A Small Taste from My New Book: Episode 10 Explorations in analytic number theory, asymptotic analysis, and unsolved problems, written by a mathematician and software engineer.

Between sums and integrals, a constant quietly reveals itself.
#EulersConstant #HarmonicSeries
#IntegralRepresentations #DeepStructure
cortexdrifter.blogspot.com/2026/02/a-sm...

Why Natural Harmonics Are Amazing!

The track I play at the end of the video is called

Tim Scott - Dirty Mule

#naturalharmonics #guitartechnique #guitarists #guitarteacher #guitarlessons #harmonics #harmonicseries

Swanrise

youtu.be/rtL3Vo7yAeM?...

To find out more about this track, and about @chrispthompson.bsky.social please go to: pipeastop.bandcamp.com/track/swanrise

#acoustic
#classical
#frenchhorn
#piano
#sibelius
#harmonicseries
#hornsection
#microtonal
#naturalhorn
#handhorn
#swans

Swanrise, by Pip Eastop track by Pip Eastop

pipeastop.bandcamp.com/track/swanrise

This work started off as an amazing piano piece by Chris. P Thompson
Check him out @chrispthompson.bsky.social

#piano
#harmonicseries
#NowPlaying
#handhorn
#naturalhorn
#hornsection

A madness most discreet, by Pip Eastop track by Pip Eastop

pipeastop.bandcamp.com/track/a-madn...

A work for two harmonic-series-tuned pianos and two natural horns, much influenced by @chrispthompson.bsky.social

#frenchhorn
#handhorn
#piano
#harmonicseries
#naturalhorn
#NowPlaying

process of calculating the constant part of the value of the harmonic series

By treating the blue areas in the graph as triangles, I worked out an approximation for the #HarmonicSeries: Hn ≈ ln(x) + 1/2 (x ≥ 1). With the exact constant (~0.577, the #EulerMascheroniConstant), I wasn’t far off!

graph showing the functions 1/x and ln(x)

The fact that the #HarmonicSeries, ∑(1/n) from n=1 to ∞ diverges to ∞ felt so counterintuitive at first—but it was surprisingly easy to prove with this magic graph! Truly one of the most beautiful things I’ve ever seen. #Math #KhanAcademy #Calculus

A newish piece of mine for guitar and electronics. #classicalguitar #electronics #harmonicseries #overtones #spectral #electroacoustic Performance by Julien Payan FR youtu.be/ke9j8_CaRtI?...

Hayward Gallery tonight at the end of the #HarmonicSeries concert where Carsten Höller's Pill Clock was before.

Hayward Gallery Art Gallery in London, Greater London

Now, our final time in here for 2yrs, for a #HarmonicSeries performance (@ Hayward Gallery) http://4sq.com/1NcqzNe