Wednesday, November 24, 2021

Metal in 6/8

Following up on this post about that 80s Heavy Metal triplet groove— a student who is mainly a Metal drummer requested some help working out some vocabulary for a song in 6/8, and these are some things we went over in our lesson. The fill portion will be good for other things, too— like in a slow swing feel, a la Jack Dejohnette on the one John Scofield record, where he plays some fast stuff at a slow tempo.  
 


It's hard to improvise in this type of groove environment; the main groove is easy, but the usual tempo range puts everything else at awkward rates of speed for drummers— the main dotted-quarter note beat is typically an uncomfortable moderato, the 8th notes feel kind of slow for fills, the 16th notes may be very fast. Your hands will want to lapse into four-note subdivisions, and that will usually sound very wrong. So you mostly have have to stay on the 8th notes— the triplet-feel subdivision. We had this same problem on Lopsy Lu, and any number of things using that 70s triplet feel, across a number of genres. 

Here's another item that may be helpful in this general feel. 

The fast doubles can be done with one or two bass drums— that's up to you guys who do that stuff to figure out.  

Get the pdf

Tuesday, November 23, 2021

Robyn Flans fundraiser

Scott Fish has shared a fundraiser for fellow former Modern Drummer writer Robyn Flans— her name was all over MD in the 80s, and she's a major contributor to the literature of drumming. Please read and donate.  

Monday, November 22, 2021

World's shortest jazz solo exercise

A quick little item— I know I've posted it before in other forms, maybe this time will be the best. For jazz students, this may be the most useful thing on the site for soloing and filling.  

This is a summary of a very well known right hand lead solo method used with the book Syncopation. You play the rhythms in the book with your right hand, accented, in a swing rhythm, and fill out the triplets quietly with the left hand. Following that rule, the first triplet exercise below is an interpretation of this rhythm— this is background, it doesn't even matter if you get this part:  


So practice this: 


Move your right hand around the toms however you like: 


Also play with your right hand on the cymbal, with bass drum in unison: 


Then improvise— play the RLL portion for as long as you like, transition with a RLR into the LLR pattern, which you can then play as long as you like, going straight back to the RLL sticking whenever you like: 



Add hihat on beats 2 and 4. 

The actual solo method using the book is a little more involved, but this will be extremely useful even without doing that. Practice trading improvised 2s, 4s, 8s, and Blues choruses this way, with all of the moves, and bango, you're a jazz soloist. 

Friday, November 19, 2021

CYMBALISTIC: Second Line Chinese cymbal!

CYMBALISTIC: Oh, I also have for sale a sweet little 14" Second Line Chinese cymbal— paper thin, at 550 grams. It took awhile for Cymbal & Gong to settle on a design for their Chinese cymbals, but what they're doing with them is great, in my opinion. I have a 20" C&G paper thin and it's the best Chinese style cymbal I've ever played.  

If you've played a few Swishes, Pangs, China Types, you know they can be quite obnoxious— with some wildly offensive overtones, or they'll be too heavy, and make a long horribly loud GAAAA when you're just looking for a fast accent. Many/most of them are unusable in moderate-volume situations. 

This one, named “Bambang”, has everything you want: a fast, washy, high energy crash, and a perfect musical exotic sound, very crisp choke effects. I normally would not get excited about a 14" effects cymbal, but this is great. I keep talking about playability with all C&G cymbals— after years of playing so many things that demanded some kind of special touch to sound good, Chinese style cymbals especially. When you get a line of cymbals that just hangs right there with you, and plays and sounds exactly the way you want whether you're playing big or softly— you get excited about it. 

This one is very zippy— it's fun to play a lot of fast stuff on it, as you can see: 


This particular cymbal may already have a buyer, but there will be more of them. I played three others at C&G HQ, and they were all excellent. We'll be seeing more of this type. Let me know by email if you're interested.

Visit Cymbalistic to see everything else I have in stock. 

Tuesday, November 16, 2021

Gaps in our counting system

In the comments on that extremely valuable izquierdadiddles post, a friend of the site from the Czech Republic remarked on stickings in his native language, and on the American system for counting 16th notes:
 

[We] Czech drummers get to deal with two syllables per hand, making everything sound as if it were meant to be eight-note based.

