In the last few lectures, I have introduced the problem of classifying an observation into one of the two populations. I discussed various procedures. In particular, I showed that one can define Bayesian classification rules or what you can say as good classification rules. So, we call them the admissible rules or the class minimal complete class that means the rules beyond which you need not discuss. In particular, we consider applications to the classification of an observation into two multivariate normal populations. The first case was when all the parameters are known and then second case we discussed when the parameters are unknown. Now, I will generalize this concept to the problem of classification of one observation into several populations. So, let me introduce the concept of optimal rules here and how to derive these rules. So, classifying an observation into one of several populations. So, suppose we are having populations pi 1 pi 2 pi m these are m populations and we are considering the density functions associated density functions say p 1 x p 2 x p m x etcetera ok. So, we wish to classify or we can find out m mutually exclusive reasons. We want to specify say mutually exclusive and exhaustive reasons of the sample space say r 1 r 2 r m. So, if the observation x belongs to say r i we classify x into the ith population for i is equal to 1 to m. We can also consider the cost of misclassification as we have done earlier. The cost function we can introduce the cost of misclassifying an observation which is actually from say pi i, but we classify into pi j then we call this function as say c j i. Now, we can define it like this c r j given i equal to see the observation is initially from the ith one, but we have classified it as into jth one. So, the probability of misclassification or the cost of misclassification can be considered like this. Now, if you remember the case of classification into two populations I had considered one particular case when we fix the initial proportions of the populations as say q 1 and q 2 where q 1 plus q 2 is equal to 1. In a similar way if I have m populations I may consider the case when the initial proportions of these populations are known. We call them prior probabilities say q 1, q 2, q m. Suppose q 1, q 2, q m are prior probabilities of populations pi 1, pi 2, pi m respectively. That means, 0 less than q i less than 1 and sigma of q i is equal to 1. If I am considering the expected loss of classifying i into j then I can consider based on the prior probabilities the total expected loss. So, the total expected loss can be defined as the expected loss. So, let us consider see we are having the I just made a small mistake here this should be p r that is the probability of misclassification this is the cost. So, this is actually the probability of misclassifying an observation from pi i into pi j. So, this is p r j given i and the cost of misclassifying is c j i. So, if I consider c j i into p r j i then this will become the expected cost. Now, let us consider the total expected loss. So, let us consider this c j given i p r j given i this r denotes the classification rule. This is the classification rule. Now, what we have done here is that observation is from ith population and we are classifying it as into the jth population. So, this is the expected cost or expected loss you can consider. Now, you may put it into any of the remaining populations. So, we vary j from 1 to m where j is not equal to i. Now, this term which is written here. So, now the observation is from the ith one and we can put into any other population other than the ith population. So, this is the total expected loss that is coming there. Now, the probability of or the proportion of the ith population that is q i. So, if I multiply by that and then I sum over all i from 1 to m then this is the expected loss using rule R classification rule R ok. So, this is the expected loss that we can consider. You can remember the value which I wrote for the case of two populations. In the case of two population let me write let me show you the expression here which we discussed earlier. It was given by just I will show you the thing and then you can compare. So, it will be clear that how this has been obtained here. If you remember the case of two population we had only two values c 2 1 and c 1 2. In this case we have several values c j i where i and j both can vary from 1 to m where i is not equal to j. So, this is the difference that is coming here in place of two values c 2 1 c 1 2. Now, I have c j i for all j not equal to i and for all i. So, total number of values will be m into m minus 1 that you will get here. Let me also show you the expected loss that we had considered here. So, the term that I wrote here p r j given i. In the case of two population we had only two values p r 2 given 1 and p r 1 given 2.  Now, you compare this with the value that I wrote just now because any observation from the ith one can get into any of the other other than the ith one then you consider all such cost then you add them. Then you look at the ith one and multiply with the prior probability of that and then you sum over. So, this is the expression that you will be getting. So, this is the full explanation of the expected cost as compared to the case of two population. So, as you can see here the expression becomes much more complex here. However, our aim or the motive remains the same that is to minimize the expected cost of classification expected loss of by misclassification. So, our aim is to find a rule r so that the expected loss 2 is minimized. So, now we can consider the as again in the case of one we had considered q 1 p 1 x by q 1 p 1 x plus q 2 p 2 x in a similar way we can consider the conditional probability of an observation coming from a population given the values of the components of x. So, the given that it is coming from coming from pi i. So, that is defined as then q i p i x divided by sigma q k p k x earlier it was q 1 p 1 x divided by q 1 p 1 x plus q 2 p 2 x or q 2 p 2 x divided by the same term, but here now I will have all the m terms in the denominator. If we classify the observation as from pi j then the expected loss is q i p i x divided by sigma q k p k x k equal to 1 to m multiplied by c j i, i is equal to 1 to m i not equal to j. We minimize the expected loss if we choose j so that 4 is minimized that is we consider the term q i p i x c j given i because the denominator is common here for all j and select that j that gives the minimum. So, in principle if you look at this is a direct extension of the case of two populations and if of course, there may be a case when two different j's give you the same value in that case you can choose the one which is well it does not matter because then whichever you choose it will give the same minimizing constant. So, now I consider this procedure assigns the value. So, we are assigning towards a j so that is the reason r j here. So, we consider then the following result then that if q i or q 1 q 2 q m are prior probabilities of pi i and the cost function is given here then the region of classifying r k is given by so r k region is sigma q i p i x c k given i less than sigma q i p i x c j given i. Here i is equal to 1 to m i not equal to j and here it is i is equal to 1 to m i not equal to k that means for the kth one if this is the minimum then you are getting the rule that is you should classify classify x into pi k if this is happening. I will not get into the proof of this in fact the proof is almost the generalization of the proof for the two population that means if I consider any other rule which is minimizing then I can consider the expected loss from the two given rules and write down the difference and as in the case of two population you can consider the condition you can consider the conditions for greater than or equal to thing. So, it will come immediately so I am skipping the proof here. Like the case of two population we can consider the optimality criteria like admissibility base rules etcetera let me just formally define that here. We can consider the conditional expected loss if the observation comes from pi i that is sigma c j given i p r j given i this term I wrote earlier this one basically so I am writing this one. So, this is for j is equal to 1 to m j not equal to i I will use a notation r r i here. So, a procedure r is at least as good as procedure r star if and only if we are having r r i less than or equal to r r star i for i is equal to 1 to m. If strict inequality holds for at least for at least some i then r is said to be better than r star r is said to be admissible if there is no procedure better than r. A class of procedures is said to be complete if for any rule not in that class a rule within the class is better. So, these definitions are similar to the one which I gave for the case of two populations and we can consider that this result is also the similar as we had earlier that if Q i's are positive then a base procedure is admissible. Once again the proof is almost the same let me exhibit at least this proof here.   Now, let us take say one of the components to be strictly smaller than the corresponding component for the rule r. So, what I am saying is that actually if I want to show that r star is better than r then we should have r star i less than or equal to r r i for all i and strict inequality for at least one value. So, for the time being I am assuming less than or equal to for 2 to m and strict inequality at least for the 2 then let us see what happens. So, if we substitute it here.   