Patent Application
VanRaden, Paul
2002
Scalable piano keyboard
Abstract
A scalable piano keyboard or synthesizer
keyboard allows the user to vary the number of notes per octave, to apply new
mathematical rules for tuning the piano, and to easily rearrange the notes on
the keyboard. Instead of a repeating pattern of seven
white keys in a front row separated by five
unevenly spaced black keys in a back
row, two rows of color-coded, evenly spaced keys are used. Every other front key
extends to match every third key in the back row. The back row of keys are the traditional width while the front row of keys are
7/8 the traditional width or 3/2 the width of those in the back. The color
pattern repeats every 8th key in the front row and every 4th key in the back
row, with the result that harmonic notes have
similar colors. Harmony is improved by tuning note n to a frequency
proportional to n / w (linear tuning) or to w / n (reciprocal tuning) instead
of 2 to the power n / w (traditional tuning), where w is width (traditionally
12), defined as the number of notes per doubling of frequency. The user can
choose w for the front row and the width for the back row is then automatically
3 w / 2. The front row of keys divide an octave into
halves, quarters, and eighths while the back row provides thirds, sixths, and twelvths. With linear tuning, the front row gives frequency
ratios such as 3 / 2 and 5 / 4 while the back row gives ratios such as 4 / 3
and 5 / 3. The back row of keys can be tuned to the traditional 12 note scale. Or, the front row can be tuned to the traditional 7 notes A
to G and the back row provides sharps and flats for all 7 instead of only 5. By
choosing w equal to 4, 6, or 8 instead of 7, musical scales are in step with
musical measures. By separating even-numbered notes to the right and
odd-numbered notes to the left, or by grouping together the notes that were an
octave apart, or by using smaller w (fewer notes per octave), even very small children can play nice chords by
pressing the palms of their hands onto a new, scalable piano keyboard.
Invention of the
Scalable Piano
Paul VanRaden
History of the Invention
Year / month |
Idea |
~ 250 BC |
The first organ was
invented by Ctesibius in Greece, but it
had no keyboard and the pipes were played individually. Development continued
among Arabs, primarily in Baghdad, until 757 AD,
when an Arab organ was imported to France. |
~ 900 AD |
Organ keyboards
were developed but had only one row with less than 10 keys. The keys were
large and were played with a fist rather than with the fingers. A keyboard
built in 1090 AD had 16 keys with the repeating letters A to G engraved into
its keys. History books give no reason for the choice of seven notes per octave. |
~ 1350 |
The back row of semi-tone
keys was introduced. The color pattern
on many early organs was reverse: the front keys were black
and the back keys were white. History books give no reason for the uneven pattern of five semi-tone keys per octave. |
~ 1450 |
Organ keys were
reduced to their current width and length. The clavichord was developed and
used a keyboard to play strings instead of pipes. |
~ 1500 |
The harpsichord was
developed in Italy. Its keyboard was copied from that of the clavichord and
organ. |
1709 |
Bartolomeo
Cristofori of Florence, Italy invented the piano. The piano could play soft
or loud by using a row of hammers instead of plucking the strings, but the
keyboard was copied from the harpsichord, clavichord, and organ. |
1824 |
Ludwig van
Beethoven composed his ninth symphony in Vienna, Austria. |
1970 |
Paul VanRaden took
piano lessons at age ten for a year and played Beethoven’s ninth symphony at
a small recital in Forreston, IL, USA. Paul’s
teacher, Leroy Krum, told him that fancier arrangements of the ninth symphony
exist which one person can’t play because the notes needed are beyond the
reach of the fingers. That was the beginning of my idea to re-tune the piano
so that needed notes would be within reach. |
1999 |
Angel VanRaden, Paul’s one-year-old daughter, began playing the
piano with the palms of her hands. Paul wondered why the two notes that sound
the worst when played together are placed right beside each other. He noticed
that the two pairs of white keys that are
not separated by a black key (B,C and E,F) sound
especially bad when played together. He could think of no reason why some
pairs of white keys should be a full
step apart (separated by black keys) and others only a half step apart. He concluded that the
standard keyboard and the C scale with its pattern of two full steps, a half
step, three full steps, and another half step between keys is not ideal but
has been copied without thought since the dark ages. |
1999 Aug |
Paul began research
on mathematical formulas for tuning the piano and purchased a Technics
