Vibrating strings and Chladni Plates (Cymatics) have been used to demonstrate or explain harmonic vibrations. Per these examples, Jacob’s Ladder may or may not define a valid concept for a harmonic, sub-harmonic, or a harmonic distribution. Vibrating strings and Chladni Plates define harmonic vibrations based on the concept of a standing wave with the associated antinodes and nodes. Jacobs Ladder is based on sequential, exponential values of golden ratio proportions. It is independent of the system it is being used to evaluate. Per this color research, Jacob’s Ladder has been applied to vibrations in free space (midair). Music theory allows Jacob’s Ladder to be applied to the actively vibrating strings of a piano. This color research believes that there are differences between things that vibrate, things that are vibrated, and things that ring when impacted. The electromagnetic spectrum is a constant vibration. Vibrating string and Chladni Plate experiments are examples of things being vibrated. The mechanical vibrations of sound and piano strings are examples of things that ring when impacted. Something that is ringing could also be or produce pressure waves. At the atomic level, everything vibrates, with few exceptions. The color theory of this research developed while this researcher was attempting to define color within the visible light spectrum, by using numbers and geometry. A numerical and geometric color pattern was discovered within the visible light spectrum. If the entire electromagnetic spectrum is light, then the color pattern should be applicable to the entire electromagnetic spectrum. A repeating color pattern was discovered within the electromagnetic spectrum, and it was named Jacob’s Ladder. The frequencies at the lower end of the electromagnetic spectrum are also found within the range of audible sound (20 Hz to 20,000 Hz). If frequencies are frequencies, cycles/second, then Jacob’s Ladder would be applicable to audible sound (mechanical vibrations). To test this assumption, the color pattern was applied to basic music theory. Pythagoras doubled or halved Primary Tone ``A'' at 440 Hz to obtain four octaves above and below the Primary Tone “A” reference. Nine music octaves are defined which partially overlap their adjacent music octaves. As a group, the nine music octaves, A0 to A8, have little correlation to the 13 color octaves, C0 to C12 (A0 to A12) for the range of audible sound. Individually, a single music octave and a single color octave can approximate each other. Color octaves divide the range of audible sound into 13 color octaves, compared to the nine octaves of basic music theory. Color octaves are color harmonics and color harmonics are color octaves. Each music octave contains 12 semitones, even temperament, and arranged per the counting of the Perfect Fifth. It results in the chromatic scale of the Circle of Fifths. The Circle of Fifths is like a spiral staircase. Ascending 360° clockwise defines a rising color octave or color harmonic. Descending 360° counterclockwise defines a lowering color octave or color sub-harmonic. Jacob’s Ladder promotes the concept of color harmonic vibrations with a correlation to color, radiation, sound, and basic music theory. It is based on the music octave and chromatic semitones as described by Pythagoras’ Circle of Fifths. We are in Primary Tone “F”. Sunlight is in Primary Tome “F”. Jacob’s Ladder is an exponential, 12th-root, “golden ratio-based” distribution of harmonic frequencies (vibrations) along the x-axis. Jacob’s Ladder is not linear. It is on an exponential, logarithmic, and golden ratio curve. There are 12 color references (Six Primary Colors and Six Primary Color Interfaces). Within Jacob’s Ladder, adjacent color harmonics or color octaves meet at the same point, but they do not overlap. Vibrating string and Chladni Plate experiments, with their associated standing waves, antinodes, and nodes are accepted methods of defining a harmonic vibration. Jacob’s Ladder as, a harmonic distribution, color harmonics, and color octaves, calls the definition of a harmonic into question. An effort will be made to contrast vibrating string and Chladni Plates experiments with the mechanics of Jacob’s Ladder.

Color Theory: Basic Color Models 10.0 Basic Music Theory 5.0: Harmonics

章节
发表日期：

2026年

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Carl Swopes

摘要

Vibrating strings and Chladni Plates (Cymatics) have been used to demonstrate or explain harmonic vibrations. Per these examples, Jacob’s Ladder may or may not define a valid concept for a harmonic, sub-harmonic, or a harmonic distribution. Vibrating strings and Chladni Plates define harmonic vibrations based on the concept of a standing wave with the associated antinodes and nodes. Jacobs Ladder is based on sequential, exponential values of golden ratio proportions. It is independent of the system it is being used to evaluate. Per this color research, Jacob’s Ladder has been applied to vibrations in free space (midair). Music theory allows Jacob’s Ladder to be applied to the actively vibrating strings of a piano. This color research believes that there are differences between things that vibrate, things that are vibrated, and things that ring when impacted. The electromagnetic spectrum is a constant vibration. Vibrating string and Chladni Plate experiments are examples of things being vibrated. The mechanical vibrations of sound and piano strings are examples of things that ring when impacted. Something that is ringing could also be or produce pressure waves. At the atomic level, everything vibrates, with few exceptions. The color theory of this research developed while this researcher was attempting to define color within the visible light spectrum, by using numbers and geometry. A numerical and geometric color pattern was discovered within the visible light spectrum. If the entire electromagnetic spectrum is light, then the color pattern should be applicable to the entire electromagnetic spectrum. A repeating color pattern was discovered within the electromagnetic spectrum, and it was named Jacob’s Ladder. The frequencies at the lower end of the electromagnetic spectrum are also found within the range of audible sound (20 Hz to 20,000 Hz). If frequencies are frequencies, cycles/second, then Jacob’s Ladder would be applicable to audible sound (mechanical vibrations). To test this assumption, the color pattern was applied to basic music theory. Pythagoras doubled or halved Primary Tone ``A'' at 440 Hz to obtain four octaves above and below the Primary Tone “A” reference. Nine music octaves are defined which partially overlap their adjacent music octaves. As a group, the nine music octaves, A0 to A8, have little correlation to the 13 color octaves, C0 to C12 (A0 to A12) for the range of audible sound. Individually, a single music octave and a single color octave can approximate each other. Color octaves divide the range of audible sound into 13 color octaves, compared to the nine octaves of basic music theory. Color octaves are color harmonics and color harmonics are color octaves. Each music octave contains 12 semitones, even temperament, and arranged per the counting of the Perfect Fifth. It results in the chromatic scale of the Circle of Fifths. The Circle of Fifths is like a spiral staircase. Ascending 360° clockwise defines a rising color octave or color harmonic. Descending 360° counterclockwise defines a lowering color octave or color sub-harmonic. Jacob’s Ladder promotes the concept of color harmonic vibrations with a correlation to color, radiation, sound, and basic music theory. It is based on the music octave and chromatic semitones as described by Pythagoras’ Circle of Fifths. We are in Primary Tone “F”. Sunlight is in Primary Tome “F”. Jacob’s Ladder is an exponential, 12th-root, “golden ratio-based” distribution of harmonic frequencies (vibrations) along the x-axis. Jacob’s Ladder is not linear. It is on an exponential, logarithmic, and golden ratio curve. There are 12 color references (Six Primary Colors and Six Primary Color Interfaces). Within Jacob’s Ladder, adjacent color harmonics or color octaves meet at the same point, but they do not overlap. Vibrating string and Chladni Plate experiments, with their associated standing waves, antinodes, and nodes are accepted methods of defining a harmonic vibration. Jacob’s Ladder as, a harmonic distribution, color harmonics, and color octaves, calls the definition of a harmonic into question. An effort will be made to contrast vibrating string and Chladni Plates experiments with the mechanics of Jacob’s Ladder.