Wednesday 18 March 2020


Is teaching music any different than other subjects so that its methodology
requires a different approach?
Compare these questions about Music and Math. Answer these questions.
Do we learn Math for fun ? Do lonely singles suddenly decide to take a Math class? Is Math like Music as just a pleasant way to waste time?
Is there such a thing as serious music? If so, is it better than unserious music?
Can you teach "good taste" in music ? Would you even think about "good taste" in Math class ? Would you feel sadness, or joy over a particular Math problem? Would you prefer to write a song or a new Math problem? Is music really a creative subject ? Is Math a creative subject ? Is there always a perfectly correct result for a musical performance?
Is there always a perfectly correct result for a Math calculation?
Is Math physically involving?
Is Music physically involving?
Is one easier than the other?
Is one more important than the other? I won't answer these questions about differences between teaching Math
and Music. They are just to get you thinking.

A learner's motivations might be very different as is the subject matter.
A kid comes to a music lesson for different reasons,
sometimes the kid deeply wants to learn music,
sometimes the parents want to live vicariously through the child's success,
sometimes they are just curious to see where it goes,
sometimes the parent wants the kid to be busy and not with them.

An adult comes to a Music lesson because
they might have a hole in their life
they need to fill or find distraction from (lost love)
they simply love music
they might enjoy the social experience that music can provide
they might find music a form of escapism from a life of adult responsibilities.
they want to return to a nostalgic moment in their life through music.
they wish to gain confidence, social status & poise via music.

Are you noticing some of the important differences between Math and Music?

So there are differences in teaching and learning different subjects. Will that affect the lesson ?
Let's examine some of commonly important things about teaching both
Math and Music.
Both involve: practice. reading. stepping up through levels. concentrating on the processes. memorizing information. using models for practice & applying those models to different situations. organizing lesson materials. evaluating the results. improving consistency. using tools.
Examine some major differences in learning & teaching Music. Choice of being in that music lesson. Emotional connection to the subject music. High levels of multitasking with mental and physical connections in music.
e.g. reading, playing, looking ahead while tapping a foot,
naming notes simultaneously while thinking about countable value,
where it is played on different hands and coordinating this information
with 2 hands, feeling the right amount of tension and angles in picking
and fretting notes and listening and responding to the quality of sound
& possibly an external partner playing. Possibly singing to this at the same
time. Public performance which comes with subjective judgement of the task.

I often hear people talk about music as a "creative" subject.
Is it creative ?

If your purpose is to make exacting copies of existing work, is it creative?
Is creativity an important part of music education?
I know several high level teachers of music who have not written a song or tune.
Are they creative? It is certainly skillful.
I do write songs and tunes. I didn't at the start. For me it is skills, knowledge and
practice first. With some basic ideas, creativity can begin.
Creativity is enhanced by having a toolbox of these inputs.
Creativity is also enhanced by having the suggestion that making
something of your own can be part of the process.

Comparing Music to Math might lead you to think that Math isn't creative.
It could be but isn't often taught that way. A student could be asked to
solve a real life problem or question using Math.
This is very different from being told to answer Exercise 7b questions 1 to 10.
Think about it.
Cheers for now.


Years back I started work in Japan as an English Teacher.
I’d worked in Australia as a teacher prior to this, in schools and as a
private music teacher with a thriving practice. 
At orientation day some 200 recruits entered our company.
The question was asked “why are you in Japan?”  
The answers involved: travel, adventure, making some money, curiosity,
Some of those people spent many years there and I would hear some talk
about leaving to "start their career."
It may surprise you, not everyone who teaches actually considers teaching
as a career, or education as a subject itself worth studying. 
A study of Teaching binds the psychology of teaching & learning with the
micro-skills of teaching and core subject knowledge.
Professional teachers are more consistent, more likely to prepare for lessons,
not just show up. 
It’s generally better learning from someone who sees teaching  as a career,
not a stop-gap measure between gigs, like just something to do until they hit the
big-time with their hit recording, find a real job or win the lottery.
Some people  working as “teachers” have no interest in the subject of
Give this some thought when choosing teachers.
Some people  working as “teachers” have no interest in the subject
they teach.
Give this one some thought when choosing teachers.
Yes I said that twice.
In music, the best player might not be the best teacher simply because
they are not interested in sharing their knowledge. A good music teacher
should be good at music AND interested in teaching.