Now, let us look at these two I am writing for 2 to m. So, for 3 to m it is less than or equal to and at least there is one strict inequality and all Q i's are positive. Therefore, this will be strictly less than 0 as all Q i's are positive. If this is happening this is implying that r r 1 is strictly less than r r star 1. So, r star cannot be better than. So, that means, the base rule must be admissible base rule r must be admissible. Actually you can see that the proof is similar to the case for the case of 2 population that is m is equal to 2. There I had taken only strict inequality for 2 and then for 1 I got the reverse 1 and similarly for the other case. Now, if the cost functions are given then also the base procedures are admissible. And the converse of this result is also true that is every admissible procedure is a base procedure. Every admissible procedure is also a base procedure. I will not give the proof of this also as the proof is similar to the case of 2 populations. Now, what we want to do is that let us consider the classification of multivariate normal population. So, let us look at this problem which we had considered for the case of m is equal to 2. So, let us consider the problem of classifying an observation into 1 of several multivariate normal populations. The populations are pi 1, pi 2, pi m where pi i is the population normal mu i sigma. So, let us define say u j k function that is equal to log of p j x by p k x actually here p j x will be 1 by 2 pi to the power p by 2 determinant of sigma to the power half e to the power minus 1 by 2 x minus mu i j I am writing. So, it should be j here prime sigma inverse x minus mu j. So, I am assuming sigma is positive definite because I am writing down the existence of the density function for j is equal to 1 to m. So, this quantity that is the ratio here log of p j x by p k x you can consider here see this term will get cancelled out. So, you will get e to the power half and the term will be corresponding to k in the numerator and j in the denominator and then you take log. So, e will go away. So, you will get basically half of x minus mu k prime sigma inverse x minus mu k minus x minus mu j prime sigma inverse x minus mu j that is equal to after simplification x minus half mu j plus mu k prime sigma inverse mu i minus mu j then the regions of classification if we apply this method that is we are considering sigma q i r r i less than r equal to this if basically we have mentioned here that the one which is minimizing this. So, the procedure will become if we assume the cost functions that is c j i to be say equal then the base rule base classification rule is that is r j that is classify the observation into jth population if u j k x is greater than log of q k by q j for k equal to 1 to m k is not equal to j. We can notice here that this functions u j k they satisfy the symmetry property. So, actually what kind of regions are these if you see it carefully they are nothing, but the r i's are actually bounded by the hyper planes type of region because x minus half mu j plus mu k prime sigma inverse mu i minus mu j. So, what kind of regions you will be getting you will be getting the regions of the type of the hyper plane. So, if the means span an m minus 1 dimensional hyper plane then r i is bounded by m minus 1 hyper planes that you will be getting because the x value that will give you a hyper plane x greater than something or less than something and if the prior probabilities are not given then in place of log of q k minus q k by q j you can put some value and in order to maintain some sort of symmetry of representation we can consider something like actually what is the value of log of q k minus log of q j because these are probabilities. So, basically you are getting them to be negative because they are lying between 0 and 1. So, we can write log of q j see log of q k minus log of q j. So, with the minus minus signs we are getting. So, we can put log of q j before because there is a minus sign. So, we can term put it in terms of the non negative values. If no prior probabilities of populations are assumed we can consider r j as u j k x greater than or equal to c j minus c k for k equal to 1 to m k not equal to j where c j's are positive constants. Actually any rule of this type is a base rule. So, in place of prior probabilities if we are putting some other numbers we can actually define respective probabilities in such a way that they will be equal to something. So, all such procedures they will be giving you the base and admissible rules. So, basically this is the you can say minimal complete class of the classification procedures for classifying into one of several populations. These rules are admissible rules they are also base with respect to they are also base because the class of base rules and admissible rules is the same here. Now, if we want to find out a minimax procedure then we can consider say probability of the correct classification and we can make them to be equal for minimax procedure we may find r. So, that p r i given i are all equal. Let us look at what is the probabilities of correct classification probabilities of correct classification which we can also call PCC. So, x is the observation to be classified then we can consider say u j i that is equal to x minus half mu i plus mu j transpose sigma inverse mu i minus mu j. This is the classification function that we got and of course, u j i and minus u i j they are related here. And so that means, basically we can consider m c 2 classification functions because we do not have to consider both here m c 2 classification functions are there. And of course, this is because if they span in m minus 1 dimensional hyper plane. So, now if x belongs to pi j that means, x is having n p mu j sigma distribution then what is the distribution of u j i. So, u j i that will have see this is normal and we can apply the linearity property. So, this will become mu j minus. So, this will become actually mu j minus mu i and here also you are having this thing here. So, this is mu i minus mu sorry this is mu j minus mu i I just wrote it reverse here.  So, this if I define the term say delta j i square which is a generalization of the malanobis d square function which I wrote in the case of two populations then this is equal to mu j minus mu i prime sigma inverse mu j minus mu i. So, in terms of this. So, this is actually malanobis d square as a distance function of distance function between populations pi i and pi j. So, then this is equal to normal half delta j i square delta j i square also we can look at the covariance of u j i and u j k. The covariance matrix will turn out to be the covariance matrix the covariance between. So, this is a scalar because u j i is a scalar function the covariance between u j i and u j k. So, that is equal to I use a notation delta j k j i that is equal to mu j minus mu k prime sigma inverse mu j minus mu k. In the classification rule when prior probabilities are not fixed in advance then we have to determine constant C j C k etcetera which I mentioned that we can choose them to be non negative. So, we can consider the probability of classifying in 2 j when it is from j then it is equal to f j that is the observation is from the jth one d u j 1 d mu j 1 and so on d mu j j minus 1 d mu j j plus 1 and so on d mu j n and these are C j minus C 1 and so on C j minus C n because the upper side is infinity here where f j is the density of u j i per i not equal to j. So, we can choose this should be u not mu I think the we can choose C j is so that p r j given j is equal for all j. Now, the another situation arises if the parameters are not equal not known then we can substitute estimates for example mu i head can be x i bar and similarly you can have sigma head is equal to 1 by sigma n i minus m i is equal to 1 to m and x i j minus x i bar prime no x i j minus x i prime j is equal to 1 to say n i i is equal to 1 to m when we have random samples x i 1 x i 2 x i n i from pi i then we can consider these estimates and the analog of u i j this will become w i j that will be x minus half x i bar plus x j bar prime s inverse x i bar minus x j bar. Now, as we discussed the case of two normal populations the distribution theory for this part is somewhat more complicated. However, the exact distribution theory is not very difficult because strong law of large numbers will hold and if I take here large sample sizes and then you can consider here that x i bars will converge to corresponding mu i's x j will go to mu j s will go to sigma s inverse will go to sigma inverse in probability and so on. Therefore, the asymptotic distribution of u j i w i j will be almost the same as the u j i. So, the problem can be handled. So, the exact distributions of w i j are quite complicated. However, for large sample sizes we can use laws of large numbers the asymptotic distribution of w i j will be same as that of u i j. So, this problem can be solved. Now, let us also go back to one of the problems that I discussed earlier that is classifying into two multivariate populations when the variance covariance matrices were unequal. I discussed the rule when the two populations had known parameters. So, if you remember the rule that I had mentioned here it was given by this that is when sigma 1 and sigma 2 are different I mentioned that in place of hyperplanic regions you are actually getting much more complex regions because this is becoming I mentioned that one of them becomes central chi square another is becoming a non-central chi square distribution. So, this region becomes much more complicated. Now, we also consider this case for the unknown sigma 1 sigma 2 case in that case we have to substitute the estimators. So, let me briefly discuss this case also. Next we consider the case of unknown and unequal covariance matrices. So, in particular let us consider say pi 1 as the population n p mu 1 sigma 1 and pi 2 is the population n p mu 2 sigma 2. So, let me go back to the expression that I derived earlier the expression that we obtained was in fact, there was a power here which I would have missed that time it should be power half here and power half here also and it is e to the power half x minus mu 2 sigma 2 inverse x minus mu 2 minus x minus mu 1 sigma inverse x minus mu 1. So, we can consider a likelihood ratio procedure