Musical Mathematics
on the art and science
of acoustic instruments
●
Table of Contents

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© 2000–2013 Cristiano
M.L. Forster
All rights reserved.
www.chrysalis-foundation.org
Musical Mathematics Advance Orders
2005–2009: 117 advance orders,
from
24 different countries;
138
copies ordered.
AUSTRALIA
Please keep me informed as I would be interested in obtaining a
copy of your book once published.
Regards
-B.
* * *
Dear Board of Directors,
The publication of Cris Forster’s book Musical Mathematics
sounds wonderful. I’m a pianist trained in the classical and
jazz tradition and over recent years have been looking for
greater satisfaction in the world of music. An interest in
alternative tunings has led me to your site.
A new chapter in my musical journey has begun and I would love
to reserve a copy of Cris’s book. How does one do so? I live in
Adelaide, South Australia, Australia. I understand that postage
and handling need to be added to the cost of such a purchase.
Well done all of you. I look forward to your reply.
Yours Sincerely,
-P.
* * *
I am writing to express interest and support for the
publication of Cris Forster’s Musical Mathematics: On the
Art and Science of Acoustic Instruments. I am a lecturer as well as a postgraduate student
in the School of Music and Drama, Faculty of Creative Arts,
University of Wollongong, NSW 2522, Australia. As a composer,
teacher and student of tuning, I am sure this publication would
be an invaluable resource for musicians interested in tuning
theory and its practical applications.
Kind regards,
-T.
* * *
My name is [...]. I
have recently made a bass marimba by trial and error and I am interested in
obtaining a copy of Forster’s book. Please contact me.
-T.
CANADA
Dear Reader,
As
a professional musician, academic, educator, instrument
builder, wholesale and retail distributor, repair shop and
manager of one of the worlds greatest private collections of
percussion instruments, that of the group NEXUS, I simply
cannot imagine a more useful and essential project than the
Chrysalis project to publish Musical Mathematics.
This project promises to bring together, in exquisite detail
all the information that brought the end of the last
millennium, a world that experienced Cage, World Music, Partch,
a revival of baroque music, Contemporary Gamelan, the Glass
orchestra,... and countless other disparate influences.
I
see this project as not only an exceptional overview of the
world history of tuning systems in a comparative analysis, and
a practical theoretical technical manual and most importantly a
foundation with which to look forward, into the future, opening
doors that we would otherwise not see but for the influence of
this presentation. I strongly urge all interested parties to
support this project.
Please put me down for 3 copies.
-A. (M.Mus)
Woodshed Percussion Inc.
* * *
To Whom It May
Concern:
I would just like to
let you know how beneficial Mr. Forster’s chapter on “Simple Flutes” was while I
was completing a high school physics project. The task was to build and demonstrate
a musical instrument and my choice was the flute. When the time came to calculate
the locations of the tone holes for the flute, Mr. Forster’s page was my primary
resource – it had absolutely everything I needed to know! As well, the presence of
both theoretical and practical examples made it far easier to understand the at
times complicated material covered.
I am currently in
Grade 11 in Toronto, Canada. I play piano and violin, and am planning to pursue a
career in engineering. Music and mathematics are my two foremost passions, and I
would love to see this book go to print!
Thanks again for a
superb resource!
Yours truly,
-E.
* * *
Dear Chrysalis Foundation,
As an instrument builder and professor of music composition, I
would very much like to see Musical Mathematics in
print. Please accept this message as my advance order and feel
free to use it in any grant applications that you apply for. In
addition to a copy of the book for myself, I will ask my
university library to purchase a copy as well, so you can count
this message as two advance orders. Please let me know when the
book becomes available.
With thanks and best wishes,
-J.
School for Studies in Art and Culture: Music
Carelton University
Ottawa, Canada
* * *
Dear Sir,
I would very much be interested in seeing Musical Mathematics in print. I am
a professor. My affiliation and address is provided.
-K.
Department of Electrical and Computer
Engineering
University of Calgary
* * *
Dear Cris,
Praying that it comes through for you so I can buy your book.
Sounds amazing. It will probably do for modern cats what
Helmholtz did for Harry Partch!
Cheers!
-L.
* * *
Greetings,
Yes, count me in on your
grant proposals if you need more names. Please keep me on your mailing list when
this book is published. I would like to get a copy.
-R.
Regina Symphony
Regina, SK Canada
* * *
Dear Chrysalis Foundation,
As a qanun player, I read about the Canon with
interest, and then bumped into the Partch connection.
I’m very glad that Musical Mathematics has
been written. I expect it will be an invaluable resource for everyone involved in
creating new sound. I plan to put it in my frequent reference shelf next to the
OED.
I look forward to hearing some of the instruments
eventually, either in SF or Toronto. We are working on a multidisciplinary centre
here and we’d love to host Cris if he ever comes through this way.
Best,
-T.
CHINA
Dear Sir:
I am writing to
contact you for Musical Mathematics.
My name is [...], a
visiting scholar from China and now in Department of Ethnomusicology of UCLA. Told
by a friend, I knew that you are compiling Musical Mathematics, which I hope
to have. In China, I am a associate professor in China Conservatory of Music,
teaching The History of Chinese Music, and a member of the council of China
Temperament Academy. My dissertation for M.A. is [...] which was published in 1992
and obtained the first national prize in 2002. Besides, I also published many
articles on temperament.
Temperament is a
highly developed study in China and I have been being interested in it, so I hope
to have Musical Mathematics very much. Would you like to contact me
before it is printed? I will buy two copies.
Thank you very much!
Best wishes.
Sincerely yours,
-L.
CROATIA
Greetings from Croatia! I am looking forward to your book; your
work is so inspiring. Wish you all the best.
Impatient one.
-I.
ENGLAND
Dear Cris,
Just a brief email to
support your plans to get your book in print. Lots of us, myself included, have
been looking forward to this book for years and I wish you good luck in getting it
into publication.