I never realised the English speaking players had a certain advantage in this regard, but what I am really envious of is your ability to count subdivisions in such an organized manner as one-e-&-a. While it's obvious for you, it's nothing short of genius for us.


He's right— the #-e-&-a system is extremely effective, for reading and singing a rhythm, while relating it to a metric grid. You can get very fluent at playing complex 16th note passages accurately while counting some very fragmented series of numbers, as, es, and &s. I've been doing it so long I don't even know what the alternative systems are.

But the world is imperfect, and our counting system is nevertheless incomplete, and so it's only a partial tool for learning rhythm— combined with playing, and with working personally with teachers, conductors, and other musicians. 

In my music career up until now I've only counted beats using numbers, plus 8th notes using added &s, plus 16th notes using added es and as, plus &-a for triplets and compound 8th notes. For teaching I sometimes need a little bit more. We're talking about counting rhythm only, here— leaving aside counting for keeping track of phrases or form. 

Here are a few of the gray areas, and blank areas, and how I deal with them:  [2023 UPDATE: As I've noted several times below, I've since settled on some better ways of handling these situations.]

More than one &
“And” is a convenient sound to put between two numbers. Yes, the rhythmic & is most familiar as an off beat 8th note (counted 1-&-2-&); but it may also be the middle triplet partial (1-&-a-2-&-a), or middle 8th note in compound meters (e.g. 6/8 or 12/8, also counted 1-&-a-2-&-a). We'll find some other places for it later on. 


Ultimate confusion sets in when we talk about swing 8th notes, where the & falls (broadly) on the last triplet partial, but if we happen to play a triplet in that setting, the middle triplet partial is also called &:



When talking through jazz rhythms, I deal with that by distinguishing between the swing & and the triplet &. Most people get it.  

You could avoid that ambiguity by counting triplets 1-tri-plet-2-tri-plet— sometimes I do. But I'm put off by all those flammy consonant clusters. It's also just kind of childish to be saying the name of the rhythm while counting it, like: 

this-is-a-tri-pul-et-this-is-a-tri-pul-et 

six-teenth-notes-are-fun-e-&-a


Forget it. 


Sixtuplets
I consider sixtuplets to be generally uncountable, and I never count them— except one time, very slowly, for students who have never played them:

1-tri-plet-&-tri-plet, or 1-&-a-&-&-a

[2023 UPDATE: lately I'll count sixtuplets 1-ada-an-ada— it works very well.]

When playing sixtuplets, I count 8th notes. When counting or singing a rhythmic passage, I'll sing something like digada-digada for any sixtuplets in the passage. Digada-dat for a single 16th triplet followed by a release. 


32nd notes
I also do not count 32nd notes, and do count 8th notes while playing them. They're usually played too fast to say a syllable for each note, or to differentiate the partials during a complex 32nd note passage. 

On complex passages (like you see in some etudes in Portraits in Rhythm), we just apply our acquired knowledge of 16th note rhythms, in double time, without counting. A few times in my teaching career, for a student, I've probably counted them out as 1-e-&-a-&-e-&-a.

Again, when counting through a passage, I may sing 32nd notes as diga-diga-diga-diga-datdiga-diga-datdiga-dat:

[2023: It's crazy, but you can simply add an a or da in between the normal 1e&a syllables: 1-da-e-da-&-a-a-da. Thankfully there's rarely a need to count a lot of 32nd notes fast.]

16th notes in compound meters
That's 6/8, 12/8, 9/8, etc. I've never seen a good system for this, or any system, which may be a hindrance to people becoming fluent in this area of rhythm. We also just don't see much of this type of thing day to day. Usually we just deal with it as best we can knowing what we already know about rhythm. When you know something about rhythm, and use it all the time, that's not difficult.  

To precisely block out rhythms for students new to these meters, I'll sometimes count them out in 6, or 12, or whatever the top number of the meter is: 

1-&-2-&-3-&-4-&-5-&-6-& 


That's the only time I count that way. In compound meters generally the dotted-quarter beats are counted, or dotted quarter notes plus the major subdivision: 1-&-a-2-&-a, as in one of the examples above.

After thinking about it for a few minutes just now, I may phase in something like 1-e-&-a-&-a:



I just counted through a couple of snare drum pieces in 6/8 that way, and I like it a lot. It's a little weird to call the last 8th note in a beat a when there are only 8th notes involved, and calling it & when there are any 16th notes in that beat. And there's some ambiguity in having two &s and two as, but it's far superior to the alternatives. It took me about five minutes to become fluent with it. Open up your Podemski/Goldenberg/Peters and give it a try. 

