Blog » 432Hz Saxophone Redesign Lobby

Reading Time: 5 minutes October 14, 2014

432HZ SAXOPHONE REDESIGN LOBBY

I started this 432Hz Saxophone Redesign Lobby in December 2011, without much success. All companies I wrote e-mails and letters to did not seem to be interested. But In December 2014 – 3 years later – the 432Hz Sax was a fact, thanks to Enrico Marchioro and Borgani Saxophones.

► Read more about it in my blog article “Borgani 432 Sax“.

► Skip the introduction about this lobby and read more about “alternative solutions” for playing saxophone “in 432”.

WHY A “LOBBY” FOR REDESIGNING A SAXOPHONE FOR CONCERT PITCH A4=432HZ?

The Saxophone is an instrument with relatively limited tuning capabilities. The pitch of a saxophone can only be adjusted a little “mechanically” by pulling out or pushing in the mouthpiece. Yes, a saxophonist can use his/her embouchure and use alternate fingering to make intonation changes, but the instrument itself should be overall in tune to start with. 

A saxophone can not be pitched by adding extensions (unlike instruments with a cylindrical bore like Flute or Clarinet). The tone-holes have been placed in exact relationship with the length of the instrument and the change in diameter of the conical bore. If one would only extend the instrument, the position of the tone-holes would no longer be correct and there for result in some tones being out of tune.

In order to be able to play in tune with Concert Pitch A4=432Hz without limiting it’s playability the sax needs to be “redesigned”.

This “lobby” does not intend to replace the existing saxophones used. Instruments are often too much part of who we have become as artist and human being to set them aside. But we like to create the option for sax players to play in 432Hz when possible and desired. To add “new members” to the “saxophone-family”.

ADDITIONAL INFORMATION ABOUT THE SAXOPHONE AND THE CHANGE OF CONCERT PITCH

Most saxophones stay reasonably in tune when the pitch difference is small, +/- 2Hz higher or lower then the concert pitch instrument was designed for. So, a saxophone designed for the standard 440Hz concert pitch, would still sound reasonable when using by example concert pitch 442Hz or 438Hz.

Larger changes in concert pitch though, would cause an intonation difference between the registers that would be too large to correct with the embouchure alone, specially with uptempo music.

Mr. Fletcher James (Schiller Institute) mentioned about saxophones and pitch change (440Hz – 435/432Hz): 

  • There are 20-23 keys and keyholes to be adjusted, and there are all sorts of inter-linked mechanisms which would need to be re-sized. Existing jigs for manufacturing (which are essential for inexpensive mass production of metal parts) could not be used at all.
  • Because of the length of the scale, just pulling out the headjoint will affect the highest note 4 times as much as the lowest.
  • Because of the length of the scale, any attempt to just insert a little space at a couple of points in the instrument would probably end up causing a lot of tuning issues. 

PITCH STANDARDS BRASS & WOODWINDS

There are at present time two different concert pitch standards used for Brass and Wood-Wind instruments. These are the so called “Low Pitch” (LP = 440/442Hz) and “High Pitch” (HP = 456/457Hz). The High Pitch instruments are/were designed and build for American Brass bands and some Military Orchestras. Their sound is sharper / louder then the sound of the Low Pitch instruments in order to not be “overtaken” (sound/volume wise) by larges numbers of noisy people, street noise and battle noise. Most Brass and Wood-Winds (like Saxophones) are engraved with “LP” or “HP” to clarify the concert pitch the instrument was build for.

There use to be another pitch standard used in France only, the so called Diapason Normal with A4=435Hz. Till WWII such instruments were made in Europe (mainly in France, Belgium and Germany). There are also brass & woodwind instruments available at A4=394Hz and 410Hz, specially designed for particular classical music genres such as Baroque and there are some old historical wind instruments in museums that use A4=425Hz to A4=430.5Hz. These are rare instruments though and do not represent an international pitch “standard”.

ALTERNATIVE SOLUTIONS

Besides the option of having a 432-Sax build by Borgani, are there perhaps other solutions? The answer is yes, there are 3 alternative approaches of playing Saxophone in 432Hz.

1. USING HIGH PITCH (HP) INSTRUMENTS
Alan Gen, a member of the Sax On The Web forum, made a suggestion that could solve the issue of 432Hz and saxophones. He suggested using a HP (High Pitch) instrument (in various sources set as A4 = 456Hz / 457Hz) and transposing a semitone down. It might sound like a contradiction to “raise the pitch” in order to “drop it” but in practice it ain’t.

When lower A4=456Hz with a equal tempered semitone (-100 cents), you will end up with A4=430.4Hz. When lower A4=457Hz with a equal tempered semitone (-100 cents), you will end up with A4=431.4Hz. In both cases close to 432Hz. With other words, a HP instrument is pretty much “in tune” with A4=432Hz and can be perfectly in tune by pushing the mouthpiece in a tiny bit more the usually. The only thing one should do, is instead of providing sheet music for Bb (Soprano & Tenor) and Eb (Alto & Baritone) saxophones, is now to provide sheets written a semitone lower then normally for the saxophone is done.

2. USING INSTRUMENTS DESIGNED FOR THE “DIAPASON NORMAL”
Using a vintage sax made for the old French standard (Diapason Normal) of A4=435Hz would put you on a 3Hz difference. This would still require you to “pull out” your mouthpiece more then usual and might mean you have to make some additional intonation “corrections” with alternative fingering and/or embouchure, but is very well possible. More info in my blog article Vintage 435Hz Saxophones.

3. USING ALTERNATE FINGERING
With woodwind instruments like the saxophone it is possible to generate tones outside the normal 12-tone range of the instrument by using “alternate fingerings”. Examples of this are the 24-tone scale by Tony Hicks and the 128-tone scale by Philipp Gerschlauer. Some of the tones generated in 440Hz with the alternate fingerings in the 128-tone scale come pretty close to the tones of the 432Hz scale.

The exact fingerings used might differ with the instrument brand and model used and it will take you a lot of time to master those additional fingerings. It would be an interesting option to explore, because you would not need to purchase a different instrument. It is though very time-consuming if you wish to master your instrument this way.

WHAT’S NEXT?

At present time saxophone manufacturer Borgani is the only company who has produced a 432 Saxophone. This is a great step forward for those musicians, composers and music lovers that wish to play, compose for or listen to live saxophone using Concert Pitch A4=432Hz. Read more about it in my blog article “Borgani 432 Sax“.

The Borgani saxophones are handmade professional instruments. They are worth the investment if you are a pro, but for hobby saxophonists and beginners these great horns might be too costly.

The willingness for other manufacturers to (re)design saxophones for concert pitch A4=432Hz as well might increase if the number of saxophones requested to be build increase first. So, if you are a sax player, or know a sax player that would like to be able to perform tuned to 432 Hz, then feel free to join the 432Hz Saxophone Redesign Lobby group on Facebook so we can share thoughts  and ideas about it and stay “up-to-date” on the developments. 

KUDOS: the background image used for the banner of this article was made by Ian Monk.


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Blog » Why using a lower Pitch then the standard of A4=440Hz?

Reading Time: 11 minutes October 14, 2014

WHY USING A LOWER PITCH THEN THE STANDARD OF A4=440HZ?

There would be various subjective reasons I could give, like that it sounds and feels better to me, but that might just be a matter of taste … I could also quote various authors that shared philosophical and/or “spiritual” point of views, but you could set that aside as a form of belief, superstition or religion … or even “pseudo-science” … right?

So, I will share some general information about sound, vibration and resonance in this blog article and will try to explain what the possible results can be when changing the pitch, on both instrument sound and the surroundings (room acoustics).
I this article the following topics:


SOUND, VIBRATION, RESONANCE AND HEARING

The human ear can nominally hear sounds in the range 20Hz to 20,000Hz (20kHz). The upper limit tends to decrease with age; most adults are unable to hear above 17 kHz. The lowest frequency that has been identified as a musical tone is 12Hz (under ideal laboratory conditions). Tones between 4 and 16 Hz can be perceived via the body’s “sense of touch“.

Higher frequencies tend to be more directional than lower frequencies. Low frequencies, due to the bigger distance between the peaks and troughs of the wave tend to “bend around” objects that are in their path (sometimes maintain it’s shape). High frequencies have smaller distances between the peaks and troughs of the wave, they are very tightly packed and have the tendency to “bounce off” or get “reflected” by objects in their path.

Frequency resolution of the ear is 0.9Hz within the octave of C4=256Hz and C5=512Hz. With other words, changes in pitch larger than 0.9 Hz can be perceived by most. Musicians and sound engineers (“trained ears”) can pick up smaller pitch changes than that. Smaller pitch differences can also be perceived through other means, the interference of two pitches can often be heard as beating

Sound travels through air, water and solid matter, all examples of mediums for sound. Without a medium (vacuum: space) there are no particles to carry the sound waves. Particles vibrate at a specific frequency for each source, called it’s natural frequency. Steel, brass, wood, (et cetera) all have different natural frequencies. Objects vibrating at their natural frequencies will cause resonance. Most vibrating objects have multiple resonant frequencies.

The frequency of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium. The frequency of a wave is measured as the number of complete back-and-forth vibrations of a particle of the medium per unit of time. As a sound wave moves through a medium, each particle of the medium vibrates at the same frequency. This is sensible since each particle vibrates due to the motion of its nearest neighbor. 

When an object is forced into resonance vibrations at one of its natural frequencies, it vibrates in a manner such that a standing wave is formed within the object. The natural frequencies of an object are merely the harmonic frequencies at which standing wave patterns are established within the object. Objects are most easily forced into resonance vibrations when disturbed at frequencies associated with these natural frequencies.