It’s reasonable to expect that if you’re hungry, tired, sick or urgently need a toilet
your readiness to learn is hampered. You cannot easily focus when your body is
not in balance.
Some needs are obvious, others aren’t. Stress from abuse or loss of loved ones
leave mental scars far less noticeable than visible physical impairment.
Emotions can disrupt physical and mental stability.
Like an iceberg which is mostly underwater, humans can look right but haveissues such as health which are not obvious at first glance.
Humans have “drives” beyond satisfaction of hunger, some controlled by instinct
like sex, or adrenalin response to fear and pain revving up our bodies.
Maslow was a prolific psychologist who famously developed  a list of needs
starting with basic things like food and water & progressing to “self-actualization”
where the drive to reach personal goals was recognized. Maslow wasn't the onlyone to develop these kind of lists but his list has stood the test of time.


Different ages require different  teaching.
All ages are teachable but in Music Education, you will spend a lot of time &
effort to get a baby to a stage where they accept direction, let alone play
an instrument. There is physical readiness & there is emotional and intellectual
A most asked question is “how old is old enough to start?”
In theory, any age is fine. Even babies can be introduced to instruments & show
a bit of sense about them in a quiet moment. The baby pictured was very curious
to the sound & touch of the guitar. Now at 9,  she is singing well and expressing
her musicality with a strong desire for formal lessons.
An interest and curiosity is not always ‘readiness’ to hire a teacher and commit a
budget to developing your child’s musical progress.
Suzuki started teaching violin to very young children with exceptional supportive
parents and achieved great results from children of preschool age. Most families
don’t have an Asian tiger mum to bring this level of discipline & dedication to daily
practice.  Most parents won’t take the time to turn their child into a prodigy, even
if the child shows interest & aptitude.
Some parents are disappointed after spending big money on lessons with their 5
year olds to get little or no results.  5 year olds are usually not disciplined to
independence & need a lot of hand holding & encouragement to play an
instrument proficiently. You simply can’t say to a 5 year old “ now go to your room
and do your practice” and expect this to happen. 
Some can, but in general terms most can’t.
Older children have more ways to absorb information. Reading skills compound
their other existing senses, they have more independence & experience to take
on a new hobby more easily. They still need support and parents who can push
them in a good way (as distinct from bullying them into practice). From around
age 7 a good learner may have developed many tools to learning that will speed
their ability to learn music.
Adults have a rich history to draw upon. A child  has to learn a song first, but an
adult may know already what it sounds like and have a head start to the learning.
A child needs to learn to move little fingers first but most adults have at least
basic dexterity. Adults often have commitments which reduce their practice time.
An (imagined) ambition isn’t the same as a commitment.
That said, many late starters do very well.
Every person is different. Even adults drop out so readiness to commit to
a budget and time on music education needs to be thought out
well in advance. 

If money is no object, music lessons can be just an amusement that might lead
If getting skills is the main object, preparing the time and resources and support
to make it happen are all part of getting a good result from your spend.
Most people realize quickly enough that without practice, skills don’t develop.
Space in your life to set aside time to practice won’t happen if you can’t prioritize
a commitment. Bite off more than you can chew and maybe you can chew like
mad, or, you could choke. Ambition without commitment to time and energy
through your body is wishful thinking.
We don’t teach driving a car to a 5 year old generally because it bears no
relevance to their lives. Learning happens best when ideas, information and skills
come at a relevant time.
Some of the seeds of learning planted will nurture and grow before fruition.
Others never find a place in learning because they are perceived as irrelevant by
the learner.


Having tools that don’t hinder a performance are a minimum.  A terrible musical
instrument can be part of learning experiences but its limits are low.
Quality instruments can inspire your consistent attention. It won't make you play
well, that is a separate issue. It is fortunate with modern production most tools
(musical instruments) are at least usable. Be certain that the tool you choose is
usable and suitable to the size and physical characteristics of the user.