KN-5000 keyboard with tunable keys for $4,189.50 from Jordan Kitts Music in
Annapolis, MD so that he could hear the results of his theories. |
1999 Aug |
Paul showed the
piano salesman, Jamal Orr, how to get eight even steps on the log 2 frequency
scale on the piano’s white keys (plus F#) and six even steps on the black
keys (plus C). He also showed the salesman a drawing of a new scalable piano
in which every fourth key in the front row lined up with every third key in
the back row (Figure 1). Instead of just black and white keys, shades of grey were used to highlite
every other and every fourth note between octaves so that notes that sound
alike would look alike. A few months later, daughter Angel helped Daddy by
scribbling all over Figure 1 while Daddy was programming his keyboard. |
1999 Sep |
The 8-note and
6-note log 2 tuning was demonstrated to Paul’s coworkers at the USDA
Agriculture Research Service in Beltsville, MD. One coworker, Suzanne
Hubbard, complained that the keys were no longer all in order from low to
high. Paul’s response was “It’s not my fault that the keyboard has two black keys, and then an empty space, and
then three more black keys, and then
another empty space.” He showed his drawing of a scalable piano (Figure 1) to
Ed Lewis and a few other coworkers. |
1999 Nov |
The eight even
steps and the six even steps on the log 2 scale did not include the standard
note G which provides very nice harmony for C. Paul calculated that note G is
halfway between the C below it and the C above it on the frequency scale, not
the log 2 scale. The relative frequencies of C, G, and the next C are 1, 1.5, and 2. Thus, evenly spaced notes on the
frequency scale give better harmony than evenly spaced notes on the log 2
scale (Figure 2). If the piano were tuned with even steps on the frequency
instead of log 2 scale, relative frequencies would increase from 1 to 2 to 3
to 4 instead of 1 to 2 to 4 to 8 across the keyboard. Paul then developed new
theories of harmony including intersecting linear harmony, parallel harmony,
and negative notes (anti-sound). He tested the new types of harmony on his
keyboard and liked what he heard. Beethoven’s ninth symphony sounded better
when played with linear tuning than with standard tuning. |
1999 Dec |
Reciprocal tuning
using the formula w / n instead of n / w, where n is the note number and w is
width or number of notes per octave, was discovered by Paul. These formulas
seemed simpler and better than standard piano tuning, which is based on
relative frequencies of 2 to the power (n / w), with w set to 12. The KN-5000
also allowed the user to set w to 24 or 48 instead of 12, but the uneven
pattern of black keys prevented the use of any w smaller than 12. |
1999 Dec |
Paul sent a letter
explaining log 2, linear, and reciprocal piano tuning (Letter 1) to Technics
/ Matsushita Corporation in Secaucus, NJ. Tables of note frequencies, a
program to compute these, and a diskette containing songs and scales with new
or standard tuning were included. These ideas on tuning were provided free of
charge because Paul believed that simple math was not patentable and because
he hoped that the company would provide these new tuning options on its
standard keyboards and thereby help create demand for a scalable keyboard.
Few people will listen to new music theories, but many will listen to new
music. |
1999 Dec 31 |
The new keyboard’s
physical structure (Figure 3) was drawn by Paul while he watched the new
millennium celebrations on New Year’s Eve. He finished the drawing at about 1
am January 1, 2000. |
2000 Jan |
A color coding system
for piano keys was developed so that keys which sound similar (for example,
one octave apart) would look similar (Figure 4). With unevenly spaced keys, the pattern of black keys helped users to
locate similar notes. With evenly spaced keys, color coding provides a similar visual aid. Paul
drew raised bumps on the front and/or
back of every other, every fourth, or every eighth key to help users easily
locate notes by sight
and feel (Figure 5). |
2000 Jan |
Rearrangements of
the notes onto the piano keyboard were developed such that the notes which
sound best together would be located on keys that are side by side. For
example, even numbered notes could be separated to the right and odd numbered
notes to the left, or all A notes placed together, B notes together, etc.
This would allow the user to play many more harmonious notes that previously
were out of reach of the fingers. |
2000 Mar |
Improved music
notation was developed by Paul. Colored
lines
on white paper match exactly with the colored
piano keys (Figure 6). |
2002 Feb |
Paul placed this
patent application and this document on his web site. |
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