Acoustic resonance is important for hearing. For example, resonance of a stiff structural element called the basilar membrane within the cochlea of the inner ear, allows hair cells on the membrane to detect sound. Hearing is not a purely mechanical phenomenon of wave propagation, but is also a sensory and perceptual event; in other words, when a person hears something, that something arrives at the ear as a mechanical sound wave traveling through the air, but within the ear it is transformed into neural action potentials. These nerve pulses then travel to the brain where they are perceived.

The speed of sound in air is much less than that in water (and the human body is contains for a large part water).  When sound changes mediums, or enters a different material, it is bent from its original direction. This change in angle of direction is called refraction. Because of the angle, part of the wave enters the new medium first and changes speed. The difference in speeds causes the wave to bend. This means that there is an acoustic impedance difference between the air and the body.

The amount of energy that is transported past a given area of the medium per unit of time is known as the intensity of the sound wave. The greater the amplitude of vibrations of the particles of the medium, the greater the rate at which energy is transported through it, and the more intense that the sound wave is. Loudness (intensity) does primary depend on the amplitude of the wave, but it could also depend upon the frequency. If the sound is not a single frequency (sine wave), then the “loudness” depends upon the distribution of overtones of the fundamental (the ‘pitch’) as well.

Everything, even air, absorbs sound. One example of air absorbing sound waves happens during a thunderstorm. When you are very close to a storm, you hear thunder as a sharp crack. When the storm is farther away, you hear a low rumble instead. This is because air absorbs high frequencies more easily than low. By the time the thunder has reached you, all the high pitches are lost and only the low ones can be heard. The displacement in a medium of a high frequency wave is more than a lower frequency wave, more energy is lost with the higher frequency. With that energy lost, the overall amplitude of the higher frequency wave would have decreased a lot more than of a lower frequency wave.


VIBRATION AND RESONANCE OF ACOUSTIC AND ELECTRIC STRING INSTRUMENTS

When we pluck or strike a string of a string instrument this string (source) starts to vibrate. Waves of sound energy then move outward in all directions from the string. The string vibrates at all the frequencies present in the impulse (an impulsive function theoretically contains ‘all’ frequencies). Those frequencies that are not one of the resonances are quickly filtered out — they are attenuated — and all that is left is the harmonic vibrations that we hear as a musical note. Usually a vibrating string produces a sound whose frequencies in most cases are constant. 

Part of the vibrations generated by the string will transfer through the “bridge“, “tailpiece” and “pegbox” or “headstock” to the body of the instrument. With other words: the instrument itself will vibrate and resonates along with the vibrating strings. The tendency of one object to force another adjoining or interconnected object into vibrational motion is referred to as a “Forced Vibration“. In the case of the guitar string mounted to the sound box, the fact that the surface area of the sound box is greater than the surface area of the string means that more surrounding air particles will be forced into vibration. This causes an increase in the amplitude and thus loudness of the sound.

“Air resonance” plays a role as well with acoustic string instruments. The f-holes of a violin for example form the opening of a cavity resonator (sound chamber of an instrument) which in the resonance curve for the Stradivarius shown enhances frequencies close to the open string D4 at 294Hz. The larger the opening to the cavity, the higher the frequency (air can rush in and out faster). An air cavity will exhibit a single resonant frequency. A larger volume gives a lower frequency (more air needs to move out to relieve the pressure exess).

Using a different tuning system is not uncommon among guitarists. One of the most used alternative is the so called “E♭ (E‐flat) tuning or D♯ (D‐sharp) tuning“. All of the strings are lowered by one semitone (100 cents). This is where the present A4=440Hz pitch standard and the “Baroque Pitch” of A4=415Hz come together (the difference between 440Hz and 415Hz is 101 cents). The reason why various guitarists tuned this way are a heavier tone / change of timbre, the possibility to use of heavier strings without decreasing playability and/or greater string flexibility (for “pull-ups”) without losing compatibility with 440Hz tuned instruments. Some of the most famous guitarists tuned their guitar this way, like Jimi Hendrix and Stevie Ray Vaughan.

A semitone (or even whole tone) pitch change is not what this blog article is about, but is useful information for a better understanding of the effects of pitch change.

VIBRATION OF THE VOCAL FOLDS

The vocal folds, also known commonly as vocal cords or voice reeds, are composed of twin infoldings of mucous membrane stretched horizontally, from back to front, across the larynx. They vibrate, modulating the flow of air being expelled from the lungs during phonation. The perceived pitch of a person’s voice is determined by a number of different factors, most importantly the fundamental frequency of the sound generated by the larynx.

Some vocalists – who have experimented with various pitches – do seem to prefer pitches lower then 440Hz. To keep a tone stable the vocal chords (muscles) need to “hold” the tension required for that particular tone. The higher the tension on the vocal chords required, the harder it will be to hold that tension. When the pitch is lowered, the tension on the vocal chords decreases as well.

VIBRATION AND RESONANCE OF WIND INSTRUMENTS

A wind instrument contains some type of resonator (usually a tube), in which a column of air is set into vibration by the player blowing into (or over) a mouthpiece set at the end of the resonator. The resonant frequencies of air columns of wind instruments depend upon the speed of sound in air as well as the length and geometry of the air column. 

The woodwind instruments use only the first few resonances of air columns and depend upon opening holes in the sides of the air columns to ascend in pitch. 
The brass instruments employ a large number of resonances (harmonics) of their air columns and make use of valves or slides to lengthen the air columns for a downward progression of pitches.

A cylindrical air column with both ends open will vibrate with a fundamental mode such that the air column length is one half the wavelength of the sound wave. The open air column can produce all harmonics. Open cylinders are employed musically in the flute, the recorder, and the open organ pipe. 

A closed cylindrical air column will produce resonant standing waves at a fundamental frequency and at odd harmonics. The constraint of the closed end prevents the column from producing the even harmonics. The clarinet consists of an approximate closed cylinder, and this makes clarinet acoustics quite different from the other woodwind instruments.|
 
A conical air column will produce the same fundamental frequency as an open cylinder of the same length and will also produce all harmonics. Conical air columns are employed in several of the woodwind musical instruments: oboe, bassoon, saxophone, and others. 

ELECTRONIC INSTRUMENTS AND PITCH CHANGE

Changing the pitch of electronic music instruments such as (software) synthesizers and (software) samplers has less effect in comparison to that of acoustic instruments (and electric musical instruments). The physical characteristics (mass, weight, volume and density, vibratory nature of the medium, et cetera) of electronic instruments (the hardware) does not play a role in the creation of its sound itself, the “synthetic” or “sampled” sounds of the instruments will be generated with exactly the same algorhythms

The only effect that the change of pitch can have for electronic instruments, is when the sound becomes “airborne”, starts floating around and “collides” and “interacts” with the room and objects in it. 

!!! What is important to be aware of though, is that it is pretty useless to change the pitch with exactly one semitone (to 415Hz, the “Baroque Pitch”) if you are using electronic instruments. There is after all no change of timbre – as mentioned above – and the frequencies responding to the keys are still the same (they simply have moved a key up or down) and thus the frequency “response” of all 12 tones, the resonate with and “reflection” of the sound with the room is practically the same.


SO, WHY LOWER THE CONCERT PITCH? (CONCLUSION)

“What changes at the source?” and “How does these changes at the source effect the surrounding space?”.

CHANGES AT THE SOURCE

For some instrumentalists a lower pitch could make a performance easier. A lower pitch would mean less tension on the strings of an instrument (and vocal chords as well), there for less “energy” is required to set the source “in motion”. Lower tension on a string would also mean that you could pull a string further up, with other words you have more flexibility to pitch-up a tone. 

A lower pitch would also mean a possible difference in natural frequency response, generating difference in resonance of the instrument itself. Due to the change of resonance of the instrument the “timbre” could change as well (also depending on the material the instrument is made of and the vibratory nature of that material).

Low frequencies do not displace as much energy as high frequencies do, but they contain the energy better. By lowering the pitch the vibration and resonance (within the instrument and the air in resonators) could lasts longer (more sustain / longer decay time).

THE EFFECTS ON THE SURROUNDING SPACE

As mentioned earlier in this article we know that high frequencies tend to “bounce of” anything in their path, while lower frequencies tend to “bend around” those objects. Even though the difference between using Concert Pitch 440Hz or 432Hz is relatively small, the “reflection” of sound from the objects it is surrounded by and the room (where the the source is in) is a little less. This is most clear with the hi-end frequencies like for example hi-hats and cymbal splashes. In particular in places with a lot of hard surfaces (concrete, glass, et cetera) a (small) difference in reflection/absorption and resonance can be heard. In the open air the difference in reflection and resonance between using Concert Pitch 440Hz and 432Hz is not really detectable though.

When using powerful sound systems or loud acoustic instruments, a part of the vibrations generated with that sound system or instruments might find resonance in the room where the sound is generated. The natural frequencies of the matter of this this room might resonate differently. After all, lower frequencies generate less energy displacement then high frequencies do, thus a little less response in resonance from the natural frequencies of the room.

HOW LOW SHOULD YOU GO?

Well, you might like to try 435Hz (Diapason Normal) or 432Hz … or lower? I suggest you start exploring the options yourself, at the end music is about you expressing yourself the way that suits you best, right? I will though sum-up a few low pitches used in music history, you can start your own “research” from there …

THE HISTORICALLY LOWEST MENTIONED PITCH USED FOR A4 (AT 360HZ)

If we take a look at the last couple of centuries we notice pitches as low as A4=360Hz (English pitchpipe organs) have been used. To put that in perspective: 370Hz is exactly to 3 semitions (300 cents) below 440Hz.