-B.
Senior Research Fellow
in Music
Dartington College of
Arts, England
* * *
What a fascinating
prospect this book is.
If I could I would fund it... But instead, could you put me down for three copies
when you publish?
Good luck and I hope you
can bring it out soon.
The Chrysalis Foundation web site is extraordinary and inspiring. [...]
-K.
Architect
* * *
Dear
Chrysalis Foundation,
I read the excerpts of Mr. Forster’s excellent book on the
mathematics of tuning. I do think it deserves to be published -
a very informative and useful book.
-M. B.Mus (Hons); M.Mus; Ph.D; PGCE
* * *
Hi There,
I came across your site linked from here:
http://www.oddmusic.com/gallery/om07100.html
I am extremely interested in a print copy of Musical Mathematics.
I am based in the UK.
I’m a sound engineer; I run my own recording studio - Beliefspace Studio in
Plymouth.
I have an honors degree in Media Lab Arts from University of Plymouth.
I’m also a qualified tutor (7407 and Cert. Ed. qualifications) and have worked part
time for 4 years at Deep Blue Sound in Plymouth, which is affiliated to The
University of Plymouth, Plymouth College of Further Education, Estover Community
College and Plymouth College of Art and Design. Here I teach basic music and basic
to advanced sound engineering.
I also build (strange) instruments and ‘noise makers’ - these are a range of
acoustic, electric or computer based instruments. I am interested in the where
these disciplines meld - for example: Acoustic control interface into electronic
interfaces into a computer or vice versa - computer controlling and acoustic
instrument. I plan to start a PhD doctorate based on these systems over the next
few years at University of Plymouth.
I have also written several short eBooks (pdf) on music, to do with learning modes
& scales on guitar.
I am currently putting together a small eBooklet (pdf) on how (Western) musical
notes relate to Control Voltage and control systems for electronic instruments.
This book will be an excellent resource for all instrument builders alike. The
contents table is looking excellent.
Many kind regards and good luck with the grants, funding, etc.
-S.
* * *
Hello There,
I am a young British musician, and I am very interested in your
book Musical Mathematics. I believe your thoughts on
tunings and new music to run true in my own compositions as I
find myself only able to write in alternate tunings.
My name is […], and I would love to see this book in print, and
to own a copy of it.
-W.
FRANCE
Dear Musical
Mathematics [writer],
I would like to know,
when the book On the Art and Science of Acoustic Instruments would appear. I think it’s contents could interest me. (I am a
mathematician and an amateur in music.)
I thank you for your
attention.
Yours Faithfully,
-E.
GERMANY
Hallo,
As a teacher at a German school, I would like to see Musical Mathematics in print.
Thank you very much!
-H.
* * *
Hi,
I’m [...], teacher of ear training, tuning, music theory and
teacher in the (Experimentelle elektronische Musik) of the Academy of Musik in Würzburg, Germany.
Please let me know the printing of Musical Mathematics. I belong to the buyers!
Best wishes for this great adventure!
-H.
* * *
Cris,
Many thanks for your
comments, and please do keep me posted. I am yet far behind you, having just
started to read myself into the topic, and at the moment I am reading Farmer’s
“A History of Arabian Music” (London 1929, reprint New Delhi
2001) and Kiesewetter’s
“Die Musik der Araber”. The latter was published Leipzig 1842
(facsimile by Saendig Reprint Verlag, Vaduz 1983), but is astonishingly precise and
specific about the mathematical side of Arab tuning. But it also proves that a
modern text like your forthcoming one is badly needed.
-M.
* * *
Dear Sirs,
According to your
announcement on the Chrysalis Foundation website, I should be glad to hear from
you, when Musical Mathematics will be available in printed form or as a
downloadable (against fee, of course!) pdf-file.
I’m physicist but also
instrument builder living in Germany.
Many thanks and
greetings,
-R.
GREECE
Yes, I am also
impatient to read the Musical Mathematics treatise, as soon
as possible.
-C.
Film Director, Music
Producer, Author, etc.
* * *
Dear Chrysalis
Foundation,
I
am a high school student heading towards the last year of my
International Baccalaureate Diploma. I must mention how much
Cris Forster’s manuscript has helped me with my Extended Essay
which is on flute acoustics - it gave me great insight and
understanding.
Although I haven’t
read any parts of this manuscript apart from sections of Chapter 8, from the
contents list it looks very wide in scope and thorough in detail; I would really
like to see this book in print.
Best wishes for
publication,
-I.
* * *
Hello Cris,
I am [...] from
Greece. We had contact before 2 months about. I am contemporary music composer and
I am interested about Musical Mathematics.
Please send me e-mail
as you are ready to sell the book and inform me about how can I pay you.
Thank you very much.
-K.
* * *
Dear Sir,
I interested to
acquire the book Musical Mathematics. I hope so that I will find answers of
certain questions about flute dimensions and calculations. I will like to make my
own flute! I am flutist and I teach in national school of music in Tessaloniki in
Greece.
-N.
INDIA
Hi,
I am a music student from India. I am very impressed with the
depth of knowledge shown in Mr. Forster’s writings. I would
like to express my support for this cause. I think it is very
important to preserve this history and cultural heritage. It is
also a compendium of mathematical knowledge of musical
structures across the world’s cultures.
Regards,
-V.
IRAN
Hi,
My name is [...]. I have a Ph.D. in electrical engineering. I
am interested in researching musical instrument modeling. I
would like to see Musical Mathematics in print.
Best regards,
-A.
ISRAEL
Hi,
I’m very interested on
buying this book. I’m a qanun and piano player from Israel. I’m a student in the
faculty of music in Haifa, and my main interest is in Arab music.
Looking forward for
your book.
-A.
ITALY
To whom it may
concern:
I’m writing because I would like to see Musical Mathematics
on paper (and buy it, of course). I am a musician, as you can
see by visiting my web site. So, please let me know when it
will be available.
