Private lessons available in person in San Diego, or online using Discord: composition, music-theory, tuning-theory, piano, and all woodwinds (sax, clarinet, flute, bassoon, recorder). Current rates US$ 80 per hour (negotiable). Send an email to: monzojoe2 (AT) gmail. Also please consider making a donation to Tonalsoft using the PayPal button at the bottom of this page. Thank you.

. . . . . . . . .

[Joseph Monzo, 1999]

David Beardsley wrote, in Onelist Tuning Digest # 206, message 9:

So what does your book offer that one can't already find in the writings of Partch, Helmholtz or Doty? Or even a trip to the library wouldn't dig up?

Here's my response (from Onelist Tuning Digest # 207):

. . . . . . . . .

Primarily, a comprehensive collection of lattice diagrams illustrating historical tuning systems and harmonic gestures, from c. 400 BC to 1999 AD, along with my prime-factor adaptation of regular staff-notation to notate these systems.

Partch and Helmholtz devote a lot of space to experimental
investigations and other aspects of acoustics and composition
which are not specifically descriptive of tuning *systems*.
For instance, Helmholtz describes his experiemental apparatus
and Partch describes his instruments and the dramatic aspects
of his compositions, all of this in great detail. And Partch's
primary concern was with his own single ~43-tone system of
Monophony; when he does explain historical systems, he generally
presents them as subsets or adjustments of his own system.

Doty's book is intentionally limited in scope to suit beginners,
and, altho still quite extensive (and probably the best
introduction to the subject), it doesn't cover
anywhere near as many *specific* tuning systems as my book.

None of them give analyses of specific pieces or gestures (with the two exceptions of Partch's 'modulation' and 'tonality flux' explanations), which I do.

This last point is especially important. As many of us here have argued, theory divorced from actual music is rather pointless. (Boethius's opinion notwithstanding). Partch certainly emphasizes that fact, but he still doesn't give analyses of his harmonic practice, except the very sketchy examples of 'tonality flux' mentioned above.

. . . . . . . . .

As far as a trip to the library: if you live in or near New York (as you do), go for it - there's a lot there.

But away from New York, I've had a *LOT* of difficulty finding
the information I was researching, even in large cities like
Philadelphia (surprisingly, especially considering all the
good university libraries here), Phoenix (even with a brand new
and very good central library), and San Diego (LOL here).
[that means 'laugh out loud' for those who don't know]
[Note from 2022: San Diego has since built a new main library
to replace the really small and antiquated one which existed
at the time of this writing, however, its inventory still leaves
much to be desired. The libraries of San Diego State University
and especially of University of California, San Diego have much
better resources in their music literature collections.]

On that last point, I find it shameful that the city where both Partch and Darreg spent the last years of their lives has such a poor representation in its libraries of anything concerned with their work (or of anything, period, for that matter).

And believe me, I've done some serious digging. People living in more rural areas will generally have even greater difficulty.

(Are any civic administrators listening to me? University librarians? Perhaps you, gentle reader, can write or email your preferred library about stocking books on microtonality. Give them specific titles to order.)

I know that for a lot of New Yorkers, the universe ends at the Hudson River, or perhaps somewhere in New Jersey and Long Island. But lots of microtonal folks live out here in the hinterlands, and I suppose we suffer accordingly.

OK, enough ranting about libraries...

. . . . . . . . .

Besides, my particular lattice design, which is different from all the others, isn't available anywhere else, except here on my website, and on the Tuning List.

Much of the historical information in my book is based on the
systems analyzed by those three authors, but my objective
was to diagram those
ratios all from the same 'perspective'
(i.e., from the same 1/1), to gain an understanding of how
the different systems *in toto* relate to each other.

In addition, there is much new information added stemming from
Barbour, *Journal of Music Theory*, *Perspectives of New Music*,
*Xenharmonikon*, and from my own interaction and correspondence
with contemporary theorists and composers.

I've also been able to take advantage of several recent
English translations of such classic treatises as those of
Aristoxenus, *sectio canonis*, Nicomachus, Ptolemy, Boethius,
*musica enchiriadis*, Hucbald, Guido d'Arezzo, Marchetto,
Prosdocimus, Zarlino, Riemann, and Schoenberg.

