Re: [tuning-math] Re: skhismic

> From: genewardsmith <genewardsmith@juno.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Tuesday, March 12, 2002 3:24 AM
> Subject: [tuning-math] Re: skhismic
>
>
> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
>
> > it's spelled this way sometimes. pronounce it. there's
> > no reason one should think it might be spelled "shismic".
>
> I used to spell it that way, but quit because everyone
> seemed to spell it differently. Still use "sk" to mean
> 2^(1/612), though.
>
> how do you pronounce "schism"? like "shism"? naah . . .
>
> Usage Note: The word schism, which was originally spelled
> scisme in English, is traditionally pronounced (szm).
> However, in the 16th century the word was respelled with
> an initial sch in order to conform to its Latin and Greek
> forms. From this spelling arose the pronunciation (skzm).
> Long regarded as incorrect, it became so common in both
> British and American English that it gained acceptability
> as a standard variant. Evidence indicates, however, that
> it is now the preferred pronunciation, at least in American
> English. In a recent survey 61 percent of the Usage Panel
> indicated that they use (skzm), while 31 percent said they
> use (szm). A smaller number, 8 percent, preferred a third
> pronunciation, (shzm).

thanks for that note, Gene ... with my penchant for history,
i found it very interesting. here's a little history on
the musical use of the terms "schisma" and "skhisma":

the earliest reference i know of is in Boethus, _De institutione
musica, liber III_; here's Freidlin's text of the original:
http://www.music.indiana.edu/tml/6th-8th/BOEMUS3_TEXT.html

>> De minoribus semitonio intervallis.
>>
>> VIII. Philolaus igitur haec atque his minora spatia
>> talibus definitionibus includit. Diesis, inquit, est
>> spatium, quo maior est sesquitertia proportio duobus
>> tonis. Comma vero est spatium, quo maior est sesquioctava
>> proportio duabus diesibus, id est duobus semitoniis
>> minoribus. Schisma est dimidium commatis, diaschisma
>> vero dimidium dieseos, id est semitonii minoris.

Bower's translation, _Fundamentals of Music, book 3_, p 97 ,
with my interpolated mathematical explanation:

>> 8. Concerning intervals smaller than a semitone
>>
>> Philolaus incorporates these [the two sizes of
>> Pythagorean semitones, which we today call _limma_
>> and _apotome_] and intervals smaller than these in
>> the following definitions.
>>
>> the _diesis_, he says, is the interval by which a
>> sesquitertian [= 4:3] is larger than two tones [= (9/8)^2].

2 3 ratio ~cents name

[ 2 -1] 4:3 498.0449991 sesquitertian
- [-6 4] 81:64 407.8200035 two tones
-----------------------------------------------
[ 8 -5] 256:243 90.2249957 diesis

our term for this interval is the _limma_.
http://www.ixpres.com/interval/dict/limma.htm

>> the _comma_ is the interval by which the sequioctave
>> ratio [= 9/8] is larger than two dieses -- that is,
>> larger than two minor semitones.

2 3 ratio ~cents name

[- 3 2] 9:8 203.9100017 sesquioctave
- [ 16 -10] 65536:59049 180.4499913 two dieses
-----------------------------------------------------
[-19 12] 531441:524288 23.4600104 comma

this is the same interval which we today call the
"Pythagorean comma".

>> the _schisma_ is half a comma.

2 3 ~ratio ~cents

[-19/2 12/2] ~148:147 11.73000519

so Philolaus's _schisma_ is very different from the
interval we know by that term today. the modern usage
of "skhisma" or "schisma" is due to Ellis.

note the spelling with a "c" by Boethius, and also
presumably Philolaus. (none of Philolaus's own work
exists today.)

>> The _diaschisma_ is half a _diesis_ -- that is,
>> half a minor semitone.

2 3 ~ratio ~cents

[8/2 -5/2] ~39:38 45.11249784

_diaschisma_ is another term that was given a different
meaning by Ellis -- ratio 2048:2025 = ~19.55 cents; see:
http://www.ixpres.com/interval/dict/diaschisma.htm

note Margo Schulter's observation that medieval (and
perhaps earlier) theorists recognized that Philolaus's
"diaschisma" is nearly equal to 2 commas, which is what
gave rise to the idea that "1 tone = 9 commas", a concept
which persisted in common practice as late as Mozart's
lifetime, and could be used in connection with both
53edo (quasi-Pythagorean and quasi-JI) and 55edo (meantone).
/tuning/topicId_29025.html#29025?expand=1

Ellis, who is responsible for the modern usage of the term
"skhisma" or "schisma", deliberately chose the spelling with
a "k", in order to avoid any connotation or reference to
the religious views associated with the "Great Schism".