we are having the samples here say x i 1 and so on x i n i this is from a random sample from pi i i is equal to 1 2. We can consider a likelihood ratio test procedure for null hypothesis that is the observations x and x i 1 x i 2 x i sorry x 1 1 x 1 2 x 1 n 1 they are from pi 1 and x 2 1 x 2 2 x 2 n 2 this is from pi 2 and the alternative hypothesis will be that is x 1 1 x 1 n 1 this is from pi 1 and x x 2 1 and so on x 2 n 2 this is from pi 2. Now, in the likelihood ratio procedure I have to consider the maximization of the likelihood function under both null and alternative hypothesis. So, in the null hypothesis I will have n 1 plus 1 observations from pi 1 and n 2 observations from pi 2 in the alternative hypothesis I will have n 1 observations from pi 1 and n 2 plus 1 observations from pi 2. Since all the parameters are unknown and unequal this is simply reducing to the problem of finding out maximum likelihood estimators for these cases. So, we can easily write down the maximum likelihood estimators. In the likelihood ratio procedure we are required to determine the maximum value of the likelihood function under null as well as alternative hypothesis. Thus we find MLEs under both cases. So, this we can write easily because the procedure for finding out the MLE is known in the case of multivariate normal distribution we know actually that the sample mean and the sample variance covariance matrix they are the maximum likelihood estimators. So, under the null hypothesis MLEs are so we write it as mu 1 head 1 that will be equal to n 1 x 1 bar plus x divided by n 1 plus 1 because this is the sum of all the observations from the first sample plus x because we are saying that it is coming from the first population mu 2 head 1. So, 1 means basically under the null hypothesis this is given by x 2 bar and sigma 1 head 1 that will be 1 by n 1 plus 1 sigma. So, we call it say a 1 plus n 1 by n 1 plus 1 x minus x 1 bar x minus x 1 bar transpose and sigma 2 head 1 that will be simply equal to 1 by n 2 a 2 here a i's are x i j minus x i bar x i j minus x i bar transpose j is equal to 1 to n i under h 1 that is the alternative hypothesis actually this null hypothesis I am calling h naught and this alternative hypothesis I am calling h 1. So, under h 1 this will turn out to be mu 1 head 2 that will become x 1 bar and mu 2 head 2 now here I will have n 2 plus 1 observations from the second one.  So, if we consider the likelihood ratio criteria that will give us the likelihood ratio.  If we consider the costs of misclassification to be the same and the priori probabilities to be equal, we can consider this ratio to be 1 to be greater than 1 then you classify into pi 1. So, we classify x into pi 1 if the ratio is more than 1 else classify x into pi 2. Now, this is one criteria that is the likelihood ratio criteria. Let me also again come back to this original observation that I got here. Another thing could be that I substitute direct estimates that means here I put x 2 bar, here I put s 2 inverse, here I put s 1 inverse, here I put x 1 bar. So, in both the cases the exact distributions of the criteria are not easy. The exact distribution of the criterion is quite complicated and alternative approach can be simply plug in estimates into this function. That is x minus x 2 bar prime sigma that is s 2 inverse x minus x 2 bar minus x minus x 1 bar prime s inverse x minus x 1 bar. So, that is you put this as some greater than or equal to something and so on less than something. So, this could be another one. Once again the distribution of the criteria is quite complicated even if I look at the asymptotic distribution for the large sample sizes by applying the laws of large numbers I will get this one. I have already discussed that if x belongs to pi 1 then this is non-central chi square this will be something like a central chi square. So, the difference of 2 and it is going to be quite complicated. In case it is from pi 2 then this one is a central and this one is a non-central. Once again the exact distribution of these things are difficult to obtain. So, in particular we are saying is that when the variance covariance matrices are unequal the classification rules no doubt can be easily found out, but in order to obtain desirable rules such as a minimax procedure among them is a difficult task because the probabilities of correct classification or the probabilities of misclassification will be quite complicated. Friends, so we have actually discussed so many classification rules. In fact, I framed a general decision theoretic approach to the classification problem by considering the Bayes decision rule, the criteria of admissible rules, the minimax classification procedure, the minimal complete class etcetera. And in particular I showed applications to the classification of multivariate normal populations. We have considered two normal populations and multivariate normal population. So, I actually wind up the discussion on the problem of classification now. Now one can consider some other classification procedures which are available nowadays, but that can be a subject of full-fledged discussion. I will move over to another topic that is the problem of principal components. So, in the next lecture I will briefly introduce a problem how to determine the principal components and also may be I will touch upon the canonical correlations. So, that will be the topic of the next lecture.


Welcome to the drum history podcast. I'm your host Bart van der Zee and today I'm joined by John Palmer, who is the sales strategist from Hoshino USA. John, welcome to the show. Thank you very much, Bart. Good to be here. Yeah. Man, we've been working on this one for a while and it's just one of those things where sometimes the stars don't align with scheduling, but we're here now. And I have had many people reach out and say, hey, you should do a Tama episode and I go, we're working on it. We're, it's coming together. Yeah. So yeah, I appreciate it. You guys sent me some books here, which are awesome, which is the history of Tama, the story behind the strongest name in drums, which I just blew right through because it was so cool and it's kind of a little handy pocket size book. So yeah, how long have you worked at Tama? Hoshino, I should say. Yeah. So exactly. We'll get into Tama and Hoshino and the relationship, certainly, Bart. And I've been here, I'm in my sixth year, so I started late 2015 and have been in the industry for many years.  So it's just, it's great. The people are great. And, you know, I'm kind of living the dream. So things are good. Yeah. Yeah, Tama, I know I've said this on the show before and it's probably confusing because I'll say this was my first, this drum set and this was like, I started off with a big old Ludwig set. But then when I actually, you know, I worked at a butcher when I was really young, like a grocery store butcher for a few years. And I saved up and I bought a brand new Tama Star Classic kit, which I would deem that my first real drum set when I was like 12 or something. And that was just the most beautiful. I had it forever. I actually ended up selling it when I was like, I mean, I was probably 25 or something. But beautiful drums. There's something, the Star Classic line in general, obviously all of the lines are just great, but they are so well respected, so innovative. I think that's something we'll obviously talk about is just the innovation, which before I read the book, I didn't really realize how many things Tama invented. It's just amazing, such a cool company. Yeah, exactly. I think that is the essence of what the Tama brand has become and was when it was finding its way. It's the innovation. And I always look at the product, say the product is the star for Tama. And they just, when I say they, the R&D team, the design team, the market research team, which is centered in Japan, they do their students and do an incredible exacting job of finding out what's happening at a very detailed level in the market and then working to improve any way possible. And it's pretty impressive to watch the work on the R&D side happen because I think it fuels the brand. That's exactly what it is. It's two, I think this should be said, it's one of those brands where kind of like Pistie or some of these others where there is, you hear people say the name differently. Tama, which is just sort of a thing, but obviously you're saying Tama. That's kind of what I, I think I started saying Tama is a kid. And then I just kind of realized like, I think it's Tama and just sort of, but we get to hear straight from you. It's Tama, correct? So that was my very first question on my very first day, you know, formally. And even, you know, I started, and I'm in Benz sale in Pennsylvania. It's where I work. It's where the Hoshino Distribution Center is and offices for the USA. So I started my first day and I said, okay, let's just get this question out of the way. How do you pronounce the name? And I was told by Charlie Hayashi, Tama.   And so they're not going to say Tama in Japan. And so when they say Tama, I say Tama. I say Tama, but I'm cool. However, it's pronounced. I meet a lot of people that say Tama, Tama, Tama. You know, all kinds of great pronunciations that are Americanized and fine with me, you know. And I think it is like piste and vinyl, you know, and, you know, Zilchian and there's so many colorful brand names in the industry. So we're just one of them. Yeah, that's so true. Tama, it's that very American. It is.  