> If you choose the frequency 440hz, jump down one 7-semitone step and up 5, you have an A major scale
Also I have one more question about - when making chords using the 3rd and 5th step, for a note on the right boundary of this n <-> 2n interval, I would jump into 2n <-> 4n interval, right? But I'd I were not using chords then is "all" (simplified) music made in only only one x <-> 2x range and it's not crossed?
Another question- why do pianos have different black and white keys? Do you plan on doing a blog post that explains how "your " explanation of music theory fits various instruments? I've always wanted to understand music from a mathematical perspective and your post was eye opening!
I am going to try out your tool once I get hold of a computer.
Each doubling of frequencies is divided into twelve somewhat evenly-spaced semitones. If you go up seven out of twelve (using index 0 for your initial frequency), that's essentially half way to the doubling of the frequency with a ratio of 3:2. E.g., if your starting frequency is 440, going up seven steps will give you a note with a frequency of 660.
Another way of dividing up the space between a frequency and it's doubling uses eight of the twelve semi-tone divisions . The eight notes form an 'OCTive'. The octive has a 1-based index for the starting frequency. You can see seven out of twelve highlighted notes in the dashboard circles . The eighth note has the same name as the first one as you complete the circle but it would either be double or half the frequency. Going up seven semi-tones using the twelve division 'chromatic' scale is the same as going up five steps in the more selective eight note octive scale.
Yes, the circle continues from 2n<->4n and 4n<->8n and n/2<->n and n/4<->n/8 etc. The boundaries are those of human hearing from about 20hz to 20khz.
The white keys on a piano are the key of C Major. The black keys are the 'accidental' notes--the five notes of the twelve division chromatic scale that are discarded when selecting the notes for the eight (7 + the 1st/8th note that is counted twice to complete the circle) note octive.
Even nonmusical people can almost always tell that, for example, 110 Hz, 220 Hz, 440 Hz, 880 Hz etc. sound like the same note.
So if you take an A major chord:
A (220.00 Hz), C# (277.18 Hz), E (329.63 Hz)
and then switch to
C# (277.18 Hz), E (329.63 Hz), A (440.00 Hz)
or also
E (329.63 Hz), A (440.00 Hz), C# (554.37 Hz)
and also something like
A (110.00 Hz), A (220.00 Hx), E (329.63 Hz), A (440.00 Hz), C# (554.37 Hz)
it makes pretty much no difference. People will hear and feel it as the same chord, the same notes, the same musical meaning.
There are some nuances in color, especially about which note is the lowest. And other concerns, like at which frequency ranges the other instruments (or your other hand on a piano) are playing at the same time, and if you want to spread out to avoid the others, or make the frequencies more crowded to put more emphasis. And also purely mechanistic concerns, how you are able to reach the notes with your fingers, for example, on guitar fretboard or piano keyboard.
> why do pianos have different black and white keys?
The 7 white keys match the C major (same as A minor) scale: C D E F G A B (and C).
I don't know why the ancient musicians thought to make C major as kind of the default scale, but that's how we now tend to see it. You can start a scale from any of the 12 semitones, but piano, and some other instruments, and the traditional musical writing notation are build so that C major is the default, and the remaining 5 semitones (the piano black keys) are written as how they deviate from the default scale.
A suggestion: show pitch constellations[1]. Piano/violin music theorists have written me that these were helpful in [2]. (I'd offer you code, but it's so ancient that it's probably not helpful :-( )
Just a heads up that your fingerboard app seems to be working incorrectly regarding displaying the names of sharps and flats on the fretboard diagram (in some cases).
For example, if I load the page and immediately click on an Eb on the piano, the fingerboard layout is correct, and the correct scale degrees are highlighted, but Eb are labeled as Db in the fretboard diagram. Similarly Bb are labelled as Abm etc. It seems like you just switched the sharp/flat symbol without also switching the note letter.
Otherwise awesome tool, this will be very useful for me!
