Kakan Day 235: Little Things Add Up…

果敢

果敢

As I mentioned in the first post of 2016,  I have chosen the Japanese word kakan (果敢: かかん): to be bold, determined, and/or resolute) as my motivational theme for this year. So today, on Day Number 235 of our Year Of “Kakans” I want to discuss numbers themselves.

We have been putting the idea of kakans: ‘little daily boldnesses’ to work for us for 235 days. That seems like a lot, but we got here one day at a time. There was a Day One, a Day 53, a Day 198, and so on, and now here we are at Day 235. That’s just over 64% of the year gone by, over 20 MILLION seconds! Factoring sleep into the equation, we have had at least 10 million seconds of waking opportunity, at least 117 days of “awake-ness” within which to act (and obviously even more since we don’t sleep 12 hours a night every night). So even if we do not have the full 235 days of kakans, due to sleep, illness, work, and so, on the numbers do eventually add up big time. These little boldnesses make big things in time.

For example, I have spent much of my adult life teaching, lecturing on, and tutoring saxophone, music, Japanese language, and so on in high school, college, university, clinics, and such  for many years. The average class size over the years has been at least 30 students. The average amount of classes ends up being two different classes a semester, and the average two semester year is 8 months. So at least 120 students a year, minimum. I have been doing this on and off over 20 years, so I have taught at least 2000 students in 7 countries (and from 8), since 1995.

I began this blog in October 2012, so I have been blogging for 3.8 years. In that time over 8100 people from 122 countries (over 62% of the entire world) have visited my blog. Small potatoes indeed in terms of how many “hits” I might get, but at least one person from nearly 63% of the world has come here to take a peek, and many countries have visited many, many times That is amazing for a little blog like mine. It is not an accomplishment, nothing I did (as other people made the choice to come here). But it is for me a humbling affirmation of what just being yourself can provide for you. 

My blog is designed to be educational rather than a place designed to merely attract customers or views. I love sharing a wide variety of perspectives on things with people and love this method when I am teaching. I want what I write to be like what I teach, so this means I have tried to help educate in some small way over 8100 people. That means I have ostensibly “taught” over 2130 people a year, from 32 different countries a year, in the last 3.8 years. That would be like teaching 120 students a year (from all over the world) for over 67 years!

In 3.8 years of blogging I have reached 67 years worth of international classroom students!!

 

At this pace, after blogging  for a full 5 years I will have been read by over 88 years worth of “students!”

This shows the power of doing something small in a way that adds up. The work behind putting together my educational post is not little at all (it’s hard to condense academic information down into readable posts), but the form (blog) in which I deliver it is just one tiny, tiny drop in an ocean of at least 170 million blogs on the Internet. But the numbers reveal that more than 8100 people from 122 countries have come to see what is here. It all started with my choice to be be bold, and actually start a blog. Not a bold choice for millions of people, but a small bold choice for me, as I spend so little time online.

So once again in Our Year Of Kakans I want to once again encourage you to be kakan-ized: be bold and ready to make small, powerful moves consistently, without stopping. Boldness + time = an amazing life. Kakans are a lifestyle, not “events,” and every day is a kakan day no matter what week, month, year, decade, century, millennium, megaannum (a million years), gigaannum (a billion years), or teraannum (a trillion years) it is in! We are living a Kakan Life: one tiny kakan at a time. 

Today is a Kakan Day…

August 23rd, in the year 283,954 will a Kakan Day too!!

毎日が大胆な日でなければなりません!

 

numbers

The Art of Drum Brushes

The Art Of Playing Drum Brushes 

The art of playing drum brushes is indeed an art unto itself, yet many take this aspect of their training for granted. To them it is old fashioned, best reserved for traditional jazz, thus a rudimentary ability to play swing on the snare is all they care to develop. But I suggest that this technique is very much a modern technique when done well, and with all the many hybrid forms of pop and jazz music occurring theses days, the ability to make original music with brushes is in one’s own economic as well as artistic interests. So, to help the novice drummer start building a solid set of brush skills, I have put together a few (road-tested) tips.