Regards,
-C.
* * *
Hello Mr. Forster,
Thanks for your kind
and early reply.
I have already
realized a plastic pipe by drilling the holes and adjust them with the tuner. Apart
the problem you mentioned to play all the bagpipe together it seems to work well.
Next step will be the realization of an identical wooden pipe.
This method, of trial
and error, was the empirical method I approached to understand how tone holes
works.
I have begun to read
chapter 8 of your book. In section 1 you say:
...On the other hand,
we may realize a given tuning by making a flute according to another sequence of
equations...
On this way I would
like to learn more about wind instrument. I hope, upon reading chapter 8 (or your
book, when available), be able learn where to place the tone hole on the pipe
without destroying my beautiful bagpipe.
I am not an instrument
maker or researcher and furthermore I am not experienced about wind instrument. I
want just to play my bagpipe and learn more about its behavior from mathematical
point of view. All the material get from your site will be for personal use.
As you mentioned,
bagpipe need continuous tuning for 4 pipes at same time. Because I am a beginner
player, I hope that to learn more about modeling and mathematics of wind
instruments will help me to overcome any related troubles.
Thank you very much
again for your support and any suggestion you would address to me.
Enjoy your weekend.
Regards.
-F.
* * *
Dear
Sirs,
I am a
professor of physics at Pisa University in Italy, who since
some years started a teaching program in the physical aspects
of music, finding it to be a rather successful teaching
approach.
I recently found the information on the Musical Mathematics
book on your web site, and I would like to know whether this
work - which from the excerpts appears to be a very interesting
one and a valuable source of teaching material - is available.
In case it is not, following the information on the site I
would indeed support its publication as a valuable contribution
to the field.
Regards,
-M.
* * *
Dear friend,
Excuse me if my
English isn’t good. I’m Italian and writing you about your e-pages of Musical
Mathematics. I’m a sales engineer of a precious metals company and play flute
for fun from more 20 year. I like mathematic, physics and chemistry. A dream born
in my head few month ago: make my flute, only one for me! I have materials (gold,
silver, platinum, etc. etc.) and technologies of metals but I haven’t know-how for
to design flute (head joint also), to calculate dimensions and best hole tune
position of flute...
I have some questions
about but I haven’t who can request to them. Now, I found your e-page and I think
you can help me. In your page you write:
“If you would like to see Musical Mathematics in print, please
write...” OK, I writing you for to know how can to receive your book or
CD Musical Mathematics: On the Art and Science of Acoustic Instruments.
I have:
1) precious metals
2) Metals technology
(micro-fusion, wax-lose tech.)
3) one old flute for
model (but I prefer to make a modern flute and not to replicate old model...)
I haven’t:
1) design of modern
flute
2) how to find
location and dimension of tune holes
Can you help me? If
you can’t, can you show me where I can to find a helper?
Thank You.
Regards,
-M.
LITHUANIA
Dear Cris,
I found your book Musical Mathematics. Can you tell me how I
can order a copy? I am very happy to find this material and
the work you are doing. It is really amazing...
Greetings,
-E.
Composer
THE NETHERLANDS
I
am interested in a printed copy of your book.
-H., The Netherlands
Artist & Amateur Instrument Maker
NORWAY
Hello.
My name is [...]. I am a 28-year-old man from Arendal, Norway,
who would very much like to see Musical Mathematics in
print.
Regards,
-S.
PAKISTAN
Hello,
I would be very interested in the print version of Musical
Mathematics. After going through some of the content being
published, I cannot wait to get my hands on the wealth of
knowledge stored in this book. I wish the Chrysalis Foundation
all the best and good luck in successfully launching this
publication.
Regards,
-R.
PORTUGAL
I
am [...] writing from Portugal. I am a teacher, and I am
studying in Lisbon University about the relationship between
Math and Music. I would like to receive a print copy of
Musical Mathematics. Thank you.
Sincerely,
-M.
PUERTO RICO
Hello.
We manufacture cuatro
puertorrique. This is a five double steel string acoustic wood instrument.
We are interesting in
create school of luthiers to teach Puerto Rican children how to manufacture and
tune our folklore instruments.
Our interest is to
explain student with mathematic and physics how to manufacture the cuatro.
We are interest to buy
your Musical Mathematics book.
See attachment.
Thanks,
-J.
SPAIN
Hi
Cris.
Nice to talk with you again. [...] I am interested to buy your
book titled Musical Mathematics.
Please let me know how I can buy the book. I hope that your
life is wonderful. [...]
-M.
* * *
I
would like to see Musical Mathematics in print.
I am an amateur builder of replicas of old musical instruments
and I find it very difficult to obtain technical information to
modify designs, except by methods of trial and error.
Please, let me know when your work will be ready to be shipped
to Spain.
Many thanks.
-V.
SWEDEN
Subject:
“Grant Applications Support”
Hi
there.
I’m [...].
PhD Student; MidUniversity of Sundsvall, Sweden.
Inventor in all fields, sound analysis is one.
Antenna designer; 4 patents in that field only.
Human factors.
-S.
“If you would like to see
Musical Mathematics in print, please write to us so that we
may include your emails and letters in our grant applications.
Kindly let us know. . .”
SWITZERLAND
Sir,
Very interested [in] your
book. I would like to know if you achieved to print it. In that case, I would be
very interested in buying one. Could you tell me about it ? Thanks in advance.
-E.
(Assoc. Prof.)
Ecole
Polytechnique Fédérale de Lausanne
* * *
Dear Mr. Forster,
I would like to order a [copy] of your
monumental work... ...we hope that you [will] succeed in printing it.
Sincerely yours,
-R.
TURKEY
Dear Sirs,
I am interested in the book Musical Mathematics to study
the tunings and the makam scales of Turkish music, as I am
studying the nay flute.
