A study of musical scales (2017)
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A study of musical scales (2017)
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Re: A study of musical scales (2017)
#2Oddly enough, I just finished watching this video which explains
all the scales succinctly. I was struck by all the permutations that are possible.
Simple method to organize ALL MUSICAL SCALES of harmonies: https://www.youtube.com/watch?v=Vq2xt2D3e3E
Re: A study of musical scales (2017)
#3A bit of a tangent, but what I always found confusing about music theory is which parts are arbitrary historical legacy and which are fundamental to human enjoyment of music. 12 notes in a scale? Their particular frequencies? That whole multiplying and dividing business? Why the letters are in the wrong order. Why have sharps and flats instead of just more letters? I always get stuck wondering how much of this is just a big ugly edifice and how much actually matters.
Re: A study of musical scales (2017)
#4A bit of a tangent, but what I always found confusing about music theory is which parts are arbitrary historical legacy and which are fundamental to human enjoyment of music. 12 notes in a scale? Their particular frequencies? That whole multiplying and dividing business? Why the letters are in the wrong order. Why have sharps and flats instead of just more letters? I always get stuck wondering how much of this is jus…
I can help with a couple of these. 12 notes is a kludge, because powers of 2^(1/12) well approximate simple ratios. These simple ratios (such as 3:2) sound good. I like this video for explanation: https://www.youtube.com/watch?v=1Hqm0dYKUx4
Also, the reason that the letters are in the wrong order is that we're playing the wrong scale. The monks who invented the scale usually sang in A-minor (so we use the first letter for that scale). Nowadays, we use the major scale, which has the same spacing between notes, but in a different order. It just so happens that C-major has the same notes as A-minor, so that's why we count from C. A great channel for this is Michael New, he explains everything very clearly: https://www.youtube.com/watch?v=UcviIQg_BlU
Music, much like language, has a lot of technical debt.
Re: A study of musical scales (2017)
#5A bit of a tangent, but what I always found confusing about music theory is which parts are arbitrary historical legacy and which are fundamental to human enjoyment of music. 12 notes in a scale? Their particular frequencies? That whole multiplying and dividing business? Why the letters are in the wrong order. Why have sharps and flats instead of just more letters? I always get stuck wondering how much of this is jus…
> 12 notes in a scale? Their particular frequencies? That whole multiplying and dividing business? Why the letters are in the wrong order. Why have sharps and flats instead of just more letters?
The number of notes and the ratios between their frequencies are fundamental. The rest are historical accidents.
A good place to start is David Benson's 'Music: a Mathematical Offering'. Available free online here: https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus....
Re: A study of musical scales (2017)
#6A bit of a tangent, but what I always found confusing about music theory is which parts are arbitrary historical legacy and which are fundamental to human enjoyment of music. 12 notes in a scale? Their particular frequencies? That whole multiplying and dividing business? Why the letters are in the wrong order. Why have sharps and flats instead of just more letters? I always get stuck wondering how much of this is jus…
The timbres of almost all (pleasant) physical instruments, including the human voice, make octaves and fifths (1/2 and 1/3 frequency ratios) important (and pleasant) intervals (the clarinet is a rare exception where the twelfth is the important interval, but even then that's an octave plus a fifth - music intervals use 1-based indexing which is definitely historical legacy).
The circle of fifths and equal-temperament tuning is a kludge, and there are alternatives (and you can go back to baroque times and hear pieces written for different tunings), but no approach is perfect; fundamentally 2^x will never equal 3^y so you have to compromise somewhere.
7-note scales are not the only one possible - a pentatonic scale produces pleasant sounds, as do the various medieval modes - but you can't go much finer without things sounding unpleasant (and eventually with microtone tuning you reach a point where people will hear beats instead of distinct tones). A 7-note scale also fits conveniently with the circle of fifths to allow you to have a single instrument that can play in multiple keys.
Fundamentally you do want to be able to write runs up and down the scale, so a notation of 7 points with sharps/flats is a lot more convenient than a notation of 12 points where a run would have seemingly-arbitrary gaps and off-scale notes look the same as on-scale notes.
If you're actually interested, I'd highly recommend doing some practical musicmaking and/or conventional academic study rather than trying to theorise everything from first principles yourself. After all, many of these principles were refined over centuries of trial and error, while the fundamental physical underpinnings were only discovered very recently.