[2023: More recently I've settled on 1-e-&-a-a-da. If one were using trip let syllables in compound meters, there's even a way to make that work.]


Odd tuplets
This  is the first time I've ever thought about it, but you can try these out: 

16th note 5s: 1-e-&-a-da
16th note 7s: 1-e-&-a-&-a-da 
8th note 5s: 1-&-a-&-a
8th note 7s: I don't know, man. 1-&-a-&-a-&-a 

Hell, why not: 
32nd note 9s or 16th note 9s (triplets nested in a quarter note triplet): 1-&-a-&-a-da-&-a-da

Those all work great. They're nice and flowing, and are easy enough to say fast, that there's no reason not to use them. 

Monday, November 15, 2021

Funky 7s on the drums

Some street-beat style 7 stroke roll related things that came up spontaneously when I was practicing today. This had a little bit of a funky Maracatu-type street beat feel the way I was playing it— usually too slow for a quality 7 stroke roll when using a 16th note pulsation. That's not the concern here. Mash the buzzes into the drum and let it be funky.  



Play all roll strokes closed— multiple-bounce strokes. Find your own way to play these that sounds cool, that gives the vibe of somebody who doesn't live in fear of incorrect technique. 

Get the pdf

I was proud of myself for pulling 80 bpm exactly out of the air when I was estimating a tempo for this. I did that another time during a recording session, and impressed some people— “How fast is X bpm?”, snaps fingers, they check the click, and it's exactly on the money. I'm not saying I can do it all the time, but my time has gotten pretty damn decent, I think. See this time post from awhile back for how to work on that. 

And here's a little Maracatu— I wasn't playing it this funky, but it was in the ball park: 

Friday, November 12, 2021

CYMBALISTIC: New Turks are in!

UPDATE: Videos are up! 

CYMBALISTIC: I just got some great Cymbal & Gong custom Turks in stock— two 20" jazz rides, two 17" medium-thin crashes, one 22" Special Half-Turk jazz ride.

They're quite interesting: the Turks have a thin lathed band at the edge, similar to what Bosphorus does. It seems to give them some more high overtones— they sound like cymbals, they don't just go thud when you hit them, like some Turks we have all played. 

The 20s are light—1651 and 1673 grams. One is high, one is moody. Lively, expressive, playable Turks. Everybody loves playing light Turks because they sound like the record— whatever 60s jazz recording you want to sound like— from the playing position. By their nature they're best for recording and intimate situations, rather than high volume unmiked situations.


At 1167 and 1137 grams the crashes are approximately medium thin. Since they're Turks, they don't fully open up for an huge explosive crash— the crash is available, as you can hear, but it's not a huge sound. They're excellent for riding, should be great for a combo setting where a controllable, reasonable-volume left side cymbal is needed. I'm really favoring a 17" on the left these days. They do everything I want, and they're... agile. 



The 22" half-Turk is really interesting— at 2015 grams it's very light, top is lathed, bottom is unlathed. It's a rather airy, delicate traditional K sound, that decays rather quickly. Small bell. A 22" for lower volume situations— not unlike a Bosphorus Master, but not as delicate as that. It should record magnificently. There is also a 24" of this design available at C&G, if anyone is interested— shoot me a note. 



Visit www.cymbalistic.com to see what else I have for sale— I have a number of great 20" Holy Grails right now. Everybody should own one of those.  

Wednesday, November 10, 2021

Page o' coordination: basic triplet texture in 5/4

Continuing this little series. You could warm up for this by just playing the original 4/4 page, repeating beat 1 at the end of each measure— effectively playing ||: 1-2-3-4-1 :||. Like we originally played it in 3/4 by just chopping off beat 4. That's kind of fun. 

But I wanted to place the bass drum differently— this page better suits what I want to do with 5/4: 


It's very straightforward. Just play them down, and begin improvising similar textures on your own. 5/4 is a peculiar time signature, and not easy to feel at all at first, so you should probably be counting your way through. See my old series Cracking 5/4 for some pointers on that, and try playing along with my corny Jesus Christ Superstar loop.    

