(ARTICLE LAST UPDATED ON: 24.02.2015)
432 TUNING BASICS - INTRODUCTION
When you browse the internet for information about “432 Tuning”, you come across various interpretations and rumors on this topic. But, is the argumentation used correct?
If might be useful to read a bit more about the various rumors and myths before we focus on the actual tuning specifications. Therefor I compiled a blog article that shares more information about some the more persistent "claims" often made in 432-related articles, presented as "evidence" to "validate" the 432-tuning concept. To me those claims generally look more like "sales pitches" - (rather then tone pitches ;) - or a method to appeal to people's desire for "mystical" and "uber-magical" experiences.
So, if you like to sort out what is of real importance about 432-tuning and what not, you might like reading my article:
432... WHAT IS RELATED AND WHAT NOT?
432 TUNING IS:
What a Tuning System is: Concert Pitch + Musical Interval System / Temperament.
(If you do not know these terms, then please read this first!)
A Concert Pitch WITHOUT a Temperament defined is NOT a Tuning System. For more information about the difference between Tuning System and Concert Pitch, read this blog: "Concert Pitch vs Tuning System".
- C4=256Hz (Scientific Pitch)
IMPORTANT: When using the Scientific Pitch (C4=256Hz) there are no proper alternatives for the Pythagorean Temperament! Any other temperament used with C4=256Hz, will not result in A4=432Hz. The difference between C4=256Hz and A4=432Hz is 905.8650025961624 cents. This interval is known as the "Pythagorean major sixth" (ratio 27/16).
For example if C4=256Hz, then:
- (5-Limit) Just Intonation: A4=426.6Hz (426,666∞Hz)
- Werckmeister I: A4=427.6Hz (427.5650147473363Hz)
- Werckmeister II: A4=428.5Hz (428.45503625389244Hz)
- Werckmeister III: A4=430.5Hz (430.53896460991314Hz)
- 12-Tone Equal Temperament: A4=430.5Hz (430.53824925657256Hz)
According to John Charles Francis Bach might have used various temperaments that (in relationship with C4=256Hz) would set A4 to: 426.6Hz, 428.5Hz, 429.8Hz, 430.3Hz, 432hz and 433.8Hz. The temperaments mentioned by J. C. Francis created by Bach were based on a combination of Perfect Fifths and tempered Fifths (1/3 syntonic comma).
MUSICAL INTERVAL SYSTEM
12 tone closed system.
The Pythagorean temperament (stacking of perfect fifths) is been noted as the only correct temperament when we talk about 432-tuning. The Most Harmonic Numbers concept is based on it, as is Maria Renold's "Scale of Fifths".
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2, "found in 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.
More information: Wikipedia
RECOMMENDED (ALT.) INTERPRETATION OF THE PYTHAGOREAN TEMPERAMENT:
"TWELVE TRUE FIFTHS TUNING" - RENOLD I & II (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)."
ALTERNATIVES FOR THE PYTHAGOREAN TEMPERAMENT?
Within the "432-Tuning community" there are those who favor other temperaments due to certain "limitations" of the traditional 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:
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 ] ►
A VARIANT I SOMETIMES USE DUE TO INSTRUMENT LIMITATIONS
MOST HARMONIC NUMBERS - TONIC CONCERT PITCH CONCEPT
The MHN TCP variant is a (partly modified) implementation/interpretation of the 432-Tuning concept. It's made for those instruments that can not be "Micro-tuned" (From Equal Temperament to Pythagorean).
[ Read More ] ►
PITCHING ... HOW TO?
A common misunderstanding about "432 Tuning" is the idea that one would simply change the concert pitch from 440Hz to 432Hz (-8Hz, -0.31766... cents). As mentioned in the beginning of this blog, "432-Tuning" and "Concert Pitch A4=432Hz" is not the same thing. [ "Concert Pitch vs Tuning System" ]►
How to change the Concert Pitch + Temperament of existing audio files? [ Read More ]►
How to change the Concert Pitch only of existing audio files? [ Read More ]►
REAL-TIME 432 AUTO-PITCHING MUSIC PLAYERS
For all who have some difficulties working with sound editors, maybe a music player with real-time pitch control provides the solution. If you just like to listen to your music from your PC or Laptop (Windows, OS X and a Linux alternative), iPhone and Android, using some applications might provide the easiest method to get in tune with Concert Pitch 432!
[ Read More ]►