pls consider my apology for nit-picking. I suspect you were only referring to the first harmonics anyways. I think you made a good and interesting point that they are octaves of the fundamental.
No apology needed!
The first harmonic is the fundamental, and my incorrect statement regarding all even order harmonics being octaves was much larger than a nit 😳
Harmonics are multiples of the fundamental frequency “H1” in Hz (cycles per second).
The harmonic series is an arithmetic series where the difference between consecutive harmonics is constant and equal to H1, even and odd orders of the fundamental frequency, H1, H2, H3, H4, H5 etc.
The octave series is a geometric progression of even order multiples doubling the previous number, H2, H4, H8, H16, etc.
In musical terms, being one octave higher, H2 sounds the same note as H1.
H4 sounds the same note two octaves above H1.
A major chord consists of the root note, a third (two scale degrees above) and a fifth (five scale degrees above).
For example, a C major chord consists of the root note “C”, the third, “E”, and the fifth “G”.
A minor chord flattens the third, using a note a half step (a semitone) below the third.
Omitting the third forms a dyad, also known as a “power chord” in pop or rock music, which works with both major and minor keys.
H3 sounds like a perfect fifth, forming a “power chord” with H1.
https://www.audiolabs-erlangen.de/resources/MIR/FMP/C1/C1S3_HarmonicSeries.html
The MaxxBass patent describes a “residue harmonics generator“ which generates a sequence of harmonics that includes at least three consecutive harmonics from the fundamental frequency within the range of interest.
H2, H3, H4 could be used in this sequence and convey the effect of the missing fundamental notes below the set frequency range used, without affecting the perceived note value.
If the consecutive harmonics H2-H4 are below the range of the speaker using the harmonics generator, the non-consecutive H6, H8, H12, and H16 could also be used without affecting the perceived note value.
The first harmonic is the fundamental, and my incorrect statement regarding all even order harmonics being octaves was much larger than a nit 😳
Harmonics are multiples of the fundamental frequency “H1” in Hz (cycles per second).
The harmonic series is an arithmetic series where the difference between consecutive harmonics is constant and equal to H1, even and odd orders of the fundamental frequency, H1, H2, H3, H4, H5 etc.
The octave series is a geometric progression of even order multiples doubling the previous number, H2, H4, H8, H16, etc.
In musical terms, being one octave higher, H2 sounds the same note as H1.
H4 sounds the same note two octaves above H1.
A major chord consists of the root note, a third (two scale degrees above) and a fifth (five scale degrees above).
For example, a C major chord consists of the root note “C”, the third, “E”, and the fifth “G”.
A minor chord flattens the third, using a note a half step (a semitone) below the third.
Omitting the third forms a dyad, also known as a “power chord” in pop or rock music, which works with both major and minor keys.
H3 sounds like a perfect fifth, forming a “power chord” with H1.
https://www.audiolabs-erlangen.de/resources/MIR/FMP/C1/C1S3_HarmonicSeries.html
The MaxxBass patent describes a “residue harmonics generator“ which generates a sequence of harmonics that includes at least three consecutive harmonics from the fundamental frequency within the range of interest.
H2, H3, H4 could be used in this sequence and convey the effect of the missing fundamental notes below the set frequency range used, without affecting the perceived note value.
If the consecutive harmonics H2-H4 are below the range of the speaker using the harmonics generator, the non-consecutive H6, H8, H12, and H16 could also be used without affecting the perceived note value.
All cell phones and small bluetooth speaker has this feature. They play with much much "more" bass than the physically can achieve.
My guess is that they below 200Hz use 4th and 6th... etc harmonic to create bass notes.
My guess is that they below 200Hz use 4th and 6th... etc harmonic to create bass notes.