categorical perception of scale degrees

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categorical perception of scale degrees

Post by abminor » Sun Apr 28, 2013 2:40 am


from what I read, you seem to have a very good relative pitch. Can I ask you what kind of training you did ?

Do you use scale degrees or interval. If you use the former. Do you recognize scale degrees only in familiar patterns or do you have like an independent grasp of them.

I ask this question because although I have an independent grasp on the tonic and the fifth (sometimes the third), I think a lot of time when several notes are played relatively fast, I perceive more a movement in a scale that a succession of degrees if you see what I mean.

So I wonder if it's possible to perceive music entirely as a succession of degrees in a kind of semi-absolute way.Each degree who have a color that you could perceive instantly and that would not be blurred the different music contexts. That seem to be the key point here because I find often that, for example, the third degree of key can sound very differently depending on the current chord. If it's a I, it's ok but if it's the 7th of the V chord, it's another story.

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Post by Space » Sun Apr 28, 2013 5:50 am

Hey, I almost didn't catch this!

RP is so much more complex than AP. There can be so many different pitch relationships being perceived at one time.

I guess my RP training history would be in order:

Initially I was exposed to mild interval training at the CCM (Cincinnati Conservatory of Music) preparatory program in high school. I did ok, but it wasn't very intensive. Then when I was 18 I bought Burge's RP course which is pretty intensive with all the drills and such. It took about a year for me to complete. I learned all my intervals to pretty much instant recognition, the 20 some odd chord types as well as inversions for major and minor chords, etc. Also, Burge's course covers the 7 degrees of major and minor scales but only one very short tape covered IDing all 12 pitches against a key center.

So, a few years later I got into Bruce Arnold's contextual eartraining method, which is ALL about hearing all 12 scale degrees against a key center. It is kind of like having AP as long as you're firmly established in a key. (here is a good place to start with his methods:

I basically did his 'one note' method using Alain Benbessant's "Functional Eartrainer" program. I got to the point where I could easily ID scale degrees with random keys for each example with all 4 cadence types. From there, I got the 'Keynote Recognition' CD and the 'Fanatic's Guide to Sight Singing and Eartraining' book and CD and did a skittle ton of learning to sing all 12 degrees against a key center.

Then I got his "2 note" bundle with the first 6 CDs which is supposed to be the next level which is to begin learning how to follow modulations. I worked on that for a while and did well but I'm kind of stuck at REALLY getting the modulation stuff. I've come up with some of my own ways of working on modulation but it's pretty exhaustive and takes a long time. Basically, you go through all combinations of notes and learn what kinds of tonalities they generate when randomly played across all octaves (I do this with Pitch Player). I've taken a break from that though, to go back to AP eartraining.

Here is a good place to start with Arnold's methods. In all honesty, It's almost completely unnecessary to bother with interval training. Music really isn't intervals. The natural human ear I believe is more geared toward scale-degree hearing. Intervals are an arbitrary extrapolation and I really feel that after studying contextual eartraining, I may even have been better off if I'd never spent all that time on interval training - or at least, worked on interval training WITHIN the context of scale degrees.

For example, take a perfect 5th interval. You could do Burge's 'grand round' (which I did myself many times) and really learn to hear and sing this interval. But when heard in actual music, a P5th interval will be in relationship to a tonality. You might hear a P5th, but which one is it? There are 12 of them against a key center!

So I guess the trick is to learn to hear a P5th as a textural unit (a set of pitches with its own type of 'buzz' or 'vibration') but not as a tool for learning to ID the pitches themselves. Scale degrees are better for IDing individual pitches in a real musical situation.

One thing I spent a lot of time on is doing Burge's 'grand rounds' with different intervals but doing it against a key center. This way, if I'm in the key of C, the C/G P5th is I/V, the Db/Ab P5th is bII/bV, etc.

