Yahoo Tuning Groups Ultimate Backup tuning the Harmonious Blacksmith

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
>
> Do any of you remember this simple piano piece (which
> I think is by Hayden, for from the time of Hayden) which
> is often given to beginning piano students?

The piece you're thing of was composed by George Frederic
Handel ... a bit before the time of Haydn. (BTW, you spelled
Haydn's name incorrectly.)

> Didn't the noises from a blacksmith's shop inspire
> Pythagoras' discovery of string length and simple
> integer ratios? I wonder if that is just a coincidence.

It's an apocryphal story -- we'd probably call it an
"urban legend" today. It was propogated in antiquity
by Nicomachus, Gaudentius, Iamblicus, Aristotle Elias,
and Boethius. Because of its appearance in Boethius,
it became a standard part of the teaching of music
during the medieval period, and was finally shown
to be wrong in the 1600s by Mersenne.

The story is that Pythagoras was passing by a smithy
and noticed that the sound of the hammers hitting
the anvils produced consonant intervals. At first he
thought the different intervals were due to differences
in the strength of the men hitting the hammers, but
when he went home and did some experiments he supposedly
found that it was the weights of the hammers that produced
the harmonious ratios. But this is incorrect.

It is true that the Pythagorean ratios apply to lengths
of strings and, somewhat less accurately, to pipes. But
it does not apply to weights of hammers.

Here's the relevant section from Boethius, in Latin:

Quemadmodum Phitagoras proportiones consonantiarum inuenerit.

HAEC igitur maxima causa fuit. cur relicto aurium iudicio
Pytagoras ad regularum momenta migrauerit. qui nullis
humanis auribus credens. quae partim natura. partim etiam
extrinsecus permutantur: partim ipsis uariantibus aetatibus.
nullis etiam deditus instrumentis. paenes quae sepe uarietas
atque inconstantia nasceretur. dum nunc quidem si neruos
uelis inspicere. uel aer humidior pulsus obtunderet. uel
siccior excitaret. uel magnitudo cordae grauiorem redderet
sonum. uel acumen subtilior tenuaret: uel alio quodammodo
statum prioris constantiae permutaret. Et cum idem esset
in caeteris instrumentis: omnia haec inconsulta minimaeque
estimans fidei. diuque estuans inquirebat. quanam ratione
firmiter et constanter consonantiarum momenta perdisceret.
cum interea diuino quodam nutu praeteriens fabrorum officinas.
pulsos maleos exaudiuit diuersis sonis unam quodammodo
concinentiam personare. Ita igitur ad id quod diu inquirebat
attonitus accessit ad opus. diuque considerans: arbitratus
est diuersitatem sonorum ferientium uires efficere. Atque
ut id apertius colliqueret: mutari inter se malleos imperauit.
Sed sonorum proprietas non in hominum lacertis haerebat.
sed mutatos malleos comitabatur. Ubi igitur id animaduertit:
malleorum pondus examinat. Et cum quinque essent forte mallei
dupli reperti sunt pondere. qui sibi secundum diapason
consonantiam respondebant. Eundem etiam qui duplus erat alio.
sesquitertium alterius comprehendit. ad quem scilicet
diatessaron sonabat. Ad alium uero quendam qui eidem diapente
consonantia iungebatur: eundem superioris duplum reperit esse
sesqualterum. Duo uero ii ad quos superior duplex sesquitertius
et sesalter esse conprobatus est ad se inuicem sesquioctauam
proportionem perpensi sunt custodire. Quintus uero reiectus
est qui cunctis erat inconsonans. Cum igitur ante Pitagoram
consonantiae musicae partim diapason. partim diapente. partim
diatessaron quae est consonantia minima uocarentur: primus
Pitagoras hoc modo repperit qua proportione sibimet haec
sonorum concordia iungeretur. Et ut sit clarius quod dictum
est: sint uerbi gratia malleorum quattuor pondera quae subter
descriptis numeris contineantur. XII. IX. VIII. Hi igitur
mallei qui XII. et VI. ponderibus uergebant diapason in
duplo concinentiam personabant. Malleus uero XII ponderum
ad malleum VIIII ponderum et malleus VIII ponderum ad
malleum VI. ponderum secundum epitritam proportionem
diatessaron consonantia iungebatur; VIIII uero ponderum
ad malleum VI. ponderum. et XII ad VIII: diapente
consonantiam permiscebant; VIIII uero ad VIII: in
sesquioctaua proportione resonabant tonum.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Aaron Krister Johnson <aaron@akjmusic.com>

🔗traktus5 <kj4321@hotmail.com>

I thought it might be a legend, but does anyone think there is any
chance that Handel was refering to the legend when he named the
piece "Harmonious Blacksmith"?