People are born with various levels of physicality and intellect.
Everyone has strengths and weaknesses. People through nature or environment
will have more or less of the ingredients we might call "talent".
Having less isn't a reason to give up before starting.
Having more from the beginning doesn't necessarily guarantee success either.
As a kid, I couldn’t be a great golfer. After hitting any ball further than 100 metres,
I couldn’t find it. Wasted time searching for balls hurt my ability to achieve.
At some point somebody might have noticed a set of glasses would have made
a substantial difference, but a poor start killed my enthusiasm for the game
Accurate senses have a profound effect on your level of success. Accurate
senses & robust physicality eases the transition to learning pretty much anything
This may be recognized as TALENT ADVANTAGE.
An enriched environment of family, school or community where people sing or
play instruments brings in cultural influences of role modelling & ready help that
compounds native knowledge & skill into that well of TALENT.
Some people come from a virtual cultural desert. They must work harder to
equal the basic level of those who have experienced a steady stream of able
people through their lives. 
INTELLIGENCE  has aspects that compound the springboard of TALENT.
A great MEMORY: visual, symbolic, audio & physical,  particularly helps.  
Intelligence is more than memory.
Ability to problem solve, emotional intelligence & communicative skills are aspects that slow down or rocket a
person to success. Intelligence can be nurtured, taught & improved.
A developing talent needs critical reflection.
Imagine we play or sing well, but replaying an audio/video performance highlights areas of strength &
weakness. Having feedback of your performance that doesn’t crush your spirit
helps you rise.
Music and Art  isn't always about complexity. Most of us don’t need a competitive
scorecard to enjoy music. There's joy in knowing that humanities are generally
not just a race for points. Anyone can participate & many succeed by virtue of
the fact that they use their abilities to an individually high level with discipline
to pursue goals.
It’s not just what you’ve got, it’s what you do with it.
Native ability is a starting point yet it isn’t the finish line. Even talented individuals
won’t succeed without practice. Figures like 10,000 hours of practice to mastery
are often quoted for pretty much anything. That’s about 4 hours a day practice
over 7 years. It would certainly get you some skills.

Monday 24 February 2020

PEDAGOGY OF MUSIC PART 6: the art, science & organization of teaching music


A lot of attention has gone to writers and theorists who maintain that the
arts are right brain activities and therefore “intuitive, emotional, expressive,
visual or aural “ as opposed to “verbal and analytic. “
That would be an exaggeration, because the best artists are often those who
have both an ability to analyze  (ANAL EYES ?) and merge the intuitive emotive
components with the simplicity of their musical sounds. 
That said, using both sides of the brain is better than half a brain.  In truth
it’s pointless to have one without the other. That would be half-brained.
Teachers should nurture the duality so that they freely interact.
So why did educators jump up and down in excitement at the work of Betty
Edwards who wrote “Drawing On the Right Side Of the Brain.” ?    
Probably because there was a time when we struck so many teachers who had
analyzed the arts to the degree that there was nothing for the student to discover for
themselves, music or art lessons were simply an exercise in getting through
your list of exercises.  
It's important to both view a piece of work holistically and view it as a series of details.
Some people can't see the trees for the woods and vice versa.

As a musical example I can view Pachenbel's Canon as many detailed single and harmonized
notes or more simply I just consider it as a bunch of chords in C.
Inevitably you need both views to fill in the detail but both points of view have their place.
I need a pretty big toolbox of techniques and exercises to be a functional artist.  
But, realize that having something to say, enjoying the absence of rules, making
and allowing mistakes through your own experiments are important steps to
developing the “whole” brain. 
Ownership of the art needs to come from the artist.
Similarly, ownership of learning "ideally" is the responsibility of the learner. 
This won’t happen when students are spoon fed every step of the way. 
Beginners need more support with learning. Most texts ignore the creative side.
In fairness many are simply trying to cover their area well.
Gaps in learning need to be addressed by teachers clever enough to allow for learners
to input and own their own learning.
Playing an instrument or being a visual artist means that the focus is on the work, not
how much you talk about it. Art isn't always clever. Art isn't always improved by complication.
Art doesn't always have a clear purpose. Art isn't always loved by audiences.
To break the dominance of the analytic side of the brain, and enhance creativity,
you need to put yourself into situations where you don’t actually know what will
happen so you can’t foresee and thus plan out everything. Merged with the
analysis and rules of music, these combinations lead to a synergy of excellence.

I can't look inside a brain to see how to improve those brain connections but I can use a
variety of approaches rather than a single way of doing things to encourage wide range

Piaget was a French educator and researcher who noted the differences in
reasoning ability between  younger children and older children.
He was tasked with developing questions for intelligence tests and was curious
about why different ages kids made the mistakes they did.
He started writing his ideas down.