(i've looked around in Ellis's translation of Helmholtz
for this info but can't find it; perhaps Ellis mentioned
it in another paper he published, which i'd read in a
library but of which i don't have a copy.)

here's a quote from a webpage with an excellent explanation
of the Great Schism
http://www.mcauley.acu.edu.au/~yuri/ecc/mod5.html

(note that much that is said here has a bearing on the future
development of music and music-theory, because of: 1) the
increasing secularization of European society -- establishment
of universities at Paris, Padua, Naples, Prague, Vienna,
Heidelberg and Cologne, at least the first of which became
an extremely important center for developments in music, and
2) the rediscovery in the West of the ancient Greek writings.
Both of these were direct results of the sack of Constantinople
in 1204.)

>> The Church had, by the time of Innocent III [ruled as
>> Pope 1198-1216], taken on the organisational role of the
>> Crusades with all its political and economic ramifications.
>> Crusades were to be launched against heretics at the
>> discretion and direction of the presiding Pontiff and
>> were used as a means of imposing the rule and will of the
>> Church on the unbeliever. Augustinian teaching that
>> justified the use of torture and death as legal instruments
>> to be used by the Church to convert the heretic became
>> widely accepted. This acted as a prelude to the legitimisation
>> of the Inquisition, which was to receive papal approval
>> under Gregory IX in 1233. Heresy was to be punished for
>> the spiritual "good" of the individual as well as for the
>> preservation and enhancement of the status of the Church
>> and State - an attitude and mentality equally accepted
>> by future Western reformers such as Calvin and Luther.
>> Such was to be the patrimony and inheritance of the Crusades.
>>
>> An even darker shadow was cast over Innocent's pontificate
>> by his involvement in the Fourth Crusade, which led to
>> schism between Eastern and Western Christendom in the
>> eleventh century, an event which is one of the greatest
>> calamities in the history of the Church. The main aim of
>> the Crusades was to try to free the Holy Land from the
>> Seljuk Turks who had conquered Jerusalem in 1071. This
>> was not accomplished, but rather in its consequences it
>> seriously undermined the powers of resistance of the
>> Christian East to the advance of Islam. It also encouraged
>> the excessive growth of papal power in the West, and this
>> over-centralisation of Church government resulted in many
>> abuses and provoked widespread discontent. Thus the
>> Reformation itself, which split the West into two hostile
>> camps, was one of its results flowing from the split
>> between East and West
>> ...
>> Roman Catholics have accused the East of an obstinate
>> refusal to accept the leadership of the Pope, and of
>> undue submissiveness towards the secular power. The Orthodox,
>> in return, have hurled against Western Christians charges
>> of arrogance and pride, and have insisted that both Latins
>> and Protestants have wilfully departed from the sound
>> tradition of the early Church and perverted their religion
>> by arbitrary and harmful innovations.
>>
>> Many controversial books have been written on this subject;
>> but if the simple question is asked, "What was the cause of
>> the Schism between Rome and Constantinople, and when exactly
>> did it occur?", too often no clear answer is forthcoming.
>> The absence of an agreed statement on such a vital issue,
>> one which has so profoundly and so disastrously affected
>> the life of all Christians, is puzzling indeed. Yet an
>> explanation of it is to be found in the study of the
>> political and ecclesiastical events which led to the break
>> of communion between East and West.
>>
>> Though conflict, disagreement and tensions in politics and
>> theological interpretation existed from the fifth century
>> onwards, this gradual process of open hostility and bitter
>> hate reached its climax between the ninth and thirteenth
>> century. It is often thought that the lasting split in the
>> Church must have been caused by some major doctrinal
>> disagreement. The history of the schism does not confirm
>> this opinion. The growing alienation between the Christian
>> East and West was provoked by political competition, petty
>> quarrels and personal rivalries. It was a slow movement;
>> for the Church organism vigorously resited these attacks
>> of destructive forces. The final blow to the unity of the
>> Church was inflicted by no heresy, but by the drunken and
>> undisciplined mob of Crusaders who sacked Constantinople
>> in 1204 and massacred its Christian population.
>> ...
>> This day, April 13, 1204 marks the end of the fellowship
>> between Eastern and Western Christians. The split was brought
>> about, not by quarrelsome theologians or ambitious prelates,
>> as is usually suggested, but by the greed and lust of those
>> men who, in the name of the Prince of Peace, had embarked
>> upon a war of aggression and conquest.

i stick with "skhisma" out of respect for Ellis's sensitivity
in this matter, but it's necessary to note that nearly everyone
else today uses the "schisma" spelling.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com