>
>
> It's an apocryphal story -- we'd probably call it an
> "urban legend" today. It was propogated in antiquity
> by Nicomachus, Gaudentius, Iamblicus, Aristotle Elias,
> and Boethius. Because of its appearance in Boethius,
> it became a standard part of the teaching of music
> during the medieval period, and was finally shown
> to be wrong in the 1600s by Mersenne.
>
> The story is that Pythagoras was passing by a smithy
> and noticed that the sound of the hammers hitting
> the anvils produced consonant intervals. At first he
> thought the different intervals were due to differences
> in the strength of the men hitting the hammers, but
> when he went home and did some experiments he supposedly
> found that it was the weights of the hammers that produced
> the harmonious ratios. But this is incorrect.
>
> It is true that the Pythagorean ratios apply to lengths
> of strings and, somewhat less accurately, to pipes. But
> it does not apply to weights of hammers.
>
>
> Here's the relevant section from Boethius, in Latin:
>
>
> Quemadmodum Phitagoras proportiones consonantiarum inuenerit.
>
> HAEC igitur maxima causa fuit. cur relicto aurium iudicio
> Pytagoras ad regularum momenta migrauerit. qui nullis
> humanis auribus credens. quae partim natura. partim etiam
> extrinsecus permutantur: partim ipsis uariantibus aetatibus.
> nullis etiam deditus instrumentis. paenes quae sepe uarietas
> atque inconstantia nasceretur. dum nunc quidem si neruos
> uelis inspicere. uel aer humidior pulsus obtunderet. uel
> siccior excitaret. uel magnitudo cordae grauiorem redderet
> sonum. uel acumen subtilior tenuaret: uel alio quodammodo
> statum prioris constantiae permutaret. Et cum idem esset
> in caeteris instrumentis: omnia haec inconsulta minimaeque
> estimans fidei. diuque estuans inquirebat. quanam ratione
> firmiter et constanter consonantiarum momenta perdisceret.
> cum interea diuino quodam nutu praeteriens fabrorum officinas.
> pulsos maleos exaudiuit diuersis sonis unam quodammodo
> concinentiam personare. Ita igitur ad id quod diu inquirebat
> attonitus accessit ad opus. diuque considerans: arbitratus
> est diuersitatem sonorum ferientium uires efficere. Atque
> ut id apertius colliqueret: mutari inter se malleos imperauit.
> Sed sonorum proprietas non in hominum lacertis haerebat.
> sed mutatos malleos comitabatur. Ubi igitur id animaduertit:
> malleorum pondus examinat. Et cum quinque essent forte mallei
> dupli reperti sunt pondere. qui sibi secundum diapason
> consonantiam respondebant. Eundem etiam qui duplus erat alio.
> sesquitertium alterius comprehendit. ad quem scilicet
> diatessaron sonabat. Ad alium uero quendam qui eidem diapente
> consonantia iungebatur: eundem superioris duplum reperit esse
> sesqualterum. Duo uero ii ad quos superior duplex sesquitertius
> et sesalter esse conprobatus est ad se inuicem sesquioctauam
> proportionem perpensi sunt custodire. Quintus uero reiectus
> est qui cunctis erat inconsonans. Cum igitur ante Pitagoram
> consonantiae musicae partim diapason. partim diapente. partim
> diatessaron quae est consonantia minima uocarentur: primus
> Pitagoras hoc modo repperit qua proportione sibimet haec
> sonorum concordia iungeretur. Et ut sit clarius quod dictum
> est: sint uerbi gratia malleorum quattuor pondera quae subter
> descriptis numeris contineantur. XII. IX. VIII. Hi igitur
> mallei qui XII. et VI. ponderibus uergebant diapason in
> duplo concinentiam personabant. Malleus uero XII ponderum
> ad malleum VIIII ponderum et malleus VIII ponderum ad
> malleum VI. ponderum secundum epitritam proportionem
> diatessaron consonantia iungebatur; VIIII uero ponderum
> ad malleum VI. ponderum. et XII ad VIII: diapente
> consonantiam permiscebant; VIIII uero ad VIII: in
> sesquioctaua proportione resonabant tonum.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

🔗traktus5 <kj4321@hotmail.com>

Here, with the quote at the end, he's just trying to show that he
knows Latin, and I don't. (Self-satisfied smugness over knowledge
that others don't have is a far thing from wisdom.) People like him
turn music students off from the tuning list, which is too bad. Can
someone moderate him?