Not really groundbreaking stuff in my opinion but younger children do know less,
have less experience and need differences in teaching. 
They do not have the same ability as adults to deal with abstractions such as
number and need more sensory experience and concrete learning experiences.
What Piaget did in his outlining of 4 learning stages was create a new vocabulary
for it. Many teachers, well good teachers (and parents) were probably making
the same observations about their kids but didn’t write a book on it.
Voila, psychology is high-brow common sense combined with experience of the
subject matter.  
Hands on approaches are an important part of musical education. Just don't buy your
kid a set of drums.

PUTTING THINGS IN BOXES :Thinking inside or outside the box. 
That’s what we do to make our world understandable. Give labels to things and
the creation of “subjects” at school into some sort of specialty helps us learn. 
Remember “big picture” thinking must see the relationship between all the parts
and notice that many of those parts overlap. 
I’ve hated teacher meetings when we collectively fill out a planner for a course we
teach and somebody isn’t sure which box to put it in so they have overlong discussions
as to where it belonged. 
The correct box would be labeled “time wasting.”
There are many instances where a concept overlaps several subject areas.
That really shouldn’t be a problem.
Much of in the box thinking could just as easily be out of the box. 
“Out of the box thinking ” has limits. Paradoxically,  no limit has limits. The paradox is simple.
Bringing in too many ideas doesn’t facilitate completion. 
My real-life example:
I tried to write a tribute song over a long period of time. I’d scratch out ideas, add and subtract,
but I wandered my way to no particular destination. 
I joined a song-writing course. The task was to follow a rule with a simple structure to write a
song. 5 minutes later I had it in a fairly complete state.
Thinking inside the box has validity. 
Teachers are sometimes told ‘the best questions are open-ended.” They could
be, but they’re also  a chance for someone to wander further and further from
the subject under discussion so let’s not get carried too far away into the world
of aimless pursuit. Teachers are supposed to guide learners to some sense of
completion, with the maturity to understand that no one can complete everything.

Intrinsic Strength your own capacity to learn, share, to grow, to nurture, to
independently manage yourself, to cooperate and collaborate, is just one of our
potential powers.
Referred Power  is a power we can use such as, when a team leader who can’t
control a staffer might use their appointed power ( a higher level boss) to fire 
their problem person or collaborate with their boss to dismiss or correct behaviour of
that worker.
A teacher might call on the principal or parent for back up when dealing with a
problem student. It doesn’t have to be negative or positive, it’s just the power is
not owned or earned directly.  
The principal might call in the parent to back-up the behaviour modification.
(Borrowed strength can produce weakness but at times is necessary.)

Collaborative Power of a team which includes colleagues, parents and
students would synergize all the possibilities.
As they say “it takes a village to raise a child.”

Monday 10 February 2020

PEDAGOGY OF MUSIC PART 5: the art, science & organization of teaching music

As a hardworking well-behaved primary schoolkid I was seated at the back at the classroom
as I wasn't a troublemaker.
I could however barely read the blackboard text.  Teachers were dangerous in those days
so I would never complain.
An alert teacher would have considered individual differences within the classroom
mix. An alert teacher would have checked these things.
Some teachers got excited when people started writing about sensory learning preferences
and strengths.
Some people are certainly stronger/weaker in specific areas: sight,sound, touch, smell & taste.
Good teachers don’t just cater for sensory mode preferences, they consciously
develop strengths across the other modes.
As I teach music I notice how diverse people are. Some struggle with written formats of
any kind, even formats which are essentially pictorial. 
Music at first glance might seem to be just about sound, but look closer and you will see that
there is a vast overlap of skills using all senses. Yes even smell and taste come into at least
the language components of music.(lyrics)
Using and varying the senses used in lessons uncovers a load of extra detail both
within the subject and the way we learn, including favoured senses.
A lesson might focus on listening, physical dexterity, interpreting charts or mixed use of senses.

