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Chords and keys and note spacing was soo confusing . I struggled all the time with what chords to play where . If I only let my mind think of the numbers and follow their positions it all is soo simple now . Why could I not get it when I was younger? It all made sense when I saw John Hartford call out the chord numbers instead of the chord names on a video , made it click , the key is the key
Edited by - laguna21dc on 02/05/2025 00:42:00
I would not go so far as to call the practical description of musical tones "math." Arithmetic is really the more appropriate description.
Music was once considered a science, and along with Arithmetic, Geometry and Astronomy was among the Quadrivium of sciences within the Seven Liberal Arts. Analysis of the interrelationship of musical intervals is really just about counting, addition and subtraction. Mathematics has to do with broadly different theoretical concepts.
As for why a more mature mind can more easily grasp the concepts, it's about combining left and right brain functions. When a person is first encountering music and attempting to make sense of the aural experience, he or she is using the right brain, which is centered on creativity, spatial awareness, and emotional response. The left brain processes language, logic, and analytical thinking. If it's easier to understand now, I reckon you've achieved the proper combination of the hemispheres.
I've never been able to figure out how math/arithmetic/?? helps get the music from the brain to the fingers.
I was pretty decent at math/arithmetic/sciences through high school, though age and dormancy (?) is taking a toll. I started banjo about 13ish years ago ... IF the past is any indicator of the future I doubt there's enough time left for my mind to mature and grasp the concepts.
[And, fwiw, that's just me thinking out loud, not a call for referrals to a teacher/method/program ............ unless it's something pretty unconventional. ]
Edit: Chicken/egg question re. "The equal tempered scale is based upon a logarithmic relationship."
Edited by - Owen on 02/06/2025 08:52:09
quote:
Originally posted by RB3The equal tempered scale is based upon a logarithmic relationship; I think that would put us into the realm of mathematics.
Certainly, when you enter the realm of the division of the octave into intervals (Pythagoras), and of fudging the distance between those intervals to arrive at a temperament of the scale, that involves math. But for the practical purpose of determining how to build a chord from a scale and how to describe the sequence and interaction of chords, that's arithmetic.
I think OP is referring to assigning numbers, a system to describe as numeric relationship; as opposed to fixed letter names. Mostly it's just counting to 7, if consider that as doing some math.
I suppose could be related to having familiarity in doing algebra, using a variable starting point "x". Then x+2; x+5... but again just counting.
quote:
Originally posted by Owen
Edit: Chicken/egg question re. "The equal tempered scale is based upon a logarithmic relationship."
Not sure what asking.
Music based on idea of dividing the octave into 12 seemingly equal like parts goes way back; approximately but not exact; and predates the accurate math and tools ability to even accurately measure frequency.
Observation that pitch it's not linear, the space between notes gets shorter as get higher, thus concept of logarithmic relation, is pretty old. The idea taking that into 12 equal, to play in any key, was pragmatic solution to instruments like on fretted lutes; applied later to keyboards. But as calculations/formulas were more understood, it ran into obvious contradictions with other aspects of how defined intonation of fifths, thirds, sixths; which felt more important; (12TET just didn't sound good to them).
But then as composers wanted to create music that more to expand harmonically, any key and modulate on the fly (without retune); 12TET favored over the better harmony.
Owen,
Everything I've read, and common sense, indicates that your "a)" is correct.
In the beginning there was music; the mathematical/scientific analysis came later.
"These imaginary and vital forms and cultural experiences of a people [i.e. poetry and music] appear before the philosophical and rational developments that are in fact entirely derived from them." (Joseph Luzzi, Dante biographer, summarizing a revolutionary proposition of the early Enlightenment scholar/historian Giambattista Vico.)
Thanks Tim. That's kinda how I see it, but then guys tell me that music is "as simple as ABCDEFG / 1234567," or that I have the prerequisite smarts (?) IF I can come up with the next item in a pattern: A B B A B B A B ___ .
Maybe the relationship is comparable to, or can be explained (?) by:
I'd be surprised if there much positive correlation between proficiency at music and proficiency at math/arithmetic.
Edited by - Owen on 02/06/2025 17:39:46
the major chord notes can be described by exact ratios --their excursions meet quiet often-- -our dna wants harmony-- even our hearing cochlea sends separate files to the brain ,in octave divisions ---
all the rest--the in between stuff -that is not so harmonious to our ears - has not been found in mathematic explanation--in other words--minor sad chord--suspenseful 7ths,diminished,blue notes etc --
my view --I ask no agreement
quote:
Originally posted by OwenI was wondering which came first .... a) was the music already being played and then math was applied to "explain" it, or b) did the math lead to new music being written or advanced upon that wouldn't/couldn't have happened without the math..
Sort of both...