It's that got that feel to it. Yeah. Yeah, it's a little drawl happening, you know, and that's cool. So no worries if you say Tama, Tama, Tama, whatever you say, it's all good. So, you know, so I think, Bart, can I jump in because we're kind of, you know, hitting the umbrella topics of the brand? And so can I can I hit into the history a little bit and kind of give an overview? Please do. Because there's there's a great story about why we call our drums Tama. And so here's the story. So, you know, and what is Hoshino, you know, and people are like, well, what is that? So here's the deal. So Hoshino was established by in 1908 in Japan, family owned business by a man named Mr. Yoshitara Hoshino. Okay. And he had a bookstore in Nagoya, Japan, and he sold music books to school back in 1908. So he he's in kind of the music, you know, education business. And then he added musical instruments to his business. So that's how he got into the musical instrument business. Way back in 1908, his wife was named Tama Hoshino. So there's the brand name. And it's pretty cool story. So Tama Hoshino and she was involved in the business as well. So, you know, that's a pretty cool story. And a couple other cool things is so for Hoshino, Hoshi, that part of the name means star and no means field. So you put it together Hoshi star and no one field your star field. And then we are Hoshino Gaki and Gaki means musical instruments. So basically Hoshino Gaki means star field of musical instruments. And then the name Tama has a name that has a meaning as well. And it means plenty fullness. So there it is star field. And so what a cool thing is, is we have this really natural kind of organic naming for the brand. And for obviously you've mentioned it already star classic.  Star cast star, you know, everything star. So that's why we do it. It's really super, you know, natural naming convention that just follows our legacy. So that's that's an important part of the history that it lets people know that, you know, we're just kind of true to our roots, really. Yeah, man, that's so beautifully Japanese. Just to have that that I didn't know that really it's cool to think that the Hoshino star field. I mean, it really kind of makes it all. It all makes sense then. Yeah, it really pulls it together, doesn't it Bart? Yeah. Yeah. Okay, so 1908 unbelievable. I mean, this is a hundred and 13 year old company. Right. And that's unbelievable. Right. Right. So yeah, we have quite a legacy. And we do also we do Ivan as guitars. So I think probably some of your, you know, listeners know that, but we own the Ivan is guitar brand and the Tama drum brand. But there seems to be a real close connection with Hoshino and the Tama brand because it is, you know, it's the founder's wife's name. Right. So there's a huge family legacy and we're still family owned by people named Hoshino.  So the legacy of the company is four generations long and continues to evolve under the Hoshino direction. Wow. So cool. Pretty cool. Yeah. All right. So then we start off selling, you know, musical books and everything. Yeah. How long did that go before he got into, you know, producing musical instruments? In the 30s, I think the kind of the story goes that I know. So Govia comes over and plays some classical music in the 30s and the classical guitar craze in Japan went pretty fervent. So there's interest in people like, can I get a guitar? So there was a guitar brand, Spanish guitar brand called Ivan as no, not Ivan as in Spain. It's called Ibanez. So, you know, that's the guitar brand in Spain, Ibanez. And I'm not sure the details, but we ended up acquiring the Ibanez brand and everybody calls it Ivan as. So that was in, I think the 30s, 40s. So we get into musical instruments then. And then post World War II, you know, this is really, it's quite a history, company history and how it mirrors world history. Obviously, World War II is a major, you know, nothing's happening. It's, you know, as far as production of musical instruments. And so it's the evolution of the company after World War II. And just as it is the evolution of Japan, and it really mirrors, I think, the manufacturing and, you know, the evolution of the country post World War II. And Hoshino is very tied, very much of a, you know, a corporate sort of, not even corporate, that's a strong word. But just a developing manufacturer that took steps like many other manufacturers did after World War II. It's so interesting with World War II how it affected so many different industries.  But it definitely rocked the world of drums and everything kind of changed after that. Right, exactly. So the MIJ phenomenon that we're experiencing now, you know, that all happened back in the 60s. And I think the Beatles, you know, certainly had an influence and 1964 hit and people want to play drums. So we realized, okay, we started a factory in 1962 in Japan to build OEM, which is original equipment manufacturing. And that's basically to supply other brands a product. So we build it, they buy it, they put their name on it. And that happened for a while in the 60s. The factory in 1962 was named the Tama Factory. But we were not making Tama drums at that point. So we were making original equipment manufacturing drums. Some of those drums were sold to big box retailers at the time, such as Montgomery Ward, which was an old school retailer that was like a Sears competitor. And you would see different brands coming out of the OEM factory that were certainly not Tama. And then in about 1967, Tama realized, well, let's put our own name on the drums. And of course, because of the Hoshino name called the drum Star. So that was the first Hoshino branded drum set with Star drums back in like 67, 68. Wow. And you can always typically tell something that's related to Hoshino because it says world supreme quality, correct? Which is kind of a neat little thing to know. It's a cool thing. And absolutely, I think the gestalt of the Japanese culture in the 60s was to imitate and take the best of anything they imitate and then try to improve on that. And what a formula for success. And you can certainly look at the photo photography industry or the bike industry or so many different industries, the television industry, and then the automobile industry, which everybody knows. And I think that is a blueprint to the formula. And certainly, I'm not qualified to speak about that, but I'm sure there's manufacturing experts and history experts that can go deep and it's quite a fascinating study. But we were just one company that was trying to do that very modestly in the drum industry. Yeah, it's so neat to see the... And I've talked about it with other people where there's just something... Obviously, they call them stencil drums too, as I'm sure you know, where it would be like, hey, all the kids are buying Ludwig and Slingerland let's make the drums look like Ludwig and Slingerland. And a lot of them are very close representations of like a Rogers throw-off or like I have a Hoshino kit and the badge from 10 feet away. It's like, is that a Slingerland set? Yeah. Oh, no, it's not. So just that sort of... It's just very interesting. And I think a lot of it... I've talked with people before about it where a lot of it is because it's the Japanese market. It was like the American brands weren't really going to... Who were they going to go after to say, hey, quit using our style? So not that it's... I mean, I guess there are some legality, but I've run into that too with European brands where like the turret lug, the George Way turret lug where Heyman drums was using it.  It's different with copyright and all that. It is. I mean, it depends where you file the patent. And so sometimes it's just USA only. Sometimes now obviously with globalization, those intellectual properties are very sensitive and more far-reaching. And certainly China has become a major source of recognition and paid a lot of attention to that. So even the Tama brand name, is that a brand name that's registered in Europe and in Asia and Africa and really every continent? Because you have to register it for it to be protected. So it's a lot of money to protect the brand integrity globally. So that's... Yeah, you see certain pockets of things that maybe aren't protected and then you got to go after it and then you got to recognize it. So that's another discussion about the business legal part. And I'm, again, not an expert on that, but I have an awareness. But that's a fascinating topic, Bart. I think you should get a patent attorney or copyright attorney on at some point and have that discussion because that's a pretty fascinating topic. I think it is. And it's just, I've learned with my wife as an attorney and there's so many... Like I would bring that up to her. I would bring something up about whatever, intellectual property or something. And it's like speaking a different language because it's so many different... I guess you'd call it verticals of law that it'd be like, it's not what they do. You need to find... I just think that's interesting with law. It's like, oh, no, no, no. I'm a elder care law lawyer or I'm a estate lawyer. So even to a lawyer, that stuff is confusing if it's not the right field that they're in. So I imagine for a drum company or whoever, it gets a little hairy to... It's brand protection. I mean, every brand goes through that and they have legal teams to work on that stuff dedicated. The industry, the drum industry is... The perception is, oh, those big drum companies, it's not that big. And we're not that big of a business. We're just kind of a humble... Just some dudes who, yeah, of course, we're into business and functionality of business, but it's not like heavy corporate meetings and starch in the shirts. There's none of that going on here. We're just trying to build a product that inspires people and the entire drum industry is like that. What you see, you meet people at NAMM, the guys from the other brands, they're all cool dudes and it's a cool little community. Just like the people who are not in the industry but play the product and we go to retail stores and certainly non-COVID times, there's a flow that happens and there's sort of a gentle vibe that permeates the industry and that's one of the beautiful parts of the industry. Just like yourself, you're a laid-back dude and we're going to get there and everything's going to be cool and I dig that. Yeah, I agree completely. And I