Gardner in 1983 described abilities as different facets of intelligence.
There are similarities to the sensory mode preferences helping us build a better picture of how
intelligence works. If you ignored any of these facets in education you wouldn't be considering
the complex process of building intelligent thought. Gardner chose the following categories.
  1. musical-rhythmic,
  2. visual-spatial
  3. verbal-linguistic
  4. logical-mathematical,
  5. bodily-kinesthetic
  6. interpersonal,
  7. intrapersonal,
  8. naturalistic

Prior to cheap, modern sound equipment, most early stage school departments had a piano
playing teacher. Teachers understood the developmental stages of children & used music
deliberately to enhance and develop skills.
Movement to music with singing & action songs using finger-play were preparing students to
listen as well as ready their fingers and hands for fine motor skills used in writing.
They also helped maintain physicality and achieve these goals in a fun way. These
lessons ensured kids were present in the lesson.
Engagement is a pressing issue for educators- how do we keep students engaged?
Even good students drift off in private thoughts in classrooms everywhere.
Good teachers still know the importance of pre-writing-reading activities and
presenting them in ways that are palatable to the students. Relating these same
concepts to music lessons means getting fingers ready in small steps, getting wobbly
eyes focused on visual cues including charts, lyrics, diagrams and the instrument
itself, listening for a purpose, organizing and caring for materials.
Young students can have trouble focusing on small detail. BIG Print in beginner books is for good reasons.

Now households have media on tap, parents have drifted away from many of the
traditional nursery rhymes, action songs and poems that were once good preparation for fine
& gross motor co-ordination and auditory memory.
The repetition of rhyming sounds is also often part of the focus of early reading and spelling training.

Memory is not just a mental process but involves your body. Some educators underplay
the importance of memory as an essential component of learning. This probably came about
because too many tests were measuring memory, not thinking ability. True but memory is
undeniably important.

The logic is “why should I try to remember everything (even anything)  if I can just have good
research skills and look it up?” 
Research and having a theory about something is not the same as doing it, practicing it
and perfecting it.
A failure to commit anything to memory hampers growth in the skills and knowledge to get
anything right.
Memory is a platform to build on. When we encounter a challenge we draw on memory for
help and ideas. If we are sad, recalling a happy time can supply the feeling we need to lift
ourselves. Memory is much more than a bunch of dry facts that have no particular use.
Memory has been really misunderstood because some teachers placed far too much attention
on retaining facts instead of training more advanced problem solving skills.
Memory is not just a symbolic or pictorial thing filed in a brain.
Our brains will file generalities for convenience. A quick look at a flower gives you that recognition
of what it is but a glance won’t give you all the information there is to be seen.
Smell it, touch it, in some cases taste it. There actually is a physical side to the memory process
which in that case includes visual and textual. Can you close your eyes and see the object
after you are no longer looking at it? It's a mistake to bypass the effort required to be good at
"visualizing" or any other memory component. Would you want to employ an architect, engineer
or designer who hasn't practiced and refined this visualizing skill?
You cannot master anything without some commitment (often great commitment) to memory of
your subject material.  Yes, it’s very useful to understand what it is, or what it means.
Understanding won’t go too far if you can’t lock it into the memory banks and actually dynamically
and physically manage the skills.
If I teach guitar, I might not need a long winded explanation of the theory before we start.  
We just do it.  After this we might have some concrete experience on which to pin symbolic
Many initial stages of playing music are locked onto the physical actions of getting your
body parts into the right places at the right time and actually listening.
The ‘anti-memory lobby’ use the words “understanding is the most important thing” as their
excuse not to bother memorizing anything. Well often it is better to do the activity, then add
in other information.
Physical, visual, auditory, sense of smell & symbolic memory have to be trained and mastered. 
How we learn is heavily connected to how we remember. 
We listen to it, read it, do it, write it down, repeat it, think it, play games with it, use mnemonics,
fall in love with it. Draw it. Touch it, listen to it.
The more ways we do something the higher the chance that learning will stick.
There are more types of memory than just the superficial “thinking memory banks”. 
Simply having  thought about it doesn’t cut it as far as deep learning goes.
Your computer like brain is attached to a series of tools:  eyes, ears, nose,
touch, muscles, etc that all require use to get skill. There is also such a thing
as muscle memory, auditory memory etc.  
Music lends itself to repetition. 
Readers of books tend to see the end of the book and think "it’s done.”  In many
situations, (particularly young children) people become better readers if they
read a book more than once as they often glance over things in superficial ways
& make incorrect assumptions in their predictive reading skills. When challenged
to explain a meaning or colloquial expression, they are often way off base.
Refreshing & reviewing through singing are often an enjoyable way to improve
reading. Repetition is necessary for both effective memorization & deeper understanding.   
The mnemonic is a memory training tool.
When reading scored music, we remember  “Every Good Boy Drives Ferraris" or similar which
denotes the names of the lines on each stave.