Oh and to answer your question about hearing the 7th of a V7 chord, I think it's just a matter of time and practice, like everything else. Eventually, you'll hear the notes of a V7 chord as the 5/7/2/4 degrees much more strongly than a 1/3/5/b7. One thing that helps IMMENSELY is learning to sing the notes against a key center. You could set up a drone with a piano or guitar or maybe find one on youtube. Or use groove builder: . There, you can just set up 4 bars of one major chord, then slowly sing each note of the V7 chord against that key center, from root, to 3rd, to 5th, to b7. Only don't think of the notes as 1/3/5/b7. You want to be thinking of and singing them as "5", "7", "2", and "4" of the key you're in. So if it's the key of C, you'd be singing G, B, D, F and thinking and hearing those notes as 5, 7, 2, and 4.

Ok, now I'm gonna go crazy. One thing that will totally bring this home is singing all 24 combinations of those 4 degrees. So for those degrees, you'd sing:





I know it sounds insane, but it's totally possible to go through them all in a 20 min session, and to really start to get it down in a few of those 20 min sessions.

At first, I had trouble with IVmaj7 chords. I would hear the 7th as a 7th and not the 3rd of the overall key. With time and practice that changed and I began to hear it as the 3rd more clearly. I also worked on all of those combinations for a few days and it was a wrap!

I hope some of that makes sense. Sorry it was so long. Figured I'd try to be comprehensive :)


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Post by Space » Sun Apr 28, 2013 6:02 am

Just for s***s and giggles, I went ahead and sang all those combinations in groove builder in the key of F (it's a good key for comfortably singing things in my personal vocal range). Fun stuff!

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Post by Axeman » Sun Apr 28, 2013 8:40 am

Hey Space! I did the same RP Supercourse by Burge too. It took me a long time to complete although I didn't really complete the last tape or two. I found it to be ok but it didn't really perform as promised. I was hoping to be able to hear chord qualities as they were playing in jazz music. The degrees thing was quite fun but very brief. Have seen the software (functional ear trainer) you mentioned for hearing degrees but found it quite laborious and slow. I am currently trying out Ear training HQ. He seems to do similar things to Bruce Arnold. I found recently that if I am listening to certain jazz songs I can hear the root of the piece and found that singing that as the music plays gives different sensation to what I am hearing.

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Post by Space » Sun Apr 28, 2013 1:41 pm

Yeah, jazz is definitely a challenge. It took some time for me to hear keys and degrees in jazz as well. It's just more complex. Rock and pop are easy. I can listen to a pop song and walk right over to the piano and start playing along right away.

But even jazz has its cliches. Over time, it has gotten easier to follow things in jazz but I still can't really play it at all. That's my dream. To really figure jazz out and be able to play it.

Bruce Arnold told me that he essentially did the exact thing that I listed for you, singing all combinations of all the different jazz 7th chords within the context of jazz standards. Said it took about a year to get through it. Of course, that guy's probably more obsessed than you or I will ever be and was practicing like 12 hours a day.

I also think that doing the 'Cuddy' method is really good for both AP and RP. I've worked on IDing random 3 note chords in Pitch Player with a 12-bar blues running in the background in Groove Builder. You learn to hear each pitch in the chord the same way you'd do with prolobe, only against a key center. You get to where you could have a dissonant cluster chord like b2, 2, b3 and hear each note and its degree sound distinctly.

There are so many ways to approach things. Just gotta find what works for you. But some exercises I really feel are indispensable whether you enjoy doing them or not, like the singing. That really lodges the sounds in your head probably better than anything. Also, Bruce Arnold's emphasis on 'prehearing' things in your head before singing or playing is SO beneficial. Training yourself to 'play' notes in your mind as clearly as possible is a huge tool to bettering your RP and especially AP.

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Post by Space » Sun Apr 28, 2013 1:47 pm

Oh and I agree about Burge's RP course. It did do a lot for me in terms of getting all of my interval and chord spellings down, and I got really good at hearing chord qualities, like the b9, #9, and all the different 7th chords, etc. but the idea that you could follow a melody by stringing the notes together interval by interval is ridiculous.