To start, make sure to keep the brush’s wires not too spread out, and the angle of the brush low. Also, own a couple of pairs of brushes that have differing wire gauges and take advantage of their extension capacity, as sometimes you will need a little more dynamic power e.g. on an outdoor or unamplified gig. Personally, I use 5” (heavy gauge) Vic Firth jazz brushes fully spread outdoors, and the light gauge VF Heritage brushes at a 3” spread indoors, and find this to be the ideal set-up. Brushes are most useful at an acute angle of about 7º to 10º degrees, though personally I like to keep my right hand at around 12º to 15º degrees since I use traditional grip. Also, keep your wrists completely devoid of pressure, putting zero weight on the brush. Then once you get used to letting the brush make all the sound, even tiny amounts of added pressure can make the brushes sound totally different. Let the brushes do the work, and you will be amazed at how easy it is to play evenly and musically at any dynamic marking.

Second, you should be able to swish the brushes around the full circumference of the snare’s batter head or in the smallest circles with no difference in consistency, creating a lush kind of drum ‘white noise.’ No changes in dynamics or slightest hints of a pulse: your foundational technique should be as smooth as silk no matter what you are playing. Also, be able to use all parts of the snare in as many ways as you can. The sound of the head near the rim is different from the middle, and dampening the head while tapping with one brush can also create many types of sounds depending on how much pressure you use in the dampening hand. The rim can also act as a closed hi-hat for high-pitched taps mixed with rim shots and batter head dampening, which is especially useful in a small jazz combo when creating multiple percussion parts on a Latin tune. Also, make sure that the batter head on your snare is a decent quality one-ply, coated head that is not too old, as the type and age of the head you are using makes a huge difference in your sound. Also make sure your snares are not too loose, and both the batter and resonant heads are properly tightened and tuned.

Furthermore, you should study the various brush patterns that different drummers find most comfortable using. Everyone is unique, and there is no one ‘official’ way to move the brushes around the snare. Taking your wrist flexibility, hand positions, and coordination into account, find the ways that you most easily create a good sound and develop them. You should also be able to create not only a traditional swing sound, but be able to creatively mimic anything from a South Indian mrdangam drum to a beat from a Slayer song. Your drum brush control should be to a degree that you can vary any aspect of it any time you want without it affecting any other part of your music making.

Brushes are such an expressive set of tools it would be a shame to waste their potential for highly developed phraseology during your solos. Thus, learning well-known standard jazz melodies and a number of sticking/swishing variations to help accent the key points of these melodies becomes an extremely useful and wise activity. Charlie Parker compositions not only have fantastic melodies, but are also a wonderful source of rhythmic material for you to memorize, and improvise with. Also, working through the first couple of pages of Stone’s book Accents And Rebounds For The Snare Drummer in conjunction with Charlie Parker tunes can also help build extra strength, control and independence in your hands.

It is also important to develop the ability to play with combinations of sticks and brushes. There are many places where this can enrich your playing as well the music you are performing, especially if there is improvisation involved. For this technique I use combinations of a Vic Firth SPE2 Erskine ride stick (or a Vic Firth 8A), one of my Vic Firth Heritage brushes, a Pro Mark Lightening Rod, and a Solutions ST-1 mallet because the extra heaviness of these particular mallets helps create luscious, round tones in my toms. This ability can also help you create your own unique beats and patterns for composition or improvisation.

Having said that, start working on your brush technique today, and don’t forget to have fun in the process. Practicing and playing music is a joyous affair, so go for it with gusto.

Ω

Odd Time Signatures: 奇数拍子

奇数拍子

There has been so much technological and musical advancement in the last twenty years it is almost dizzying. But even with such change there still is not as much discussion in woodwind circles about the organized, practical study of odd time signatures as I feel there should be, so I thought I would discuss them with you in this post.

“Odd” time signatures are any that are divided into non-even numbers: 3, 5, 7, and so on. Also, it is almost always the case you will eventually encounter, or be required to play in, time signatures such as 5/4, 9/8, or 7/16. What makes them feel “unusual” at first is that since most Western music (jazz, rock, classical, etc.) is in 4/4 or 2/4, a time signature like 7/4 feels “uneven,” or often hard to keep track of. But there are three basic approaches that will help you understand and feel comfortable with odd time signatures.