(In particular, I've gathered so much information about Schoenberg that I've decided to write an entire second book exploring in more detail his theories and the work of his students and predecessors - which is only natural, since I admire Mahler so much, and I dig Webern a lot too.)

. . . . . . . . .

The book grew out of my frustration in dealing with ratios of very large numbers in Partch and Helmholtz, and most of it was finished before I ever saw Doty's book, which does have a fair amount of the same information (in particular, his use of lattices, which are, however, a bit different from mine).

Another thing you won't find anywhere else (except my website): I have a few very speculative theories on possible examples of higher-prime systems at earlier dates than those usually cited - readers of this list will already be aware of these (one example is that of Boethius which I just mentioned yesterday, another is Marchetto of Padua).

In addition, I explore blues and rock music styles (for example, Louis Armstrong, Robert Johnson, Etta James, Jimi Hendrix) which, to my knowledge, have never been subject to extensive microtonal analysis before, excepting Sims's work on Armstrong. (Note that all these artists were African-American, which may or may not be significant - at any rate, there's certainly a gap in the understanding of microtones in African-American music, which I hope to fill at least partially.)

Also, the work of several contemporary composers and theorists
- for example, Erv Wilson, Ben Johnston, Lou Harrison, Ezra Sims,
Terry Riley, Johnny Reinhard, Denny Genovese, Sasha Bogdanowitsch,
David Beardsley : ) - is included, which obviously was impossible
for Helmholtz and Partch, and which lie outside the scope of Doty's
introductory *Primer*.

To a large extent, the differences may be summed up with the statement that Partch and Helmholtz argued polemically in favor of their JI or tempered systems, and Doty explains and illustrates more-or-less basic concepts and ends there, whereas I've assumed what all three of them said as given, expanded from there, and tried to find underlying principles of unification.

ORDERING INFORMATION

*JustMusic* is available!

for US$ 125.00 plus postage

See: US Postal Service shipping prices

Send me an
email
notifying me of your interest *before* sending money.

Thank you.

A text of the 3rd edition (212 pages) is available for free download [291 K zip file, in Microsoft Word .doc format]. It does not include any musical examples or lattice diagrams, and these diagrams are really the whole point of the book.

*NOTE, FROM 10 APRIL 2004:*

Since beginning my website in June 1998, i've devoted almost all of my spare time to writing webpages, and my website is now a huge source for tuning theory information.

Also, for the past few years, i have been actively
developing my microtonal music composition software,
Tonescape^{®}.

So work on the book really has not progressed since late 1998.

I will ** not** finish the current (4th) draft of

For those who really want the book as it is now in its present condition, I will make copies of the book as needed. The draft from which i make these copies still has these problems:

- many diagrams are hand-drawn
- there is no index
- the text needs major editing
- the page numbers are not consecutive

Eventually, Tonalsoft Press will publish a clean, edited version of the book in its final form. Those who purchase the book in its present condition will be entitled to a clean copy at a nominal cost when it is published.

. . . . . . . . .

Please make a donation to help keep Tonalsoft online. A recurring monthly contribution would be apprecitated.

Thank you!

a&b temperament [a&b are numbers]

55-edo / 55-ET / 55-tET (comma) (Mozart's tuning)

1/1 or 1:1 (ratio)

2/1 or 2:1 (ratio)

a&b temperament [a&b are numbers]

apotome (Greek interval)

aristoxenean (temperament family)

atomic (temperament family)

augmented / diesic (temperament family)

augmented-2nd / aug-2 / #2 (interval)

augmented-4th / aug-4 / #4 (interval)

augmented-5th / aug-5 / #5 (interval)

augmented-6th / aug-6 / #6 (interval)

augmented-9th / aug-9 / #9 (interval)

blackjack (tuning)

cent / ¢ / 1200-edo (unit of interval measurement)

centitone / iring / 600-edo (unit of interval measurement)

chromatic-semitone / augmented-prime (interval)

daseian (musical notation)

dekamu / 10mu (MIDI-unit)

dexl / 540-edo (unit of interval measurement)

diapason (Greek interval)

diapente (Greek interval)

diatessaron (Greek interval)

diatonic semitone (minor-2nd) (interval)

diesic (temperament family)

diezeugmenon (Greek tetrachord)

diminished-5th / dim5 / -5 / b5 (interval)

diminished-7th / dim7 / o7 (interval)

doamu / 2mu (MIDI-unit)

dodekamu / 12mu (MIDI-unit)

dominant-7th (dom-7, x7) (chord)

dorian (mode)

eleventh / 11th (interval)

enamu / 1mu (MIDI-unit)

endekamu / 11mu (MIDI-unit)

enharmonic semitone (interval)

ennealimmal (temperament family)

enneamu / 9mu (MIDI-unit)

farab / 144-edo (unit of interval measurement)

fifth / 5th (interval)

flu / 46032-edo (unit of interval measurement)

