT NOTE: When only changing the pitch and not the tempo, there will be resolution loss, and the high-end sounds might sound “fake”. That’s why option 1 (changing the speed) is the preferred option!


Q: CAN YOU RE-TUNE AND (RE-)TEMPER A COMPLETE SONG AT ONCE?

A: A complete song (1 file, for example .wav or .mp3 file) with various instruments tuned to 440Hz + 12-TET, can NOT be re-tuned to 432-Tuning (432Hz + Pythagorean or related Temperament). 

You can still pitch it -31.667…cents down, so the Concert Pitch changes from 440Hz to 432Hz, but the piece will not be “in tune” with the 432-TUNING SYSTEM, simply because the temperament has not been changed from 12-TET to Pythagorean (as explained at the introduction to 432-Tuning).

IF you have recorded the instruments on separate tracks though, a lot can be done! 

Some instruments that can not change the Concert Pitch and/or Temperament – or might be too hard to intonate when used with another concert pitch and/or temperament then they were designed for – can be re-pitched and (re-)tempered in post production (after recording). This is sometimes the “only option”, specially when working with instruments with tone-holes / valves / pistons (particularly conical wood winds / brass) or those that are made out of one piece (Didgeridoo, Penny Whistle, et cetera), as well as melodic percussive instruments (like Vibraphone, Marimba, et cetera). Unfortunately there is no solution for these (acoustic) instruments when performing live. 

How to: Change Concert Pitch + Temperament with Software

Some online sources proclaim re-pitching music from Concert Pitch A4=440Hz to 432Hz will positively effect the “overtones”. This is not true! [ Read More ] ►


RECORDING IN THE RIGHT PITCH & TEMPERAMENT IS BEST!

Every form of “manipulation” will cause loss of quality to a recorded sound. The better the algorithm used with the software, the smaller the loss. Nonetheless, it is always preferable to tune the instruments you like to record to the right pitch and temperament, if possible.

Some online sources proclaim 432-recorded music has more “Overtones” then 440-recorded music.
This is not true! [ Read More ] ►


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