Bruce Arnold has a newer course on secondary dominants which I'm sure is a huge key to following jazz progressions. I should check it out here soon and report back.

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Post by abminor » Sun Apr 28, 2013 9:15 pm

Hi space,

thank you for your very complete answer. That seems to be a an awful amount of work :-) I thought I had put a a lot of work myself but when I read your ear training history, I realize that I did very little.

I think I lacked the grit needed to really complete a course or method in a systematic way so I tried a little bit of everything without any real focus. It makes sense that your ear is better that mine. You just get rewarded for the amount of work you put, no surprise here.

How many years has it taken to do all that ?

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Post by abminor » Sun Apr 28, 2013 9:32 pm

I was thinking,

maybe the APA game would be a great tool for functional ear training if it was tweaked a little. I mean it should be possible to adapt the same principle of perceptual differentiation to hearing a scale degree instead of an absolute pitch. Of course the main difficulty comes from generating some melodies with a tonal center.

I think for this to work, you have to vary the key often enough, otherwise you can just lock on a given pitch without really having to feel the degree. So the basic principle would be for example: do you hear the 4th degree in that egg ?

Do you people think it could work ? Can we develop categories for scale degrees one at a time or does it develop the categories: scale degree x/not scale degree x instead ?

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Post by Space » Sun Apr 28, 2013 11:59 pm

I actually already apply something like this. As part of my eartraining 'regime' I'm on now, I have groove builder play a 12-bar blues in the background while I do APA. I've been thinking for a long time of doing a video where I do a session and record my computer screen as I work and maybe get a mic up and provide some narration to explain what and why I'm doing what I'm doing :op

Oh, and as for the time this has all taken me, I had that little bit of eartraining in high school, but it wasn't until I bought Burge's AP and RP courses in the spring of 1998 that I really started taking it seriously. So this month actually marks 15 years since then and I tend to go through phases of maybe 3 months or so of hardcore daily obsessive eartraining until I burn out and take a month or 2 off. Though, when I recently did the 'Cuddy' method with the note, G, I went for about 6 months straight which totaled 300+ sessions or so of just IDing pitches against a 12-bar blues in G with Pitch Player at each weight from 99 to 0, and doing singles, doubles, and 3 note chords for each weight.

To be completely honest, though, I've been very dedicated and determined (although it's an on/off thing), but I consistently question my methods after working for a number of months and then want to switch to doing something else. I really feel that pang of "if I knew then what I know now". I would've approached everything SO completely different from the beginning. I haven't been entirely efficient. There are so many ways to approach the AP/RP thing that I feel the best thing to do is to pick one path and stick to it. Switching around all the time ultimately slows you down.

Currently I've landed on a particular way of combining the basic idea of simply adding notes one by one, the Cuddy method by using groove builder to anchor my ear into the key of whatever pitch I'm working on, and melody triggers.

This way I'm doing a little bit of everything so I'm less apt to want to stop in the middle of the trajectory I'm on to focus on something else. I've spread myself too thin over the years and it has slowed me down. Now that I'm 33 and getting older by the minute I really feel that I need to pick something and focus until I see it through.

So even though I've been at this off and on for 15 years, if I would've had the foresight to do this kind of thing back when I first started, I could've had it knocked out in a few years. So don't think it's gonna take that long for you!

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Post by Nikolaus » Mon Apr 29, 2013 2:40 pm

there are great extremities that one can go with scale-degree recognition. for instance, recently i got my recognition of many four note triads down to one second! that's four notes, or degrees per chord! totally beats intervals, or other tricks for hearing triads. (such as listening for quality, the bass tone or even the function). in fact, the ability to hear function could just be thought of as the ability to hear the collective sound of scale-degrees. when you hear I, what you're really hearing is the collective sound of 1, 3, 5. and when you hear V, what you're really hearing is 5, 7, 2. for inversions, all you're doing is listening for what degree is in the bass. for V, if 7 is in the bass then that's first inversion. it's an artificial way of saying 7, 2, 5. i don't think major first inversion with a b in the bass. i think 7, 2, 5. it's an automatic, one step process. then you can get it super fast even with four note, and then speed it up to one second so that you can use it in real music. like i said - knocks the snot outta interval training. but it takes work to get down, as with anything.

i like bruce arnold's stuff too but it's WAY too technical after a bit! i stopped after getting fanatic's down to one sec per pitch.