First, one must get used to note groupings less common in 4/4. We get so comfortable playing even eighth or sixteenth note groupings of four (in bebop for example) that playing odd note groupings feels strange. Thus, first learning to accent groups of five and seven in 4/4 is an excellent way of first getting the feel of odd numbers in a comfortable setting. A relatively easy way to do this is through scale practice. Using the C major scale in 4/4 for example, play the scale very slowly, in sixteenth notes, accenting the first of every three notes in sequence (C, F, B, etc). Thus we play [C d e F g a B c d E f g A…] and so on. Doing this makes it sound like we are playing triplets over 4/4, like we are playing in 12/8 simultaneously. This effect is a cross-rhythm (often mistaken called a polyrhythm) that plays against the main pulse.

Once you are comfortable with accent triplets, then accent in groups of five: C d e f g A, and so on. Another fun way is to accent notes in groups of two and three: C d E f g A b C d e, etc. What this does is introduce the feeling of playing in odd time signatures without counting in your head, which you want to avoid. This preliminary exercise also moves you out of old habits and clichéd (comfortable) patterns. Another really effective method is studying/adapting the first ten pages (pg. 4 – 14) of George Lawrence Stone’s book Accents And Rebounds For The Snare Drummer, to your scale studies. It will simultaneously strengthen both your motor and intellectual skills.

Second, one must actually listen to odd time music in order to get used to hearing its ebb and flow in traditional Greek folk music, for example. A classic example of simple yet brilliant usage of 7 and 5 are the songs on Dave Brubeck’s albums Time Out and Time Further Out, (including the wonderful “Unsquare Dance”). Many songs by Sting are also excellent examples of using odd time signatures very musically, and not just for show. “Seven Days,” for example is an excellent, minimalistic use of 5/4, while “Straight To My Heart” is an excellent example of creating a catchy riff in 7/4. It is important to start with music that is easy to analyze, as many groups  (e.g. Animals As Leaders, Frank Zappa, Meshuggah, King Crimson, etc.) often play with such complexity that it is difficult to follow and analyze what their music by ear.

So I suggest listening to as many examples as you can in order to find what you are initially comfortable with, and progress from there. Then, when you have found a few songs you like, memorize the main theme or pattern as a kind of mental guide. For example, the main guitar riff from RUSH’s live version of La Villa Strangiato (starting just after 5:30) off the album Exit Stage Left is such a fantastic riff that for years I used it as a mental rhythmic guide if I had to improvise in 7/4.

Lastly, when you have begun analyzing odd time you will notice that many feel “lop-sided,” like they kind of limp along. This back and forth quality may feel strange at first, but it is a quality that other cultures enjoy. In Turkish folk music, for example, these rhythms are known as aqsaq (“stumbling”) rhythms. What is important to note about such rhythms is that they are divided into groupings of two or three counts in a (repeating) chain, e.g. 3 + 2 + 3 + 3 = 11/8. This stumbling or wobbling quality of threes and twos gives the music a pleasurable bounce, often figuratively compared to a young woman carrying sloshing pails of river water back to her village. Knowing this then you can begin to create your own odd time songs and riffs, using groupings of three and two that you feel comfortable with, as composing is often the most effective musical education. There are six basic combinations of two and three you can begin to play with: 232 (i.e. 2+3+2), 223, 332, 323, 322, and 233, before creating longer chains of 19/16 or 21/8.

For more on odd time studies, see my previous articles on aqsaq rhythms or South Indian solkattu, or read Trichy Sankaran’s fantastic book The Art of Konnakkol. Good Luck!

sankaran

Ω

The Density Referent in Jazz Improvisation

ジャズの即興

Young woodwind players (jazz saxophonists especially) often ask me how to develop the ability to “play really fast.” The truth is that playing fast is meaningless, unless it is really musical and enhances the performance aesthetically. So the better goal would be to seek out how to develop your mind and body to be able to use a variety of tempi and note values musically.

For jazz saxophonists the gold standard for speed and musicality combined are artists such as Charlie Parker, Lester Young, Paul Desmond, Stan Getz, and others. But having studied their music, one will find that they were always extremely musical, and that even at high speeds their tone was rich and their improvisations were lyrical and dynamic. And, the true “secret” to their success is revealed in how they approached slow ballads (!).

It is often said that ballads are the surest test of a jazz musician; being able to play a ballad with intelligence and sophistication separates the average musician from the masters. Jazz ballads expose a musician’s ability to keep time at slow speeds, organize their thoughts, and demonstrate their understanding of harmony and space. Most importantly however, ballads reveal how well a musician understands what is known as the density referent.

