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?
432HZ - A SHORT TIME-LINE
Before 432Hz became the "core frequency" of the 432-tuning concept, there was no pitch standard and various other concert pitches were used. One of these concert pitches does has a "connection" with the 432-tuning concept. This pitch of C4=256Hz is called the "Scientific Pitch", or "Sauveur Pitch" or "Verdi Pitch". Due to it's "connection" these historical references will be listed below as well.
C = 128Hz & 256Hz
French physicist Joseph Sauveur suggested in 1713 using C4=256Hz as concert pitch. In the years that follow, Ernst Chladni (a leading acoustician in his time), defined C=256Hz as the "scientific tuning" in his textbook on the theory of music. What temperament should be used was not specified, it is thus unclear if 432Hz would actually be used.
Italian composer Giuseppe Verdi supported and promotes C4=256Hz for a period of time in the middle and/or late 1800's. Verdi is said to have supported the French pitch standard (Diapason Normal) of 435Hz as well, but NOT 432Hz in particular. What temperament should be used was not specified by Verdi.
Rudolf Steiner (the founder of Anthroposophy) mentioned C=128Hz, representing the "Sun" during one of his lectures. He did not specify the temperament to use, nor did he mention 432Hz.
Hans Cousto discovers the "original frequency" of the sun (32.312,52Hz) and calculates its 8th lower octave to 126,22Hz.
A = 432HZ
Maria Renold publishes the first edition of her book "Intervals, Scales, Tones and the Concert Pitch 128 Hz" — a book based on Rudolf Steiner's suggestion of using C=128Hz. This is one of the better documented tuning concepts called "the Scale of Fifths" where both 256Hz and 432Hz appear "side-by-side".
The Schiller Institute (the organization of activist Lyndon H. LaRouche) and Dr. Jonathan Tennenbaum insist that 256Hz is the correct reference frequency (middle C), that consequently sets A4 to 430.5 cycles (12-TET) and 432 cycles (JI / Pythegorean Temperament) and associate the frequency of 432Hz with the name “Verdi Tuning” (perhaps not a good "choice": Verdi supported 256Hz and 435Hz, not 432Hz in particular.
The first issue of “Fidelio Magazine” got published by the Schiller Institute together with LaRouche’s own political magazine “Executive Intelligence Review” (Volume 15, Number 32) from 1988, are the principal sources that "triggered" the entire 432Hz campaign. The articles “The Foundations of Scientific Musical Tuning” and “Revive Verdi's tuning to bring back great music” are both available online.
Ananda Bosman publishes his article “Universal Dances: A Musical Congruence towards the Global Song of the Omega Revolution” after reading 'classical musicians Jonathan Tennenbaum’s essay on 432Hz tuning' (“The Foundations of Scientific Musical Tuning” from “Fidelio Magazine” mentioned above), founding a new music trend first envisioned by him in 1997. The purpose is to "implement a harmonic music revolution in rave culture, using 8Hz and harmonic tuning in equal tempering."
Brian T Collins starts the Omega432 website. He strongly supports the Maria Renold Temperament "Scale of Fifths" (see Roel's World article).
Jamie Buturff makes a few videos and publishes them on YouTube, advocating a "Pythagorean" scale where A4=432 Hz. Jamie Buturff introduces a multiplication table of doubles and triples of the number 1, called “The Most Harmonic Numbers/Frequencies” (see Roel's World article) which lists all the tone-numbers of the chromatic scale in "Pythagorean" tuning.
Eric Rankin publishes his “Sonic Geometry: The Language of Frequency and Form” video, where he introduces the “Factor 9” Grid tuning of tones, which is nothing more than overtones 14 to 28 from the harmonic series (27 omitted), having as 1/1 the many-fold doubling of 9 Hz: 126. In hist first video several frequencies are missing in his grid though ... more information about his video in the Roel's World article "432Hz & the Factor 9".
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 ]►