Gentle introduction to Fokker periodicity-blocks (by Paul Erlich)

fourth / 4th (interval)

(English translation by Monzo)
Gentle introduction to Fokker periodicity-blocks (by Paul Erlich)

grad (~614-edo) (unit of interval measurement)

hexamu / 6mu (MIDI-unit)

Hurrian Hymn (Monzo reconstruction)

hypate (Greek note)

hypaton (Greek tetrachord)

hyperbolaion / hyperboleon (Greek tetrachord)

hypophrygian (Greek mode)

imperfect (interval quality)

iring / centitone / 600-edo (unit of interval measurement)

1/1 or 1:1 (ratio)

2/1 or 2:1 (ratio)

jot / 30103-edo (unit of interval measurement)

JustMusic: A New Harmony [Monzo's book]

JustMusic prime-factor notation [Monzo essay]

kwazy (temperament family)

leimma / limma (Greek interval)

lichanos (Greek note)

limma / leimma (Greek interval)

locrian (mode)

lydian (mode)

magic (temperament family)

Mahler 7th/1 [Monzo score and analysis]

marvel (temperament family)

meantone (temperament family)

mem / 205-edo (unit of interval measurement)

meride / 43-edo (unit of interval measurement)

mese (Greek note)

meson (Greek tetrachord)

millioctave / m8ve / 1000-edo (unit of interval measurement)

mina / 2460-edo (unit of interval measurement)

minerva (temperament family)

miracle (temperament family)

mixolydian (mode)

monzo (prime-exponent vector)

Monzo, Joe (music-theorist)

morion / moria / 72-edo (unit of interval measurement)

mutt (temperament family)

mystery (temperament family)

octamu / oktamu / 8mu (MIDI-unit)

octave (interval)

oktamu / octamu / 8mu (MIDI-unit)

orwell (temperament family)

p4, perfect 4th, perfect fourth (interval)

p5, perfect 5th, perfect fifth (interval)

pantonality of Schoenberg [Monzo essay]

paramese (Greek note)

paranete (Greek note)

parhypate (Greek note)

pentamu / 5mu (MIDI-unit)

prime-factor notation (JustMusic) [Monzo essay]

proslambanomenos (Greek note)

quarter-tone / 24-edo (unit of interval measurement)

savart / 300-edo (unit of interval measurement)

schismic / skhismic (temperament family)

Schoenberg's pantonality [Monzo essay]

second / 2nd (interval)

semisixths (temperament family)

semitone / 12-edo (unit of interval measurement)

seventh / 7th (interval)

simplified Sumerian tuning [speculations by Monzo]

sixth / 6th (interval)

sk / 612-edo (unit of interval measurement)

skhismic / schismic (temperament family)

entire old Sonic Arts website

sruti tuning [Monzo essay]

studloco (tuning)

subminor 3rd (interval)

Sumerian tuning [speculations by Monzo]

Sumerian tuning, simplified [speculations by Monzo]

synemmenon (Greek tetrachord)

temperament-unit / tu (~36829-edo) (unit of interval measurement)

tenth / 10th (interval)

tetrachord-theory tutorial [by Monzo]

tetradekamu / 14mu (MIDI-unit)

tetramu / 4mu (MIDI-unit)

third / 3rd (interval)

thirteenth / 13th (interval)

tina / 8539-edo (unit of interval measurement)

tone (interval, and other definitions)

triamu / 3mu (MIDI-unit)

tridekamu / 13mu (MIDI-unit)

trihemitone (Greek interval)

trite (Greek note)

tu / temperament-unit (~36829-edo) (unit of interval measurement)

Türk sent / 10600-edo (unit of interval measurement)

twelfth / 12th (interval)

whole-tone (interval)

woolhouse-unit / 730-edo (unit of interval measurement)