THE “BAROQUE PITCH” (A4=415HZ)
This pitch was commonly used during the “Baroque period” (1600-1760). 415Hz is 101 cents or 1.01 semitone below the present 440Hz standard. With other words, Concert Pitch 440Hz is 415Hz transposed a semitone up. A4=415Hz as Concert Pitch might be an option when using acoustic instruments (due to differences in resonance and timbre). When using electronic instruments this pitch-shift is useless (see information earlier in this article).

THE “SCIENTIFIC PITCH” C4=256HZ (A4=430.5-432HZ)
Also known as also known as philosophical pitch, Sauveur pitch or Verdi tuning, was first proposed in 1713 by French physicist Joseph Sauveur, promoted briefly by Italian composer Giuseppe Verdi in the 19th century, then advocated by the Schiller Institute beginning in the 1980s. All the octaves of C are an exact round number in the binary system. The exact pitch of A4 depends on the Temperament you use. If you use Equal Tone Temperament we find A4 at 430.5Hz, but if you use the Pythagorean Temperament you will find A4 at 432Hz. Other Temperaments could generate different results for the exact pitch of A4 when using C4=256Hz as Concert Pitch.

THE “DIAPASON NORMAL” (A4=435HZ)
In 1859 (February 16), the French government passed a law to set the National Standard to A4=435Hz, the only official (law binding) National concert pitch in recorded history. 

ARE THERE ANY DISADVANTAGES USING A LOWER PITCH?

Unfortunately YES, there are …
The biggest disadvantage of using a lower (or higher) pitch then the present standard A4=440Hz is the tuning difficulties/issues that occur when using particular instruments. Not all instruments can change Concert Pitch!!! It is important to be aware of this when composing and producing music.

  • If you intend to perform live using a different Concert Pitch, then make sure the instruments of the the musicians you invite for the gig can handle a pitch change. I the blog article “Instruments & Tuning” you can read more about this.
  • If you only compose and produce in order to release music, then it is possible to change the pitch (and temperament) in post production for those instruments that do not handle the pitch change well, if all instruments were recorded on separate tracks. More info about this in the articles: “How to: Changing the Concert Pitch” and “How to: Changing the Concert Pitch + Temperament“.

Another disadvantage about using a different Concert Pitch is one for DJ’s. Mixing tracks that use different Concert Pitches does sound horrible, the dissonance can be mood-killing. Naturally DJ’s could re-pitch their whole repertoire (time consuming), or play only tracks produced using the same Concert Pitch (limits repertoire). Fixing the difference in Concert Pitch real-time is at present time (2014) no proper solution, not even with modern DJ gear such as “Traktor” or “Serato“.


AFTERWORD

Now, I do like to make clear that the difference between the present A4=440Hz pitch standard and the A4=435Hz (“Diapason Normal”) or A4=432Hz & C4=256Hz as Concert Pitch will not be a difference of “night and day”.

Using another (lower) Concert Pitch such as A4=432Hz is not like some “magic trick” that will make a piece of music suddenly sound great that if played and recorded the same way but 8Hz higher (at 440Hz) would not sound very well. The “intention” (passion, energy, et cetera) of the performers and “mastery” of both musicians and sound engineers still play the biggest role when it comes to something sounding great. 

A different pitch might create a different “perspective” … A lower pitch (then A4=440Hz) might enlarge the sensation of an extended “dimensionality” at best, but only if that dimensionality was there to begin with. 432-Tuning nor any other Concert Pitch or temperament can “create” what isn’t there to begin with … and that does start with the composition itself, the story that is going to be told, and stands or falls with the accomplishments of the total of artists involved.

Concert Pitch 432Hz is perhaps more something you could call “fingerspitzengefühl” … that is, for those who have “ear” for it. 

What really changes the way a piece of music sounds like is the change of Temperament … 

 SOURCES:

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Blog » 432Hz … A “Special” Frequency?

Reading Time: 3 minutes June 20, 2014

432HZ OR 444Hz/528Hz… “SPECIAL” FREQUENCIES?

In this article I will share my OPINION about this matter. It is how I see it … you may agree or you may disagree, or perhaps you have a completely different idea about it all. In case you don’t agree, I would like to ask you kindly to have the decency to respect my personal point of view and treat it as such.

From my experience with sound I can say that the effect that sound has on us is often underestimated or misunderstood.

On various sites and fora “special qualities” are given to the frequency of 432Hz (432-Tuning), as well as to frequencies like 444Hz and 528Hz (another tuning concept, the “Ancient Solfeggio Tones“). Some would describe this frequency as “divine”, “mystical” or “magical” and even claims of great healing power are subscribed to it. Sound to me is not that kind of “special”, to me it’s simply part of nature, of all. I do not feel the need to place “fancy labels” on it like it’s some “sales pitch” or so. Nothing is more (or less) “special” then anything else, everything simply is.

I think pretty much everyone has experienced sound physically, for example when standing close to a sub-woofer one can not only feel the air displacement caused by the movement of the speaker, but you can actually feel the low frequencies “wobbling” in your stomach. Or what about the reflexes triggered by a sharp squeaking sound (like for example fingernails scratching over a chalkboard): goosebumps, cold shivers and pulling up your shoulders unintentionally. Sound can also effect us mentally. The sound of crashing waves on the beach, the wind gently blowing through the tree leaves, or perhaps the gentle dripping of the rain on a roof window could sooth the mind. Nervousness and irritation can be experienced with sounds that annoy us, like a neighbor drilling holes in the wall or pounding drum beats coming from the party next door. 

I think it is safe to say that the sound that we are surrounded by (or we surround ourselves with) can have a direct relationship with our well-being. The idea of “sound-healing” is thus not as strange as you might think.

BUT … I personally do not “believe” in “one size fits all”, specially when it comes to spirituality, life and the universe we live in. We are all unique beings with our own unique characteristics. We have our own unique brainwave responses (responses to external “stimuli”, together forming a “brain fingerprint”) and even features as bone density, mass, et cetera could effect the way we perceive the sound that surrounds us. Even the shape our ears plays a role in how we perceive sound. 

If our perception of sound differs, then it is logical to assume that a particular frequency could effect people differently. With other words, particular “divine”, “mystical” or “magical” frequencies do not really exist, other then in the minds of some people who wish to “believe” in something special, or perhaps do so to keep faith in life. 

That there are particular frequencies that might effect you (the individual) positively is undeniable and that within certain frequencies ranges more people seem to respond is not strange either. There are besides differences similarities as well between us human beings. Nonetheless, the proclamed “healing frequencies for all” concept seems to me like an over-simplification of nature itself and lacks the awareness and understanding of the diversity and uniqueness of every individual. 

Besides that … that someone can compose and produce music is one thing. To be able to “read” people correctly to provide a custom “piece of music” for a particular medical problem is something else. Healing is a gift … all posses it, but not all master it.

Ofcourse … this is just my opinion …

Now, just a short audio-fragment from something Abraham Hicks shared … just because it’s interesting and I like it.

https://youtu.be/IO06wKzr5tI?si=5BbYzjDC4Cu-mXKf

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Blog » ⚠ 432Hz and “the Factor 9”

Reading Time: 7 minutes March 1, 2014

432 & THE “FACTOR 9”

The Factor 9 concept is mentioned in the video called “Sonic Geometry: The Language of Frequency and Form” (by Eric Rankin and Alanna Luna). In this article we will take a closer look at the Factor 9 “formula”, it’s relationship to the Harmonic Series and the difference between the Factor 9 and “standard” temperamental implementation. 

Official Website: www.sonicgeometry.com

SECOND VIDEO (2016) 

FIRST VIDEO (2015)

NOTE: The number grid shown in the first video (12:52) contains some mistakes, more about this later

FACTOR 9 AND THE HARMONIC SERIES OF D=9HZ

The “base frequency” or “Fundamental” of this grid is 9Hz. The other tones are the result of the implementation of the Harmonic Series. Depending on the Harmonic used as “starting point” of the a scale a different Musical Interval System is formed. 

The number of tones in the scale formed from the Harmonic Series relates directly to the number of the Harmonic you start with. If you start from the 15th Harmonic, you would end up with a 15-Tone scale. This is not only the case when you use 9Hz as base frequency for this concept, this is simply the “nature” of the Harmonic Series.

For example:

12TH HARMONIC (TONIC A): 12-TONE SYSTEM

When we use A2=108Hz the first degree of the scale (12th-24th Harmonic of 9Hz) to it’s octave A3=216Hz, we would end up with a 12-Tone Temperament. On octave above 216Hz we find A4=432Hz.

14TH HARMONIC (TONIC C): 14-TONE SYSTEM

When we use C3=126Hz the first degree of the scale (14th-28th Harmonic of 9Hz) to it’s octave C4=252Hz, we would end up with a 14-Tone Temperament.

16TH HARMONIC (TONIC D): 16-TONE SYSTEM

When we use D3=144Hz as the first degree of the scale (16th-32nd Harmonic of 9Hz) to it’s octave D=288Hz, we would end up with a 16-Tone Temperament. D4=288Hz is a pretty familiar frequency for those who have been exploring 432-Tuning. We find the D4 at 288Hz with various 12-Tone Temperaments, such as the Pythagorean Temperament (in combination with Concert Pitch C4=256Hz or A4=432Hz) and Maria Renold’s “Scale of Fifths“.  If you would like to use the 16-EDO system with Concert Pitch A4=432Hz, all frequencies (listed in the 3rd column) need to be pitched up with approximately 62 cents, the 16-EDO scale has “A4” at 416.8Hz, instead of 432Hz.