Re: A study of musical scales (2017)
#7A bit of a tangent, but what I always found confusing about music theory is which parts are arbitrary historical legacy and which are fundamental to human enjoyment of music. 12 notes in a scale? Their particular frequencies? That whole multiplying and dividing business? Why the letters are in the wrong order. Why have sharps and flats instead of just more letters? I always get stuck wondering how much of this is jus…
The timbres of almost all (pleasant) physical instruments, including the human voice, make octaves and fifths (1/2 and 1/3 frequency ratios) important (and pleasant) intervals (the clarinet is a rare exception where the twelfth is the important interval, but even then that's an octave plus a fifth - music intervals use 1-based indexing which is definitely historical legacy). The circle of fifths and equal-temperament…
> with microtone tuning you reach a point where people will hear beats instead of distinct tones)
That's a fantastic notion. Music consists of rhythm melody and harmony. Harmony is created by relations of frequencies. But Rhythm itself IS a frequency, and there can be several overlapping rhythms in a piece of music. Melodic steps are also ratios between frequencies, but pieces of melody also repeat in a piece of music. So its all about frequencies and frequency of changing the frequencies. Something like that. The simple point is that rhythm is a frequency. A note is a frequency.
Re: A study of musical scales (2017)
#8A bit of a tangent, but what I always found confusing about music theory is which parts are arbitrary historical legacy and which are fundamental to human enjoyment of music. 12 notes in a scale? Their particular frequencies? That whole multiplying and dividing business? Why the letters are in the wrong order. Why have sharps and flats instead of just more letters? I always get stuck wondering how much of this is jus…
I spent lots of time during the quarantine on learning music (theory). My consensus is: 99% of what is considered "music theory" is purely interpretative cruft. 1% of it is based on physics.
The only reason why we (westerners) learn the same cruft is because we have been agreeing that this cruft is the least confusing one we have come up with (so far).
Re: A study of musical scales (2017)
#9A bit of a tangent, but what I always found confusing about music theory is which parts are arbitrary historical legacy and which are fundamental to human enjoyment of music. 12 notes in a scale? Their particular frequencies? That whole multiplying and dividing business? Why the letters are in the wrong order. Why have sharps and flats instead of just more letters? I always get stuck wondering how much of this is jus…
All of it matters, as a lot of what you find enjoyable about music is learned. Today's music might sound dissonant to someone a few hundred ago. Eg. a particular interval the _tritone_, also known as the devil's tone was considered particularly unpleasant before, but is now ubiquitous. Even today you might find music with 12+ tones not enjoyable (try listening to Indian or Middle Eastern scales).
To understand what the physical fundamentals are, think of a taught piece of string that produces a note when you pluck it. The length of it is arbitrary (frequency), what you call this note is arbitrary (letters, sharps, flats etc.). But if you start cutting the string and compare the note it makes to the original, that _ratio_ of strings (frequencies) is a fundamental property of sound and the basis of all music. The simpler the ratio, the more 'pleasant' it will sound when played together, eg. 1-2 is the octave, 2-3 is the fifth. As you can cut the string any number of times, the number of these ratios (the number of notes in a scale) is unlimited, but western music settled on 12 because that number has some nice properties.
*Note - 12 tone equal temperament, that allows for the kind of transformations in the article does not exactly match these fundamental ratios. If we were using pure ratios, the distance between any 2 notes in the scale would differ slightly. Meaning you would have to retune a piano if you wanted to play in a different scale.
Re: A study of musical scales (2017)
#10Earlier quoted context omitted.
The timbres of almost all (pleasant) physical instruments, including the human voice, make octaves and fifths (1/2 and 1/3 frequency ratios) important (and pleasant) intervals (the clarinet is a rare exception where the twelfth is the important interval, but even then that's an octave plus a fifth - music intervals use 1-based indexing which is definitely historical legacy). The circle of fifths and equal-temperament…
> with microtone tuning you reach a point where people will hear beats instead of distinct tones) That's a fantastic notion. Music consists of rhythm melody and harmony. Harmony is created by relations of frequencies. But Rhythm itself IS a frequency, and there can be several overlapping rhythms in a piece of music. Melodic steps are also ratios between frequencies, but pieces of melody also repeat in a piece of musi…
"Beats" is a specific term of art. It's not related to rhythm.