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Post by abminor » Mon Apr 29, 2013 8:02 pm

to space:
Hi, I'm not really familiar with the Cuddy method. Where does it come from ? If you stay in a given tonality, how can it we beneficial for AP ? How do you know you're not using only scale degrees for note identification ?
I like your idea, of practicing APA with a musical background. I hear a lot of people complaining on the forum that they don't have a musically useful AP but THEY DONT TRAIN FOR IT ! It's like complaining one cannot swim without ever getting into the water.

to nikolaus:
Pretty impressive. What kind of exercise have you done to achieve that level ?

I looked more into bruce arnold stuff. I like his advice of not using any trick into your scale degree recognition: don't count degrees to tonic, don't compute interval, don't use common resolutions to a more familiar degree.
I makes really sense that it should be faster like this and that you should have a more context independent sense of degrees. I realize that I do use those tricks myself and that may be a reason why this process is not spontaneous (except for few degrees).

Initially, I kind of developed those technics to check if was correct, but now they have become engrained. An habit hard to break down. Mostly I use familiar tonal patterns starting with a degree to recognize it. It's a little like melody triggers adapted to functional ear training. It can be pretty fast but, it's not fast enough to recognize every notes going on in normal speed music.

While you where doing bruce arnold course, could you guys develop instant recognition of degrees just by color, without any additional trick, as recommended by him ?

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Post by abminor » Mon Apr 29, 2013 8:34 pm

Now that I think about it,

there seems to be a strong parallel between developing instant degrees recognition by color and AP. If you truly hear every degrees in music instead of relying on learnt tonal patterns, then the process of music decoding is very similar to the one used by AP (it's down to the note level) except you need to know the key to really get the note names.

It would be interesting to know what percentage of the people that were able to develop functional AP, also have this kind of instant degree recognition.

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Post by Space » Mon Apr 29, 2013 9:57 pm

Yeah, I'd say essentially, my scale degree recognition of all 12 degrees is instant, especially in the context of what Bruce Arnold would call 'one note'. I can ID 2 and 3 note chords this way as well (cuz I've practiced doing random 2 and 3 note chords against a 12-bar blues background.

Still, I wish functional eartrainer took things farther. I emailed Alain Benbessant about it, tried to describe what I was aiming for but he didn't seem to get it, oddly enough. I just wanted 2, 3, and more note chord options. Basically the same set up as FET basic but after the cadence is played, you have to identify an interval or chord instead of a single note. The aim of this is to learn to ID ALL 12 degrees of all possible intervals, triads and most common chord types in jazz and such. Actually, what I'd really like to have is a fully customizable option where you could input the specific chord with a specific voicing or whatever and learn to hear and ID that chord at any of the 12 possible tonal 'locations'.

Does that make sense? It didn't seem to make sense to Alain in spite of the fact that FET Advanced does this for intervals within the major and minor scales (but that's all it covers) :P

I'm going to implement a buzz word here: "Chunking". I think that's a good way to explain the way a person can learn to ID groups of multiple pitches by their overall sound without having to count up specific pitches or degrees. Like Nicklaus was referring to, if you know the textural sound of a major chord and how it sounds from all 12 degrees, and you know all 12 degrees of all 12 keys, AND have AP for all 12 pitches - you only need to have AP to cover the absolute sense of the key you're in, then you can hear the degree of the root and the overall texture of the chord (in this case 'major'). So, if you're listening to a piece of music, you will, for example, hear that it's in the key of D, and you hear the V chord and you know 'A' is the 5th degree of the key of D and you hear the overall sense of 'major' over the whole chord and you know it's Amaj. You're hearing all of these things at once, essentially, because it has all been integrated. You hear the whole thing all at once as a harmonic 'chunk' of "Amaj, V chord in the key of D" and it happens pretty much instantly. This also includes inversions, so you might be hearing the 'major' chord quality of the V chord with a C# in the bass and brain hears all in one flash of recognition "Amaj, V chord, 1st inversion, key of D".