FACTOR 9 12T vs. 12-EDO vs. FIBONACCI-8 vs. RENOLD-I

The most “common” 12-tone scale belongs to 12-TET (12-Tone Equal Temperament) or 12-EDO (Equal Divisions of the Octave). I will try to “visualize” the difference between the “Factor 9 Temperament” and 12-TET in this article.  If you do not know what a tuning system is made of, then please do read this article on my blog: Tuning Basics.

ABOUT 12-TET or 12-EDO

12EDO, perhaps better known as 12TET since it really is a temperament, is the predominating tuning system in the world today. It achieved that position because it is the smallest equal division which can seriously claim to represent 5-limit harmony, and because as 1/12 Pythagorean comma (approximately 1/11 syntonic comma) meantone, it represents meantone.

It divides the octave into twelve equal parts, each of exactly 100 cents each unless octave shrinking or stretching is employed. Its has a fifth which is quite good at two cents flat. It has a major third which is 13+2/3 cents sharp, which works well enough for some styles of music and is not really adequate for others, and a minor third which is flat by even more, 15+2/3 cents. It is probably not an accident that as tuning in European music became increasingly close to 12et, the style of the music changed so that the defects of 12et appeared less evident, though it should be borne in mind that in actual performance these are often reduced by the tuning adaptations of the performers.

Source: Xenharmonic 

Below a table with cents, ratios and more, comparing 12-EDO with FACTOR 9 12T, Fibonacci-8 and Renold-I, based on A=108Hz. I have transposed the complete scale in order to include 432Hz in the table so we start from A3=216Hz.

Degree Tone 12-EDO Factor 9 12T Fibonacci-8 Renold-I
0 A3 216 216 216 216
1 A#/Bb 228.8 234 230,4 229,1
2 B 242.5 252 240 or 243 243
3 C 256.9 270 259,2 256,4
4 C#/Db 272.1 288 270 273,4
5 D 288.3 306 288 257,7
6 D#/Eb 305.5 324 303,8 305,4
7 E 323.6 342 324 324
8 F 342.9 360 345,6 343,6
9 F#/Gb 363.3 378 360 364,5
10 G 384.9 396 384 or 388,8 386,5
11 G#/Ab 407.8 414 405 410
12 A4 432 432 432 432

All frequencies above are rounded up to 1 digit behind the decimal point.

Below an example of a piece using the Factor 9 12-Tone scale (as listed above) by Derrick Scott van Heerden:



FACTOR 9 16-TONE By Derrick Scott van Heerden

The factor 9 scale is really a harmonic scale, a one octave portion of the harmonic series repeated over octaves and played as a music scale on a multi-tonal instrument.

The long vertical column on the right (of the chart) shows the harmonic series for 9 Hz, while the bottom half shows the portion that makes the factor 9 scale repeated over 4 octaves to the right and left. There are a few missing notes in the factor 9 scale chart in the movie, here you can see that there are really 16 tones in each octave (16th to 31st harmonic). 


Image on the right:
This scale / slice of the harmonic series contains many intervals found in ‘pure’ versions of our 12 tone equal temperament scale and makes it seem obvious that our modern day 12 tone scale must have it’s roots in the harmonic series.

More information at the source article: http://mathemagicalmusic.weebly.com/


DISADVANTAGES OF THE FACTOR 9 TEMPERAMENT

The most significant disadvantage of the Factor 9 Temperament is the specifications of some instruments, in particular acoustic instruments. Some acoustic instruments without temperamental issues are for example: the human voice, fret-less string instruments (like the Violin family), Trombone (a wind instrument without valves or tone-holes), the Harp and percussive instruments. 

Naturally one could compose and produce music with modern Synthesizers, software with micro tuning capabilities or design / invent a new instrument based on this Temperament. 

For instruments without micro-tonal tuning capabilities would be difficult to use the Factor 9 system, even in a 12-Tone scale. 

NOTATION (SHEET MUSIC)

Up to a 14-tone scale the present notation system would work fine (adding a B#/Cb and E#/Fb to the scale). Notation of a 15-tone scale (or larger) using the traditional notation system can be a bit “tricky” and would require some time to study to be able to read it “prima vista“. 

A 15-tone scale would look something like this (Easley Blackwood‘s notation system for 15 Equal Temperament):

 

A 24-tone scale would already require 3 variations in sharps and flats (24 Equal Temperament “Arab Tone System”):

 

SONIC GEOMETRY FIRST VIDEO: MISTAKES IN THE FACTOR 9 GRID

IMPORTANT FOOTNOTES ABOUT THE MOVIE “SONIC GEOMETRY:

Some numbers listed are simple miscalculations, but a more crucial mistake is that tones are missing in their grid!!! The scale/temperament displayed in the movie is a 13-tone system. But, after comparing the grid with the Harmonic Series we can conclude the grid shown in this video (12:52is incorrect. Instead of a 13-tone system it would generate a 12 / 14 / 16-tone system if the implementation is done properly.

Also the “build-up” of the grid starts wrong, the “Factor 9” temperament is based on the tone D being 9Hz. If we set D as the first tone of the scale, then the first two frequencies listed in the 1st column belong to the “great octave” (stacking of 4.5Hz), while the rest of the tones listed in the first column belong to the “small octave” (above the “great octave”, stacking of 9Hz).

Movie screenshot:

Missing frequencies

  • 130.5 (between C and C# in column 1) – “great octave” (stacking of 4.5Hz)
  • 139.5 (between C# and D in column 1) – “great octave” (stacking of 4.5Hz)
  • 243 (between 234 in column 1 and 525 in column 2) – “small octave ” (stacking of 9Hz)
  • 486 (between 456 in column 1 and 504 – missing – column 3) – 1-line octave” (stacking of 18Hz)
  • 504 & 522 (between 486 – missing – and 540 in column 3) – 1-line octave” (stacking of 18Hz)
  • 972 (between 936 in column 3 and 1008 in column 4) – 2-line octave” (stacking of 36Hz)
  • 1044 (between 1008 in column 4 and 1080 in column 4) – 2-line octave” (stacking of 36Hz)
  • 1944 (between 1872 in column 4 and 2016 in column 5) – 3-line octave” (stacking of 72Hz)
  • 2088 (between 2016 in column 5 and 2160 in column 5) – 3-line octave” (stacking of 72Hz)

Miscalculations
B in column 2 has to be 468 instead of 456643 in column 3 has to be 648 and 3755 in column 5 has to be 3744.

Another footnote to make is related to what is being said in the movie about Concert Pitch and instruments. In the movie Eric Rankin mentions that most modern musical instruments have been tuned to 432 for decades (until A4=440Hz became the International Standard). This is not correct, 432Hz has never been a standard, and only some old instruments seem to / might have been build for (or close to) 432Hz as Concert Pitch such as 435Hz (Diapason Normal). There are many old instruments in museums, as well as old Pitchpipe (Church) organs with various pitches ranging between A4=360Hz up to A4=460Hz. Instruments for Baroque music (1600-1750) for example, were designed for a Concert Pitch 415Hz.


OTHER REFERENCES:


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Blog » How-To: Changing the Concert Pitch and Temperament

Reading Time: 2 minutes February 21, 2014

HOW TO: CHANGING THE CONCERT PITCH + TEMPERAMENT (POST PROD.)

USING SOFTWARE TO CORRECT TEMPERAMENT
Antares Auto-tune / Melodyne Editor / Waves Tune

When you have the separate instrument tracks of a song, then you do have the option to re-tune and RE-TEMPER the instrument tracks individually changing not only the concert pitch but the temperament as well.

This is possible due to software like the Melodyne Editor.

The videos below provides information on how to use different Temperaments and Concert Pitches. These videos aren’t turorials about 432-tuning in particular, but 432Hz as Concert Pitch is being mentioned in the second video (03:46 – 04:00).

Other plugins that can be used to change the temperament, are Waves Tune and Antares Auto-tune. With both plugins you can select the scale, in the case of 432-Tuning we set it to Pythagorean. Now, it is important to know how to work with these plugins, so if you have never worked with them before, then I suggest you check some youtube videos and read the manuals. 

Important is that you have to make sure that you do select the correct root (Waves Tune) / key (Antares Auto-Tune) and use formant correction. Also pay attention to the range (Waves (Tune) / Input Type (Antares Auto-Tune) settings of these plugins.

     

RECORDING IN PITCH & TEMPERAMENT IS ALWAYS BETTER!

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.


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Blog » How To: Changing the Concert Pitch (post prod.)

Reading Time: 5 minutes February 21, 2014

HOW TO: CHANGING THE CONCERT PITCH (POST PROD.)

A blog about using software and/or plugins to change the Concert Pitch. There are various applications (sound/wave editors) and plugins that can be used for changing the Concert Pitch. I am not going to blog about every available piece of software, most applications and plugins work pretty much the same, so I’ll just write something about the most popular applications used by “members” of the “432 Community”.

NOTE: if you like to change both Concert Pitch and Temperament of recorded material then read this article

USING AUDACITY (FREEWARE: WINDOWS, OS X, LINUX)
Website: http://audacity.sourceforge.net/download/

Audacity is probably the most popular freeware sound editor among members of the “432-Community”. This freeware application is available for all major operating systems (Windows, Mac OS X and Linux). 