It would be cool if you supported a kapo and turning it flat. That way I could tune it to e flat without having to do the mental math, and I could put the kapo on whatever fret so I could visually see quickly.
That's a very good question. I had plans to add major and minor pentatonic scales until it became clear that they way they are used, especially in rock and other blues based music is a subset of dorian modes. There's some real insight to be gained, especially with regards to harmony, or more practically, what chords you can play against a major or minor pentatonic. It's a lot more than one would think!
So, to answer your question, I'm not going to add pentatonic scales, but I do plan to record a video showing how GD can give you some really cool insight into how they work harmonically.
How about an option to overlay the pentatonic scales over other scales, similarly to the way you color the root notes but with a different color? You could use a similar idea to overlay root-third-fifth or other chords. I think this would be useful for those of us who are still trying to build muscle memory, but still present information in a way that minimizes "stuck thinking."
It's also Dorian and Phrygian without the 2 and 6. Plus you can use it in other keys, the A Pentatonic in the key of Bb is lydian, in G it's dorian, in C it's major, etc..
I agree with you. It's prevalent and is also one of the very first thing most guitar players learn. It definitely feels like it should be a prominent part of the UI and not just hidden away in some video.
My favourite book on music theory is 'Songwriting Secrets of The Beatles' by Dominic Pedler. The title doesn't do it justice. It's a magnificent treatise on music theory and song writing using the Beatles songs as examples. If you're a Beatles fan like me, it's a must read!
Richard Lloyd (formerly the guitarist for the proto-punk band Television) has a few great lessons on YouTube that teach theory and the circle of fifths very effectively:
While these tools are useful, I recommend oldschool hard copy books to get started properly, if you're relatively serious about it. There are some great books for guitar put out by Berklee, I don't recall the names right now, but I do remember a series that had 4 books from intro to advanced.
I spent a lot of years learning guitar technique while not progressing much on the music theory side until I started reading Mark Levine's Jazz theory book. It's probably the best material on music theory I've read, though it's slightly based on jazz, or at least references it a lot. But I think you could use it as a general theory guide.
Another favorite of mine is Yusef Lateef's Chord and Melodic Patterns book, though it's more advanced/exploratory.
Levine is a great resource, but music theory, and jazz theory in particular, is a super dense subject. Having an experienced teacher to guide you through and help you internalize it is very valuable, even if it's only for the occasional lesson.
Another perspective: Jazz pianist here. I looked at Mark Levine's book when I was in my early/mid 20s, by then I already knew everything in it - and I'd learnt almost all of it from the music, from the greats. I don't believe in (theory) books, or teachers, really. I don't wish I'd read that book before I knew any of it.
I played classical for years as a kid, then played any songs I could get my hands on - folk songs, pop, Beatles etc. So I learnt basic chords and how they work by playing that stuff a lot. Then when I got into jazz, you learn by listening and transcribing. Transcribing tunes, solos, chord voicings, anything. All different instruments. I've transcribed piano, trumpet, sax, guitar, bass, drums.. and Indian classical, funk, reggae etc. Anything you hear and like but don't know what it is, transcribe it, and learn to play it yourself. (If it's simple enough, you don't need to write it out) You learn a lot of things by doing that. There are books of transcribed solos, I think they're absolutely worthless. Do it yourself. Besides that, books of songs, solos etc always have mistakes, sometimes a few, sometimes thousands. I've written out orchestral scores to play on piano, studied those. I studied/played/sang Debussy's opera for over a year, that felt like a complete musical education, a lot of it is simple combinations of notes. In my 20s I learnt a lot about what pianos can do by playing a lot of piano pieces by Debussy, Ravel, Rachmaninov etc. Also playing other instruments is good - I've spent a fair bit of time playing drums, bass, guitar, trumpet, trombone, clarinet, etc. Also learning who the great musicians are is invaluable, so you can find who appeals to you most. Check out a lot of different stuff. Study, analyze, learn from the music you listen to and love. All that is so much easier since the internet! (I started in the 80s) It should all be a great joy. I enjoyed every minute of it.