Music was largely played by just what sounded good; and then later discover what explained why those harmonic interval relation sounded good, and math of that; for example 3:2 or 5:4, 6:5... and so on; works well for one diatonic key scale and chords.
However, that had limits, esp when dealing with very fixed pitch instruments, and playing in different keys/chords; ability to utilize all 12 notes to octave. So solution was that some notes had to be tempered, slightly out of tune in order to achieve a balance. The idea of tempered, still based on general quality above, just that the some of tempered notes will be close enough to sound okay. They were using math to work out many different/various meantone temperaments, and what they thought worked better. Meantone typically made some intervals closer to pure for some keys/chords, not others, and that gave different keys different relationships and flavors; and some composers did write for that.
Eventually they worked out solution, math for a temperament of 12 equal (logrithmic spaced) pitches. Which allows music to be written with that in mind, that it has freedom to modulate, pieces that moves outside of one diatonic key/chords; which just wouldn't work well in pure intonation, nor meantone temperaments played on fixed pitch instruments.
Edited by - banjoak on 02/07/2025 16:30:40
quote:
Originally posted by laguna21dcIf I only let my mind think of the numbers and follow their positions it all is soo simple now
Everyone seems to stop at the I IV V. This PDF shows the simple 1-7 mathematical relationships between the CHORDS AND THE MELODY.
quote:
Originally posted by OwenI was wondering which came first .... a) was the music already being played and then math was applied to "explain" it, or b) did the math lead to new music being written or advanced upon that wouldn't/couldn't have happened without the math..
As usual, both. Not only equal temperament, but many compositions where written starting with mathematical relationships (Bach being prominent IIRC).
Thank you kindly.
every time the root note has executed 4 excursions (complete phases of a wave)--so-anyway -- at four excursions mark--the third of the scale makes exactly 5 excursions --it is faster at 1.25 waves--next --on up to the 5th (a G note in a C chord) it is even faster at 1.5--every time the c hits twice the g hits 3---at 8 C excursions the E note has made an exact (kinda)number of10 and the G note has done12--this is all hitting in sync in micro seconds
Edited by - Tractor1 on 02/08/2025 08:16:03
I dunno ... it might have some correlation with school/community size and what other opportunities there are/aren't. Small sample size, but back before my wife was my wife, in her smallish, rural-ish N.S. community sports were pretty ifffy .... the Citizen's band was "where it's at." [She wasn't in the advanced math track ... if there was one .... but she was smart (?) enough to marry me. ]
I am just explaining the place where math shows the property of being in harmony--music also has other tricks up it's sleeve--I kinda guess -that certain sounds match other sounds----- that occur to us during emotional events--Even notes extremely out of basic harmony--ring the same mood on and on--
as far as being a better player--there is not a drop of -(free ride) in knowing this--Earl's book shows how to build the scale by cutting each semitone section by a ratio on the end --then the left over gets cut by the same ratio--he said it was a logarithmic action--until then I had no idea what logarithms were--and never found a need to use the info-- to make the tempered scale somebody had to be sharp to come up with it-- or maybe diligent in trial and era method------
my opinion I ask no agreement
Edited by - Tractor1 on 02/08/2025 10:40:44
quote:
Originally posted by OwenI'll take your word for it, Tom. But how does being fairly proficient at math thru public school [and still not too, too terrible] help me with learning to play the banjo... i.e. all of ^^, especially the "micro seconds" part?
You are probably overthinking this.
"Playing" banjo does not really need to involve doing any math calculation. Mostly just basic assigning/counting numbers represent a scale. As in what OP was referring. No need to overthink it.
A bit of conflation to the other question brought up, was getting into bit of under the hood, physics explanation of how sound works, frequencies, sound waves, fine intonation. So involves a bit of math involved with figuring that out, or in explanation to question.
But the latter is not "playing" the banjo, nor any prerequisite needed to learn to "play". I don't think anyone as "playing" banjo, is mentally trying to do calculations of frequency to some multiple of the square root of 2; nor calculating interval difference in ratios like 8/5 to 15/8. So can ignore it, just don't really need to know.
Bill (Brad) Keith liked to go down the circle-of-fifths rabbit hole
"A trained mathematician, (Ben) Eldridge juggled a day job at Johns Hopkins University’s Applied Physics Laboratory while gigging first with Cliff Waldron & The New Shades of Grass. The strain of working both jobs led him to quit Waldron’s band, but the music never left his soul. "
"Eldridge helped form The Seldom Scene soon after that in 1971."
Check out Ben's opening break on this one; cosines, slopes, and logarithms l blended into one...... https://youtu.be/bX12kzod0RI?si=HlM2dky7m-YYUBBX
Edited by - chuckv97 on 02/08/2025 16:10:17
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