The “density referent” in a song is the fastest unit of time that a piece of music contains or is based upon, i.e. if you are improvising over the jazz song Take The A Train at mm = 130, and the fastest subdivision of the time you can improvise in comfortably is sixteenth notes, they are your density referent. This is why it seems easier to play fast runs on a ballad, as the tempo may be so leisurely that the density referent could be as high as 32nd notes yet still be comfortably playable. This is also why young jazz saxophonists struggle with musicianship. They assume ballads are “easy” because they are slow, and have lots of space to fill up. Thus they play a density referent that crowds the music with too many notes. Likewise, when they try and play a fast number they rush and stumble, as they attempt a density referent beyond their skills.

But specifically focusing on the density referent in the practice room and in performance has many great benefits. It teaches you that musical time is not primarily a case of speed alone, rather one can move at different speeds within a given timeframe, which means we can be artistic with our time/referent choices. Thus, you are then given a better understanding of what your strengths and weaknesses are in terms of metric modulation at various tempi. You also develop a greater technical and creative control over your improvising, and are able to be more musical at higher speeds. You train you mind and body to react faster to the improvising of others, as well as play more of what you hear in your head instantaneously. Also, developing finger and mind dexterity while applying your conceptual understanding of the density referent is a transferable skill you can apply to other instruments that you double on.

To start studying density referents first go through the various jazz standards you know and find out what they are and which tempos you can handle them at. Most songs you will at least be able to play quarter notes in, so the next three densities will be eighth notes, eighth note triplets, and sixteenth notes. Catalogue the various metronome markings and referent values in your practice journal, and then begin to work on slowly increasing the tempo of the song. You’ll notice that even a small increase in tempo will increase the difficulty of the referent while hardly affecting the remaining densities. This is why you should keep track of the tempo at which you can play the density referent, not just the tempo you play the song at. If you know you can’t play sixteenth notes at certain tempi just yet, you will save yourself from playing a song too fast. Also, work on being able to play the density referent in jazz breaks or cadenzas. For faster numbers, work on being able to shift to your density referent from the note value beneath it, gradually building the ability to spend longer lengths of time at the ‘top.’

You should also gradually increase the metronome marking, noting that you can only physically play so fast. If you just can’t play sixteenth notes any faster than a certain tempo, make a note of it and then focus on making as much music as you can with the other densities remaining. A fun way to do this is to invent your own scale exercises that combine different densities (“density shifting”), i.e. create exercises that move from quarter notes to sixteenth notes with a few eighth notes and eighth note triplets in between, and so on. You should also spend some of your practice time dedicated to improvising through various density shifts. If you can’t play the density referent for more than a short burst here and there, turn this seeming “weakness” into a strength by making density-shifting part of your overall style.

By using your knowledge of density referents thusly you will be able to build something new and exciting out of what you thought was an obstacle. 

371 Days: Reflections On Ornette Coleman

 

vn tem flags

It has been 371 days since my saxophone teacher and beloved friend wandered off to Elysian fields, to God, to Paradise, to the place where thoroughly kind and wise people go when the body cannot contain such a soul any further. Ornette Coleman, Pulitzer Prize winning genius and man of peace, encouraged me to pursue my passion for free improvisation and Asian/Buddhist aesthetics, and was the spark that lit any/all greatness that I am able to muster. I loved him madly, and he was in my thoughts when I walked the streets of Ha Noi, Vietnam recently. So as I wandered words began to come to me in a particular form: part haibun: a 17th century Japanese literary form mixing autobiographical haiku and prose, also involving travelogue., and part zuihitsu: (literally “following the brush”) a scattered selection of essays and fragmented ideas inspired by one’s surroundings. The following haibun/zuihitsu hybrid is for you and Uncle Ornette.

Canto One

(I will be your today, and rejoice!)

“Wonderful, wonderful” said Ornette and the Buddha; Ha Noi is a genre

its passages scooters improvising counterpoint in composed roads

…having dreamed a thousand dreams… I dream him.

Ornette singing peace upon a flag, and the earth seeing war no more….

Every waking rhythm, every note = cars all fending for themselves

bio-industrial bebop, a love letter to such girls named Minh and Kanh.

I sit inches from Ha Noi’s street/songs; arteries swarming with drum solos

A traffic light; merely a fermata all ignore

the beautiful dust; the motorcycles screaming [everythingallatonce].