Sincerely,
Dr. -D.
Specialist in
Psychiatry and Psychotherapy
* * *
Dear
Sir,
I am so glad
to read about the book
On the Art and Science of Acoustic Instruments will be published in 2006 end of spring. First of all I would
like to congratulate the publisher and writer(s) due to this very important
project. Secondly, if it is possible I and my staff want to be among of your
academic-customers for the publication either. I will appreciate if you inform me
about circumstances of subscription or to order the book in a near future.
Thanks for
your very kind attention and interests indeed.
Best regards.
-R.
(Assoc. Prof.)
Turkish Makam
Music Theory and Qanun instructor
YTU Music
Department
Besiktas –
Istanbul
* * *
Dear Authority,
I visited your web
sites...
Musical Mathematics pages are really effective... Congratulations...
-O.
UKRAINE
Hello!
I read about plans in publishing Musical Mathematics
manuscript and decided to write you a letter.
I work in telecom industry and I’m musician and instrument
maker as my main hobby. I mainly concentrate on
ethno-instruments as instrument maker, winds first of all. As
musician, I study and play Western stringed (such as guitar,
violin), ethno-instruments (winds and percussion), woodwinds
(Boehm flute, clarinet, sax).
As I have MS degree in applied physics, I am very interesting
in physics and mathematics of music and musical instruments,
deep understanding of which would help me a lot in making
instruments. I’d be very happy and would order a book without a
doubt if such a comprehensive work would be published!
Thanks for your work!
-Y.
UNITED STATES
Concerning Mr. Forster’s Musical Mathematics, I would
like to know if that book is already available and, in such
case, how can be it ordered and paid. My best wishes to your
Organization and specially to Mr. Forster for his excellent
work.
Thank
you.
-A.
* * *
Dear
Reader,
My name is [...]. I am a Freshman at Reed College in Portland
Oregon. I am very interested in non-tempered tunings, both
Western and non-Western, and hope to start building new
instruments for which I can compose soon. Right now, however,
I’ve been working only with pre-existing instruments, primarily
strings, because the lack of frets makes them a practical
choice. I believe that Mr. Forster’s book would be an
invaluable resource to an aspiring instrument builder such as
myself, as one of the largest practical concerns I find with
instrument building is a lack of proper or complete
information. I hope to see Musical Mathematics in print
soon and look forward to buying a copy once it comes out. Thank
you for your time,
-A.
* * *
Hi, my
name is [...]. I am a composer/guitarist/student/tuning fanatic
contacting you in hopes of possibly increasing Musical
Mathematics’ chances of publication. From what I have seen and heard,
anything written (and made) by Cris Forster must be heard.
-A.
* * *
I am
very interested in seeing Musical Mathematics: On the Art and Science of Acoustic Instruments
in print. I am a student, a musician, and an aspiring luthier.
I have also taken an interest in homegrown instruments of the
type the Chrysalis Foundation is based upon. Unfortunately, I
have no institutional connections, unless you can figure out a
way to make the printing of the manuscript beneficial to the
United States Army.
I would be more than happy to have my name and any other
pertinent information included in grant applications, and I
hope to be able to purchase a copy of the manuscript within the
next few years.
Best of luck.
Cheers,
-A.
* * *
To
whom it may concern:
I am
writing this letter to express my support for Cris Forster’s
book. I am a violin student at the Mannes School of Music, and
I have always been interested in the science behind the music
that I play. I would be very interested in seeing Mr. Forster’s
manuscript in print.
Sincerely,
-A.
* * *
Hi,
I am a builder professional concert Bansuri bamboo flutes. I am based in Maryland.
The subject and the content Musical Mathematics is absolutely enthralling for me and I would
love to see it published.
Thanks.
-A.
* * *
Hi,
Please contact me when the book is published. I am a music
editor and composer very interested in non-tempered tunings. I
am particularly interested in Al-Farabi.
Thanks,
-B.
* * *
My name is [...]. I am a
musician, both studio and live performance oriented, and a teacher of music of all
sorts. I also have dabbled in building guitars. I am currently attending the
University of Memphis in Memphis, TN. I am a senior in college pursuing a degree in
Recording Engineering Technology. I am absolutely thrilled at the information that
is available in this manuscript. It would be a certain tragedy for this wealth of
information not to be available in print for whoever wanted it. If it doesn’t go to
print, at least let me know how I can get a hard copy.
-B.
* * *
Dear Cris,
I’m
delighted to see that your plans for self-publication are proceeding, and that you
think you will be able to publish your whole book for under $90. Please put me down
for a copy. I hope that all is going well with you.
With best wishes,
-B.
Professor Emeritus
Department of Mathematics
Stanford University
* * *
Hi,
I read some of
Musical Mathematics online. I am a bassist in 8th grade (going into 9th). I
also play a little guitar and keyboards. I am interested in seeing Musical Mathematics in print. I go to Rye middle school and am
involved in the music program there. Is it possible for me to buy the book you show
excerpts of on your website? Please send me an email at [...]
Also, I have a
question. Is there a device or method that would allow me to tune the bass to C=256
instead of C=263 (A=440). C=256 is the way instruments were tuned in the classical
era and I would like to be able to tune a bass that way. Any help would be greatly
appreciated.
Thank you for your
time.
-B.
* * *
I would love to
purchase a copy of your book when it becomes available. Is there a waiting list I
can sign up for?
Thanks.
-B.
* * *
Hi - Hoping you will go forward with
the publication of the manuscript - the sample of flute holes reminds of the
inspiring work of Benade: Benade, A.H.,
“The Physics of
Woodwinds,”
Scientific American, October 1960.
Please publish it, and count me in
for a copy.
Keep up the good work.
-B., MD
* * *
I like to see Musical Mathematics in print.
Thanking you...
-C.
* * *
Hi,
I am an amateur cellist and instrument designer/builder. [...]