Get the pdf

Tuesday, November 09, 2021

Back to Dahlgren & Fine

Basic unit of Dahlgren & Fine
UPDATE: I've been hitting this all week, covering most of the pages in question every day, tempo around quarter note = 126. It's very interesting— all kinds of unrelated stuff just starts flowing. Practicing all of these illogical disjointed unisons seems to smooth out a lot of hidden structural hang ups keeping that other stuff from flowing, or from coming out easily. It's pretty cool.  

I did something very cruel to a student recently— we did two entire lessons on the harmonic portion of Four-Way Coordination by Marvin Dahlgren & Elliot Fine. Perhaps you've heard of it. The book is famously a real pain in the A— I feel like I've complained pretty copiously about that fact in the last 8-10 years. 

I mostly stopped using the book— my own harmonic method covers the same territory, and is vastly superior; it has a clearer musical purpose, and it can (and should) be adapted for students of all levels. Scroll through these posts to learn more. Or, heck, call me for a lesson. 

But 4WC is a famous book, a lot of people own it, and they want to know how to deal with it, so let me give you my strategy for learning that brutal harmonic section on pp. 15-18. We'll talk about playing single measures repeating— eight note patterns. Doing just the four note patterns seems like a good way to start, but that's not necessarily easier. 

There are no instruments indicated on the staff, just RH, LH, RF, LF. I recommend: with the hands, hit a cymbal on notes that are in unison with the bass drum (right foot, presumably), and hit the snare drum on notes that are in unison with the hihat (left foot). Your hands will have to move between the snare and cymbals. That's a normal orchestration, with normal hand moves you want to be practicing. It's the whole point of doing this. Musical independence has to involve the parts of the actual instrument, used in their normal roles.  
 

The first two numbered systems on p. 15 are straightforward; the top staff has the right hand in unison with the bass drum, the bottom staff has the left hand in unison with the bass drum. Use them as a warm up. Starting on system 3 are the harder combinations, where either hand could be played in unison with either foot, on the cymbals or snare drum. 

First, look for all the measures that have four notes in a row with either the hands or the feet. On page 16, that would be these: 


Job 1: Play all of those on pp. 15-18. Hit cymbal when in unison with the bass drum, hit snare drum when in unison with the hihat played with the foot. 

Then look for patterns with four in row on the hands or feet when you repeat the measure. On p. 16, that includes most of the remaining patterns: 


This vastly simplifies our problem— just play a sticking pattern with the hands or feet, along with four notes played with one opposite limb. Very importantly, this gets us away from the idea of starting everything on the 1— to do it this easy way, start playing the pattern wherever in the measure the four in a row starts.  


Job 2:
Learn all the remaining measures with four notes in a row with that hands or the feet. You've now learned 80% of the material on these pages. 


Next, look for the patterns with a RLRL-LRLR in the hands or the feet— that we haven't already played in Job 1 or 2. There are two of those on p. 15: 


This will be more of a challenge. You could start by playing just the RLRL (with the opposite part), and then the LRLR— one time only, or repeating. Then play RLRL-L, and LRLR-R— one time only.
  

Job 3: Learn any remaining patterns including an RLRL-LRLR in the hands or feet. 

Some people may find it easier to do this portion based on the RRLR-LLRL sticking— in that case, look for all instances of that in the hands or feet, that you didn't do in Jobs 1 or 2. 

Once you've done this, you've essentially learned all of the full measure patterns on these pages. 

Observe: 

If you look closely and don't always start reading on the 1, you'll notice that all of the remaining patterns are based on that same RLRL/LRLR pattern— a paradiddle inversion. The highlighted spots below from p. 16 show the RLRL or LRLR in each of those measures— so you'll be playing the exact patterns you already learned, just not starting on the 1:



Note that there will be more than one option— on all of these remaining patterns, both the hands and feet are playing paradiddle inversions, each of which can be played as RLRL-LRLR, starting at different places in the measure. 


Job 4: Learn the few remaining patterns orienting off the RLRL-LRLR in the hands or feet, wherever that begins in the measure


The upshot: after the first two easy systems, there are 56 measures total, each played two different ways— hands reversed on the lower staff. A whopping 45 measures have that easy four in a row with the hands or the feet; the remaining 11 have the RLRL/LRLR in the hands or feet, or an inversion of that. Learn that one hard pattern, and learn to start it off the 1, and you've learned the system. 