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
> >
> > Do any of you remember this simple piano piece (which
> > I think is by Hayden, for from the time of Hayden) which
> > is often given to beginning piano students?
>
>
> The piece you're thing of was composed by George Frederic
> Handel ... a bit before the time of Haydn. (BTW, you spelled
> Haydn's name incorrectly.)
>
>
>
> > Didn't the noises from a blacksmith's shop inspire
> > Pythagoras' discovery of string length and simple
> > integer ratios? I wonder if that is just a coincidence.
>
>
> It's an apocryphal story -- we'd probably call it an
> "urban legend" today. It was propogated in antiquity
> by Nicomachus, Gaudentius, Iamblicus, Aristotle Elias,
> and Boethius. Because of its appearance in Boethius,
> it became a standard part of the teaching of music
> during the medieval period, and was finally shown
> to be wrong in the 1600s by Mersenne.
>
> The story is that Pythagoras was passing by a smithy
> and noticed that the sound of the hammers hitting
> the anvils produced consonant intervals. At first he
> thought the different intervals were due to differences
> in the strength of the men hitting the hammers, but
> when he went home and did some experiments he supposedly
> found that it was the weights of the hammers that produced
> the harmonious ratios. But this is incorrect.
>
> It is true that the Pythagorean ratios apply to lengths
> of strings and, somewhat less accurately, to pipes. But
> it does not apply to weights of hammers.
>
>
> Here's the relevant section from Boethius, in Latin:
>
>
> Quemadmodum Phitagoras proportiones consonantiarum inuenerit.
>
> HAEC igitur maxima causa fuit. cur relicto aurium iudicio
> Pytagoras ad regularum momenta migrauerit. qui nullis
> humanis auribus credens. quae partim natura. partim etiam
> extrinsecus permutantur: partim ipsis uariantibus aetatibus.
> nullis etiam deditus instrumentis. paenes quae sepe uarietas
> atque inconstantia nasceretur. dum nunc quidem si neruos
> uelis inspicere. uel aer humidior pulsus obtunderet. uel
> siccior excitaret. uel magnitudo cordae grauiorem redderet
> sonum. uel acumen subtilior tenuaret: uel alio quodammodo
> statum prioris constantiae permutaret. Et cum idem esset
> in caeteris instrumentis: omnia haec inconsulta minimaeque
> estimans fidei. diuque estuans inquirebat. quanam ratione
> firmiter et constanter consonantiarum momenta perdisceret.
> cum interea diuino quodam nutu praeteriens fabrorum officinas.
> pulsos maleos exaudiuit diuersis sonis unam quodammodo
> concinentiam personare. Ita igitur ad id quod diu inquirebat
> attonitus accessit ad opus. diuque considerans: arbitratus
> est diuersitatem sonorum ferientium uires efficere. Atque
> ut id apertius colliqueret: mutari inter se malleos imperauit.
> Sed sonorum proprietas non in hominum lacertis haerebat.
> sed mutatos malleos comitabatur. Ubi igitur id animaduertit:
> malleorum pondus examinat. Et cum quinque essent forte mallei
> dupli reperti sunt pondere. qui sibi secundum diapason
> consonantiam respondebant. Eundem etiam qui duplus erat alio.
> sesquitertium alterius comprehendit. ad quem scilicet
> diatessaron sonabat. Ad alium uero quendam qui eidem diapente
> consonantia iungebatur: eundem superioris duplum reperit esse
> sesqualterum. Duo uero ii ad quos superior duplex sesquitertius
> et sesalter esse conprobatus est ad se inuicem sesquioctauam
> proportionem perpensi sunt custodire. Quintus uero reiectus
> est qui cunctis erat inconsonans. Cum igitur ante Pitagoram
> consonantiae musicae partim diapason. partim diapente. partim
> diatessaron quae est consonantia minima uocarentur: primus
> Pitagoras hoc modo repperit qua proportione sibimet haec
> sonorum concordia iungeretur. Et ut sit clarius quod dictum
> est: sint uerbi gratia malleorum quattuor pondera quae subter
> descriptis numeris contineantur. XII. IX. VIII. Hi igitur
> mallei qui XII. et VI. ponderibus uergebant diapason in
> duplo concinentiam personabant. Malleus uero XII ponderum
> ad malleum VIIII ponderum et malleus VIII ponderum ad
> malleum VI. ponderum secundum epitritam proportionem
> diatessaron consonantia iungebatur; VIIII uero ponderum
> ad malleum VI. ponderum. et XII ad VIII: diapente
> consonantiam permiscebant; VIIII uero ad VIII: in
> sesquioctaua proportione resonabant tonum.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