I would definitely like to preorder your book [...]
Please let me know when it is available.
Thanks,
-C.
* * *
I have found the sections out of Musical Mathematics to
be very interesting.
The sections that I have looked at, Chapter 8, Simple Flutes,
and Chapter 10, Western Tuning Theory and Practice, Part
VI, Section 37: Just Intonation is great. With both
history and actual theories presented, and the interim
transitions in between, has helped me understand the basics of
both the trumpet, that I played some years ago, and the flute,
which I have taken up recently.
Being a professional engineer, I enjoyed the derivation of
equations.
Keep up the good work,
-C.
* * *
To the Chrysalis
Foundation:
I am a student at Sam Houston State University in Huntsville, TX. I stumbled upon
this website while pursuing my personal studies in music. I am thinking about
turning music into my major or minor. I am also an aspiring luthier; however, it
will be some time until I can afford setting up a shop. This manuscript seems to be
a magnificent accomplishment that would expand my musical knowledge. It would be a
priceless resource in my education and aspirations.
Sincerely,
-C.
* * *
Greetings!
I’m a graduate student of mathematics, and have played piano since a young age. I
learned all the technical details of music notation and scales, sometimes curious
of why some things were the way they were, but in mostly a dogmatic manner - the
focus always being “Practice, practice, practice! Perform, perform, perform!”
Despite my curiosity and the fact I really loved the music, I realized I wasn’t
deriving all that much enjoyment from playing it, and concentrated more on
my non-musical studies.
Whenever people hear of me doing math and having musical experience, I often hear
“math and music go together” (in apparent contradiction to that other bit of
“common knowledge,” that math is left-brain and art is right-brain - this is
something I don’t believe is true at all, but that is another story). I never could
figure out exactly what they meant by that. I guessed they were noting the fact
that there seems to be a higher proportion of musically talented people among
mathematicians, or perhaps that music possesses, besides beauty, a certain logical
structure which can be analyzed. The influence of college roommates more musically
talented than I (who all worked in scientific fields!) helped me revive my
interests. I discovered a world of interesting things, answering questions like how
the Western system of music came about, and introducing concepts such as tunings
and microtonality. I never realized just how much math and music really do go
together (I don’t think very many of the people who say so realize it in this
way!).
In short, I am very glad that you are writing Musical Mathematics, and would
love to see it in print. The closest thing I have looked at (not fully read,
though) is Helmholtz’s classic, and I’d been hoping to find something with a more
modern perspective. Your book looks to be it! Please keep me posted.
Thanks!
-C.
* * *
Hi,
I am interested in the
possibility of a book version of Musical Mathematics; please include me on any updates.
Thanks.
-C.
* * *
Hello Cris and all at
Chrysalis,
I understand that the
Instruments are not for sale, and that you do not accept commissions to build
instruments. Since they are quite beautiful creations in both sound and vision, it
certainly inspires professional curiosity, inquiry regardless of their
“purchasability”. The idea of exploring
“just intonation” and in creating my own instruments for
compositions has recently grabbed a hold of me and won’t let go, as I’m sure you
must have experienced most profoundly.
My question is a request
that you point me to sources that can help me build my own instruments, much like
you have. Or, if you know of any available tutorials or designs for the composer
(such as I) that has no prior experience with the actual building of an instrument.
I of course will be looking forward to the publication of your book in 2006 as
well.
Thank you in advance for
any consideration you may afford me and congratulations on creating music in your
own way.
-C.
* * *
Hi Cris,
Thirty years working on Musical Mathematics? I’m interested in
Chapter 10. I notice that you have a bibliography. I am
currently writing something like Chapter 10 purely through
introspection. [...] I am interested in a copy. [...]
-D.
* * *
Hi!
I just discovered your website. It’s great! I look forward
to the publication of Musical Mathematics and definitely want to
order a copy. I teach high-school math and have a strong
interest in music theory and the math and physics thereof.
Thanks,
-D.
* * *
Dear Sirs,
Although I would mostly like to read details about [flutes] and
their construction, I would certainly purchase the entire book
if nothing other than for reference value. But, as can be seen
on your webpage, the content goes far beyond this simple
requirement. Well, I guess I’ll just say it: It’s the missing
link of musical details, previously unheard of to the laymen,
and able to fill in all aspects of musical theory.
Kudos...
Best,
-D.
* * *
Greetings,
I am a luthier, a musician, and a music therapy student and I
would definitely be interested in purchasing a copy of your
book Musical Mathematics: On the Art and Science of Acoustic Instruments
when it is
published.
Best Regards,
-D.
* * *
Yes, by all and any
means; I would like to see Musical Mathematics in print.
I would definitely buy this work when it arrives in print.
I am a flutist of forty years and a manufacturer of professional flutes in precious
metals and wood.
-D.
* * *
Hello my name is
[...]. [...]
I’m a musician of 12 years and I’ve been studying Just Intonation for the past 8
months. I recently began researching on how to build my own instruments for JI
tunings. Coming across the Chrysalis Foundation site was wonderful... I saw the TOC
for Musical Mathematics and got super excited to see that there was detailed
instructions on building a Harmonic Canon. But then I realized it was not in print.
Please pass this email on to those that can make this happen. I would purchase this
publication in a heartbeat.
Thanks much and put me on your emailing list.
-D.
* * *
Hi Cris,
Nice to hear from you.
That is very exciting about your book! I would love to buy a copy for myself. The
topic is right up my alley.
The drumming is going
well. I’m not getting as much practice time in as I would like but so it goes.
I’ll try to answer
your specific questions below...
-D.
* * *
Hello,
I am definitely
interested in the publication of Musical Mathematics. I am an instrument builder focusing on
electric-acoustic instruments in both standard and custom configurations. I also am
in the process of designing a series of multi-scale instruments. Having this new
publication would be an excellent resource when designing an instrument with a
certain scale (or set of scales).
