Speculation on an 'Undertone Series'

[Oscar South]

I understand that this area isn't for everyone, but I like to explore theoretical and speculative areas of music. Even if it ends up being impractical or outright pointless I like 'flexing the muscles' of my musical brain to keep things fresh, and it can be the source of new ideas or even genuinely new insight.

Anyway, this post is discussing the possible existence of an 'Undertone series'.

This is in it's essence a speculative mathematical inversion of the overtone series. Here are the first 5 notes of the undertone series including the fundamental:

Freq | Ratio | Series
440 | 1/1 | fundamental
220 | 1/2 | 1st
146.6r | 1/3 | 2nd
110 | 1/4 | 3rd
88 | 1/5 | 4th

This has generally been considered a speculative concept, with many researchers proposing that it's only possible to demonstrate through a process of arbitrary mathematical tone generation based off the overtone series. It has been discovered as a physical phenomenon however and is demonstrated in the following video, where the author holds a ringing tuning fork to a piece of paper. Sometimes the fork touches the paper every oscillation, sometimes every second, sometimes every third (etc.).
[url="https://youtu.be/Gh8k_dcG708?t=58s"]https://youtu.be/Gh8k_dcG708?t=58s[/url]

This creates the psychological effect of perceiving a series of descending frequencies which exactly inverts the ascending intervals of the overtone series. The overtone series is the perfect mathematical division of a fundamental frequency in ascending intervals. The undertone series is the formation of multiplying the fundamental frequency by values of 1, 2, 3, 4 etc. (can anyone tell me what the mathematical term for this is?). The resulting effect is an exact mirror image of the overtone series.

An interesting speculation is that the while the overtone series is used to explain the existence of the major chord as a centre point of harmony through it's presence inside the first few notes of the overtone series, the minor chord is equally explained by the undertone series as a minor triad built on the subdominant exists in it's first few degrees. This also gives the emotive properties of major and minor chords a logical explanation, because the 'extraversion' of major harmony literally comes from physical existence of the overtone series in the outside world entering our sensory systems. By contrast if minor harmony is theoretically derived from the undertone series, then it's 'introversion' can be attributed to the fact that the most tangible case for the practical existence of an undertone series is in the internal psychoacoustic perception of pitch.

I spotted this recently, which is a very nice composition based on the mathematically derived Undertone Series:
[url="https://www.youtube.com/watch?v=3tysYkxX-jY"]https://www.youtube....h?v=3tysYkxX-jY[/url]

Anyone have any thought, opinions or questions about this?

Edited July 19, 2015 by Oscar South

[alyctes]

Interesting. The major/minor idea sounds daft to me, but I can't pin down the reason.

Presumably you're going to start with high pitches (violin? flute?) and work downwards from there?