Chords and the Mathematical Fretboard | Maths and Music | N J Wildberger
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- čas přidán 27. 07. 2024
- We look at how the 12 tone chromatic scale system provides a powerful tool for learning to navigate around a guitar and to identify and locate chords, with particular emphasis on triads and tetrads (four note chords). This is a step away from the current piano-focused system of musical nomenclature and terminology which is fundamentally at odds with the more translation invariant symmetry encompassed by the modern guitar.
It will also be an important step as we move to consider more general and canonical ways of applying mathematical notions to simplify and rationalize our understanding of music and its theory.
Video Contents:
00:00 Introduction
01:51 Basic structure of a guitar and the fretboard
09:19 From one string to the next
21:26 Definition of a chord
22:14 Chords with three notes: Triads
26:03 Chords with four notes: Tetrads
29:13 Types of triads
33:42 Finding triads on the fretboard
This is one of my favorite videos ever.
Great to see this series continuing. Music theory needs this reimagining
Thanks doc, this is going to be a godsend for mapping alternative tunings for math rock and emo music.
Really I appreciate your explanation in this mathematical model.
For mathematics enthusiasts guitar oneself learners it could be interesting and also useful 😀👏
Me, as musician and guitar and piano player & composer since 12 years I think that knowing the chromatic scale, guitar afination, every fret is a semitone, the basic chord triada structure, even as the semitones of every interval it's easy to learn maybe easier...
You quickly understand the efect from moving one fret up or down, chord definition and inversions, traspose melodies or chords and so on...
What is clear is that if you try to code a computer program to edit or compose or process music the definition of the notes as a set {0 1,2..11} the mod12 , floor(12) operators, a correct notation for harmonic and melodic intervals, time scale(rhythm) and dynamics it's perfect..
Thank you for your approach !!
Maths are in my life !!
😀
Thanks
Great eye opener to me, thank you.
Color code the numbers to make the patterns pop!
i had a hard time with my guitar learning in the beginning days... but this makes things/strings so intresting.... ❤️❤️❤️❤️ them... thank you professor🙏
Hats off Professor, this has already improved my playing, thanks a lot :D
The overtone harmonics of the flute notes are also very interesting. How does the flute note of the golden section sound like?
Besides overtones, there are also undertones, which are utilized by throat singing, electronic wave manipulation etc. Relation between undertones and overtones is very interesting from the perspective of general measurement theory, as a vibrating string of any finite length can measure only the overtones it contains as shorter wave lengths, but not longer undertones.
I love it because I was good at math :D
If you change 10 and 11 to T and E or X and E then you can treat it as a base 12 system, the octave becomes 10, the perfect fifth up and octave become 17.
@Tjeva Absolutely -- our musical system provides strong motivation to think more about a base 12 system.
@@njwildberger Exactly and then heptatonic scale degrees become base 7 indexes of different patterns.
When you get a chance to look at 31-TET you can create a MUCH better sounding MEANTONE keyboard using the 0,5,10,13,18,23,28 positions for the white keys.
Hello Dr, thank you for your interesting videos, I wanted to ask if it is possible to get the position of a floating unit that we don't know how course and speed it is, just with a different radar direction at different times.
Welcome to my world.
how would you notate or graph the notion of tonal center ?
I had previously read some interesting history of musical theory related to heavy metal music, where apparently a couple of the early innovations were to tune the guitar differently (is it called 'drop D'?) and to make use of 'tritones'.
I don't play music myself, so I've heard of this but don't really know what it means in reality. Do you have any insight as to how these differences relate to your mathematical fretboard? How would the different tuning be represented? And how are tritones played (I guess they are like chords?), whether on the original tuning, or on the adjusted tuning?
Is the adjusted tuning really related to playing tritones, as I'm guessing, or are they two separate innovations that together characterize heavy metal (especially early heavy metal, I believe, such as by Black Sabbath)?
Hi Rob, While tritones (what I would call a 6-step) are generally viewed as dissonant, they are convenient theoretically, as they exactly split an octave into two equal pieces. I don't know about the heavy metal use of these though, sounds interesting.
Roughly speaking, I heard that one of the rules European composers followed was that you never ever have successive 'power chords"(they were called something else but you know what I mean...in number tabbing you got something like this:
G-----2--
D--5-0--
A--3-----
E---------)
While showing this with numbers is illustrative, I would advice getting used to interval names asap.
@Kristian -- Yes, but hopefully the numerical interval names: 5-step, 7-step etc!
@@njwildbergerThat terminology exists, just say semitone instead of step. The interval names are not based on chromatic steps but diatonic.
@@whig01 I am trying to gently get people to step back from the piano based and diatonic conventions that currently dominate. This frees us up to have notation and terminology better suited for a variety of instruments and a variety of cultural / musical backgrounds. The mathematical logical approach I believe is to base our analysis on the numerics of the 12 tone chromatic scale, for which it is the step which plays the role of the fundamental unit. Hence it deserves a more central name than "semitone" or "half-tone".
@@njwildberger I dislike the dissonance of 12-TET thirds and think we should move away from it as soon as possible, but diatonic numbering still works when using 31-TET as I specified the positions above for the white keys.
Solfeggio is the foundation of diatonic conventions, not the piano 12-TET.
A thought just occurred to me as you were talking about chords as increasing sequences of notes, and the corresponding interval sequence as the successive differences between them: This reminds me of the usage of (was it Netwon's) Forward and Backward differences, and their relation to calculus as like discrete versions of derivatives (and sums as integrals). Is there perhaps a way in which one could literally play the (discrete) 'derivative' or 'integral' of some musical 'function'??? What would that sound like?
Thinking in terms of Fourier decomposition, I would guess that the derivative brings out the overtones. Have to try it though, once I get back to my computer!
By the way another nice thing to try is to take a Bach recording, and convolve it with itself backwards. It sounds pretty nice and smooth.
@@JoelSjogren0 Wow, cool! Amazing that someone out there already has some idea of how to actually do the derivative thing. And I can just imagine the Bach convolution thing sounding really cool, too. 😃
I've never been interested in music, but your videos on the mathematics behind it have made me consider picking up an instrument. what would you recommend for a beginner?
@BananaMan That's an easy question to answer: I would recommend the guitar. It is easy to learn, and you can sing with it!
@@njwildberger Thanks for the recommendation.