learned that on other episodes with like Vic Firth, for example. I was like, you guys are huge and he was like, well, there's like seven of us here. And I'm like, you're Vic Firth and obviously there's more distribution and all that, but it's just cool to know that and it kind of has its... Obviously, it has its roots back to being a smaller kind of scrappy company, but you know, Tama is one of those brands that I think you know this, but so with the MIJ, the Made in Japan, the Stencil stuff, I mean, it rocked the world of the American brands and I think we're going to be approaching that area of like when Star became actually Tama, but it's just you can't underestimate how like I would imagine people here in America were like, oh, whatever, let them do their thing. It's not that big of a deal. Let them have the beginner drum market, these cheapo kits. I don't think people maybe realized at that point how disruptive to use like a modern buzzword. It was when these MIJ brands, which there were a few of them in addition to Hoshino and obviously Star, but I hear about it in every episode where people go, oh man, we got killed in the 70s and 80s because the Japanese brands came out. Yeah. And again, it's just a microcosm of a larger economic shift and again, look at any industry and a brand like Sony, Panasonic or Toshiba, there's so many really good Japanese brands that very much mirrored our company history and you're right, if you're a dominant American drum brand at that time and there weren't many because there just weren't that many and here come these other guys that are making, oh yeah, it's okay products, but the price was really good. So there's an economic benefit to the product. Now, were the drums as hardy and sturdy and robust as the American counterpart at that time? Maybe not at that time, but the really fascinating study is how quickly it evolved and changes were made very fast to manufacturing and feedback was gathered very quickly and it goes back to the market research and intensive market research and study. One of the cool things, so you're right, so we're moving into now the Tama, we're moving out of the 60s and getting into the 70s. So what year was that, so we know? So 67, it became Star, right? Yeah, so we're doing Star in 67, 68 up until 1974 and then in 1974, that is when Tama, the Tama brand was first put onto a drum set. So 1974, Tama's born. Okay, cool. Yeah, so there you go. And then at that point, I think there was realization that the brand had to evolve and couldn't just be a house brand, a Tama brand without some improvements. So improvements were already happening at that time as far as hardware and the shell and just things just got better and they quickly, after that launched, there was a lot, one of the cool things about the Hoshino company and certainly the drum side, the Tama side, is the people working on the projects, and I'm talking R&D people, I'm talking sales people, market research people, nobody I think or maybe very few were really drummers and so there was a beautiful humility and study to the market that was done because there was no arrogance of, hey, I know what drummers want because I'm a drummer and that's a big deal for us and I believe was really a very objective way to move forward based on informed comments by artists and informed comments by retailers and we listened really closely without the preconception of we know best and that's a huge benefit to us. Yeah, you gotta, I mean, there's that whole like, well, we do it this way because we do it this way, kind of attitude with any industry, but like, God, that makes so much sense. You gotta put yourself into that point of view then of like, it's so interesting that like, guys were working on this and inventing this and Japanese, you know, culture I guess is very like, forward thinking and efficient, but to be working and building drums for something, if you're not a drummer, it's really interesting. I remember on the Noble and Cooley episode, like the Joneses, the father and son work there aren't drummers and it's sort of, I was blown away by that, so I need to like, become more like, oh yeah, everyone's not a drummer in the world of music, you know? Yeah, I think it's rare. You know, it's how I think drum companies are permeated with drummers, but you know, that's interesting Noble and Cooley. Yeah, I mean, some of us just, we manufacture it, so we can make a round, you know, wood object or, you know, a cylinder and we can put some hardware on it, so why not make a drum, you know? Yeah, some of it. But yeah, I think the humble, you know, predisposition of not knowing, there was a big study and, you know, and that spirit continues in the company today, you know, and I, you know, sometimes I think I know, you know, the direction so easily because I've been in the industry, but oftentimes I just sit back and watch and wait and then, you know, there's maybe a new perspective that's introduced that I hadn't considered and that's due to just being super objective and asking a lot of questions. Yeah, I mean, you can't, it seems like Tama had a period where they were the ones pushing forward with everything, but as, you know, we live in a modern time, you can't be like, you know, we're the only ones who are going to progress, but when other brands do come in and it's sort of like a, like, we're going to, like, you know, brand A is going to build on what Tama did and then brand B is going to build on what brand A did and it's just going to keep getting better and better and better and better. And I think that's sort of how the world works. Yes.  Obviously that's a car example. Yeah, I think there's a great parallel there for sure. I think, yeah, you nailed it, Bart.  Yeah, you know, we didn't invent it. We just looked at it and said, how do we improve it? Yeah. So some of the things, just so maybe some of the cool things that we did bring into the market that were not there is a boom stand. And, you know, we didn't know that drummers needed to have their cymbals closer to them and drum set sizes were evolving and they couldn't get a stand close, but we asked people and somebody, so there was a visit and we do a lot of market research and their fun trips and we go around and visit informed, the informed drum community and we ask a lot of questions. And one, so that happened back in the 70s and there was a contingency of Japanese headquarters guys that came over and did a market research trip and went to a Sam Ash store in New York and someone said, hey, can you make a stand because apparently the story is people were duct taping like boom arms onto stands and then spending cymbals because they needed their cymbals closer. So that's a problem to solve, right? So our engineers were like, yeah, we can do that and we made a boom stand. Man. The nylon sleeve inserts that are, you know, they go in between the pipe clamps on a cymbal stand. It was metal to metal, metal to metal and that had problems. So an engineer came up with, let me look at this, analyze it and try to figure out a better way. So we made the first nylon sleeve that goes inside the height adjustment collar. So there's some cool things. And of course, we're not the only company to innovate and so you're right, we look, we see, how can we do it better and other companies do the same with us and who benefits the drummers? Yeah. There are, you know, scenarios where a straight stand is obviously really cool and it can work, especially like, you know, for your ride, if you can get it low enough and kind of tucked in there.  It is the worst thing when you can't get the cymbal in close enough. Yeah. And you're like tucking legs under things. Yeah. It's falling over. So. Exactly. That's a big one. Yeah. That's a cool one. Yeah. Are we at the point too, where obviously, I mean, you can't talk about Tama without talking about Billy Cobham, which I think was sort of in this region. You're definitely in this realm. Yeah. Right. Yeah. So there's a few, right? So Billy Cobham was a huge impact. And, you know, again, it's so funny, I think that because I grew up in the 70s and so this was all like real direct stuff for me. But I have to remember, you know, my age and there's a lot of listeners who are like, Billy Cobham, who's that? So my recommendation is check him out. He was blowing people's minds. You know, he was like the original gospel chops sort of drummer. Yeah. In the 70s. And he was doing things, you know, on the drum set that just were not done before. Of course, he was standing on people's shoulders and, you know, he took Tony Williams and Ginger Baker and, you know, kind of did his own thing. And it's a beautiful thing. So check him out. And he was a big icon in the drumming industry and Tom assigned him, I think around 1977. And yes, that was a big marketing exposure impact for Tom and drums. So we realized artists were key. Now, apparently, how it happened was he was just wandering around a Nam show. I think it was in Houston at that time. And he just saw some things that Tom was doing from a product standpoint. And he was open to checking out certainly ideas and ways to improve his playing. So there was, again, an organic sort of interest to the products. And that's what led Billy to us. And he was huge for us. We also, around that time, had Lenny White, who was another killer fusion guy. And then Stuart Copeland goes way back to like 1975 or 74, when he reviewed a Tom and drum set for a British music publication. And he was doing reviews. And he was sent a set and he's like, these drums are cool. And so he became, I don't know if he's our, he might be our earliest like signature artists, I believe, is stored. So he's been with us a long, long time. And then Simon Phillips also in the late 70s was another icon who joined Tom. So we had some pretty killer artists early on that enjoyed the brand and enjoyed the sound. And it was really interesting for me growing up there, because of course I know the American brands. And then I see the three primary Japanese brands, that being Tom and Pearl and Yamaha, kind of come onto the scene. And I was like, what's up with these? And then I start checking them out. And I'm like, yeah, good quality, sound good, and price is very competitive. So what's not to like? Yeah. Yeah. More modern too. Like I love the, you know, I love the American brands. I love all the brands, but there's something about the Japanese stuff, which seemed like it's almost like a scrappiness where like you had to innovate to compete.  