The reasons for looking to change tuning system are concerning both the physics of sound and its effect on musicality.
For many musicians nowadays music has become merely a circus act, a challenge in virtuosity, a spectacle, man versus beast, and musicians have forgotten the purpose of music as a language to convey emotion, to enable the mind to explore and to heal. Healing requires gentle caressing, and harmony not of sound but of the vibrations within sound.
Sound is made of vibrations, regular vibrations per second. Modern piano tuning does not maximise the numbers of vibrations which coincide.
The change to modern tuning was made between 1860 and 1920 when current tuning was hardened into the "equal temperament" currently used where each semitone is an exact same distance apart.
Here is an octave of keyboard notes
Because E is the third note from C, C-E when played together is a "third" and C-G, five notes apart, a "fifth". C-E, F-A, and G-B are thirds.
C to C# (C sharp) is a semitone. C to D is a tone. A tone is two semitones. The interval of the third, therefore, is made of two tones, from C-D and D-E and this is four semitones. The third from D therefore is not F, which is only three semitones - the third from D is F sharp, labelled F#. So this is why we have the five black notes. C-C is an octave.
1. Physics of sound.
The notes which are an octave apart are a doubling of frequency. So middle C in the middle of the piano keyboard might be 256 vibrations per second. The C above will then be 512 vibrations per second. An octave above that would be 1024 vibrations per second.
The organ as an instrument has stops which are pulled which allow all three pitches to be sounded from the same key, and more. The purpose of this is to make the sound richer.
All sound in its different timbres as flavours or colours, is made of combinations of these multiples of vibrations together.
You can demonstrate this singing a note and opening your mouth to allow the extra sounds to be heard - you can see and hear on https://youtu.be/TF2Cj3ak-Kk
Apologies for the inexpert and very ugly sight.
When a string is struck, all these frequencies vibrate exactly together to give the tone of the string and form part of the tone of the instrument.
Let's say we have our string at 100 vibrations per second - written 100 Hz - 100 Hertz. This string giving good piano tone will produce vibrations at 100, 200, 300, 400, 500, 600, 700, 800 and more vibrations per second.
We don't have a note specifically for 100 but I am choosing this to make the mathematics easy to see.
If we hold the note down for say 100Hz in the bass and we strike the notes for 200, 400 and 800 (an octave above, two octaves, three octaves and four octaves) then these tones will excite and resonate the bass string and the sound will continue to be heard in the bass string even when the upper note stops sounding. This is demonstrated on https://www.youtube.com/watch?v=Pz0B0SwKpww
where you can hear this effect.
What is interesting is that when we play two notes together, such as 500 and 600 vibrations per second, 100 times per second the vibrations of the two coincide. So the bass note is synthesized as if sounding, without actually being played, a resulting or resultant note. This gives tone and sonority to the instrument and builds the sound.
What becomes interesting also is when we sound together combinations such as 200 and 300 together. We then synthesize the resultant note 100. But the 200 string vibrates with harmonics
200 400 800 1000 1200
and the 300 string vibrates with the harmonics
300 600 900 1200
so we find that the frequency of 1200 is reinforced and adds to the sound as an extra note.
If we sound 500 with this then we add the series
500 1000 1500
so we find 1000 as well as 1200 as well as 100 is added. So the tone of the sound of the instrument becomes reinforced all the more.
The problem with modern piano tuning is that the 300 500 600 700 frequencies are nowhere tuned close enough to the perfect harmonic to add reliably except in a jangling way.
In fact as musicians we have experienced a shimmering to the sound and then we say "what a wonderful piano" - but it has ceased to convey the music as intended nor the emotion.
2. Musically this has reduced the dimensions in which the music can speak, reducing them to
a. loud versus soft
b. slow versus fast
c. discordant versus harmonious
Have you read George Orwell 1984? The new language NEWSPEAK reduced the number of words to 300 so that people were limited in their language to think. This reduction of dimension in music has done the same in music.
3. The meaning of "Chromatic"
As musicians we have been bamboozled into thinking that the chromatic scale is simply going up each note by semitones C C# D D# E F F# G G# A A# B C.
We have forgotten what the language means.
Photographers who are old enough took photographs as transparencies for projection on film called . . . KodaCHROME EctaCHROME FujiCHROME and our lenses are CHROMATICally corrected - which means that on the edges of things in our image we don't see fringes of a spectrum of colours.
In the modern tuned instrument there is no hint of anything that we can call CHROMATIC demonstrating a spectrum of sound.
4. The solution.
The tuning that I use exploits lots of perfect fifths in the exact ratios of 200:300. This brings many thirds in the ratios 500:400 very near to exact and exact enough to resonate, without making other thirds unpleasantly too far from perfect. This is enough to give back the spectrum of colour to the chromatic scale and to chromatic music as exploited in particular by Haydn, Mozart, Beetoven, Schubert, Chopin and Liszt whilst not doing damage to the music of later composers.
The spectrum of sound that we hear is demonstrated on https://youtu.be/qqS_IjKo-d8
The differences of sounds create a reward to the musician for playing sensitively and reacting to the different sounds differently as intended to be heard by the classical composers moulding the sound shapes in the phrasing of the music, conveying meanings unheard in modern tuning but intended to be heard.
We have a corpus of recordings, many of which are acclaimed by musicians who have heard them:
Music in "colour tuning"https://www.youtube.com/watch?v=oMHvl1yH1pw
Bach on Harpsichord
- see the commenthttps://www.youtube.com/watch?v=7JF3YzTG7lU
Bach on pianohttps://www.youtube.com/watch?v=SzlvFcYdVjs
Chopin on Steinway Boston played by Adolfo Barabinohttps://www.youtube.com/watch?v=p7AoF3zvcaI
Brahms violin sonata accompanied by Barabino with Steinwayhttps://www.youtube.com/watch?v=s2py2xz1hX8
Chopin 2nd sonata played by Barabinohttps://www.youtube.com/watch?v=PAPVSlKR8OM
Mozart violin sonata B flathttps://www.youtube.com/watch?v=fJT5Q6HooyA
Chopin Ballade 4https://www.youtube.com/watch?v=qdsFLIo9l88
Chopin 24 preludes https://www.youtube.com/watch?v=A34K-fj5nHshttps://www.youtube.com/watch?v=hgA1-I5MfNY
Chopin 2nd sonata in unequal and equal temperamenthttps://www.youtube.com/watch?v=QnYITP11UgQ
Chopin on Grotein Steinweg. This instrument brings to life the singing thirds.https://www.youtube.com/watch?v=EsKpxZIhc4U
effect on melodyhttps://www.youtube.com/watch?v=nCcRGSvgmz8