> 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.
Thank you, that was a detailed answer that gave me a lot of new things and I have a new question and some old questions-
You are saying there are 8 notes in an octave, but we only selected 7 notes after selecting 7th semi tone 7 times. I think you said the 8 note is 2x the original. Is that correct understanding?
So I got the point about 2^(1/12), what I didn't get is the staring point for A major and the jump structure. I thought all jumps are selecting 7th semi tone. So what is meant by "jump down one 7-semitone step and up 5"?
You partially answered my second question I think- saying that for chords it's okay to go from n <-> 2n scale to 2n <-> 4n scale. My question is for non chord music is this a common occurrence?
The music tradition sees the notes rather as intervals between two notes.
C to the same C is "unison" (You may need to instruments to play two identical C notes at the same time.)
C to C#/Db (this note has two names) is "small second"
C to D is "large second". And so on.
C to the next higher C is "perfect octave".
So if we take the C major scale, it has 7 different notes. But if we also include the next higher up C, you can pair the base C with 8 different notes, when we include pairing with itself, and pairing with the higher C. When you have two instruments playing, these are the pairings you can make when you play two notes at the same time.
> C to the same C is "unison" (You may need to instruments to play two identical C notes at the same time.)
> C to C#/Db (this note has two names) is "small second"
While C# and Db are the same note (in equal temperament [1]), the intervals C/C# and C/Db have different names: C# is called 'augmented unison' [2]. For the name, you start from the basic interval (e.g. C/C) and apply the accidentals (# or b) [3].
This is an example of why the traditional approach to music theory can be cryptic for a beginner. After the Western music moved to well and equally tempered scales (starting from the early 1700's), the context in which there is a difference between C# and Db has disappeared. But we still use terminology and notation from 500-800 years ago.
I actually didn't realize that the notes of the major scale and it's modes were contiguous on the circle of fifths until seeing guitardashboard.com last night. That's what the down one, up five is saying.
A fifth is seven semi-tones above the root. It has a 3:2 frequency ratio to the initial note. It so happens that if you jump up by seven semi-tones five times, you've got most of the major scale, albeit strewn over 3 doublings of the initial frequency. Usually, the major scale is thought of as occurring within a single doubling so in the key of C you'd have to divide the frequencies D and A by 2; E and B by 4 to get back into the original n<->2n range. Any time you double or halve the frequency you get a note with the same mood/purpose/name but one octave higher or lower. The frequency ratios end up something like this:
C = 1
G = 3/2
D = (3/2)(3/2) (/2 to get back to the initial range)
A = (3/2)(3/2)(3/2) /2
E = (3/2)(3/2)(3/2)(3/2) /2/2
B = (3/2)^5 /2/2
There's one note missing, though--the one with a 4:3 frequency ratio: F. To get that one, we invert the 3/2 relationship and take the frequency that's 2/3 of our initial frequency. That's in the halved range, n/2<->n, though so we've gotta double to get back into our starting range. This is the one time we go down seven semi-tones instead of the five times that we go up.
I'm not sure how useful it is to think in these terms but it does show that you can derive the major scale by using simple ratios which, psycho-acoustically speaking, are generally considered more pleasant than complex ratios when played at the same time. The relationship between B and C, (3/2)^5 == 243/32 is already pretty tense. E.g., you could alternate between two notes with that ratio to make it sound like Jaws is lurking somewhere nearby:
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.
I can see the construction from D onwards - jumps of 7, but how did you get to D? The instruction was 7)semi tones down, which from A is D "in previous scale"), but what about the 5 semi tones up?
One new question that popped in my mind- is this series of instructions (7down, 5up) a reverse engineering of the A major sequence to fit the 7- jump rule or is there some theory about it? I have no clue what different scales even mean or what major and minor means. Feel free to ignore the new questions (or the old one!)
The blog means two different sequences of jumps. The sequence of down-jumps begins from A. Then the sequence of up-jumps begins from A.
{jumps down: 1, jumps up: 5}
First, you start from A, and execute the down-jumps. In this case, there is only one. Then you start again from A (returning to A is not counted as a jump), and execute the up-jumps.
> Up two 7-semitone steps and down four gives you A minor.
Up-jump sequence: A, up to E, up to B.
Down-jump sequence: A, down to D, down to G, down to C, down to F.
Sort: A B C D E F G
I don't know what's behind this idea, or how useful it is. It seems to work, though. But I think there are simpler ways to construct the scales. Or just memorize them.