And I also want to say that with Simon Phillips, you get him wearing Toma leggings in his instructional tapes, which is like, that's devotion. Yeah. Yeah. It's so, again, so beautiful, the industry and the connection, you know, we're so lucky, like, maybe not lucky, but we just, maybe we're just insightful. And we appreciate, you know, the connection of music and life and the expression of our inner selves through music. And that's so personal, you know, Barton and the people who were into the brands that they play. And it's any brand, you know, I love that there's a personal connection to the brands. I love it. I do too. And there is a serious personal connection to the brand. I mean, and maybe that's a good time for me to just give, give him a shout out. There's a guy named Johnny Martin who shot me a message like a week ago, which is perfect timing because we're doing this, but just talking about how much he loves Toma. And I just want to say that because there's obviously this, in many brands, there are these groups of people who are so beyond passionate that it's just like, it's, I mean, like, I use the word obsession in a great way because obviously we're all obsessed with the drums, but I don't think it should be, you know, skimmed over that there is a very passionate group of collectors and enthusiasts with Toma, but also with every brand.  So I just totally agree with what you're saying. Very, very, very, very passionate people here and Toma has a great, which you know you're doing something right if you've got people who, from the beginning, love what you do. I think it's a testament to the company. Yeah, thanks. Yeah, I think the industry is full of that and, you know, a cool thing about our, again, our instrument category, drums and percussion and cymbals is the product's age well and it's so cool to be able to play a vintage kit from the 50s, 60s, 70s, 80s and just feel like it's like, got some personality, you know, and it's useful. It's not like an Atari game or a computer, you know, from 1986. Yeah, it's novel, it's cute, but I would never use it. No, you know, we can take these old drums out, rehead them, make them sound awesome and explore our personalities through the instrument and that's a just beautiful thing. I love hearing too. I love Stuart Copeland so it's neat to hear that he was kind of the first guy.  I mean, he's just, you know, and that's where there's kids in the front row and they're looking at this, you know, drum head for an hour of a concert or on TV and it says Tama and boom. Yeah, yeah. That's where it begins. That drum head is a nice, no pun intended, but good impact. Yeah, big time. All right, so let's, for the sake of time, let's push forward here. So we're in the 70s, obviously very innovative time. Tama's like, you know, really making the big companies kind of shaking their boots and be noticed. So take it away from there. Okay, so yeah, I mean, it's just continues. Basically the message is, the blueprint has been written, I think, as far as innovation and, you know, looking and what can we do better. So we realize drums are, you know, the sound of drums are important and we get into the crest stars and the art stars and try to do some things different sonically. Certainly we've, up to this point, a lot of birch, most, I think it's mostly birch and then we get into art star two and that's the first maple kit. Bigger kits, bigger sizes. Again, listening to the drumming community, amplification is getting louder and we need to have stronger drums, a stronger sound. So we just very humbly listened and realized we got to produce a larger sound and Dicast hoops were instituted and longer toms instituted and the metal market responded. Yeah, yeah. And I mean, I don't know if I'm getting ahead of myself, but obviously you said longer toms and it made me think of the octabons, which are kind of just they're about as iconic of, you know, just an innovation that came out as anything else in the drum world. When was that? Yeah, that was in the 70s. And I actually, now that you mention it, I believe that is the product that Billy Cobham was inspired to see at the NAMM show in the 70s and 77 in Houston. There was like a secretive, here's this little product and apparently was, you know, in a side booth or something that was not on the floor and he saw those octabons and he's like, yes, melodic, very cool. So that happened in like 77-ish. Yeah, and those obviously became important for him and important for Stuart Copeland, Simon, all the key guys that were playing had these beautifully tuned octabons. So that was then and yeah. Yeah, the gong bass drum. The other thing that Billy's like, if I come over to Tama, you got to make me a gong bass drum. So we did that. So, you know, again, we're just sort of following the artist's leads, you know, they're telling us what to invent sometimes and then we invent it and then we improve it. Now, a gong bass drum, maybe we just pause there for a sec. I've seen them many times, obviously, you know, on stages and you see some of the mega drummers use them.  So the technology, though, is basically it's a normal bass drum that's mounted typically no bottom head, right? And then the top head is bigger than the shell and it has like a timpani head. Yeah, okay. That's cool.  So again, if you haven't checked out Billy Cobb, just check them out and you'll see some incredible gong drum stuff happening there. It's amazing. It's so cool. All right. Well, now if we're getting into the 80s, I want to make sure we talk about and again, Johnny Martin, who's the big collector kind of sent me a list of stuff and he's like, make sure you talk about this. We've talked about it previously on the I did a 5000 episode, but I want to make sure we talk about with camco and the buying of the rights with DW and how did that work with camco? Like what's the deal with that? Yeah. So, okay. So I know bits and pieces like, you know, I wasn't wasn't with the company then and so that happened in like 77, I believe late, like 77-78 and there was an opportunity to purchase part of the camco like brand. So as what eventually happened is DW got the rights to the turret lug and Tama got rights to all the hardware but certainly the camco pedal, which was a leather strap drive at the time and then we realized we, you know, that part was wearing out and let's make it into a sprocket drive and so we made the camco Tama pedal with the sprocket so that was, you know, 77-78 so we still own the camco name, the brand name and DW still owns the design for the turret lug and I think it's served both companies really well. So that's where it sits and yeah. So it's pretty cool to, you know, have that. So that's that part and what else with Johnny? What were some other topics? So he just said basically in 85 and again this is I just love that this is coming from a diehard collector who, you know, these are some things he just wants to talk about. So in 85, Hoshino USA made a custom shop in Bensalem Oh, Bensalem, yeah. That's where I work now, yeah. Where you are. So it's the, to his knowledge he said it's the first time a company offered custom paint jobs to the public. I don't know if there's, if that's, you know a fact. We did do some assembly here and actually that when we to rewind back to the camco you know, era, we changed the badge a little bit and put like a camco Hoshino badge together and we did drum production here in Bensalem for maybe 78, 79 to about 1983. So we kind of had some drum production here with assembly and finishes. So we were set up for that and then as far as the mid 80s go and doing customized things, yeah we did some things but I don't have a very detailed knowledge about what we had, what we were capable of doing. So that part I'm going to sort of, you know, just respectfully say I'm not an expert. Yeah, that's fine and I mean let's just throw it out there that maybe that's something that happened but you got to be careful with saying who was first because there's always, there's frequently someone who goes well no, actually six days earlier you know, Pearl was doing it or something. Like you can't be too specific on that but that's a theory. Yeah, all right. So then 80s, that's always got for the 80s but it's just to me that it's even more of like Tama just, you know, powering through and becoming more of a powerhouse and even more of, I mean you kind of think of the 80s as like maybe not so much with Ludwig but like I think of Slingerland and I know that Slingerland went through and made amazing drums for a long time, some saying that for the Slingerland guys and girls out there but but really you think of like Slingerland sort of being really in trouble and Tama and the Japanese brands just you know, shooting to the moon to use a star kind of space but that had to be a massive time of growth for the company. Yeah, absolutely and acoustic drums were flourishing you know, during that time in larger sets and double bass kits and heavier and louder and you know more rock solid and bigger, stronger so Tama was absolutely at the forefront of that and our market perception was they, you know, super rock solid and great sounding drums that are very sturdy so it's certainly fit the times and our hardware developments were doing well and you know, Iron Cobra pedal was being certainly evolving at that point so lots of cool things and yeah we had a great run and you know, products Asian products