Online you can find various blogs, articles and step-by-step instructions how to pitch sound files created using A4=440Hz as Concert Pitch, to the prefered A4=432Hz Concert Pitch. What I have noticed is that the option to “Change Pitch” is suggested by most. Important to mention though, is that when only changing the pitch and not the tempo, there will be resolution loss, and the upper harmonics might sound “fake”.

The better method thus would be to “Change 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.

HOW TO: CHANGE SPEED

Assuming you do know how to start Audacity and open a sound file, I will get straight to “business” and assume you have loaded the file-to-be-speeded-down in Audacity. So, here’s what you need to do:

STEP 1: 
Select “Change Speed …” (found under the menu topic “Effect“).

Change_Speed_step1_2

STEP 2:
Enter -1.818 at “Percent Change” (check if the “Standard Vinyl RPM” is set to “n/a“). Then press “OK” to implement the Speed Change.

ChangeSpeed-PercentChange

Congrats, you have done it!

Don’t forget to safe and/or export the file in the prefered format (it is best to keep the original format type to prevent additional quality loss). Do check the export “Options” when you export the file to make sure the “Bitrate”, “Quality” and “Channel Mode” is the same as the original.


USING A “CHAIN” (BATCH PROCESSING)

You can make “chains” with Audacity for batch processing. This is convenient if you like to edit multiple files at once.
Scroll down to read how to make a chain yourself.

If this seems too hard for you, then you can download various chains from this website: 
440-to-432-(WAV) | 440-to-432-(MP3) | 440-to-432-(FLAC)

To download: Right-click the link(s) to safe the file(s) to your machine. Place the chain file(s) in the following folder:

  • Windows 2000/XP: Documents and Settings\<user name>\Application Data\Audacity\Chains
  • Windows Vista/Windows 7/Windows 8: Users\<user name>\AppData\Roaming\Audacity\Chains\
  • OS X: ~/Library/Application Support/audacity/Chains/
  • Linux: ~/.audacity-data/Chains

 Skip “MAKING THE CHAIN(S) YOURSELF” (below) and continue to “USING THE CHAIN(S)“.

MAKING THE CHAIN(S) YOURSELF:

  • Under “File” select “Edit Chains …”.
  • Click on the button “Add” (under the left column).
  • Enter the name of your chain, for example: “440-to-432-MP3”.
  • Click on the button “Insert” (under the right column).
  • Double Click “ChangeSpeed” and click on the button “Edit Parameters”.
ChangeSpeed-doubleclick
  • Enter “-1.818” at the “Percent Change” and press “OK”.
ChangeSpeed-PercentChange
  • Click once more on “OK” button to add the Command to the chain.
  • Click once more on the button “Insert” (under the right column) to add the export format to the chain.
  • For this part of this “How To” we double-click “ExportMp3” and press ok. The “ExportMp3” will be added under the “ChangeSpeed” to the chain. If the “ExportMp3” ends up above the “ChangeSpeed” in the chain, then use the “Move Up” or “Move Down” button to correct the order in the chain.
  • Press on the “OK” button to finish the edit and you will be ready to use it.
Saving-Chains

USING THE CHAIN(S):

  • Under “File” select “Apply Chain …” to select a Chain. For this example we will use the mp3 chain, our source files were mp3, and thus exporting it as such.
Apply-chain
  • Click on “Apply to Files …” to browse to the folder containing the files, select the files and click on “Open”.
  • 2 small windows will pop-up, one with the cue list with files, another one displaying the processing.
  • IMPORTANT: the processed exports will be stored in a folder called “cleaned” inside the folder containing the selected (original) files. 
  • When the processing has been done, select “Close” under “File“. Audacity will ask you if you like to “Safe Changes?”. Press the buttonNo“. The chain has already exported (and closed) the processed files, to safe an “empty session” would be useless.

Save-Changes-No(1)

SOME FOOTNOTES:

1) Close any files you might have opened before applying a chain.

2) Keep in mind that when exporting Audacity will use the settings last used for exporting a particular format.

  • In order check/change the quality settings, you should load a file and click on “Export …” (Shift+Control+E).
  • A window will pop-up where you can select the format. Under the “pull-down” format menu you can find the “Options …” button. This button will trigger a small window to appear, where you can set/change the “setup” for format(s) you like to use. After you have modified the setup, press “Ok” to close the small window.
  • “Cancel” the “Export Window”, after all, we did not need to export anything, just check/change the settings.
  • Close the loaded file (without saving)

3) Chose the same format to safe the piece with as the original, conversion between different formats requires additional processing and can cause loss of sound quality. There is no use to convert a lower quality format to a higher quality format. If the original was MP3, then there is no use to select the 440 to 432 Flac or Wave chain, you would only change the size of the file, but not the sound quality.


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Blog » 432Hz & Cymatics

Reading Time: 2 minutes January 26, 2014

432 & CYMATICS

Cymatics is the study of visible sound and vibration. Typically the surface of a plate, diaphragm, or membrane is vibrated, and regions of maximum and minimum displacement are made visible in a thin coating of particles, paste, or liquid.
[ Read More ] ►

Why is this of importance? Well, we do know that sound has an effect on how we feel. Not just emotional, but physically as well. It is there for interesting to see what effect particular tones (frequencies) have on matter.

In the video below on the left you see a Cymatic experiment with various tones (frequencies), both when A4=432Hz is used as Concert Pitch, as well as A4=440Hz is used. The video on the right displays various tones (fequencies) related to (or very close to) tone frequencies in 432 Tuning generated with the Software Tonoscope*.

IMPORTANT NOTE:
The thickness and type of metal used, as well as the size of the grains are of influence in the relationship of frequency and pattern. If a different kind of metal is used and/or a plate of different size and thickness and/or another type of “sand”, the same frequency might create different patterns or fail to generate a proper pattern.

The video below where they compare 432Hz with 440Hz is thus NOT PROOF of 432Hz being “better”, it just tells us that that particular “setup” of plate and “sand” used works better with 432Hz-related frequencies then it does with 440Hz-related frequencies.


*Footnote: 
On the website of the Software Tonoscope the “Ancient Solfeggio Frequencies” concept is supported/endorsed. I do NOT support that concept as you might have read in my blog article Myth: “The Ancient Solfeggio Frequencies”.


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Blog » ⚠ Myth: Mozart, Jimi Hendrix, Bob Marley, Price … 432-Artists?

Reading Time: 8 minutes January 22, 2014

⚠ MYTH: MOZART, JIMI HENDRIX, BOB MARLEY, PRINCE … 432-ARTISTS?

From time to time stories about various known artist and composers such as Bach, Mozart, Verdi, and more recent Bob Marley, Jimi Hendrix and others pop up, with claims that these artists and composers wrote and/or performed music for concert pitch 432 and/or 432-tuning. Unfortunately most of these stories are rather “speculative” … are those stories urban legends or … ?

For information about Giuseppe Verdi read this article!

About: Mozart | Bob Marley | Jimi Hendrix | Price | and others …

Q: Have the proclaimed “432 artists” and composers mentioned or noted anything themselves about using 432-Tuning?

A: In short, No (although both Verdi and Prince seem to have referred to 432Hz as reference pitch once). Most articles with these stories generally fail to provide proper references that support their claims. There are no links to interviews or documentaries nor to articles, autobiographies or memoirs by the artists in question themselves, sharing any information about the usage 432Hz as Concert Pitch and/or another Temperament then the present standard.

Q: Did the proclaimed “432 artists” and composers (always) compose for and/or perform their work using Concert Pitch A4=432Hz?

A: In short, No. I have not been able to find proper historical data (logs et cetera) about any artists and composer mentioned above of using A4=432Hz for (all) compositions. Perhaps the particular historical data has not been made “public”, but that would be odd, wouldn’t it? It is though rather strange (if not questionable) why some people proclaim composers did compose in 432, but can not deliver any proper historical evidence to proof their claim. Where is the hard evidence that proves their claims?

We do know that great composers – Mozart being one of them – traveled a lot (not only through all German-spoken countries, but in England, France and Italy as well) and must have come across various concert pitches used by musicians, orchestras, instrument builders and composers locally. A composer – when asked to compose a piece – had no other choice then to compose for and work with instruments with the pitch locally used. Naturally the choice of instruments used for a piece would influence the possibility and flexibility of tuning as well. A string quartet would be able to use a large range of possible concert pitches and temperaments, while a church organ would only work with the particular concert pitch it was designed for.

RECORDING METHOD

Various people have noticed that some mostly older recordings sometimes do sound a (little) bit lower (or higher) in pitch then 440Hz. Nowadays most artists record digitally, but a couple of decades ago all artist would record on tape. The “problem” with tape is that in time – when played often – tape could “stretch”. A direct result of tapes getting stretched out is that the pitch (and tempo) of a piece would drop a little. Another thing that we should keep in mind, is that the tape decks used had electrical (mechanical) motors to spin the tapes, that like any mechanical part got “worn-out” in time. Fluctuations / changes in pitch when using tape was there for not uncommon. Even using the same tapes on different tape-decks could result in a variation of pitch (and tempo).

INSTRUMENTATION

Another important thing to keep in mind is that not all instruments can change Concert Pitch. If also the Temperament needs to be changed, then some instruments like the guitar will be problematic. Almost all guitars and bass guitars have a 12-Tone Equal Tempered fret-board. Trombone is pretty much the only wind instrument that could play in any Concert Pitch and Temperament. Fretless String instruments have (generally) no problems with changing the Concert Pitch.