All of the one measure patterns, anyway. You can do different combinations of the lettered 4-note patterns to make different one measure, 8-note patterns. We've been doing AC and BD. You could also do AB/CD, and AD/BC. Now you have a strategy for doing that. 

Make no mistake, this is a nightmare mission, but at least now we can make some kind of systematic assault. Figure it out, and you'll be one of the elite few— for all the tens of thousands of copies of this book sold— who has ever done anything meaningful at all with this part of this book. 

Saturday, November 06, 2021

Izquierdadiddles

Tenue des baguettes
I've got 6 hours of driving to do a 90 minute gig today, gang, so I'm going to leave you with this:

I spend a good part of my life singing stickings in rhythm, for students. We're very lucky in the English-speaking world that we have nice one-syllable words for left and right, and for many of the other possible four-way stickings— bass, kick, hats, hands, feet, both. Others— Spanish-speaking people, for example— are not so lucky. To tell someone the sticking for a paradiddle, you have to say: 

derecha izquierda derecha derecha
izquierda derecha izquierda izquierda


It's only possible to do it at baby speed, with a giant space in between words. Derecha. [Whack]. 

Italian is almost as bad, they shaved off a syllable:
 

destra sinistra destra destra
sinistra destra sinistra sinistra


If you say it fast you have a Bulgarian rhythm.

German is acceptable, with rechts (or rechte?) and links. French droite and gauche are a mouthful, but sound cool, especially the word gauche has a good sound for percussion, like a Pinstripe on a snare drum. Goosh. Drummers speaking most other languages are burdened with extra syllables. I don't know what they do, call stickings by their letter name? Assuming the letters themselves are only one syllable?

Sidebar, step into my office: Where the hell did the Danish get venstre for left? It's similar to das Fenster in German, meaning window. We can only speculate on that etymology, remembering that usually words meaning left are derived from weird, dirty, evil, weak, clumsy, suspect. The left hand is out the window, like the rotten herring seems the likely word source.  

[...] 

Fellow drumming blogger Ted Warren suggested you could have a whole new rudiment if you played a note for all the syllables in that Spanish version. We have the choice of keeping the beat the same, or keeping the rate of notes the same: 


That first one will give you a little left hand workout. I imagine in a parallel Star Trek universe where I speak Spanish, I say izquierda in a lesson, and the student says so I hit it four times, IZ-QUI-ER-DA? [whack whack whack whack] and I say NO! It's quite simple! etc endlessly.

Lots to think about.   

Thursday, November 04, 2021

Very occasional quote of the day: the instrument itself

“If you get too involved in the playing of the instrument itself, you forget that the whole purpose of what you're doing is to add to the music. 

There's more to music than having control over the instrument.” 

- Steve Gadd, 1978 Modern Drummer interview with Aran Wald


Lots of great quotes lately, from MD interviews with Gadd and Shelly Manne. This one is worth commenting on, because it fits so neatly into the ridiculously polarized, eternally pointless and misguided internet "chops vs. groove" debate. It's a hobbyist's topic, conveniently framed by and for hobbyists. It's not real. Gadd is not supplying you with an excuse to not practice. 

He was no doubt referring to himself as much as anyone else here. When he first became known as a star player in  the 70s, he was as technically able as anyone else active. It takes a lot of involvement in the playing of the instrument itself to play as well as Steve Gadd. 

The point is that it's not the only thing to be involved with.   

Wednesday, November 03, 2021

Hemiola funk patterns in 5/8

Here's a nice easy page of hemiola funk patterns in 5/8— based on our friend the 3:2 polyrhythm. World's fastest way of getting your students playing hip stuff in 5, if you already (wisely) ran them through my previous hemiola funk pages


These will also work in a bright 5/4— 8th notes = quarter notes, in that case. You can also swing the 16ths, add hihat (on 2 and 5) and alter the cymbal rhythm (add skip notes on 2 and 5) to make a 5/4 jazz feel, which is an excellent idea.