were still kind of getting refined as far as the build quality and the price value and I think there were some big improvements there that allowed drummers to say that's a really nice sounding kit that I can afford and I think I'm going to buy that kit because it feels good, it looks good, it sounds good it looks durable and it's a great value so yeah, I meet so many drummers Bart, I'm sure you do everybody's like, oh yeah, I had a swing star kit man, I threw that my first kit was a rock star I hear that all the time and much like, you know, the Pearl export kits and you know, they're just you know, certainly there were Pearl and Tama entry level kits were allowing drummers to enter you know, their drumming you know, spirit class basically or their path at a really really good price point and their real drums, they're not you know, the Macy's catalog drum set that is sort of a toy, these are more real deal yeah, absolutely real deal yeah, the rock stars and the swing stars and stuff are to this day obviously very, very, very good not even beginner because I feel like with any drum set like that you can throw good heads on them and make them sound great, so they're not a toy, they're nothing to be like not ashamed of, but you know what I mean, they're nothing to be kind of like, oh, this is just my beginner set you can use these things for a long time no question, huge value and I see them all the time you know, on Reverb or Facebook marketplace or wherever and yeah, those drums you know, you get a nice kit, use kit you know, 250, 200 exactly like you said, you put new heads on them, foam their tone is great yeah, and you mentioned the Iron Cobra which I've, that was probably my first real deal bass drum pedal that I got was an Iron Cobra which I still have still love it's obvious, I have a double pedal, but I think I'd basically just use it as a single because I haven't done as much double drumming double bass drumming in the last couple years but it's such a good pedal, I mean there was just something about it or it was like buying it for the first time which you know, obviously no double bass drum pedal or a single pedal is a different story, but they're not cheap any double pedal you get is not cheap so just buying it, it was like whoa, this is the real deal and it just is such a cool design, I just love the name Iron Cobra is in itself such a cool thing, which now that I think about it is kind of a departure from the space theme yeah, yeah for sure, you're right and yeah, some of our hardware is first chair thrones and road pro stands, so the star naming more on the drum side than the hardware but that was a marketing decision again preceded me by a long shot, but it is, it's just form follows function and we were able to with a connecting rod and a secondary pedal on the left side with a connecting rod put two beaters into the single frame and that was our big breakthrough because there was another company on the west coast real big company two letters, I think you know I think we know they were super good at innovation too and much respect and they were using I think they had created a double pedal but the second beater was not inside the single frame, so when that happened that changed the feel to something that was more realistic and expressive yeah, and I have to nerd out and say that was the 5002 invented by Dwayne Livingston who is actually on Facebook and is just like a super nice guy and you know, which is just so cool to be like it's just a drummer like us who came up with that the history of drums is filled with people that were just dudes just innovating exactly, yeah that's the coolest part alright, so then what is our, so like if we're in 80's getting into the 90's, maybe we take a second here and just talk about some of the lines that are out because then this is getting into more like you know modern era of drums so there would be like you take it away but it would be, you know what's the lowest to the highest they had on the market then as far as the range of drums well, so Star Classic was born in 1994 so that's the kit you have and that was our high end kit at that time and going through the Star Classic performer then was also developed and that's with bird shells the I want to say rock star kit with different orientations, finish orientations and then swing star and then imperial star so that basically was what we were looking at and then obviously out of Star Classic so much kind of flowered out of that, Star Classic Bobinga, Star Classic Burj Bobinga and now we have Star Classic Walnut Burj and a brand new series Star Classic Performer which is Maple and Burj so that's that's new for 2021 so you know there's a lot there and then in 2013 we launched the Star Series which are handmade in Japan at our Japanese Katsuki factory and that's the epitome of our high end so that's Star Bobinga and Star Maple and Star Walnut drums come out of there so that's kind of where it sits and they're just really gorgeous instruments so it's cool for us to have that and we did then also in that time period lots of development on snare drums Star Phonic snare drums the artist signature pallet and then SLP snare drums so that as you said it's sort of the modern product offering so from that you know side of things that's really that's where things were you know where we are now we also have Superstar in the line back as a name different than the original Superstar drums that were from the late 70s and 80s but yeah yeah what is the deal with SLP which stands for sound lab project what is the what's the story with that because I've played some I think I played a kit at at PASIC last year or the year before I've lost track of when things were normal at this point right yeah 2019 I think 2019 yeah so but they're just awesome like so what is what is the sound lab so that's exactly what it is so it's evolved from our snare drums which the concept of the snare drums was to develop snare drums that were each unique and different not so conventional in a way like here's your brass 6.5 and your brass 5.5 and your brass 5 you know 5x14 or whatever and here's your steel and here's your wood that's really the traditional way that snare drums have been offered in the market so the concept that Tama came up with was to create kind of boutique differentiated snare drums that each have a different voice within the SLP line so one might be brass one might be aluminum one might be maple one might be walnut and they're super accessible price points that each have a unique sonic personality that's cool and you know jumping around here I'm just like looking through the website the Tama website and I just think that there's a a heritage of like I think things got a little far out in the 60's and 70's which I love with the finishes but there's still very cool finishes to the Tama drums I'm just looking there's like a beautiful green kit they're very unique and I say the 60's and 70's if anyone looks at those old kits I mean they are just like there are the satin flames and stuff it would be cool if they brought that stuff back but that being said you guys have very unique and beautiful finishes and I think I saw online a video of someone doing gosh what was it it's almost you're going to know right away the name of it but it's like a red kind of like streak. Yeah, phantasm lacquer oyster. And there was a video of them creating that and it was not just print out you know a wrap and throw it on it was like hand painted. Yeah, that's that's part of the so our factory you know it gets into manufacturing stuff so we have a texture star in Japan and then most other drums are coming from our Tama owned factory in China which we started in about 2004-2003 so that's our own factory that we own and we develop our projects and products and then take that information and then go implement it in China. So we have our painters there are really skilled and they hand paint shells and that's what you're seeing and that's what's creating these beautiful lacquer oyster finishes that we're able to offer within our our star classic line that are super just super compelling and different and you know interesting and intricate and really good price points. I mean it's kind of it's kind of incredible. Yeah, there was a when I was in high school I worked at Guitar Center and there was a Pink Sparkle Bubinga kit there that I would just sit on and play because I mean that was sort of the downfall of retail stores where minus people dropping their kids off to be babysat by a drum set and then they'd go over to whatever stores next door I would just be sitting there a lot and those drums, the Bubinga line I remember just when it first got there it was just this like holy grail of a drum set it was just so like present and it just felt like honestly one of the most out of all the drums there it felt like one of the most professional high-end drum sets I've ever played at that point. What is Bubinga? I know it's obviously a type of wood but maybe a little little info on that. Yeah, so yeah awesome. So we were somehow the company associated most with Bubinga. Yeah it is a type of wood. It comes from I believe Africa and we just started using it and implementing it and then realized it had super deep low tonal qualities to it and making a whole drum set out of Bubinga just created a different sonic imprint of a drum set and rich and fat low-end they do sound awesome. I remember when those came out and I checked out a kid and I'm like I'd never heard a bass drum sound like that. Just super dense and present but with this huge rich low end. So that's something that you know we cultivated a lot and we still offer Bubinga on the star line it has been removed on the star classic line due to the cities trade restrictions of endangered woods even though the wood sourcing that we use is cultivated wood and farmed wood and sustainable. It's just complicated to get the clearance of the wood all the different processes that you