I would definitely
like to purchase a copy of the book when it is published. I would also love to be
able to demonstrate how the information applies to instrument design.
Keep me posted on the
progress and when the book will be available. This research is definitely needed
and wanted.
Thank you,
-D.
* * *
Good Morning Chrysalis
Foundation,
I would definitely be
interested in purchasing one of the books once they have been printed. I find the
subject matter most illuminating to someone who is interested in acoustics and
audio engineering. I am an electrical engineer and a novice at playing the flute. I
am interested in constructing a flute to obtain a particular scale, dynamic range,
and tonal quality. Your presentation regarding the placement of tone holes will
assist me in accomplishing this quite nicely. I would like to create a working
model using MathCad to simulate the tone hole placements and produce the desired
note(s) and subsequent waveform. Using a Fast Fourier Transform, I should then be
able to precisely calculate the amount of energy (power density) within each note
as well as review the tonal and composite bandwidth.
Scale analysis is
something I have been studying for many years as a hobby.
Please inform me of
how to obtain a copy of Mr. Forster’s book once it is published.
Thank you for the
enjoyment you have provided me and Good Luck in your endeavors.
Warmest Regards,
-D.
Microwave Hardware Development Engineer
Staff
Lockheed-Martin Systems Integration
* * *
Hi,
I am interested in learning about the possible publication of
this comprehensive book. Please keep me informed on this great
work.
Blessings,
-E.
* * *
I
am very interested in designing and making simple flutes, and
Mr. Forster’s work would be a great help to me. I hope you can
get your grant and publish this work. Please let me know when
it is in print. I teach Highland and Lowland Scottish pipe and
play wooden flute, and am researching their design so I can
make my own.
Sincerely,
-E.
* * *
Hi
--
I’d like to order a copy of Musical Mathematics --- very
important work --- put me on the list please. I’m a writer,
playwright, teacher of geometry at Jung Institute. I build
stuff.
-F.
* * *
Dear Mr. Forster,
As a person with special interest in the publication of your monumental work
entitled Musical Mathematics, please accept this as my order for ten copies
of such work upon publication at a price of approximately $90.00 per volume plus
shipping and handling charges. It is my belief that this book must be made
available to universities and other centers of learning for the advancement of
knowledge in the field of acoustic music. It is my intention to donate copies to
selected institutions where they will have the most far-reaching effect.
-F.
* * *
Hello,
My name is [...]. I am a New-York-based pianist/composer and music theorist. How
might I go about seeing and learning from the Musical Mathematics
writing? I am always thirsting for
knowledge.
-F.
* * *
Dear Sir/Madam:
I would like to see Musical Mathematics in print. Please
use my email in support of your grant applications.
I am an instrument builder.
Thank you.
-G.
* * *
Hello,
My name is […], and your proposal of this
book is entirely overdue in our world, not just an absolute priority. I am amazed
it hasn’t yet been [published]. I am a student of an art high school full of
musicians, just like me. However, the passion that claims most of my attention is
mathematics. My fascination with physics brought me to a deep understanding of
mathematics to a philosophical level, a privilege I know most of my peers may never
understand, because of the way they always seem to trudge home to finish algebra
homework on Fridays. As a musician as well, I wanted to know why this theory I know
works down to it’s very core, and I knew math would be where that lies. So
weeks of research have led me far across the internet, gazing at yet another
amateur musicians page of ‘well this is how to construct a triad’. Your book sounds
like the absolute epiphany a world of struggling musicians needs to stop all the
memorization, and to have the realization that these musical phenomena all happen
as a bi-product of energy and vibration, not because ‘the pattern of a major scale
is and always will be 2-2-1-2-2-2-1’. Thank you very much for wanting to document
what should rightfully be documented.
-I.
* * *
To Whom It May Concern:
I would like to purchase Musical Mathematics if it
becomes available. [...] Please email me with information how
and when I can obtain a copy.
Thank you
-J.
* * *
As requested on a web site, I write to say I would like to see Musical Mathematics: On the Art and Science of Acoustic
Instruments in print. I have no
affiliations of interest, but am a physicist who plays and
builds instruments.
Cheers,
-J.
* * *
I am currently finishing a B.M. in Music Technology this
semester. I am a guitarist and a composer. I have been
interested in the mathematics of music ever since my mother
showed me what a harmonic was when I was a kid. As a scholar, I
have become somewhat frustrated with the serious lack of just
intonation and musical mathematics in the standard music
department. For my degree in music technology I have taken
courses that cover acoustics and psychoacoustics, which has
furthered my obsession with just intonation, along with
studying the music and writings of Partch and his lineage of
students.
Just Intonation and the art of temperament in the academic
world is not something that should be disregarded while 12-tet
is taught as the one true king of tunings. I would love to have
a copy of your book when it’s published, it seems like it will
be a fantastic reference that I would use all the time.
Hopefully it reaches a large number of libraries and makes it’s
way into the hands of many musicians.
-J.
* * *
Hello,
I’m very interested in Musical Mathematics. I am a
student of woodwind making. I would like to purchase your book
when it is published!
Thanks very much.
-J.
* * *
To Whom It May Concern:
It baffles me that this work is not
already in print. I have seen numerous books on the subject of temperament and
acoustics in all major bookstores. But it is the same thing every time. Either way
too complicated for the layman, or not complicated enough. I have read quite a few
extracts from Musical Mathematics, and I find it to be a perfect balance
between these extremes. The material is always presented in an understandable
fashion, and it always treats its readers with respect by not over-simplifying the
subjects. Namely, because Mr. Forster takes the time to lead you into the concepts
with historical anecdotes, lots of pictures and diagrams, and careful writing so as
to not obscure the material. I believe there is a strong market for this book, and
anxiously await seeing a publisher pick it up, as someone should have long ago.
I’ll be first in line for a copy when they do.
-J.