Oh, and one more thing. To answer some questions about the 'Cuddy' method. It basically just involves 'weighting' a particular pitch so that while IDing notes, that pitch is sounded more often than all others which tends to put one into the key of that pitch. Then, you successively drop the weight of that pitch session after session until the pitch is equally weighted with all others. By the time you get to that point, you have most likely internalized the weighted pitch and are using your memory of that pitch to ID the other pitches against. So it involves scale degree recognition but you are hearing the keynote as an absolute. So the reasoning is, if you did this for all 12 pitches, you'd end up having them all internalized.

So yes, I *AM* using scale degree recognition to ID pitches but over time, AP becomes more and more involved in the recognition as well. With experience, you learn to tell when you are using 'chroma' and when you are using scale degrees because it feels different. Also, over time, you begin to do both at the same time with many pitches. The ultimate goal is to have all 12 pitches cross-referenced and integrated with all 12 keys, so that you basically have 144 different simultaneous absolute/relative sounds.

Personally, I've achieved a useable amount of this integration that involves the most common keys that we tend to hear on a daily basis in western music (particularly pop and rock music). I think it came about as a result of constant exposure, not only listening, but learning and playing over top of the eartraining I was doing. It's like a kind of matrix centered around all of the 'cowboy' chords on guitar (so, E, A, D, G, C, F, Bb, and the relative minors of those). Recently, I've begun to hear F#m, C#m, and Eb more often as I progress further.

And example of how I can still make mistakes or get confused is that 'Daltry' guy that had that song "I'm Comin Home". The song is in F# with the guitars tuned down a half step. Initially I always used to get confused and think it was G, I guess because I had the relationships and overall sound of the guitar chord voicings memorized. I haven't heard it in quite some time so I don't know if I'd hear it correctly if it popped up on the radio now.

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Post by abminor » Wed May 08, 2013 1:21 pm

Ok, I've been trying to spontaneously sing the major 2nd degree against music. I currently hear music from the bar next to my bungalow. It's a mix so the tonality is changing rapidly. It's been quite difficult so I guess I have a lot of work to do in perspective.

I try to sing the degree without starting from the tonic or using familiar tonal patterns, only by feel. I guess it's a logical first step to really internalize the degrees. I also try to recognize them as they are played in music. This step is easier for me, but I notice it's because I recognize tonal patterns I'm familiar with. What I really want, is develop a categorical perception for degrees independent of tonal patterns so I can recognize them on the spot no matter if it's a context I'm familiar with or not.

I think working with real music is also much more beneficial than working with a computer generated cadence because I'm exposed to greater variety of modes, rhythms etc... Plus, I have to be able to sing the degree at any point during the chord progressions rather than having to wait the end of a cadence that (too?) clearly establishes the tonic. The latter would probably influence me to compute the interval between the degree and the tonic which I try to avoid as I believe It would not help me internalize the feel of degrees.

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Post by Space » Wed May 08, 2013 3:44 pm

I spent a lot of time focusing on that kind of thing myself. I had Bruce Arnold's "Fanatic's Guide" book which came with a CD of 12 tracks with each track being a I-IV-V-I and then a drone chord every 4 second for 5 mins in one of the 12 keys.

So I came up with a little exercise where I would pick a scale degree and cycle through each track playing the beginning cadence and then imagining the scale degree purely by 'feel' and trying to sing it as fast as I can.

I'm really still not perfect at it but I'm pretty decent.

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