Most drum/percussion instruments – in particular membranophones – can be re-tuned. But some drum/percussion instruments – for example cow-bells – can not tunable, they are manufactured for a particular pitch.

Modern synthesizers have micro-tonal features that make it possible to change pitch and/or temperament. Older keyboards and synthesizers did not (always) come with these features.

Some instruments were designed to be played in 440Hz are for example: Fender Rhodes, Hammond Organ, Vibraphone and conical wind instruments like the Saxophone. If you see these instruments (original) on stage, then you can bet on it that the band is playing in 440Hz. When instruments that can’t change their pitch from 440Hz to 432Hz, then you can be pretty sure the recordings made and performances given were NOT with the use of Concert Pitch 432Hz.

More information about the Concert Pitch and Temperament capabilities of instruments can be read in the article “Instruments & Tuning“.


MOZART (AND OTHER COMPOSERS FROM THE “CLASSICAL PERIOD”)

The dates of the “Classical Period” are generally accepted as being between about 1730 and 1820. The “Classical period” falls between the Baroque and the Romantic periods. The among best-known composers of this period are Mozart and Beethoven.
In Wolfgang Amadeus Mozart‘s time there was still no standard concert pitch. From country to country and even from region to region and city to city the concert pitch used could vary.

The instruments used by musicians and the concert pitch they were build for would differ as well. Some instruments, like string instruments, could be tuned easily to a different concert pitch. Other instruments, like Church (pitchpipe) Organs would not have this possibility. 

You can find more information about instruments and their tuning capabilities here.

Some people have told me (through e-mail) that they have seen an authentic score from the hands of some of the great composers (like Mozart) with “A=432” written in the side-line. This might be very true (I have no reason to doubt the writers intentions). But this “evidence” has not been shared in public, so I can not deny nor confirm it’s authenticity. If it is true, why hasn’t anyone one else (then the specific individuals) have ever seen it? And why do these individuals do not share their evidence?


BOB MARLEY AND 432

This is maybe the most mentioned artist of “our time” in relation to 432-tuning. It seems though, that this claim is not based of facts, but the result of misinterpretation and perhaps mostly “wishful thinking”. So, why do some people proclaim Bob Marley to be a 432-artist? 

INSTRUMENTS USED
The most important reason though why Bob Marley did not record and perform in 432Hz (as far as is know), is the instruments used by his band members.

In many pieces of Bob Marley instruments like a Fender Rhodes (an instrument that was build for 440Hz and has no microtonal capabilities) or an original Hammond Organ is used (some sources say a change in the power frequency could effect the pitch because the motor is speed locked to it, but this I can’t say for sure). On some of his albums and at some live performances a horn section participates. In particular when a saxophone is used (conical wind instrument), there will be intonation issues if Concert Pitch 432Hz is used instead of the Concert Pitch the instrument was build for (440Hz for most brands). With other words, when using such instruments, you have no other choice then to record (and perform) using 440Hz as concert pitch. 

You can find more information about instruments and their tuning capabilities here.

LIVE PERFORMANCES
IF Bob Marley was a 432 composer/musician, would it then not be more logical if he would perform in 432Hz as well? Why then, was 440Hz used during all the live registrations? 

CONCLUSION ABOUT BOB MARLEY AND 432-TUNING
I think it is more then clear that proclaiming that Bob Marley was a 432 artists is nothing more then a fairy tale of mythical proportion …


JIMI HENDRIX AND 432

In some articles Jimi Hendrix is mentioned of using 432Hz. Similar as with Bob Marley the recording method and medium used does play a role in various pitch differences detected by listeners. Hendrix, like Marley, used 12-TET guitars.

Often musicians have to re-tune their instruments in between pieces during a concert. Changes of temperature and even amount of moisture can detune instruments. Strings also lose tension (drop in pitch) as well due to the striking/plucking.

The amount of force that the strings of guitars are stroke or plucked with is much higher with Rock music then with many other music styles.

Another reason why Jimi Hendrix – and for that matter many other rock artists – could sometimes sound a bit “off-pitch” – in particular in live-recordings – is that many rock artists tuned by ear. A classic rock formation (with vocals, guitars, bass and drums) is not bound by Concert Pitch (only by Temperament), unlike Rock bands that also used keys (for example Hammond Organ).

JIMI HENDRIX AND Eb TUNING
That Jimi Hendrix tuned his guitars different then most guitarists is fact though. He was one of the most known guitarists that used the so called “E♭ (E‐flat) tuning or D♯ (D‐sharp) tuning“. All of the strings are lowered by one semitone (100 cents). This is where the present A4=440Hz pitch standard and the “Baroque Pitch” of A4=415Hz come together (the difference between 440Hz and 415Hz is 101 cents). Using A4=415Hz instead of A4=440Hz does NOT really change anything though. The tone frequencies used with 440Hz as Concert Pitch are being used in both cases. You could say that all tone-names simply “shift” a semitone. A4 is no longer 440Hz, but A#/Bb is now. The reason why various guitarists tuned this way are a heavier tone / change of timbre, the possibility to use of heavier strings without decreasing playability and/or greater string flexibility (for legato and bending) without losing compatibility with 440Hz tuned instruments. 

Jimi Hendrix is known for using Eb-Tuning, not 432-Tuning.


PRINCE & 432HZ

To end this article with something positive (specially for those who are disappointed after reading this article) … According to various articles Price has shown an interest in the 432Hz topic. In order to promote a new album release, he offered a rare engagement with his fans via Facebook on September 30, 2014.

“Join Prince for an exclusive Q&A on Facebook right here at 12pm PT/ 3PM EST!! Submit your questions below!!!”

prince-432hz
That post is not available on Facebook though, nor is the Prince page in question active.

Who Dee J Fogee exactly is I don’t know, the website deejfogee.org is down (at least it was when I added this info) and the last post on the Facebook profile of Dee J Fogee was done on 5 December 2015.  

Here you can find the article linked to: “Here’s Why You Should Consider Converting Your Music To A=432 Hz“.

QUESTIONS REMAIN:
Is it clear why Prince decided to post that link? How did he really feel about it? Was he serious or just creating a bit more “Controversy”? Was that post really made by Prince himself? At prince.org (the online fan community) fans are not sure what to think about it as you can read in “Q&A with Prince on Facebook today!” and “The frequency of A-432hz“.  

Prince himself did not share any more thoughts or insights on this topic after that Facebook Q&A event. And we might never know the “truth” about this story, Price passed away on the 21th of April 2016.

NO RELEASES IN 432HZ
The albums he made – including those released after that Facebook posts – are not tuned to 432Hz, nor did he perform using 432Hz as concert pitch. For his music he used the standard 440Hz! 

Many (recording) artists and composers leave unfinished and unreleased work behind when they die. Often work they were not completely satisfied about yet or had not found the right moment for to release it. Perhaps in the near future some 432Hz tuned pieces pop-up from his “vault”, who knows. But, for the time being there is no evidence nor proper reason to proclaim Prince used 432Hz for his music.

YOUTUBE AND 432HZ MUSIC VIDEOS

You might have come across videos of famous artists and bands such as Bob Marley, Jimi Hendrix, Pink Floyd, Enya, Coldplay, The Doors, John Lennon / The Beatles, Dire Straits, Jamiroqui … and many more that are available tuned to 432Hz. Important to keep in mind, is that those pieces were not uploaded by the bands, their management or label, but by fans of their music. These fans have down-pitched their music before uploading it onto Youtube. 

! Only 432-tuned tracks available through the official Youtube Channel of artists/bands and/or their label are authentic. All other are not official (proper) representations of the works by those artists.


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Blog » Real-Time 432 Auto-Pitching Music Players

Reading Time: 7 minutes January 21, 2014

REAL-TIME 432 AUTO-PITCHING MUSIC PLAYERS

(For: Windows, Mac OS XLinux, iPhone, Android) 

GENERAL INFORMATION:
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, iPhone and Android, using one of the applications listed below will provide the easiest method to get in tune with Concert Pitch 432Hz!

IMPORTANT! – Keep in mind that the players mentioned in this article will not detect the Concert Pitch of the source. When another Concert Pitch is used then the 440Hz standard, the music will nonetheless be pitched in the same way as if it was in 440Hz. The real-time auto-pitching instructions as mentioned in this blog article only work for 440Hz tuned/pitched audio files. 

NOTE! – Do keep in mind that the change of Concert Pitch alone is not “432 Tuning”
432-Tuning is Concert Pitch A4=432Hz + “Pythagorean Temperament”. With most Western music (and instruments played) the “Twelve Tone Equal Temperament” (12-TET) is used. These players will NOT be able to make real-time changes to the temperament! If you like to read more about the difference between “Concert Pitch” and “Tuning System” then you can find more info here.

With some players (VLC and Foobar) there is the option to adjust the rate. If you can adjust the rate, then use this option instead of pitching down. With the “adjust rate” option you change the speed (both pitch and tempo) so there will be no resolution loss. This method is the equivalent of slowing down a turntable and preferable over the pitch-change option! 

The optimal speed (rate) is set to 0.981818 (VLC) or changed with -1.818% (Foobar). If the player/plugin you use can not use more then 2 digits behind the decimal point, then use a rate of -1.82% (A4=431.998Hz) or -1.81% (A4=432,036Hz), a “neglectable difference” (a difference that most people won’t be able to hear, actually). -1.8% will set A4 to 432,080Hz, less then 0.1Hz difference, still very close.

