jsinjin - Posted - 09/11/2025:  14:42:01

I’m fascinated by music theory and have a lot of catching up to do with people who were exposed to it growing up. I’ve been reading and working through three books that have helped me so much. I found all three at either thriftbooks website or half priced books.

The first is “Physics and Music” by white and white. It explains the general principles of sound and musical scales. It helped me understand the nodes and vibrations of a string pinned at both ends (as well as open or closed tubes). It’s interesting that I recall having this in AP physics in high school decades ago but not realizing that it was connected to music and that this defined so much of music.

I sort of imagined that music was a set of a distribution of all frequencies of sound and humans just picked the ones we liked for the notes but that was a completely wrong assumption. This was so helpful to me. I literally had no idea why the frets and selections of the keys were set up the way they are. I realized with a lot of excitement that when tuned to a G the second harmonic is at the 12th fret is first at halfway on the string length and second when I ran it through an oscilloscope it was exactly double the frequency at roughly 392 hz. This is probably a “duh” moment for everyone else but I never thought of the instrument this way.

So at a 2:1 ratio in the string length you go to an octave up

Then at 1/3 the string length at a ratio of 2/3 at the 19th fret I get 588 hz which is 3x the G frequency and a D

This then completely explained the harmonic overtones and their purity at frets 12, 7, 5, and 4 (and I suppose mathematically right between 3 and 4 at roughly 3.2 fret if there is such a thing).

This reminds me so much of optical spectrophotometrics of emitted light. I recall as a graduate student seeing a spectrum for the first time in fluorescence of an emitter and then when the spectrum was read on the diode array there were these clear peaks way down in the UV. I didn’t know what they were at the time and the post doc in the lab just laughed and said they were harmonics of the frequency doubling of the emitted light constructively adding and picked up by the detector.

So much about the instrument is finally making sense to me.

The next two books are Tonal Harmony by Kostka etal (along with the workbook for that book) and Music theory for guitarists.

These two books along with the workbook helped me so much to understand the fourths reason for the common tuning with the fifth string at a fifth jump.

I realized that the common tuning for the tenor banjo is in fifths all the way across and I tuned mine (ignoring the fifth string) over to DGCF which then I could tell dramatically moved the notes farther apart.

I think this combination of books has moved me faster farther and made me more excited and comfortable with my instrument than anything I’ve done before. This is exactly what I’ve been looking for in how to play!

banjoboyd - Posted - 09/11/2025:  15:08:38

I sort of imagined that music was a set of a distribution of all frequencies of sound and humans just picked the ones we liked for the notes but that was a completely wrong assumption.

The basic assumption is correct -- every musical system is indeed a limited set of frequencies pulled from an infinitely divisible spectrum.  And we do pick based on what we like. But that picking process is conplex, influenced by biological as well as material/technological and cultural factors. We find, for example, in cultures that make prominent use of pitched percussion instruments -- which do not exhibit harmonic overtones -- that the frequencies they pick likewise diverge from a strictly harmonic pallette. And we find in cultures that do focus on string and wind instruments but do not organize their music around vertical sonorities (that is, chords), they pick frequencies that can be explained harmonically but which do not exist in the Western 12-tone system. 

I highly recommend William Sethares's work, Timbre, Tuning, Spectrum, Scale for a scientific (but not Eurocentric) approach to understanding musical systems.

banjobob36 - Posted - 09/11/2025:  15:26:17

Exactly. Bluegrass banjo however uses a different standard 3 finger roll ...without any type of detected lighting or Lonesome Standard Time.

banjoboyd - Posted - 09/11/2025:  15:53:36

Of course, if you're interested in tracing the historical progression of this type of theory, you should start with Helmholtz's On the Sensations of Tone. 

jsinjin - Posted - 09/11/2025:  16:04:04

quote:

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Originally posted by banjoboyd

Of course, if you're interested in tracing the historical progression of this type of theory, you should start with Helmholtz's On the Sensations of Tone. 

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I'm assuming that's Helmholtz of the free energy equations and black body radiator theory.   Maybe.  I don't know if I'll go into the history but I'm absolutely feeling so much better and less random about playing now!

ALCO - Posted - 09/11/2025:  22:17:16

John, the following suggestions are somewhat related to the subject of your post.

Look at the history, science and performance of the Theremin.

If you ever decide to learn the guitar (I think you should), I highly recommend Richard Lloyd's instructional DVD, 'The Alchemical Guitarist'.

Regarding the previous conversation we had, did you ever try the chromatic harmonica?