Traffic is theater: streams of circumstantial kabuki. Even the sun sweats after 7 am…

…I fell again on my morning bed, and returned to him with sleep.

He sang peace upon a flag,

and the earth saw war no more….

 

Canto Two

 

To know Ha Noi? To find a pocket of pause in vascular streets. I love Hanoi!

vascular roads, deciding moment by moment what phố comes next

in the minimal parade of #IAmHere… abandoned by trends.

Except only now do I drink good tea,

only now am I too old to gaze with fire,

to bend my talk into a casual tai ch’i of engaged action.

Poets marry experience and honeymoon within.

How small! That is when “I don’t know”

should be their poem, honestly? Be my poem!

What if I am merely bad fiction,

and I don’t see Ha Noi as her grandness.

Only seeing myself reflected back in t-shirts

and the hookah smoke that leaves me behind like Ornette did,

glorious and ethereal, remaining only me

and my efforts to not sound the silent gong

of my failures.

Astonishment is an addiction

and Ha Noi is too busy to know me…

 

Canto Three

 

A Ha Noi street is a zither and we navigate

the 10,000 motorized things pacing the

flat harp of 7 to 9:30 am… at least.

The melody is us plucking inward.

 

Sound the Ionian! the basis, the street.

Sound the Dorian! ignore me, I am just writing stuff.

Sound The Phrygian! sweat falls like notes from an old piano.

Sound The Lydian… or is it lunch yet?

Sound the Mixolydian… the salt panel when it fell into the lake.

Sound The Aeolian… keep clams and carry on.

Sound The Locrian… the rotting roofs only I notice.

 

the zither calls us, (Ornette called us) all to fret, to mahogany,

to make harmonics of us all,

to make harmonics of us all!

 

Canto Four

 

goodbye ornette!

Your holy city is gone, the gaze is gone.

walking backwards home the silent gong, me!

real here, real…her

i am like an empty table, somewhere, lacking a feast

Ha Noi comforts me, but I am inconsolable.

tourists eat copycat pudding, they wander feeling justified, “righteous” visions

my little blue cup offers up Ha Noi’s finest, coconut espresso

the best in the world: dark jazz, minor funk!

this town is still a drum solo, played with a million sticks and mallets a day!

But who will love the 80 year old with her baskets and shoulder pole

who will love the tired quang ganh ladies? The pole basket navigators?

Their onions wilting

are the onion lifters forgotten? Noone to hold them

after they wander up and down Hang Dieu street?

All that is left is to drink the water at Nội Bài Airport

And leave for Seoul.

Goodbye Ornette

I miss your cooking, the anthology of your flavors…

I want to be unsalted

gone beyond your gone beyond,

beyond the place you left here. But,

I will be your today and rejoice….

TSOJTC

Chromatic Improvisation And The Art of Wu-Fa.

painting

中國藝術

When I mention the word ‘chromatic,’ to young musicians they most often think of the chromatic “scale,” merely running up and down their instrument in half steps. But the world of chromaticism is much more creative and complex than that, so in this post I would like to share with you one particular method I use to improvise and compose chromatic music. Before I do so, it is important to understand where I am coming from conceptually or aesthetically when I talk about such things.

In my studies of music and art I have been most influenced by Japan, and have spent a major part of my life studying Japanese aesthetic culture. But in this case, my studies of Chinese aesthetic culture inform my conceptual approach to chromaticism.

The ancient Chinese masters often used related terms to discuss form and structure in art. The most significant of these are what I call the “Three Fa-s.” The first is ku-fa, translated as “bone means.” This refers to the various structural requirements and considerations necessary to create truly masterful works. But the goal was not the mastery of purely formal properties of painting. Their greater goal was to create works that captured the nature of form, the very essence of structure: ku-ch’i, “bone spirit.” This ku-ch’i speaks to what is “above shapes” (Li), its universal principle(s). And through the expression of Li, they would achieve a natural mastery that was far beyond structure, arriving at a freedom from method (liao-fa) so natural and effortless it seemed like no method at all (wu-fa). Indeed, the great masters of any art and music create in such a manner.