Players / plugins, that use cents or semitones should be set to pitched down with: -31.76665363342977 cents or -0.3176665363342977 semitones. If case you need to “round it off”, use as many digits behind the decimal point as possible. The smaller the number of digits behind the decimal point, the less accurate the result. If for for example use -31 cents / -0.31 semitones, then A4 becomes 432,191Hz, as with -32 cents / -0.32 semitones A4 becomes 431,942Hz

If you are looking for a hardware auto-tuning high-end Hi-Fi music player, then do read the Roel’s World article about the EVO 432 Music Server!

EVO-432

PLAYERS FOR [ Windows | Mac OS X | Linux | iPhone | Android ]


PLAYERS FOR WINDOWS

#1: VLC PLAYER – Sets A4=432Hz (freeware)

I think the best freeware video and audio player available for all platforms (Windows, OSX and Linux) is the VLC player

Read more about it in this Roel’s World article!

432 PLAYER “432HZ” FOR WINDOWS 7 (freeware) – by Ophir

Ophir used the Open Source code by Alambic WPF Music Player, and modified it change the Concert Pitch to A=432Hz.

More information & Download at: http://ophirpaztao.wix.com/432player 
(bottom of the website, click on the player image to download).

FOOBAR 2000 (freeware)

NOTE: Personally I would recommend the VLC player instead though, it is more accurate and simply sounds better!

Foobar use to be the preferred software to use several years back. It was one of the first players for Windows that made listening to music pitched down to 432Hz in real-time relatively easy in reasonable sound quality. You did not needed to use sound editors anymore to manually pitch-shift your music collection anymore, a huge time-saver for most people.

INTERESTING FEATURE: You can install this application also on a portable device, like for example a Flash Drive. Then you can play the music on another PC/Laptop, without having to install the program on another PC/Laptop first.

But, for those who do prefer using Foobar, follow these instructions: 

Now … 

  1. Install Foobar.
  2. Unzip the SoundTouch plugin and place it in the map “C:\Program Files\foobar2000\components\“.
  3. After installing the player and the plugin, open under “File” > “Preferences“. A control menu will pop-up.
  4. Under “Playback” you can find the “DSP manager“. Activate SoundTouch DSP (see image below).
  5. Select the SoundTouch plugin and configure (button above the Active DSPs list). Select the “Rate adjust” option and move the slider -1.82% (see image below). If your mouse movements are not precise, use the arrow keys on your keyboard to get it right. 
  6. Click “ok”, then on “apply” and you’re all ready to start listening.  
STEP 4: Select SoundTouch    STEP 5: Adjust SoundTouch

FOOBAR & YOUTUBE

For those who prefer using Foobar for watching and/or listening to Youtube videos: Foobar 2000 can be setup to deal with Youtube streams as well.

To do so you need to download the Youtube component for Foobar 2000 here: http://fy.3dyd.com/download/.  You can choose from 3 different versions, a standard version and 2 preconfigured versions (detailed information can be found on the fv.3dvd.com site). The difference is in default component settings. Standalone variant configured to play best quality from the formats which foobar2000 can play out of the box and without problems. Variant preconf_audio configured to use wider set of formats which can be played without problems only using 3rd party plugins which it contains. Variant preconf_video also has needed DirectShow filers to be able to play video without need to install them in the system.

INSTALLING THE YOUTUBE COMPONENT

  1. Go to the Components page.
  2. Click the “Install…” button and select the component archive, or simply drag it to the list.
  3. Press “OK”, you will be prompted to restart foobar2000 in order to load the newly installed component.

WINAMP (freeware)

For WinAmp you can find a couple of plugins too. My experiences with these WinAmp plugins are less positive then the Foobar + SoundTouch plugin. I have tested 3 plugins for WinAmp, but noticed some “clicks” in the sound. Maybe those plugings work better with other version of WinAmp then I use. Nevertheless, you can give it a try if you like, here are the links:

NOTE: I personally would strongly recommend the VLC player instead of WinAmp when using Windows!

PLAYERS FOR [ Windows | Mac OS X | Linux | iPhone | Android ]



PLAYERS FOR OSX
#1: VLC PLAYER – Sets A4=432Hz (freeware)

The best freeware video and audio player available for all platforms (Windows, OSX and Linux) is the VLC player (in my opinion).  

Read more about it in this article!

NEUTRINO + AU PITCH

Download from: http://www.machinecodex.com/neutrino/ (30-days trial before purchase) 

In the ‘inspector’ window click the plus (+) at the bottom under ‘Fx Chain‘, choose AUPitch, click OK, then enter -31.7667 into the ‘cents’ field, click the x to close. To save this preset, click the file icon to the right of the plus (+), name your preset ‘432Hz’ or something and click OK, it is now saved. You may have to reselect this preset when Neutrino restarts (Instructions by Cole Hayley, using Mac OSX 10.6.8, Snow Leopard).

AU Pitch    AU Pitch (GarageBand)    AU Pitch (Ableton)    AU Pitch (Vox)
VOX + AU PITCH

Download from: http://www.macupdate.com/app/mac/24852/vox
NOTE: this setup worked for older versions of this player (see 4rd image above), the latest versions do not seem to have this option anymore.

PLAYERS FOR [ Windows | Mac OS X | Linux | iPhone | Android ]



PLAYERS FOR LINUX
#1: VLC PLAYER – Sets A4=432Hz (freeware)

The best freeware video and audio player available for all platforms (Windows, OSX and Linux), for Linux users VLC Player is the best option

Read more about it in this article!

ALTERNATIVE APPROACH FOR LINUX

Personally I would suggest you use VLC when using Linux (it’s the most accurate player for Linux so far).

But, you can run Foobar (or WinAmp if you wish) with Linux too. This is possible due to “Wine” (a compatibility layer capable of running Windows applications). More about Wine (and dowloads) at www.winehq.org

I personally like to use “PlayOnLinux“, it’s freeware and allows you to easily install (some, not all) Windows applications. More about PlayOnLinux (and downloads) at: www.playonlinux.com. An alternative for “PlayOnLinux” is “Crossover” by “www.codeweavers.com“. This application is not for free though.

 NOW … 

  1. Install Wine (and PlayOnLinux/Crossover if you like). I will not provide instructions on how to install Wine and PlayOnLinux / Crossover. If you are a Linux user, you most likely already know how to anyway. 
  2. Install Foobar (standard, not portable) on a “virtual drive”.
  3. Unzip the SoundTouch plugin.
  4. Open the application directory of the “virtual drive” and place the SoundTouch plugin in “..\foobar2000\components\“.
  5. Follow the instructions from “step 3” as described at the Foobar install for Windows

PLAYERS FOR [ Windows | Mac OS X | Linux | iPhone | Android ]



PLAYERS FOR iPHONE / iPAD

432 PLAYER “432HZ” FOR IPHONE (freeware) – by Ophir

More information: http://ophirpaztao.wix.com/432player
Download from: https://itunes.apple.com/us/app/432-player/id633600716?mt=8

PLAYERS FOR [ Windows | Mac OS X | Linux | iPhone | Android ]



PLAYERS FOR ANDROID

MAPLE PLAYER (freeware) – by SQR5

  • After installing Maple Player, open the tab called “Pitch“.
  • Click on the pencil icon on the top-right side to open the “pitch editor”.
  • Type -0.32 (or -0.31, what ever sounds best to you) and press “ENT” (enter) to set the new pitch.
  • Press the “back key” on your phone to close the “pitch editor” and you are all set to listen to your music re-pitched.

Download from: https://play.google.com/store/apps/details?id=com.sqr5.android.audioplayer
For Androind Jelly Bean download: https://play.google.com/store/apps/details?id=com.sqr5.android.player_jb 

432 PLAYER “432HZ” FOR ANDROID (freeware) – by Ophir
Ophir used the Open Source code by Alambic WPF Music Player, and modified it change the Concert Pitch to A4=432Hz.

More information & Download at: https://play.google.com/store/apps/details?id=com.appums.music_pitcher


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Blog » Renold-I Temperament (“The Scale of Fifths”) by Maria Renold

Reading Time: 8 minutes January 21, 2014

RENOLD-I TEMPERAMENT (“THE SCALE OF FIFTHS”)

I came across the “Twelve True-Fifths Tuning” concept (by Maria Renold) through a facebook friend, Brain T. Collins, who mentioned this tuning concept on his web site, the Omega432.com. Brian T. Collins refers to the page of  Graham H Jackson where the “Twelve True-Fifths Tuning” concept is explained. This concept is a great alternative implementation of the Pythagorean Temperament.

NOTES:

  • The frequencies listed in this blog article are the result of the original “Scale of Fifths” tuning method (discovered in 1962), also referred to as “Renold I” Temperament. Maria Renold later found out that Henricus Grammateus had constructed a similar scale in 1518 (source: Jorgensen, 1991, p.332).
  • In her work Maria Renold used alternative names for the black keys of the piano. C#/Db = “delis“, D#/Eb =”elis“, F#/Gb = “gelis“, G#/Ab = “alis” and A#/Bb = “belis“. For this article I will use the common tone names instead.
  • Maria Renold did continue experimenting and developing her concept, with the “Renold II” (also known as “Middle Tuning” temperament as result. This Renold-II temperament is described in the article Renold-II Temperament.

WHY AN ALTERNATIVE FOR THE PYTHAGOREAN TEMPERAMENT?

Well, the Pythagorean Temperament works with the stacking of perfect fifths. But, when we stack 12 perfect fifths, we do not end up at a the same note we started, but approximately a quarter-tone above. With other words, we don’t end up with a circle but a spiral. This actually happens with any perfect (pure, natural) interval (except for the octave) when stacked (and that does not work very well with a closed musical interval system). In order to close the circle, one or more 5th’s should be slightly decreased to end up with a perfect circle. Maria Renold though came up with an tempered version of the Pythagorean Temperament, using mostly Perfect Fifths and still create a working closed circle.

