10 Years of Trumpet Learning: Tips for Beginners

October 24, 2023 music 1 comment

I realised recently that I embarked on my journey to learn playing the trumpet a decade ago in September 2013. At the time, it was a very spontaneous idea, and I had no idea how hard it would be on the one hand, and how much I enjoy playing and learning the instrument. For the anniversary, I decided to treat myself to a new trumpet (hopefully to last longer than ten years!) Coincidentally, I stumbled upon a Craigslist ad from a parent seeking a trumpet for their child. In the spirit of sharing (and also because I had collected quite a few) I decided to give one of my trumpets away. Yesterday, that parent reached out to me for advice on how to help their child learn to play. In response, I’ve compiled some of my own experiences and insights to assist aspiring trumpet players.

The trumpet is a unique and challenging instrument. Unlike musicians playing other instruments, I have found professional trumpet players to express their unique frustrations and the experience of being constantly challenged. This difficulty stems from the fact that much of the technique required to play the trumpet is hidden inside your mouth. Initially, no one can fully explain how to make the necessary adjustments, and even if they could, you might not have the muscle control to implement them. And then, even if you do have the technique, when you happen to make a mistake it is going to be quite obvious to the listeners, because of the volume of the instrument. Patience is key, and it’s important to understand that it may take a considerable amount of time, possibly even a year, before you can produce pleasant or enjoyable sounds. Don’t get discouraged by mistakes or slow progress – enjoy the journey and celebrate every small improvement. I was happy to not have any timeframe or goal to meet — I just liked the challenge and the (small if not tiny) progress that I was making. I still think it is one of the hardest things I have undertaken.

Before even thinking about the technicalities of playing, I think it’s valuable for any trumpet player to know how to disassemble and assemble their instrument. It is also not particularly difficult, and the first step to clean it from the inside. You can find helpful tutorials on YouTube for this purpose, here is one example.

While self-learning is possible, finding a qualified teacher is highly recommended. A teacher offers valuable corrections and guidance, inspiring and encouraging you throughout your journey. I had weekly one hour lessons. (Although many beginner students do half hour lessons.) I found my (three) teachers through twitter, online search and a party. I practise around 15 – 30 minutes daily (except weekends).

The Internet is a treasure trove of resources for aspiring trumpet players. A simple Google search for “trumpet tutorial”, “how to begin playing trumpet”, or related keywords and phrases will yield a wealth of advice, lessons, and tips to suit your specific needs. Same for searching Youtube. I trust you can adapt your search terms as needed. Also, you can do an image search for scores (example, Bach Minuet Trumpet), or search for “trumpet – tune – pdf”. (example, Amazing Grace Trumpet PDF). One of the first things you may find immiediately useful are fingering charts. With the Internet, it has never been easier to learn. I find YouTube so useful I am paying for a Premium membership, in order to avoid the interruptions by ads. This also comes with YouTube music.

The first practice technique that I highly recommend is focusing on long tones. These exercises help build your embouchure, tone, and breath control. You can find a helpful tutorials on long tone exercises on YouTube, here is one example.

I really like the Second Clarke Flow Study. You can access the sheet music online, and watch recordings on YouTube. The Clarke flow studies are versatile and can be practiced starting from any note, from the low G below the staff to the high G above it. A beginner may find it easier to start on the C – F notes (32 – 37 in that PDF).

With the major scales and 3 different kinds of minor scales, you can easily spend 5 minutes a day and still take quite a while to be able to play all of them by heart. I have actually written them up myself. The thing about scales is that many melodies will have shorter or longer sections of ascending or descending notes, so it is good to be familiar. Also, even the simple scales are challenging enough — if not, just try playing faster. And it is good to be comfortable with different key signatures. (So Long Tones, Clark Flow and Scales would easily make up a good first 10 minutes of a daily practise session).

In the beginning producing a good sound will be more difficult than anything else; still it will be good to play with a metronome just to get used to it. There’s many mobile apps if you want to spare the expense. So turn it on for long tones, the flow studies and scales.

Of course, there are many other exercises, like lip slurs, articulation exercises, or sight-reading practice. But I wanted to highlight these as they seem to me to be good for beginners and advanced players alike. Happy playing!

Musical scales with inline flats and sharps

October 19, 2019 music, systems No comments

I have started to learn playing scales on the trumpet. Mostly because it should be helpful for playing faster runs, and also for improvising.