I'd recommend the Hook Theory "books" (there are two volumes). I put the word book in quotes because they are available as both interactive ebooks, i.e., Kindle & iBook, and mobile applications, i.e., iOS & Android.
The authors do a nice job of introducing basic (and then advanced) music theory concepts with text and audio/video examples using recognizable pop songs. They also have some tools for exploring themes further on their website.
I've read the books a couple times and it has given me the ability to reason about existing songs as well as better compose and improvise with songs myself.
Got quite a collection of intro books, but nothing on theory really. I had hand surgery on my frett hand a few months ago and still do physical therapy twice a week - just now getting some strength back so while I recover, trying to learn more music theory since my practice sessions are limited by a screwed up hand. I tell ya what though, practicing guitar is better than most of my PT exercises :)
I'd agree. For beginners, Guitar Dashboard is probably overkill. I really wrote it for people like me, who'd been playing guitar for a while and know all the basic chords, but want to get deeper into the underlying theory.
The basic idea: fret a string on one of the indicated spots in the diagram, pluck a string. Then pick another one, and do the same thing; now you have a melody starting.
Moving on: divide that pattern into interlocking "boxes", and memorize the fingering pattern for each box, and how it dovetails with the adjacent boxes.
Some boxes have a transition where there are two notes per string; this is good for staying in a tight position, without much finger stretch. Three-note-per-string boxes are good for shredding.
If you have this overall pattern memorized and well rehearsed under your fingers, you can easily improvise to most music (at least that with Western roots around diatonic scales). Listen to the track and play a few notes by ear. Within a bar or two, it's obvious which pattern you are in and from there you know the rest of the picture instantly, and can "break out" all over the fretboard.
If you like playing electric guitar, then Rocksmith should be part of your learning tools. Much more fun imho than any of the other methods, well except for being part of an actual rock-band.
What most articles and books I've read on the subject recommend: Learn to strum with rhythm. Learn the scales. Learn the chords. Play things that let you have fun, even while nailing down the basics.
The best ones I have read take it a little closer to the guitar: "Learn the freboard" Learn why the freboard is the way it is, why it is tuned the way it is, why no one for hundreds of years has been able to come up with a better tuning system -- then learning rhythm, chords and scales will be a bonus side effect. The very excellent book "Fretboard Logic" takes this approach
I see a lot of folks asking about resources to learn the ideas in this tool, so I’ll recommend the Guitar Grimoire series. Granted they are more reference-type books, but each one has a good introductory chapter that I found taught the theory in an accessible way to me. I picked up the Scales volume first and have gathered more over the years, like the practice exercise edition, but don’t use them much these days (it’s been like 15 years now :)
Great job!
One idea: Have some tracks ( from Spotify api?) to play along that matches the selected scales.
I've found that playing on top of songs works pretty well, improvising up and down is very easy if you are playing the safe notes of the scale, finding how the singing melody fits the scale, then how the solo fits the scale..etc is a funnier way to memorise the scale.
I've found a looper pedal a fantastic tool for learning theory. Play some chords from a particular scale, then try improvising over it. You get a real feel for how the different modes sound.
I keep being surprised at people having the same idea e.g., see also Grunfy's post from a few months ago. https://news.ycombinator.com/item?id=17272516
He has some very nice stuff there.
My work-in-progress is also derived from "first principles", although I haven't bothered to try adding alternate tunings yet.
Mostly my focus has been on using it to aid learning improvisation, so one feature i added to my little app was the ability to set up a particular chord pattern on the fretboard and "save" it, so that you can have several different diagrams on the screen at once, e.g., one for each of the three chords in a 3-chord song.