Composer, Pianist
SFSU School of Music
* * *
Greetings To Whom It
May Concern.
I am a designer/maker
of free reed musical instruments. I would benefit greatly from the publication of
Cris Forster’s manuscript Musical Mathematics.
Thank you.
-J.
* * *
Dear Cris,
I would like to see
your book Musical Mathematics available in print. The table of contents
listed is compelling and seems it would make an essential reference for the tuning
library of any musical instrument designer or composer. The proposed price of $90
is OK and understandable, provided it is published in hardcover.
I am a composer
specializing in non-octave tunings and also a modest instrument builder. I also
design musical tuning software for the Macintosh.
Please keep me
informed if and when the book is published.
Best Wishes,
-J.
Chief Musical
Instrument Designer
Red Barn Goat Farm
* * *
Looking forward to the
publication of Musical Mathematics. I am a composer, performer, educator,
broadcaster intensely involved with tunings and new musical instruments. This
volume will be a welcome addition to the existing literature, taking readers closer
to information only alluded to elsewhere.
If appropriate, I
would be interested in reserving one of the first 500 of the unabridged edition -
and if you are considering a subscription as a method of publication, I would be
more than happy to be involved.
Sincerely,
-J.
Music Professor,
Pierce College
Host/Broadcaster -
Pacifica Radio’s Global Village
* * *
Board of Directors,
The Chrysalis Foundation:
I read with great
interest of your plans to publish the book Musical Mathematics. I anticipate the book will be a valuable
reference for me, both professionally and personally.
I am a life-long
professional musician and (currently) amateur flute maker. My interest in flute
making developed after my first exposures to Native American end-blown flutes
produced by various makers in the eastern and central U.S. These flutes are made in
a wide variety of shapes, sizes, and configurations, from a variety of materials
that includes, among other things, river cane, bamboo, hardwood, and PVC piping.
Because of the natural variations in, and volatility of, these materiel, proper
placement of the tone holes which produce the various pitches on the instrument can
be extremely challenging. Proper placement is absolutely essential, as it ensures
each pitch on the instrument will be
“in tune” with all the other pitches.
That’s where I
anticipate your book may be a great help. Developing a working knowledge of the
mathematics that underlies the placement of each tone hole in reference to all the
other holes, and in reference to the dimensions of the instrument itself, should
enable me to produce a higher quality instrument, regardless of the dimensions and
material used. I’m very excited to read of your plans for this book, and would like
to offer my best wishes for a successful outcome.
Sincerely,
-J.
Performer, Composer,
Song Writer, Builder
* * *
I am a guitar designer, builder,
repairman, and singer/songwriter. Please acknowledge my interest in obtaining a
copy of your future manuscript as it will definitely expand my knowledge of this
fantastic art form.
Confidentially yours,
-J.
* * *
Heidi,
Cris -
Please
put me down for a copy of Musical Mathematics. I am looking forward to seeing it published.
[...]
-K.
* * *
To Whom It May
Concern.
No one living has gone
through such painstaking labor in acquiring the knowledge that is in this book. It
will no doubt become the standard text and will allow the field of instrument
building to take a giant technological leap forward. I strongly urge all
organizations and individuals to fully support this project.
-K.
* * *
To Chrysalis
Foundation:
My name is [...], and
I am a Degree student at Musicians Institute. I play guitar and piano, and over the
past year have started to hear about and investigate just intonation; I would love
to see Musical Mathematics in print, as I would like to further
understand the concepts of tunings and how they can be applied to music.
Could you recommend
some good books for a
“beginner” like to me?
Thanks!
-K.
* * *
Hello,
My name is [...], and I am a student at Berklee College of
Music, having previously also studied at the Indiana University
Bloomington School of Music. I discovered the Chrysalis earlier
today on oddmusic.com and found it to be absolutely haunting!
Upon my venture to the Chrysalis Foundation website, my
intrigue was only furthered. The mathematics and physics behind
music and our perception of it is something that I think I have
always been subconsciously fascinated with, only recently have
I really begun to understand, appreciate, and pursue this
knowledge though (due in large part to having read Daniel
Levitnin’s This Is Your Brain On Music).
Cris Forster’s manuscript definitely sounds like something I
would be highly interested in reading, and I wouldn’t have any
second thoughts about putting out $90 for it. If possible, I
would like to be informed of any developments in the search for
a publisher. Seeing as the proposed printing will only be 500
copies, I most certainly want to make sure that I will be able
to obtain one.
Thank you, and I look forward to exploring your site further.
-L.
* * *
I
would be most interested to own a copy of your book. I compose,
teach and play French Horn professionally. Many of my works are
composed using just intonation. My previous two degrees (MMus
Musicology and MPhil Composition) featured just intonation as
does my current degree and I expect my involvement will
continue with such tunings. Reference material as has been
written by Mr. Forster is most welcome for a continual increase
in understanding. I was pleased to see the preface by David
Canright whom I enjoyed visiting in 2003.
-M.
* * *
Hi
there, it is exiting that there is a book just about to be
published about a subject for which I have a tremendous
passion. I have been Improvising music with new music
instruments since the year 2000. All the experiences gained
through this activity led me to want to become a music
instrument builder and a sound sculptor. So I am looking
forward to Cris Forster’s book to employ and apply its
knowledge in instruments making. Let me know when it is ready.
-M.
* * *
Hello,
My name is […]. Please keep me informed as to the progress of
the manuscript. I wish you all the success in the world at
achieving the publication of Musical Mathematics.
-M.
* * *
Grant application
[committee],
Please publish this book. I’ve heard some samples of music in just intonation, and
after listening to just a few 2-minute samples, now all the other music I hear
sounds dull in comparison.
I can’t find much information about just intonation at the moment. There are one or
two books on the subject, but... the table of contents [of Musical Mathematics]
is impressive by itself; it almost looks like an encyclopedia.
We need this book!
-M.