When I play from scores with the usual presentation of scales, I find it difficult from time to time to make out whether the following note is sharp or flat. This is because that is usually indicated at the beginning of the line, in the key signature. So I have to look left, count lines, etc.

So I have prepared scores where the flats and sharps are written immediately in front of each note. There are usually no “cancelling” naturals, because it is taken for granted that if there is no flat or sharp, the next note is meant to be played natural.

To begin I started with the 4 main scales: major, natural minor, harmonic minor and melodic minor.

Of course, there is also value in learning the key signatures, and the positions of the half-tone-steps, and the whole system that holds these scales together. But I think that can be separated, and playing trumpet, and playing these scales in particular, is already hard enough.

I used the free musescore program to create these files. It works really well, and the result looks very good! WordPress doesn’t like me to upload the musescore (mscz) files of the scores – so please email me if you’d like to have a copy.

Here is a list with clickable links for the PDF files. Below are the scores as images, also clickable:

Major Scales
Major Scales
Natural Minor Scales
Harmonic Minor Scales
Harmonic Minor Scales
Melodic Minor Scales
Melodic Minor Scales

The use of superlatives in Wikipedia articles

August 2, 2019 Uncategorized No comments

You are most likely familiar with wikipedia (wikipedia.org) “the free encyclopedia that anyone can edit.” In many ways it is an amazing service,
and I often find it useful.

Some aspects of it are amusing, and here I am writing about one of them.

And that is the inclusion of superlatives and world-best about the subject of the article. Each individual point sounds interesting, relevant and informative, but after reading a few of them, they seem, to me, arbitrary and fluff.

Most-disliked-youtube-video? Most-hat-tricks-in-the-Champions-League?

Of course, these are all outstanding and talented people, and I don’t mean to doubt their accomplishments here.

I am writing here about how they are presented on wikipedia. I take it as a symptom of attention deficit (“ADD”), a lack of expression on the one hand, similar to showing off and exaggerating, or, on the other hand, reading superficially, only being able to grasp
simple, shallow points, or the quickly perceived.

Here I have put a few examples for you together. It is mostly musicians, although it also includes sports and one writer. I have strung the quotes together into one paragraph, to emphasize the point! The sequence may be different in the articles themselves.

The list is followed by a few links to articles that do not have this kind of treatment.

All the links to the wikipedia pages are by version, so you will be looking at the page as I found it when I copied the quotes. The “current link” will take you to the present version of the article (at your time).

“Without further ado.”

Justin Bieber

currrent / quoted

He has sold an estimated 150 million records, making him one of the world’s best-selling music artists, and became the second person to reach 100 million followers on Twitter in August 2017 after Katy Perry. In 2016, Bieber became the first artist to surpass 10 billion total video views on Vevo. In July 2010, it was reported that Bieber was the most searched-for celebrity on the Internet. His music video for “Baby” surpassed Lady Gaga’s “Bad Romance” (2009) as the most viewed, and also the most disliked, YouTube video ever. The music video held the record for the most video views in 24 hours when it was released, with 10.6 million views.

Beyoncé

currrent / quoted

Among numerous awards and accolades, Beyoncé has won 23 Grammy Awards and is the most nominated woman in the award’s history. She is the most awarded artist at the MTV Video Music Awards, In 2014, she became the highest-paid black musician in history and was listed among Time’s 100 most influential people in the world for a second year in a row. With the release of Lemonade, Beyoncé became the first and only musical act in Billboard chart history to debut at number one with their first six solo studio albums. Beyoncé performed at the Super Bowl XLVII halftime show, held at the Mercedes-Benz Superdome in New Orleans. The performance stands as the second most tweeted about moment in history at 268,000 tweets per minute Lemonade was streamed 115 million times through Tidal, setting a record for the most-streamed album in a single week by a female artist in history.