Like you, I also have been using Typescript and SVG, but not D3 (just drawing SVG elements directly using React seems to work well enough for my purposes)
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> If you choose the frequency 440hz, jump down one 7-semitone step and up 5, you have an A major scale
Also I have one more question about - when making chords using the 3rd and 5th step, for a note on the right boundary of this n <-> 2n interval, I would jump into 2n <-> 4n interval, right? But I'd I were not using chords then is "all" (simplified) music made in only only one x <-> 2x range and it's not crossed?
Another question- why do pianos have different black and white keys? Do you plan on doing a blog post that explains how "your " explanation of music theory fits various instruments? I've always wanted to understand music from a mathematical perspective and your post was eye opening!
I am going to try out your tool once I get hold of a computer.
Another way of dividing up the space between a frequency and it's doubling uses eight of the twelve semi-tone divisions . The eight notes form an 'OCTive'. The octive has a 1-based index for the starting frequency. You can see seven out of twelve highlighted notes in the dashboard circles . The eighth note has the same name as the first one as you complete the circle but it would either be double or half the frequency. Going up seven semi-tones using the twelve division 'chromatic' scale is the same as going up five steps in the more selective eight note octive scale.
Yes, the circle continues from 2n<->4n and 4n<->8n and n/2<->n and n/4<->n/8 etc. The boundaries are those of human hearing from about 20hz to 20khz.
The white keys on a piano are the key of C Major. The black keys are the 'accidental' notes--the five notes of the twelve division chromatic scale that are discarded when selecting the notes for the eight (7 + the 1st/8th note that is counted twice to complete the circle) note octive.
Even nonmusical people can almost always tell that, for example, 110 Hz, 220 Hz, 440 Hz, 880 Hz etc. sound like the same note.
So if you take an A major chord:
and then switch to or also and also something like it makes pretty much no difference. People will hear and feel it as the same chord, the same notes, the same musical meaning.There are some nuances in color, especially about which note is the lowest. And other concerns, like at which frequency ranges the other instruments (or your other hand on a piano) are playing at the same time, and if you want to spread out to avoid the others, or make the frequencies more crowded to put more emphasis. And also purely mechanistic concerns, how you are able to reach the notes with your fingers, for example, on guitar fretboard or piano keyboard.
The 7 white keys match the C major (same as A minor) scale: C D E F G A B (and C).
I don't know why the ancient musicians thought to make C major as kind of the default scale, but that's how we now tend to see it. You can start a scale from any of the 12 semitones, but piano, and some other instruments, and the traditional musical writing notation are build so that C major is the default, and the remaining 5 semitones (the piano black keys) are written as how they deviate from the default scale.
It's just tradition, I assume.
A (440 Hz), down to D. A, up to E, up to B, up to F#, up to C#, up to G#.
Sort: A B C# D E F# G#. This is the A major scale.
A suggestion: show pitch constellations[1]. Piano/violin music theorists have written me that these were helpful in [2]. (I'd offer you code, but it's so ancient that it's probably not helpful :-( )
[1] https://en.wikipedia.org/wiki/Chromatic_circle#Pitch_constel...
[2] http://osteele.github.io/fingerboard/
For example, if I load the page and immediately click on an Eb on the piano, the fingerboard layout is correct, and the correct scale degrees are highlighted, but Eb are labeled as Db in the fretboard diagram. Similarly Bb are labelled as Abm etc. It seems like you just switched the sharp/flat symbol without also switching the note letter.
Otherwise awesome tool, this will be very useful for me!
It would be cool if you supported a kapo and turning it flat. That way I could tune it to e flat without having to do the mental math, and I could put the kapo on whatever fret so I could visually see quickly.
Super awesome work!
I wonder: on the "scales" dropdown, why didn't you include pentatonic? It's so prevalent across so many styles of music; it seems like a must.