So, to allow for chromatic flexibility (wu-fa) while having something structural to study (ku-fa), I use rows of chromatic tone sequences (see image below). These are varying combinations of the 12 chromatic half steps available in standardized Western music, set in rows. I also use combinations of both semi-tones and quarter-tones, but as most Western saxophonists for example have not studied micro-tonal music, I will stick to semi-tonal tonal rows in this instance. Although some intervallic repetition in such an exercise is natural, this system guarantees enough variety to ensure you don’t fall into instinctual, repetitive patterns. It trains your reflexes and mind without limiting your vocabulary to pre-rehearsed riffs and phrases. By moving beyond fixed scales and chords, you can develop the ability to literally play anything without hesitation, without using conscious memory.

Tone Rows

To start creating these tone rows, I cut out twelve little paper squares and write the tone names on them. Then, I throw the squares up in the air, collect them at random off the floor, and write down their order. And, if a couple of intervals repeat from the line before, I just change their order. There are probably more efficient ways to create these rows, but I find the whole process kind of fun: something interesting to do on a rainy Sunday afternoon. And if you get tired or bored after a couple pages of these, you can always take a couple of the rows, reverse them from back to front, and put them further down the page.

So now that we have some rows, there are a number of things we can do to practice improvising chromatic ideas. Using the first three pitches from the first row of the image (B F# C), we can start by playing the first note then improvise/pick a note nearby, doing this for each tone in the row. Thus, we end up playing something like this: {B C# F# E C D…]. Go slowly so you can have the time to improvise the extra pitches without stumbling or feeling rushed. This is not about speed, but rather developing the ability to play any sequence of notes at random without hesitation. Then, when this is comfortable for you, improvise two notes between the written pitches, using random intervals, e.g. [B D Eb, F# A B, C B A…]. Then, move on to three and four notes, always making sure that you go slowly enough that you are not panicked or stumbling forward. Then when you have done this, move on to doing alternating sequences up and down so you do not get in the habit of always going in one direction. Switch up the direction, and try keeping track of it, for example two notes up, then one down: [B C Eb E, F# G Ab B, C A G# G…].

At first it will be easier to do this without a metronome. It is most important to be able to improvise these structures easily, adding time afterwards. Then, when you use the metronome, start by playing each tone on the beat (quarter note = 70). Once this is easy, move the metronome up a few clicks until you are playing at medium speed. Then move the metronome back down to where you can play eighth notes easily, each beat consisting of one written note from the row and one improvised note. Go slow and do it comfortably without stumbling. Then when you are completely comfortable with this, repeat the process with an eighth note triplet on each beat: one written note from the row, and two improvised notes. Then do this with four sixteenth notes and finally a sixteenth note quintuplet. As you are doing this keep track of the base metronome markings you are doing each of the note groupings at, and try to move each up a click at a time, playing with clarity and ease. Keeping track of your progress will also guarantee you see clear results, which builds confidence and reduces procrastination.

This exercise is designed to be a way of combining organization with chromatic spontaneity; just letting your instincts fly without hesitation. And, even spending just 15 minutes a day on the process will guarantee great results within days. Don’t forget to invent your own exercises too, and play around with the process.

ch paint

Ω

Encyclopedia of Youth Cultures

abc clio

 

The Encyclopedia of Youth Cultures in America (Vol. 1).

 

Simon Bronner and Cindy Del Clark (eds.)

Hardcover: 859 pages

ABC-CLIO/Greenwood Publishing Group. Westwood, CT

ISBN: 978-1-4408-3391-5.

I am pleased to announce that Volume One of The Encyclopedia of Youth Cultures in America (A to I) is now available through ABC-CLIO/Greenwood Publishing Group. For those of you who are interested, the encyclopedia contains an entry I wrote on “The Beat Generation” and their influence on the youth culture of the 1950s and 60s.

Many of you have probably heard of William S. Burroughs, Jack Kerouac, and/or Allen Ginsberg, whose works directly challenged the way the world viewed literature, poetry, art and music. What you may not know, however, is how these men focused on spontaneous creativity and a rather Bohemian lifestyle – traveling and living free of society’s rules – and in the process created a potent mélange of words and sounds that radically changed the course of Western (and Eastern) literature, poetry, and musical improvisation (some saying as much for the worse as the better).

To learn more about the Encyclopedia, and the great work done by ABC-Clio, visit their website and check out their catalogue. And, on a personal note, I would like to thank Dr. Bronner for his editorial insights and guidance, which I very deeply appreciate.

Ω