Lionel Messi

currrent / quoted

He has spent his entire professional career with Barcelona, where he has won a club-record 34 trophies. A prolific goalscorer and a creative playmaker, Messi holds the records for most goals in La Liga (419), a La Liga and European league season (50), most hat-tricks in the UEFA Champions League (8), and most assists in La Liga (169) and the Copa América (12). According to France Football, Messi was the world’s highest-paid footballer for five years out of six between 2009 and 2014, and was ranked the world’s highest-paid athlete by Forbes in 2019. He was among Time’s 100 most influential people in the world in 2011 and 2012. Although FIFA did not acknowledge the achievement, citing verifiability issues, he received the Guinness World Records title for most goals scored in a calendar year. He surpassed Luís Figo as the player with the most assists in La Liga;[note 4] he made his record 106th assist in a fixture against Levante on 15 February. His second goal, which came only three minutes after his first, saw him chip the ball over goalkeeper Manuel Neuer after his dribble past Jérôme Boateng had made the defender drop to the ground; it went viral, becoming the year’s most tweeted about sporting moment.  This was also Messi’s sixth hat-trick in the Champions League, the most by any player.

J. K. Rowling

currrent / quoted

In October 2010, Rowling was named the “Most Influential Woman in Britain” by leading magazine editors. In February 2013 she was assessed as the 13th most powerful woman in the United Kingdom by Woman’s Hour on BBC Radio 4. She was named the most highly paid author in the world with earnings of £72 million ($95 million) a year by Forbes in 2017. The book was purchased for £1.95 million by online bookseller Amazon.com on 13 December 2007, becoming the most expensive modern book ever sold at auction.  She is best known for writing the Harry Potter fantasy series, which has won multiple awards and sold more than 500 million copies, becoming the best-selling book series in history.

Taylor Swift

currrent / quoted

Her 2006 self-titled debut album was the longest-charting album of the 2000s in the US. The album’s third single, “Our Song”, made her the youngest person to single-handedly write and perform a number-one song on the Hot Country Songs chart. The album won four Grammy Awards, with Swift becoming the youngest Album of the Year winner. For her fifth album, the pop-focused 1989 (2014), she received three Grammys and became the first woman and fifth act overall to win Album of the Year twice. Having sold more than 50 million albums—including 32 million in the US—and 150 million singles, Swift is one of the best-selling music artists of all time. She also ranked first in the Forbes Celebrity 100 (2016 and 2019), and was the youngest to be featured in the magazine’s listing of the 100 most powerful women (2015). Swift has received many awards and honors, including 10 Grammy Awards,[406] 23 American Music Awards (most wins by a female artist),[407] 23 Billboard Music Awards (most wins by a female artist)

Queen

currrent / quoted

At the time, it [A Night at the Opera/SW] was the most expensive album ever produced. In December 2018, “Bohemian Rhapsody” became the most-streamed song from the 20th century, and the most-streamed classic rock song of all time. As of 2005, according to the Guinness Book of World Records, Queen albums have spent a total of 1,322 weeks (twenty-six years) on the UK Album Charts, more time than any other act. Also in 2005, with the release of their live album with Paul Rodgers, Queen moved into third place on the list of acts with the most aggregate time spent on the British record charts.[298] In 2006, the Greatest Hits album was the all-time best-selling album in UK Chart history. … the band is the only group in which every member has composed more than one chart-topping single, A 2001 survey discovered the existence of 12,225 websites dedicated to Queen bootlegs, the highest number for any band.

Serena Williams

currrent / quoted

Williams holds the most Grand Slam titles in singles, doubles, and mixed doubles combined among active players. She is the most recent female player to have held all four Grand Slam singles titles simultaneously. Her total of 23 Grand Slam singles titles marks the record for the most Grand Slam tournament wins in the Open Era. She also holds the all-time record for the most women’s singles matches won at majors with 343 matches.  Earning almost $29 million in prize money and endorsements, Williams was the highest paid female athlete in 2016. She also broke the record previously set by Justine Henin for the most prize money earned by a female tennis player in one year, with Williams earning $6,545,586. Williams won her fifth Wimbledon singles title, her fourteenth Grand Slam title;[140][141] setting a serving record of 24 aces by a female in a match as well as having the most aces, male or female, during the tournament (102). She is the only player in history to win all four Grand Slams at least once after having turned 30.

Discover  for yourself

Compare

Here are articles where without a doubt, superlatives may have been included. But they aren’t.

Quick note about the times tables

August 1, 2019 generic, math No comments

I was asked yesterday, why do they teach the multiplication tables in school. Wasn’t sure whether this was common knowledge, but here’s how it goes. Once you know how to multiply the numbers from 1 to 9 with each other, you can multiply basically any two numbers by hand; doesn’t matter how many digits they have.