So, to answer your question, I'm not going to add pentatonic scales, but I do plan to record a video showing how GD can give you some really cool insight into how they work harmonically.
https://youtu.be/mNmEq-cP9Oohttps://youtu.be/9lSifKZ80H4https://youtu.be/fjWFqz1Sjps
Lloyd is a bit eccentric in person and in his methods—he's very opinionated, but IMO that's one of the things that makes him a great guitar teacher.
I spent a lot of years learning guitar technique while not progressing much on the music theory side until I started reading Mark Levine's Jazz theory book. It's probably the best material on music theory I've read, though it's slightly based on jazz, or at least references it a lot. But I think you could use it as a general theory guide.
Another favorite of mine is Yusef Lateef's Chord and Melodic Patterns book, though it's more advanced/exploratory.
I played classical for years as a kid, then played any songs I could get my hands on - folk songs, pop, Beatles etc. So I learnt basic chords and how they work by playing that stuff a lot. Then when I got into jazz, you learn by listening and transcribing. Transcribing tunes, solos, chord voicings, anything. All different instruments. I've transcribed piano, trumpet, sax, guitar, bass, drums.. and Indian classical, funk, reggae etc. Anything you hear and like but don't know what it is, transcribe it, and learn to play it yourself. (If it's simple enough, you don't need to write it out) You learn a lot of things by doing that. There are books of transcribed solos, I think they're absolutely worthless. Do it yourself. Besides that, books of songs, solos etc always have mistakes, sometimes a few, sometimes thousands. I've written out orchestral scores to play on piano, studied those. I studied/played/sang Debussy's opera for over a year, that felt like a complete musical education, a lot of it is simple combinations of notes. In my 20s I learnt a lot about what pianos can do by playing a lot of piano pieces by Debussy, Ravel, Rachmaninov etc. Also playing other instruments is good - I've spent a fair bit of time playing drums, bass, guitar, trumpet, trombone, clarinet, etc. Also learning who the great musicians are is invaluable, so you can find who appeals to you most. Check out a lot of different stuff. Study, analyze, learn from the music you listen to and love. All that is so much easier since the internet! (I started in the 80s) It should all be a great joy. I enjoyed every minute of it.
The authors do a nice job of introducing basic (and then advanced) music theory concepts with text and audio/video examples using recognizable pop songs. They also have some tools for exploring themes further on their website.
I've read the books a couple times and it has given me the ability to reason about existing songs as well as better compose and improvise with songs myself.
Moving on: divide that pattern into interlocking "boxes", and memorize the fingering pattern for each box, and how it dovetails with the adjacent boxes.
Some boxes have a transition where there are two notes per string; this is good for staying in a tight position, without much finger stretch. Three-note-per-string boxes are good for shredding.
If you have this overall pattern memorized and well rehearsed under your fingers, you can easily improvise to most music (at least that with Western roots around diatonic scales). Listen to the track and play a few notes by ear. Within a bar or two, it's obvious which pattern you are in and from there you know the rest of the picture instantly, and can "break out" all over the fretboard.
https://rocksmith.ubisoft.com/
I see a lot of folks asking about resources to learn the ideas in this tool, so I’ll recommend the Guitar Grimoire series. Granted they are more reference-type books, but each one has a good introductory chapter that I found taught the theory in an accessible way to me. I picked up the Scales volume first and have gathered more over the years, like the practice exercise edition, but don’t use them much these days (it’s been like 15 years now :)
I keep being surprised at people having the same idea e.g., see also Grunfy's post from a few months ago. https://news.ycombinator.com/item?id=17272516 He has some very nice stuff there.
My work-in-progress is also derived from "first principles", although I haven't bothered to try adding alternate tunings yet.
Mostly my focus has been on using it to aid learning improvisation, so one feature i added to my little app was the ability to set up a particular chord pattern on the fretboard and "save" it, so that you can have several different diagrams on the screen at once, e.g., one for each of the three chords in a 3-chord song.
Like you, I also have been using Typescript and SVG, but not D3 (just drawing SVG elements directly using React seems to work well enough for my purposes)