Easter Bunnies Get Drunk At Easter, or Eddy Ate Dynamite, Good Bye Eddy
denotes the notes used for standard guitar tuning- E A G D A and E.

Visual Memory Can Be Enhanced Through Associations
This picture below is a D chord showing where to place fingers and what strings
to play. What does it look like ? Not much.
And now,  can you see a face with 2 eyes and a nose on the one below ?
Using visual memory cues can be developed through music training. 
Improving memory uses conscious approaches in how you do things.
Our vast and confusing world gives us too many things to remember.  
We have a generation who remember very little, not necessarily because they
are lazy or brainless. Some just haven’t had sufficient help in choosing worthy
targets to commit to memory. In previous generations, math tables drill was
routine. Just remembering the answers to simple tables was enough to make
quick everyday calculations of value to daily living skills. 
A generation of theorists entered and the claim was “ you don’t have to
remember it, you must understand it.”  Sounds fair right, except the first part.
They should have been saying at least about some especially useful things
“you must remember it and also understand it.”  
Like the Suzuki students who learnt playing violins rote style with repetition and
physical engagement, the theory could come along a bit later.
(Some) Educators have given away the goal of memorization skills and replaced
it with “as long as they know how to work it out.”  
As if explaining something with words is the same thing as doing it?
A master of any subject needs to have a ready set of memorized knowledge.
It’s handy to know how to work it out, but without core knowledge memorized,
there can be no mastery of a subject. These memories are often a complex mix including
many of our senses. 
Take an everyday example of getting your car repaired. What would you say to a
repairman who told you he couldn’t remember how to do the job but he would
work it out?  Naturally you would be billed for the time it takes him to work it out.
You might immediately look around for an expert.
As a young man repairing my own car I knew the theory to replacing a steering tie rod and ball
joint. Separate the parts with a hammer hit. Couldn't do it in 30 minutes of bashing.
The mechanic did it in 2 seconds. 
I asked a computer specialist for help with my music software.
His response was "I don't know it but I can work it out." Not at $100 an hour, I'll find an actual
user of this software to help me, or work it out myself.
Naturally many things including known “facts” change over time. Is that a reason
not to know what you are doing today?
Math lessons like most subjects involve a number of strategies which are
explicitly taught :
Observing patterns, listing, putting things in order, recording information, labeling,
pattern recognition, categorizing, predicting, summarizing, explaining, making
guesses and testing whether they work (trial and error),drawing, using processes of
elimination, taking a patterned example and applying the principles to a similar
but different example. 
All of these strategies can be similarly and explicitly taught in the context
of music and lead to orderly, systematic thinking. 
In most cases the more ways you do something improves your depth of skill:
read it, write it, say it, sing it, think it, listen to it, do it, play it, modify it,
apply a rule to a different example.

These ideas should be considered as strategies in learning and decision making but are
different from the ones mentioned already.
Edward De Bono got into the nitty gritty of thinking with his colored hats. Each
hat represented a way of thinking such as emotional, critical, positive. There
were a lot of hats and I don’t care to memorise them all but looking at issues
from many different perspectives is valid. People have benefited from listing
ways to think through problems. Comedians & their audiences have benefited
from wearing the purple hat of stupid suggestions. 
Edward De Bono had fun and earnt money at the same time training people to
wear one of six coloured hats.  Each hat represented a singular thinking role :
information, weaknesses, strengths, feelings, creativity and an overseer. 
He just divvied up the roles so all aspects of an issue were thought about,
weighed and organized before decisions were made. I guess that’s called
“doing your homework”  to a normal human.  
Other “thinking tools”  looks at the pros and cons of  ideas or plans as
positive-negative-or interesting. 
Mind-mapping is another strategy to planning. Anything that you want to plan
out becomes clearer at some point if it’s been written down. I truly should have
written a mind map before working on my “pedagogy of music” and it may have
been more orderly.

The idea of choosing the best bits and synergizing that knowledge so that the
whole thing is greater than the sum of the parts is our ideal.