Let’s say you want to multiply 132 × 18. When you learn your times-tables, these numbers are not covered. But there is a method for you to follow that will just involve multiplying numbers less than 10. It does assume that you know how to add, but learning how to add numbers with several digits is not that hard either.

There’s more than one way to do multi-digit multiplication, but you can find the descriptions here: https://en.wikipedia.org/wiki/Multiplication_algorithm.

Of course, youtube has a few demonstrations too, for example:

  • https://www.youtube.com/watch?v=FJ5qLWP3Fqo
  • https://www.youtube.com/watch?v=KiI4eZCGTLM

So, 132 × 18 = 2,376. You would be multiplying these numbers on the way: 2 × 1, 3 × 1, 1 × 1, 2 × 8, 3 × 8 and 1 × 8 (which are all really simple!)

Now if you ask why to learn how to multiply numbers in the first place? I find mulitplication comes up quite a lot just in ordinary tasks, doubling baking recipes, find distance from velocity and time, and vice versa, buying quantities of  various items. Sometimes I use a calculator, or spread sheet, but often it’s good to do without. There’s lots of different applications!

Replacing a toilet

July 27, 2018 challenge, family, generic, systems No comments

After a long time, we replaced our toilet last week. The old one didn’t work well for years and years!

We found these two videos helpful, showing in detail how to remove a toilet, replace the wax ring, and then, install the new one. The second video also comes with written instructions. The videos made it look quite straightforward, and so they were very encouraging; and it did work out quite well. It took just about 2 hours.

But here, I provide numbered steps, to follow along one-by-one, as a detailed plan. This way, you will always know what to do next—which can often be tedious, and the most challenging.

1. Empty space next to toilet, clean, etc.
2. Prepare space to lift old toilet to (Step 16)
3. Put new toilet in place to lift from
4. Flush (old) toilet
5. Wipe down toilet
6. Clean bowl, etc.
7. Turn water valve off
8. Flush until will not flush anymore (remember Step 7: water is disconnected)
9. Disconnect water hose
10. Plunge bowl
11. Sponge bowl dry
12. Scoop out water tank, sponge dry
13. Scrape off silicon connecting bottom of toilet to floor (if needed)
14. Lift lids of screws on the bottom / sides
15. Unscrew the bolts that fix the toilet to the floor
16. Lift toilet out
17. Remove the two bolts
18. Scrape out existing wax gasket
19. Clean floor which was underneath the toilet
20. Place new wax gasket
21. Place new bolts (upside down, on sides)
22. Lift new toilet into place. Make sure back is parallel to wall, level perpendicular and parallel to wall
23. Weight down to smoothe out the wax connection
24. Tighten new screws on bolts
25. Connect water, test flush
26. Cut off tops of bolts (saw)
27. Place lids on bolts
28. Connect new seat
29. Test flush
30. Clean up

This is an optimistic list; if anything goes wrong (e.g., at step 13, 18 or 29), you’re on your own. Our new toilet is just a one-piece, so I didn’t cover the case of a separate water tank.

Bezos using the I-words

December 13, 2017 challenge, economics, systems No comments

I came across a more or less generic interview with Jeff Bezos, the founder of “amazon,” a few days ago. It took place in May this year; they chat about management questions, how to run a business, this and that, etc.

But at one point he uses the I-words: impossible and inconceivable.

It is impossible for me to imagine a scenario, where ten years from now a customer comes to me and says, “Jeff, I love amazon; I just wish you delivered a little more slowly.” This is so inconceivable, …

Here’s the link to the quote in the youtube video, jumping right ahead. The context is that the “leader” of a business should “identify” 2 or 3 “big ideas,” and “enforce great execution against these big ideas.” Here, since this scenario is so “impossible” it is easy to dedicate a lot of energy to working on fast delivery. At some other point in the interview he enumerates what he calls the big ideas at amazon, the “consumer business”: low prices, fast delivery, and vast selection. (On the other hand, he is quoted with a different set of 3 big ideas, as well.)

Such a strong conviction and judgement about what is not possible is not common in my world. I almost feel like I go out of my way to avoid talking like that, and so do my friends and colleagues and people I hang out with.