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.
Definitely agree about the teacher bit, if you can find a decent one, or can afford it. I find that sitting in or jamming, or even playing over standards is really helpful just to get things going. You have to remember that a lot of the jazz greats of the 20th century had little to no formal music education, let alone the complexities of jazz theory.
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 :)
That's alright, I've had to relearn my technique after a coma. It's easier the second time around. I really recommend doing legato exercises to strengthen the fretting-hand. Look up any neoclassical shred guitar book and they should have some guitar acrobatic exercise on legato. A good one is the Frank Gambale warmup instructoinal video. Another is a Paganini for guitar book put out by Greg Howe in the 90s if I recall correctly. I had a lot of fun learning the 24 caprices from that book.
Definitely agree about the guitar practice being better than PT part. :)
Martino is perhaps my favorite guitar player and musician of all time. Was listening to his new record Formidable just earlier today! I'm familiar with his story although for him it was a brain/memory thing. While I retained all my theory/knowledge I had to train my muscle memory all over again. In his case, he had all the muscle memory but couldn't remember ever knowing how to play at all. I recall that he started learning again by listening to his own records!
I'd recommend learning theory concepts removed from the guitar, at least initially.
https://www.musictheory.net/lessons will pretty much teach you what you'd learn in two years at university. Honestly, I find it the best resource to get up to speed on common practice period music theory.
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
Not to disagree with your points, but a brief aside you made me think of:
The fretboard in its current incarnation works well for western music, at the cost of being quite poor at playing for middle-eastern and eastern music.
There have been attempts to address this with microtonal fretboards (which are complicated), but most often they use fretless necks (which are available for guitars and basses).
So, as with all things, the fretboard evolved in a route that favored local optimizations.
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)
Fantastic work. I've been learning music theory off and on to help with my guitar. I was hoping for a whole lot of interactive applications like yours, but found most lacking for me, though I did find a few on the iPhone: FretTrainer for muscle memory stuff. I figure out what to learn next based on Musicopoulus. Both are fair, each with quarks.
I've bookmarked you in my, just created, music "Toby" folder. Speaking of which, here's one last app recommendation that's totally unrelated: if you don't already have an extension for bookmark management on your computer, consider "Toby." It's a decent one for chrome, I use it as I have way too many normal bookmarks and finding stuff via scrolling becomes painful. I'd be interested if anyone else is using a different bookmark extension for Chrome as well.
This is absolutely fantastic. I've lost my guitar teacher's notes where he wrote out the modal scale patterns, and the ones online are not good for developing this kind of intuition. Perfect example of just the right amount of information while still remaining simple to digest. A+
and then the chords can all be mapped on a big torus (donut) to represent transposition, and each chord connects with 2 others that just so happen to correspond with 'complimentary' chords from traditional music theory. And there are also different ways to connect to other chord groups.
Beethoven's 9th Symphony famously traces 19 of the 24 possible chords of the torus, and remember that he was partially deaf so relied on vibrations.
More interesting that all this however is a new instrument called the 'Fluid Piano' which doesn't restrict itself to Western tuning (multiples of 440Hz etc.) Check it out
https://www.youtube.com/watch?v=t7Cq3pbcMkI
Music from the country Georgia can't be represented using on traditional musical staves. I'd be fascinated to understand how so different musical cultures developed, particularly in relationship to how our brains might have evolved over the year to regard certain frequencies and melodies as delightful, eerie, etc.
Lefty here. The options to flip the fretboard and the nut are much appreciated.
How about introducing another shading for the 3rd and 5th notes, so that the relationship between the scales and the chord shapes becomes more apparent?
If I might add a suggestion, it takes a while to fine the number of the chord. For example, if I'm trying to figure out what 1-4-5-1 would be, I have to hunt until I find the 4 and 5. Would be cool if there was another view that was the Nashville number system in sequence to make it quicker to find.
Oh my g o s h, it works with all my crazy custom FF privacy config stuff, this is awesome! I've never heard of "N Minor" and searching doesn't bring up anything. Is that a mistake?
Looks very good - I'll get a chance to look properly on a laptop tomorrow. One thing I'd like is the ability to do 9 string tuning - I have a 9,and yet to get seriously into it, partly because it's so easy to get lost and I'm yet to get on top of the patterns that I already know well on a 6 string... I know it's the same intervals as the bottom 4 strings of a 6 string, but seeing the patterns would help, I think. But as its open source, I guess I should do it myself!