Graham H. Jackson explains on his site:

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).


SO, HOW DOES THAT WORK?

We know that the perfect fifth uses the ratio 3:2. We use the following formula for calculating the fifth: 

Frequency • 3 / 2 = Frequency of the Fifth above.                                              

Now, let’s have a look at the Circle of Fifths:

When we follow the Circle clockwise, we go up a fifth. The outer “ring” with the capital letters is the Major Circle of Fifth, with inside the parallel minor Circle of Fifths. 

As suggested by Graham H. Jackson, we start with from the tonic of the the C Major scale (the white keys on the piano). Now, the C Major scale contains the following tones: CDEFGAB.

When we start with C3=128Hz (as Renold suggested) and implement the formula we get the following:

128 (C3) • 3 / 2 = 192 (G3) • 3 / 2 = 288 (D4) • 3 / 2 = 432 (A4) • 3 / 2 = 648 (E5) • 3 / 2 = 972 (B5).

In this article I will use the tone frequencies between C4=256Hz and C5=512Hz so it will be easier to “compare” to the
tone frequencies on the modern standard.

256 (C4) • 3 / 2 = 384 (G4) • 3 / 2 = 576 (D5) • 3 / 2 = 864 (A5) • 3 / 2 = 1296 (E6) • 3 / 2 = 1944 (B6).

!IMPORTANT:

If we continue stacking 5ths (• 3 / 2) after B6 (1944Hz), we pass Gb, Db, Ab, Eb and Bb, ending up with F10=22143.375Hz. If we would stack another 5th on top, we end up at C11=33215.0625Hz. 

!!! A perfect C11 relative to C4=256Hz would be C11=32768Hz, not C11=33215.0625Hz !!!

With other words, the fifth between F10 and C11 would be imperfect. If we bring that F10=22143.375Hz back to F4, we will end up with 345.990234375Hz. This is about 4Hz higher then the “harmonic mean”. So, we have to use a different method, to get the harmonic mean right. This is where mathematical formulas can help us out.

CALCULATING THE ARITHMETIC, GEOMETRIC AND HARMONIC MEANS

When we calculate the means in between C4 = 256Hz and C5 = 512Hz we get the following

The arithmetical mean formula: (256 512) / 2 = 384Hz (G, the 5th above C).
The geometrical mean formula: (256  512)362.038671968Hz (F# or Gb, the dim. 5th above C).
The harmonic mean formula: (2  256 • 512) / (256 512) = 341.333∞Hz (F, the 4th above C).

The arithmetical mean G = 384Hz was already part of the scale (the first perfect 5th we stacked on the C). Now we have calculated the harmonic mean as well, we can add F = 341.333∞Hz to the scale and we have completed the C Major scale.

C D E F G A B C
256 288 324 341.333∞
384 432 486 512

If we start from the geometrical mean between C4 and C5, the F# (or Gb), stack 5 perfect fifths, and bring them back in between C4-C5, we get the following Major Pentatonic Scale of F# (or Gb):

F#/Gb C#/Db G#/Ab D#/Eb A#/Bb
 362.039 271.529  407.294
305.470  458.205

Note: the frequencies noted above are rounded off on 3 digits behind the dot.

When we combine the C Major Scale and the F#/Gb Major Pentatonic Scale, we get the following Chromatic Scale from C:

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B C
256 271.5
288 305.5
324 341.333∞
362
384 407.3
432 458.2
486 512

In modern music we use only 12 tones. The consequence of this choice is that it is impossible to create a perfect system (a perfect circle of intervals using only perfect intervals), the natural “movement” sound makes when only using perfect intervals is spirally. And you can’t expect to see a spiral if you are drawing a perfect circle right? When we use Maria Renold’s “Scale of Fifths” concept and like to use a closed circle, then we end up with “just another” tempered version of the Pythagorean Temperament.

When we use the tone frequencies as listed above and calculate the amount of cents (rounded off) in between the Fifths, you notice that most intervals are about 0.1 cent off (lower or higher) from the 702 cents of the Perfect Fifth (Just Intonation). There are though two intervals – the Fifths between B and Gb/F# and between Bb/A# and F – that are smaller then the other 10 intervals: 

C G D A E B Gb
F#
Db
C#
Ab
G#
Eb
D#
Bb
A#
F C
   701.9 701.9 701.9 701.9 701.9 690 701.9 702.1 702.1 701.7 647.5 701.9

When we rearrange the circle chromatically we end up with semitones of 101.8-102.1 cents between every semitone, except in between between E-F and B-C, the only two semitone intervals of the Diatonic Scale:

C C#
Db
D D#
Eb
E F F#
Gb
G G#
Ab
A A#
Bb
B C
101.8 102.1 102.1 101.9 90.2 101.8 102.1 101.9 101.9 101.9 101.9 90.2

Below a list with the differences in cents and ratio between the Equal Temperament (present standard) and Maria Renold’s “Scale of Fifths” Renold-I Temperament, both using the Scientific Concert Pitch C4=256Hz.

TONE 12-TET C4=256Hz M. R. SCALE OF FIFTHS CENTS DIFFERENCE RATIO f2 / f1 DIFFERENCE
C4 256 Hz 256 Hz 0  0
C#/Db 271.2 Hz 271.5 Hz 1.9140234664560511 1.0011061946902655
D 287.4 Hz 288 Hz 3.6104998468059137 1.0020876826722338
D#/Eb 304.4 Hz 305.5 Hz 6.244825443055806 1.0036136662286466
E 322.5 Hz 324 Hz 8.033583088810076 1.0046511627906978
F 341.7 Hz 341.333∞ Hz -1.858725915674287 -0.9989269339576626
F#/Gb 362 Hz 362 Hz 0 0
G 383.6 Hz 384 Hz 1.8043087084650533 1.0010427528675703
G#/Ab 406.4 Hz 407.3 Hz 3.8296946774990657 1.002214566929134
A 430.5 Hz 432 Hz 6.021689719949426 1.0034843205574913
A#/Bb 456.1 Hz 458.2 Hz 7.952746136304442 1.00460425345319
B 483.3 Hz 486 Hz 9.644782878502031 1.005586592178771
C5 512 Hz 512 Hz 0 0

For tuning by ear three tuning fork are needed: C4=256Hz, A4=432Hz and “gelis” (F#/Gb)=362,04Hz (Renold 1). How to tune by ear is described (scheme included) in Maria Renold’s book

Here an example how the Renold I temperament sounds (in comparison with Equal Temperament):

RENOLD-II

An alternative for the Renold-I Temperament (in particular for acoustic instruments) is the Renold-II Temperament.

DOWNLOADS (MIDI & SOFTSYNTH SCRIPTS)

I have added the “Scale of Fifths” to Scala (a software tool for creating scales, temperaments and more) and exported it in various formats. If you need a different format then provided, download Scala as well as this: SoF – Scala scale.scl scala-file and export it in the format you require.

Note: I do not guarantee the files bellow will work with your hardware and software setup. In case it does not, then try creating and exporting the “Scale of Fifths” yourself with Scala. Please, do feel free to send me a message if the provided files do not work for you, preferably with some info about the hardware, operating system (version) and software you have used.

DOWNLOAD (right-click mouse button: “Safe as”):

THE BOOK BY MARIA RENOLD

“The Scale Of Twelve Fifths” (and more) can be found in the book “Intervals, Scales, Tones and the Concert Pitch C = 128Hz“. by Maria Renold. Information about “The Scale Of Twelve Fifths” can be found at Chapter 13, 21, 24 & 25 of this book.

ISBN 9781902636467
www.templelodge.com

Why is it that certain intervals, scales and tones sound genuine and others false? Is the modern person able to experience a qualitative difference in a tone’s pitch? If so, what are the implications for modern concert pitch and how instruments of fixed tuning are tuned?

Maria Renold tackles these and many other questions, providing a wealth of scientific data. Her pioneering work is the result of a lifetime’s research into Western music’s Classical Greek origins, as well as a search for new developments in modern times. She strives to deepen musical understanding through Rudolf Steiner’s spiritual-scientific research, and she also elucidates many of Steiner’s often puzzling statements about music.

The results of her work include the following discoveries: that the octave has two sizes (a ‘genuine’ sounding octave is bigger than the ‘perfect’ octave); that there are three sizes of ‘perfect’ fifths; that an underlying ‘form principle’ for all scales can be found; and, most importantly, the discovery of a method of tuning the piano which is more satisfactory than equal temperament. She also gives foundation to some of Rudolf Steiner’s statements such as: ‘c is always prime’ and ‘c = 128 Hz = Sun’.

MARIA RENOLD (1917-2003) spent her childhood in the United States, where her parents emigrated to found a eurythmy school in New York. She studied eurythmy and later violin and viola and toured with the Bush Chamber Orchestra and the Bush String Quartet. One of Maria Renold’s deeply-felt questions concerned the correct concert pitch. When she heard of Rudolf Steiner’s concert pitch suggestion of c = 128 Hz she put it into practice immediately, and experimented with it over many years in America and Europe. She also discovered a new method of tuning the piano, closer to the tuning of stringed instruments, arriving at the concert pitch of a4=432 Hz. First published in German in 1985, her book has become a modern classic of musical research.


REFERENCES:

Special thanks to Sławek Kędra providing additional information and suggestions.


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