* * *
I am interested in the
book when it is published.
-M.
Amateur Instrument
Maker
* * *
Cris,
I would like to order 2 advance copies of Musical
Mathematics. I am a custom instrument builder.
Hope all is well,
-P.
* * *
I will definitely buy your book when it becomes available.
Please inform me when it is ready. […] And I have promoted your
site by adding it to the Links section.
-R.
* * *
Hello.
I just found your webpage by searching for "chromatic lichanos
meson" or something like that. I was looking for detailed
information on Greek divisions of the tetrachord, and I was
very happy to find in your page very concise, clear
explanations on the matter.
I saw the message on top of the page, and I am interested in
print copies of the book.
Also, I have one question regarding Chapter 10, Section 7,
Figure 1 [at]
http://www.chrysalis-foundation.org/Philolaus_&_Euclid.htm.
Figure 1 shows specific intervals for the three genera of
tetrachord. Although in the text above the figure, reference is
made to Archytas’ and Aristoxenus’ divisions of the tetrachord,
the explanation for the figure itself is that of a "typical
tetrachord" for each genus. Could you tell me which source was
used to create the illustrations? [...]
Sincerely,
-R.
* * *
Dear Chrysalis Foundation,
I would like to see Musical Mathematics: On the Art and Science of Acoustic Instruments in
print. Please put me on your mailing list and let me know when
it is published.
Best regards,
-R.
* * *
I look forward to the publication of Cris Forster’s
manuscript, Musical Mathematics: On the Art and Science of Acoustic Instruments. I am especially attracted by the light that
this manuscript casts upon a subject in which I specialize: the history of
mathematics and of related sciences such as music theory, especially among the
ancient Greeks and the medieval Arabs.
-R. (Prof.)
Department of Mathematics
Schoolcraft College
* * *
Please print the
manuscript.
-R.
Web, Java, and Net
Programmer and Developer
HP Software Global
Business Unit
* * *
I am a high school student who has, in recent months, devoted a
great deal of time to the study of just intonation and the
design of musical instruments. Based upon the content of the
pages display on the website, I feel that a copy of Musical
Mathematics would benefit my research tremendously.
-S.
* * *
I’m interested in a published copy of Musical Mathematics: On the Art and Science of Acoustic Instruments.
I am a musician and an instrument builder as a hobbyist. The
book received high praise from oddmusic.com as a comprehensive
resource for building, as well as a historical reference.
-S.
Residential Designer
* * *
I would love to see
Musical Mathematics in print so I can have a copy.
I’ve been a musician my entire life. I started piano at six, but music reading was
too difficult for me to master, so my teacher encouraged me to play by ear, which I
have done ever since. At 22 years of age, I took up the concert harp after
outgrowing a small Celtic harp that I built. I went from the small harp to the
concert pedal harp in four months! I was an intermediate level student in my 2nd
year of instruction. It was then that I began to understand reading music a little
better, but once again, the instructor marveled at my ability to play nearly any
piece of music by ear.
After all the training, the practice, I barely understand the ins and outs of music
and the unseen “workings” of it all.
For the past year or so, I’ve been more interested in building instruments, rather
than playing. I’m currently building a single manual harpsichord — from scratch! —
not a kit. It’s going to be interesting to see how it turns out, since I’ve used no
drawings or plans for it, just information from various sources. Harpsichords are
nice, but now I think I would like a Harmonic Canon sitting in my living room!
Just intonation? 19-tone equal temperament? Ratios, etc.? What are those?
This is the knowledge that I am lusting after!
Please put Musical Mathematics in print so that I can have a copy!
I would be forever grateful!
-S.
* * *
Hi, My name is […], and this book is just what my son is
looking for. He is a jazz drummer who builds his own
instruments. He has a harmonic canon in his future. How do I
get a copy of Musical Mathematics?
-T.
* * *
Hi,
As a musician, and an inhabitant of this planet, I am always looking for new
methods of vitalizing art. While the equal tempered system has served us well over
the past few hundred years, I believe it is now more of a liability to humanity
than a plus. I could list a great number of reasons to support that statement, but
the issue here is the breaking of new ground for new forms of expression, with new
palettes of sound as their foundation. For this reason I would very much appreciate
being notified when this book becomes available, and/or when pre-ordering can be
done.
Thanks,
-T.
* * *
Dear Chrysalis Foundation,
I visited your website today and discovered the project to
publish the book Musical Mathematics: On the Art and Science of Acoustic Instruments. The
wealth of technical material included on so many aspects of
musical scales and instrument tuning marks this in my mind as a
very worthwhile project.
I’m a musician and armchair instrument builder with interest in
a broad range of musical instrument types, including stringed,
woodwind, percussive and electronic. The book you intend to
publish would help me in many aspects with the theory and
practice of tuning instruments and defining scales. I look
forward to your success in this and would be happy to be
informed of the publication date.
Sincerely,
-V.
* * *
Hi,
I would love to see this book in print. Please let me know if
there is any opportunity to pre-order at any time.
Thanks for your efforts.
Greatly appreciated,
-W.
* * *
I would be very pleased to see the work
Musical Mathematics in
print.
As an engineer, musician, and amateur
musical instrument builder, this book would be a valuable resource.
If possible I would like to pre-order my
own copy of the book when it is published; can you send me details on how to get on
the waiting list?
Thank you,
-W.
*
* *
|
Dear Reader,
Since July
2002, more than 560,000 visitors have logged on to www.chrysalis-foundation.org. We are
pleased to announce that Cris Forster’s book Musical Mathematics: On the Art and Science of
Acoustic Instruments is now available. We
would like to thank all readers who placed advance orders for
their visionary and steadfast support. If you would
like more information on Mr. Forster’s book, please visit
our
Musical
Mathematics page,
which shows the Table of Contents of this work.
Thank you for your interest and support of the Chrysalis
Foundation.
The Board of
Directors
|
|