have to do to get substantiated and cleared it's just it's a big administrative hurdle so we decided that we're going to move away from that and at the same time it had been in the line for quite a long time so that's why we now have walnut birch and maple birch and different drums that do different things sonically because you know we always like to keep things fresh so it's kind of it was a timely issue and also kind of forced our hand due to the trade restrictions of endangered woods so. Yeah sure and man you saying keeping it fresh just looking on the website basically on every kit you click on there's just some like little innovative detail where it's not really changed since the 70s where it's still just really running forward with the best with innovative ideas and things to keep it interesting especially with the hardware obviously the drums are beautiful but just the little like details I mean you guys are so. Yeah Starcast system is to me the most beautiful and then the most useful suspension system in the market because it's suspended we don't touch any tension rods it's all done through the hoop and the hoop has extra holes to suspend the drum so as far as in just the way it's designed there's no stress on the shell there's really no stress on the hoops so the drums stay in tune they resonate fully and it looks incredible it's such an integrated and lovely silky smooth sexy setup it just looks incredible and I I've been a long time admirer of the Starcast system and just really really appreciate that design. Yeah man that's so cool so all right as we wrap up here is there anything I know the world is kind of upside down right now when things are a little slowed down but is there anything that you know the Tama die-hard fans can be looking forward to in the future that you'd maybe want to talk about here or anything like that yeah okay so yeah this interesting your podcast is going to live on forever so so this is this is for the record we're in the COVID sort of the 2021 yep so what was that? Read all about it how scared? Here we are but yeah it's been a challenging time to product develop because we just because we haven't been able to travel and our R&D team can't go to all of our factories and go to our Chinese factory and you know check out samples so it definitely has hurt the flow of our development but at the same time it's allowed us to sort of work closer together and as I mentioned earlier we do have a new star classic performer series that is at the the easiest entry price point for star classic and it's they're maple and bird shells and they sound fantastic they look fantastic and that's brand new for 2021 so feel free to check that out there's information on the web now and and we just you know we continue to evolve our product lines and you know you're always going to see new things from Tama it's just part of our DNA and it's part of what we do as a company to keep innovating and that's really an ethos of our company is to continue to innovate and bring fresh things in the market because we feel that you know drummers want it they look forward to it and we're just feeding the curiosity so that's what we're going to keep doing that's awesome well everyone can find Tama obviously just by you know googling it or go to Tama.com Tama.com I think to this day still Tama is the the strongest name in drums as they as they the slogan says I think that's very you know well-earned and you guys continue to push forward and and I I always try and be unbiased with everything but I do really like Tama and I think they're great drums and have you know kind of one of my like I said my you know it was a great drum set to buy and I loved it it was amazing to have that star classic kid as a kid so yeah we're fans of the industry you know and we love watching you know what the other brands do and you know it's a friendly competition for sure but you know the industry is exciting and innovation happens in obvious places and not obvious places so it's fun to keep up but yeah we're humbled and you know we're just going to do our thing and keep bringing product into the market that hopefully inspires and you know as as you said it's just you know you're the drummer out there and and you're the ones expressing so you know what is it that we can do to help express that that's really our that's what we do and before we end I want to so I have this awesome little history of Tama book that they that you guys sent over and I want to give a shout out because I talked to him on the phone very I would just say lovely man is a good way to put it very very nice guy I want to say a thank you to Mitsuaki Shimada or I think his friends call him Mike for just kind of really we talked on the phone for a while and he was at the post office trying to send me a book but there was a storm and he couldn't get it over to me and just he had the great idea I've made the mistake before of I made a call to someone in Germany and I ended up having a hundred and fifty dollar phone bill where Mike was smart enough to say let's do it over you know Facebook or zoom and I'm like you know you only you only learn from your mistakes you know and just a little fun side note there but thank you to Mike and yeah Mike had a long career important career with Tama all those stories that we talked about from the 70s and 80s Mike was at the forefront of all of that so he was you know huge guy for the brand and I say that was because he recently retired and gave his life to the brand and you know I appreciate you you know appreciating him because it's people like Mike you know that you know it's the collective benefit of their work that brings it all to motion so shout out to Mike. Absolutely shout out to Mike so alright and if you're listening to this John and I are going to do a quick probably conversation about some other Tama stuff I have a couple you know smaller kind of maybe not so drum related questions I want to talk about the ventures and the electric guitar you know fad that went through Japan which I thought was fascinating in this book but so if you want to hear that little bonus conversation head over to patreon.com slash drum history podcast and you can pay you know two bucks or whatever and join the patreon and get these weekly bonus episodes so on that note John I want to thank you so much for coming on the show and sharing your you know vast knowledge and passion and love for Tama with me and the listeners it thanks for having me Bart I'm glad we could connect this up and really enjoyed talking about you know the thing we love talking about so thank you. If you like this podcast find me on social media at drum history and please share rate and leave a review and let me know topics that you would like to learn about the future until next time keep on learning


On September the 8th, we're gonna rise together as a movement to say that the science is clear and that it is enough. No new fossil fuel anywhere. 100% renewable. Fast enough as well as just.


So finally this is what Sulfuraphane looks like and I've been reliably told By my hair and health expert milder spinest that Sulfuraphane is what's Sulfuraphane again? Look at that. It's really good. Mm-hmm So I haven't tried it yet This this is Five six days worth and my hair expert is run off So this is what we have. Okay, I'm gonna try this for the first time It smells like sprouts. I do grow Brussels sprouts and it's quite me.  So How is it Is it good, okay, that's good. Oh jeez. That's good It's so bad, right? It's really lunges. I'm so good.  So you don't taste it as much So that's how I started to take it or just like do one shot in like water and then just like basically like you're taking a shot of like tequila or something just like Like that and then wash it down with something sweet. This is how I do it Nasty, yeah, it is so nasty. This is what scares all of the campus cells because it tastes so pretty much bad Yeah, you know, why isn't anybody talking about that? Why is anybody not talking about how bad this tastes? Yeah, well, yeah, I'm glad that it validates my the ones that I made They were pretty I'm still gonna eat it though. Oh, yeah, absolutely Tell me that's how you can buy cancer, you know, so But yeah, if you're gonna make this just be a way it tastes really really terrible. It really does taste terrible Be tech look at the spark it tastes it's kind of like a It's unlike anything that I've tasted before So I've tasted a lot of stuff Vegan so, you know So, yeah, when I was vegan I like to compromise sometimes on taste I know that's quite controversial. They'll be vegan saying like no, you can not really taste the things which you can but I don't know a vegan cheese though. I've had some previous cheese But this is basically the worst thing. This is really Yeah, it tastes terrible But you know what I'm a grown-up woman I spent five days rinsing this twice a day and just it's so fiddly to actually grow the summer eat it because I'm the seeds are Replacing yeah, well you gave me the seeds so I didn't have to pay them but because I spent my time in it I am gonna eat them. I have her That you freeze them it increases the bioavailability and hopefully makes them more palatable No, it makes them worse. It makes them worse. It really does. Okay, but I'm going to freeze them. Yeah, that's my last film And also makes them last longer, obviously Yeah, but yeah, it's pretty and I'll report back to you in 60 years until you if I had cancer or not


Hello and welcome to this session. Let us discuss the following problem today. Show that the function f from r to r given by fx is equal to x cube is injective. Now let us write the solution. Given to us fx is equal to x cube. Let x1, x2 belongs to r then f of x1 is equal to f of x2 which implies x1 cube is equal to x2 cube which implies x1 is equal to x2 on taking cube root f is 1, 1 from r to itself and hence f is a injective function. If you understood this problem, bye and have a nice day.