So this morning scenarios popped into my head, of what he deems impossible:

  1. Let’s say you’re at the other end of the world, and don’t want the delivery to happen until you have returned home. Then fast delivery would be undesirable.
  2. Or: your house is full, and that couch you are ordering will not fit until next week, you’re not ready till then.

So in these two cases (or call them “scenarios”), you would like amazon to deliver a bit more slowly.

Surely you can think of other scenarios?!

(Disclaimer: I don’t do any shopping at amazon, and encourage you to avoid them as well. No brown boxes in our house! I’m actually astounded how excited people are about them. You can find a few reasons starting from these search results for boycott amazon from duckduckgo.com)

Alcoholism: The Sinclair Method

November 14, 2017 challenge, economics, food+drink, generic, systems No comments

As far as I can tell alcoholism is quite a terrible disease. I think I am ok, but I used to be addicted to smoking. I stopped smoking two and a half years ago. I’m glad to not be addicted anymore. But recently I came across a treatment for alcohol addiction. I found it compelling, so I wrote this up this short article!

It is called The Sinclair Method, developed by Dr. John Sinclair in the 1960’s. I’ll try to describe it in a few words: You may have heared of Pavlov’s Dog and what is called “Conditioning”. So the bell rings and the dog salivates because the dog is trained to expect food when the bell rings.

It turns out that Dr. Pavlov also found a way to uncondition the dogs. This happens when the stimulus is presented without the reward. As wikipedia writes, “when a conditioned stimulus is presented alone, so that it no longer predicts the coming of the unconditioned stimulus, conditioned responding gradually stops.”

The Sinclair Method consists in the addicted person taking a drug which makes it so that when they drink alcohol, the brain does not perceive the reward as it was without the drug.

In other words, the Sinclair Method thinks of alcohol addiction as a learned behaviour that can be unlearned. The unlearning takes the “fun” out of drinking. But once you’re addicted and desparate, you may find that not much of a loss. And the drug is otherwise said to be harmless.

I found this approach quite convincing. (It appears the drug does not help with nicotin addiction).

The drugs are called Naltrexone, Naloxone, and Nalmefene, keyword “opioid antagonists”.

The Internet has a lot to say about this method. Please read up:

Reddit has a few related forums:

Thanks! Hope this helps. Please do send me any feedback about this if you have!

Some word searches

June 12, 2017 Uncategorized No comments

Came up with a new kind of word search.

Thing is it turns out a bit differently when your alphabet is only one letter. We’ll require that words cannot overlap.

So I’ll show you a few examples, beginning with easy, and going to very difficult.

We’ll use the letter A — first one that comes to mind, isn’t it?!

1. Simple word search

A A A A
A A A A
A A A A
A A A A

Words to find: AAA, AA, AAAA

2. Harder word search I

A A A A A A A
A A A A A A A
A A A A A A A
A A A A A A A
A A A A A A A
A A A A A A A

Words to find: AAA, AAAAA, AAAAA, AA, AAAAA.

3. Harder word search II

A A A A A A
A A A A A A
A A A A A A

Words to find: AAAAA, AAAAA, AA, AA, AA, AA

4. Hardest word search

AAAAAAA
AAAAAAA
AAAAAAA
AAAAAAA
AAAAAAA
AAAAAAA

Words to find: AAAA, AAAA, AAAA, AAAA, AAA,AAA,AAA,AAA,AAA,AAA,AAA, AAAAA

Good luck!

Testing the Soundcloud Player: On Copying and Owning

August 17, 2016 music No comments

Wanted to do a little test for the Soundcloud player (in a WordPress blog).

Here’s a tune I put together 4 years ago.

I had made an earlier version where it says, the piece is:

based on the essay “On Copying and Owning” by Chris Drost at drostie.org/on_copying.html. With sounds from LMMS and beat similar to www.home.no/mlinux/us-lmms.txt (Mikkel Meinike Nielsen). Text-to-speech by MARYTTS, mary.dfki.de; the voice is cmu-slt-hsmm (Note: Chris Drost updated his essay in the mean time; I liked the original!)

Three notes:

  • The MARY text-to-speech system was a lot of fun to work with (they have an online demo).
  • The theme of the song is still totally relevant.
  • The Chris Drost (drostie.org) website is no longer available (Summer 2016).

Snowden, NSA, etc.