I've been playing guitar for a while now and am now beginning to understand the importance of theory, but I'm kind of at a loss on how to go about learning and applying it. Does anyone have a book/mooc that they'd recommend with lots of exercises and accompanying songs?
I've gone through a few sources but most of them relate everything to a piano. I understand the underlying theory is mostly the same but I feel like I would internalize it better seeing it on a fretboard.
Another thing, I really do recommend learning music theory on the piano/keys as well as your primary instrument. Doesn't have to be a fancy keyboard, any cheap midi thing just to visualise the way the way chords and scales are structured. I've found that learning other instruments become a lot easier once you know a little bit of theory and how they're laid out on a keyboard.
When I was learning theory, my teacher taught all his students, regardless of their instrument, on piano. It's the most neutral, in terms of scales and chords.
Guitar, on the other hand, usually has multiple valid fingerings (on different strings) for the same chord inversion. Part of the process of learning new chord voicings on the guitar is learning the same chord everywhere it can be played.
This is really good advice. With all the different places you can play the same note on guitar, it makes it a little more difficult to visualize. The one note to one key ratio can help to make things like chord structures and inversions make a lot more sense.
I had a collection of hundreds of guitar books at one point I think, though that was a while ago. I've made another comment here - the Berklee modern method books are great for guitar. Also, learn a ton of songs if you can. There's no better way to work on technique than learning songs. I can suggest specific books if you mention what style of guitar you're learning to play...
I don't agree - the modes are presented here in the order of change from the major scale, which I've found is often the best way to get people to understand how they work. One man's method, etc...
This is great! I'm not actually sure how prominent the CAGED sequence is in guitarist circles, but I was thinking it might be helpful to indicate the chord shapes.
Hope you can continue hosting it - I might use this to practice my scale visualization.
> it might be helpful to indicate the chord shapes
You can select notes on the innermost ring in the circles.
For example, select G as the base in the middle ring. Then select 1, M3 and 5 on the innermost ring. The fretboard will show you all the possible ways to finger the G major chord.
I always wanted something like this. Previously I'd set up custom spreadsheets to do the fretboard highlighting like you have. Fantastic work and great effort - thank you!
Just wanted to say thanks for this, it looks great and operates great. Really nicely done, I'll be using this quite a bit and will provide feedback if there is any.
Ditto for "Open D minor (DADFAD)" tuning that I use. Being able to set up an arbitrary tuning would serve this purpose as well, although I suspect generalizing that function might be more work than it is worth.
It would also be nice to see other scales, such as major and minor pentatonic and blues scales.
I've used jguitar.com in the past for this sort of thing, but I really like visual aspect and unity of guitardashboard. Nice work!
There aren't a lot of tools for exploring fingering for non-standard tunings, and jguitar.com has served my explorations for the past couple of years.
jguitar.com is also very comprehensive in terms of chord fingering, scales, etc.
One major difference between jquitar.com and guitardashboard.com is that the facets (tuning, chords, scales, etc.) are separated from one other on jguitar.com, whereas guitardashboard.com tries to place them all onto a single screen. My initial reaction to guitardashboard.com is that this approach does succeed. However, jguitar.com has more to offer in total.
My thanks to both authors for helping us explorers of alternate tunings. Any help we can get is appreciated.
Would be neat if you could just select a standard tuning and then have a spinbox to say how many steps up or down to modify it. Makes lots of combinations available.
I haven't used D standard, but it looks like regular EADGBD tuned a whole step down. So you could basically use that tuning on the site and just select the key a whole step below what you want, and it will align on your fretboard properly, as a workaround.
the only problem with all of this is that you must ingest the entirety of the information before becoming unconsciously competent. Do you think skilled guitarists actually think about this while they play? It's a complete flow state; prefrontal activity just shuts it down.
Honestly I like seeing the fretboard patterns to identify funky triads or strange chord fingering patterns. It's especially useful for when you change tunings to something you've not used
Right now, I just want more people to know about it and get some good feedback on what works and what doesn't. I'd be super happy if guitar teachers and other music educators pick up on it. It'd be great if I got some good pull-requests too. I'd like to make more YouTube videos, relating Guitar Dashboard to the theory and showing some examples. I'm not a keyboard player, but Piano Dashboard seems like an obvious addition :)
