Musical Mathematics


on the art and science of acoustic instruments

 

Table of Contents

 

 

Buy now at  Amazon.com: click New, Used, or All.

 

Also available from the publisher at Chronicle Books, San Francisco.

 

© 2000Ė2014 Cristiano M.L. Forster
All rights reserved.

 

www.chrysalis-foundation.org

 

 

Musical Mathematics Advance Orders

 

 

2005Ė2009: 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 Forsterís book Musical Mathematics sounds wonderful. Iím 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 Crisís 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 Forsterís 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 Forsterís 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. Forsterís chapter on ďSimple FlutesĒ 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. Forsterís page was my primary resource Ė 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.
 

*     *     *

 

*     *     *

Dear Chrysalis Foundation,

 

As a qanun player, I read about the Canon with interest, and then bumped into the Partch connection.

 

Iím 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 weíd 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

 

*     *     *

 

*     *     *

 

*     *     *

 

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.

Iím 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.

Iím 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 Ďnoise makersí - 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 [Ö], 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 itís 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,

 

Iím [...], teacher of ear training, tuning, music theory and teacher in the (Experimentelle elektronische Musik) of the Academy of Musik in WŁrzburg, 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 Farmerís ďA History of Arabian MusicĒ (London 1929, reprint New Delhi 2001) and Kiesewetterís ďDie Musik der AraberĒ. 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.

 

Iím 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 Forsterís manuscript has helped me with my Extended Essay which is on flute acoustics - it gave me great insight and understanding.

 

Although I havenít 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. Forsterís 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 worldís 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,

 

Iím very interested on buying this book. Iím a qanun and piano player from Israel. Iím 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:

 
Iím 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 friend,

 

Excuse me if my English isnít good. Iím Italian and writing you about your e-pages of Musical Mathematics. Iím 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 havenít 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 havenít who can request to them. Now, I found your e-page and I think you can help me. In your page you write: ďIf you would like to see Musical Mathematics in print, please write...Ē 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 havenít:

1) design of modern flute

2) how to find location and dimension of tune holes

 

Can you help me? If you canít, 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: ďGrant Applications SupportĒ

 

Hi there.


Iím [...].
 

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.

 

ďIf 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. . .Ē
 

 

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 Fťdťrale 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 Ė 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 Iím 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. Iíd 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

 

 

*     *     *

 

*     *     *

 

*     *     *

 

*     *     *

 

*     *     *

 

*     *     *

 

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.

 

*     *     *

 

*     *     *

 

*     *     *

 

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., ďThe Physics of Woodwinds,Ē 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.

 

*     *     *

 

*     *     *

 

*     *     *

 

*     *     *

 

*     *     *

 

Hi Cris,

Thirty years working on Musical Mathematics? Iím 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. Itís 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 Iíll just say it: Itís 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 [...]. [...]

Iím a musician of 12 years and Iíve 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. Iím not getting as much practice time in as I would like but so it goes.

 

Iíll try to answer your specific questions below...

 

*     *     *

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. Forsterís 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. Forsterís 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 --

Iíd like to order a copy of Musical Mathematics --- very important work --- put me on the list please. Iím 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 writingI 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 [Ö], and your proposal of this book is entirely overdue in our world, not just an absolute priority. I am amazed it hasnít 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 itís 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 Ďwell this is how to construct a triadí. 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 Ďthe pattern of a major scale is and always will be 2-2-1-2-2-2-1í. 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 itís 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 itís way into the hands of many musicians.

-J.

 

*     *     *

 

Hello,

Iím 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. Iíll 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 Forsterís 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 Radioís 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 ďin tuneĒ with all the other pitches.

 

Thatís 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. Iím 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 ďbeginnerĒ 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 Levitninís This Is Your Brain On Music).

Cris Forsterís manuscript definitely sounds like something I would be highly interested in reading, and I wouldnít 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 Forsterís book to employ and apply its knowledge in instruments making. Let me know when it is ready.


-M.
 

*     *     *

 

Hello,


My name is [Ö]. 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. Iíve 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 canít 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. [Ö] 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 Archytasí and Aristoxenusí 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 Forsterís 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.

 

*     *     *

 

Iím 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.

Iíve 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 ďworkingsĒ of it all.

For the past year or so, Iíve been more interested in building instruments, rather than playing. Iím currently building a single manual harpsichord ó from scratch! ó not a kit. Itís going to be interesting to see how it turns out, since Iíve 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 [Ö], 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.

Iím 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.