January 20, 2014 internet, systems No comments

It’s been a while since Edward Snowden started revealing details about the global surveillance operations of the NSA. I’ve been meaning to write down a few thoughts for a long time, but didn’t quite find the time; however they still seem interesting enough now, so let’s go.

1. Insulting the whole world

It hardly makes sense to begin without stating that these actions are insulting, disrespectful and abusive to every human being (who uses a phone, or the Internet) on the planet.

How dare the American government think they are entitled to listen in on everyone’s phone conversations, read everyone’s emails and track all other online activities.

This also goes for everyone defending these actions. How dare you?!

The reporting from the American side often makes distinctions between surveillance of American citizens, and surveillance of those who are not such citizens. Sometimes it sounds as if American citizens are more worthy of some kind of better treatment. That is of course also insulting, disrespectful and abusive.

2. Spam

When I first heared of the extensive surveillance systems, I thought, well, if they really have this much equipment and so many resources, it would be nice if they could solve a real problem: namely email spam, blog post spam, and similar.

However, they do not occur to be working on that.

One concludes that this is not high on their priorities.

3. Bittorrent

Early on, one could read that the NSA stayed away from analyzing Bittorrent traffic. Which makes a lot of sense, since there is so much of it.

On the other hand, this leaves quite a gap to set up communication channels.

4. Pair programming

Within the first few weeks there were reports that the NSA switched to Pair-programming, pair administration, etc. Basically, don’t let anyone touch the systems without someone else watching. Take turns. Call it “Access Control Layer 1?”

The reports I read, didn’t point out how natural such a policy is. It is also not necessarily more expensive, some software companies use pair programming to avoid costly mistakes, programming bugs, etc.

So one wonders whether the original access  control did not have this additional layer in order to actually allow unauthorized access. After all, Mr. Snowden did not access the system for personal gain; how many others with access were not that noble? How much easier to avoid laws and cut corners without such a layer.

Also, has this policy been reverted in the mean time? It would be possible to do so without issuing a press release, of course.

5. An extra button

Also early on, it was reported that the data that passes through the NSA’s system is enormous. On the other hand, if you look at any particular person, the data traffic they generate will most of the time be quite managable.

So I am guessing that if anyone shows up in manual surveillance (an operator inspects certain communications), they will have a button within their user interface, “Track this individual closely”. Save all that traffic for later viewing. I would estimate that adding 100 people per day would be easy to manage in terms of traffic.

6. Germany

I follow German news of course. When it was first revealed that the NSA was listening in on phone calls of the German chancellor, I thought, well at least governments have the resources to set up communications based on One-time pad encryption. Also, Germany has local chip factories  to make sure the chip does what is desired by the owner, and not what the NSA desires.

(I find the response of European governments quite weak, I think it is underestimated how easy it is to argue with Americans)

7. Logging

In the wider context of privacy on the Internet (user profiling using cookies, etc), it had occurred to me a long time ago, that such policies should also cover web server logs. After all, such logs capture some information about individuals, sometimes not too much, but in the aggregate, I think it would be useful to look into stronger protection. Such protection, in one of my thoughts, would consist in having people, and organizations, be granted a “License to Log”. Such a license would be lost in the case of illegal activities, irresponsible behaviour, and so on.

These kinds of thoughts seem to be totally useless now.

8. Metadata

It hadn’t occurred to me that what they call “metadata” is useful, but now it does seem intuitive that it is very helpful. Basically every person is placed in a circle of their acquaintances, in circles of similarities according to many different categories.

This is similar to Facebook asking users to list their favourite books and music, etc. Facebook will also benefit from this as similar metadata of its users (Who to show which ads, as the most basic example).

9. Cost

One can only feel sorry for the average American. Basically these surveillance systems cost each tax payer a few hundred dollars a year. Without any benefit to them, it would seem.

10. Balance of powers

I often hear praise for the American democracy and how there is a balance of powers.

Cannot be spotted here. It’s rather obvious that there is no supervision of the NSA. Last week it was reported that a senator inquired whether they as senators are also covered by the systems. Asking the question itself was already revealing, needless to say the answer was disappointing.

One can make the case for secret courts in democracies, but I think it is obvious that these should be only used extremely sparingly. That is not the case here.

−

Ok, that’s all for now. You probably have your own thoughts about this. I’m sorry I couldn’t include links everwhere. Please share below, add corrections or other comments, if you could!