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My response to music professor Kurt Ellenberger: Noncommutative nonlocal superluminal sound signals
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The Perfect Fourth is neither an overtone nor a harmonic!
is the column article I responded to.
"Vibrational modes of an ideal string, dividing the string length into integer divisions, producing harmonic partials f, 2f, 3f, 4f, etc. (where f means fundamental frequency)."
"Anachronistically speaking, this means that, supposing both these both cycles meet, there would be m and n integers such that (2:3)n = (1:2)m, that is, 3n = 2m+n, which is impossible, since the left term is odd and the right is even. (Abdounur, 2015)"
if you play a perfect fourth above a fundamental frequency together, in natural resonance, like Indian music, the Perfect Fourth is heard as the fundamental frequency because the Perfect fourth has the lower note as its harmonic while the lower note does NOT have the Perfect Fourth as its harmonic. This demonstrates the Phantom tonic of the PErfect fourth as inherent noncommutativity of reality.
"The thesis can be expressed in the following way: If two drones either a fourth or fifth apart are sounded, one of these will 'naturally' sound like the primary drone. It is not always the lower of the two which will sound primary, but the one which initiates the overtone series to which the other note (or one of its octaves) belongs. By amplifying a prominent overtone the secondary drone lends support to the primary and intensifies its 'primary' character. Ma [Perfect Fourth as 4/3], although consonant to Sa (root tonic), is alien to the overtone series and is not evoked in the sound of Sa. On the other hand, Sa is evoked in the sound of Ma, since Sa is a fifth above Ma and is its second overtone.
For this reason it can be argued that the tendency to view Ma [the Phantom Tonic] as the ground-note has a 'natural' basis. The same cannot be said for Pa [Perfect Fifth] as Sa is not part of its overtone series." Jairazbhoy N. A. (1995). The Rags of North Indian Music: Their Structure and Evolution, Popular Prakashan.
"The thesis can be expressed in the following way: If two drones either a fourth or fifth apart are sounded, one of these will 'naturally' sound like the primary drone. It is not always the lower of the two which will sound primary, but the one which initiates the overtone series to which the other note (or one of its octaves) belongs. By amplifying a prominent overtone the secondary drone lends support to the primary and intensifies its 'primary' character. Ma [Perfect Fourth as 4/3], although consonant to Sa (root tonic), is alien to the overtone series and is not evoked in the sound of Sa. On the other hand, Sa is evoked in the sound of Ma, since Sa is a fifth above Ma and is its second overtone.
For this reason it can be argued that the tendency to view Ma [the Phantom Tonic] as the ground-note has a 'natural' basis. The same cannot be said for Pa [Perfect Fifth] as Sa is not part of its overtone series. Jairazbhoy N. A. (1995). The Rags of North Indian Music: Their Structure and Evolution, Popular Prakashan.
"Nicolas Slonimsky once pointed out, in an effort to dissuade readers from the idea that Western tonality is the inevitable result of how we hear (as opposed to a largely artificial invention), that no matter how high one goes in the harmonic series, a fundamental pitch will not produce a perfect fourth above the fundamental....Just as Slonimsky opined, the perfect fourth above the tonic is nowhere to be found....
One other dominant does exist, however: the one built on the tonic itself. It resolves, not to any note within the scale, but to a foreign pitch—the so-called subdominant. Thus the perfect fourth above the tonic enters the scene, not as part of a stable major scale, but as a tempter, a seducer, a built-in modulation away from the true tonic. The perfect fourth, and not the tritone, is the true “devil in music.” It’s no “subdominant.” It’s the phantom tonic.
This is from the book Music and Sound, published in 1937 by the English organist, composer, and theorist Llewelyn Southworth Lloyd:
All the evidence shows that, in the early stages of a scale developed in the attempt to sing melody, one of two intervals, the fourth as an interval approached downwards, or the fifth, would almost certainly provide its first essential note other than the octave. (Emphasis added.)"
is the column article I responded to.
"Vibrational modes of an ideal string, dividing the string length into integer divisions, producing harmonic partials f, 2f, 3f, 4f, etc. (where f means fundamental frequency)."
"Anachronistically speaking, this means that, supposing both these both cycles meet, there would be m and n integers such that (2:3)n = (1:2)m, that is, 3n = 2m+n, which is impossible, since the left term is odd and the right is even. (Abdounur, 2015)"
if you play a perfect fourth above a fundamental frequency together, in natural resonance, like Indian music, the Perfect Fourth is heard as the fundamental frequency because the Perfect fourth has the lower note as its harmonic while the lower note does NOT have the Perfect Fourth as its harmonic. This demonstrates the Phantom tonic of the PErfect fourth as inherent noncommutativity of reality.
"The thesis can be expressed in the following way: If two drones either a fourth or fifth apart are sounded, one of these will 'naturally' sound like the primary drone. It is not always the lower of the two which will sound primary, but the one which initiates the overtone series to which the other note (or one of its octaves) belongs. By amplifying a prominent overtone the secondary drone lends support to the primary and intensifies its 'primary' character. Ma [Perfect Fourth as 4/3], although consonant to Sa (root tonic), is alien to the overtone series and is not evoked in the sound of Sa. On the other hand, Sa is evoked in the sound of Ma, since Sa is a fifth above Ma and is its second overtone.
For this reason it can be argued that the tendency to view Ma [the Phantom Tonic] as the ground-note has a 'natural' basis. The same cannot be said for Pa [Perfect Fifth] as Sa is not part of its overtone series." Jairazbhoy N. A. (1995). The Rags of North Indian Music: Their Structure and Evolution, Popular Prakashan.
"The thesis can be expressed in the following way: If two drones either a fourth or fifth apart are sounded, one of these will 'naturally' sound like the primary drone. It is not always the lower of the two which will sound primary, but the one which initiates the overtone series to which the other note (or one of its octaves) belongs. By amplifying a prominent overtone the secondary drone lends support to the primary and intensifies its 'primary' character. Ma [Perfect Fourth as 4/3], although consonant to Sa (root tonic), is alien to the overtone series and is not evoked in the sound of Sa. On the other hand, Sa is evoked in the sound of Ma, since Sa is a fifth above Ma and is its second overtone.
For this reason it can be argued that the tendency to view Ma [the Phantom Tonic] as the ground-note has a 'natural' basis. The same cannot be said for Pa [Perfect Fifth] as Sa is not part of its overtone series. Jairazbhoy N. A. (1995). The Rags of North Indian Music: Their Structure and Evolution, Popular Prakashan.
"Nicolas Slonimsky once pointed out, in an effort to dissuade readers from the idea that Western tonality is the inevitable result of how we hear (as opposed to a largely artificial invention), that no matter how high one goes in the harmonic series, a fundamental pitch will not produce a perfect fourth above the fundamental....Just as Slonimsky opined, the perfect fourth above the tonic is nowhere to be found....
One other dominant does exist, however: the one built on the tonic itself. It resolves, not to any note within the scale, but to a foreign pitch—the so-called subdominant. Thus the perfect fourth above the tonic enters the scene, not as part of a stable major scale, but as a tempter, a seducer, a built-in modulation away from the true tonic. The perfect fourth, and not the tritone, is the true “devil in music.” It’s no “subdominant.” It’s the phantom tonic.
This is from the book Music and Sound, published in 1937 by the English organist, composer, and theorist Llewelyn Southworth Lloyd:
All the evidence shows that, in the early stages of a scale developed in the attempt to sing melody, one of two intervals, the fourth as an interval approached downwards, or the fifth, would almost certainly provide its first essential note other than the octave. (Emphasis added.)"
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