Get the pdf

Tuesday, November 02, 2021

Delayed continuity

I've been looking some piano literature lately, reading an old book called Practising the Piano (British spelling) by Frank Merrick. You can get it on Scribd without having to pay anyone but Scribd. Another site giving away a lot of content, making sure they get paid, if nobody else does. Let's talk about a thing Merrick calls delayed continuity— it's a useful phrase, whether or not we decide to practice the way he suggests: 

Some music is very easy to play phrase by phrase with pauses in between:  


 

If the pauses are so long that each phrase is mentally or actually sung a tempo before it is played, the player will benefit by this forethought and often excel previous efforts on the spot. If each phrase is also followed by a further pause for reflection and self-criticism the successful playing can be noted as worthy of retention and the unsuccessful as models of what to avoid. The threefold ritual can be abbreviated into three verbs, "plan, play, judge"[...]

Remember that the pause must always be at least as long as the phrase to come. The following shows the minimum length of pauses for Ex. 1:  


 

This leaves no extra time for criticising your efforts and if the thinking is a really expressive mental rehearsal of what is to come (rather than an apathetic conning over of the mere notes) it will be preferable to add a breathing space to the minimum pause. When the time is also taken for self-criticism, all sorts of practical questions like “Did the fingering, pedaling, etc, all conduce to give me a recognizable copy of  that mental rehearsal?” can be seriously faced. 

Sometimes the desire to try the phrase over and over again is irresistible, but think it through again first. Do not play twice on one mental rehearsal if you can withstand the violent temptation to do so which comes from an over-eager spirit. In this emulate not a hockey player but a golfer. When the latter misses the ball he repeats a very solemn and impressive ceremony known as “addressing the ball” before carrying out a second attempt. 


It's very similar to the way I teach independence/coordination on the drums— except I don't use the word “conduce” in my inner monologue. I use added stops or fermatas to group complex coordination items into manageable bits, and give time to think about what is the next thing. Drumming practice is usually very repetitive, so we'll often just be adding pauses to a single measure of a pattern. Like in my “skiplet” method*, I'll put a fermata on the 1 and 3. When teaching a Mozambique, I'll put a fermata on the rests, or quarter notes. The thinking-ahead phase takes the form of counting the rhythm of the upcoming part, and thinking through the four-way sticking. The criticism phase is instantaneous, and almost unnecessary. If you're doing it right, there will be no mistakes— you go slow enough, with small enough chunks of the overall pattern,  that you can do it perfectly. 

* - I'm too embarrassed to actually say that dumb word skiplet now. I just say spangalang for that little chunk of pattern. 

Playing the drums as a jazz musician is very different from being a concert pianist; Their job is deep learning of lengthy, very involved composed pieces, to be performed perfectly, note for note; there's a serious mental discipline involved with that, which Merrick's method serves— it should also be useful in concert percussion, when learning and memorizing a piece. 

A jazz drummer's job is to improvise a developing texture, with huge latitude for what exact notes are acceptable, if they're played in time. For a concert pianist unplanned notes are mistakes; for drummers unplanned notes are virtually the plan. But this tactic of suspending the time in logical places— usually by making a long note longer— to give yourself a chance to think through the upcoming coordination and count the rhythm, is very useful. 

Monday, November 01, 2021

Page o' coordination: prep for subtractive method with Rumba bell

Continuing this subtractive thing using another common Latin bell rhythm, a Rumba rhythm, Guaguanco. There isn't typically a bell used in Guaguanco, but played on the drum set, it's the equivalent of the bell rhythm; if you want to be slightly less inauthentic, play it on a jamblock or shell of the drum or some kind of wood sound. I'm playing it mainly on the ride cymbal. I just want to play creatively in the kind of quasi-Latin stylings done by jazz musicians— and not be totally lost playing music that is actually clave-based.  


Before getting into it, it helps to think about the bell pattern a little bit. I found it helps to orient around the 2& in the first measure, and the 3& in the second measure. For me the rest of the pattern falls naturally if I just play the 2& and 3& in the right spot. 


Also note the three right hand doubles in a row from that 3& through the repeat: 



It's also a good idea to practice each measure individually before doing the full pattern. 

And once again, these two pages are very substantial by themselves. You could practice this system while reading out of Syncopation (pp. 4-5, 10-11, 30-45), or not. I think it's worthwhile. Playing the Mozambique bell part, I was able to do all of the one-line patterns easily; doing the longer exercises is going to take more practice. 

If you get into my Latin loops archive, there are several suitable loops at reasonable tempos— look for the ones labeled Rumba. 

Get the pdf