🔗oyarman@ozanyarman.com

🔗klaus schmirler <KSchmir@online.de>

🔗Jon Szanto <jszanto@cox.net>

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
>
> Here, with the quote at the end, he's just trying to show that he
> knows Latin, and I don't. (Self-satisfied smugness over knowledge
> that others don't have is a far thing from wisdom.) People like him
> turn music students off from the tuning list, which is too bad. Can
> someone moderate him?

As someone who knows Monz personally, I can tell you that your
impression of him is completely incorrect. Monz goes out of his way to
be careful in his presentations to people, always being respectful.
The amount of work he has done (and continues to do) in his tuning
dictionary work and other related projects is virtually all pro bono
and a service to the community. If he - like all of us at times - gets
so deep into a subject that he supplies information that you don't
think relevent, way over-the-top, or just something different than you
expected, it is (I am sure) simply his enthusiasm to help others.

There might be valid reasons that people get turned off to this list,
but you couldn't find a guy more willing to help - and in a
considerate way - than Monz. And I don't understand Latin, either!

Cheers,
Jon

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:

> Here, with the quote at the end, he's just trying to
> show that he knows Latin, and I don't.

No, i'm not. First of all, i had no way of knowing when
i posted it that you don't know Latin. Secondly, i don't
know Latin well enough myself to be able to translate it
without a dictionary, and i never claimed to have any
superior knowledge of it.

I simply provided the Latin text of the Pythagoras story
as transmitted by Boethius because:

1) it isn't very long, and readers should always be
able to consult an original source for any story that
has any amount of dispute involved; and

2) i know that readers here can be too lazy to even
click on a link to check out a source, so i just copied
it and pasted it into my post, for anyone who might
find it helpful.

> (Self-satisfied smugness over knowledge that others
> don't have is a far thing from wisdom.)

Again, i don't keep tabs on what people here do or
don't know. I simply try to provide as much information
as i can to answer questions which people here ask.

I will admit that i don't go out of my way to appear
humble. If that bothers you so much, tough shit.

I'm here to learn as much as i can about a subject that
fascinates me, and to pass on what i do know to others
who want to learn.

> People like him turn music students off from the
> tuning list, which is too bad.

If you took a poll on how many music students i've
turned off from the tuning list versus how many whose
enthusiasm i've facilitated, i'm sure that you'd find
the latter far outnumber the former.

> Can someone moderate him?

No.

Stop being so silly. You want a moderator to censor
*my* posts just because *you* don't know Latin and
found it haughty of me to provide more information
than you were able to deal with? Please.

PS - If you want to use a fancy word like "supercilious",
especially in the subject line, and even more especially
when you are using it to deride an erudite scholar like me,
then please spell it correctly.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Just please don't start a tuning-latin group.

I know that was meant at least partly in jest, but
you know what? There actually *is* so much medieval
tuning theory written in Latin that starting a
separate group for it might be a good idea!

The index page of the Thesarus Musicarum Latinarum
has the most complete collection i know of, and it's big:

http://www.music.indiana.edu/tml/start.html

A Yahoo tuning-latin group would be a good way to try
to attract classical scholars who know Latin far better
than most of us here, to help get this stuff translated
into modern languages.

Here's a webpage i made of my English translation of
Patrice Bailhache's essay on Euler's music-theory, where
i used green to show my English translation of Bailhache's
translation of Euler's Latin text, and red to show my
own English translation of Euler. Along with my "T"
(for "translator's") footnotes, it points out some of
the subtle distinctions translators need to be aware of,
when working with material as technical as tuning theory.

http://sonic-arts.org/monzo/euler/euler-en.htm

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗monz <monz@tonalsoft.com>

🔗Carl Lumma <clumma@yahoo.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:

> Here, with the quote at the end, he's just trying to show
> that he knows Latin, and I don't. (Self-satisfied smugness
> over knowledge that others don't have is a far thing from
> wisdom.) People like him turn music students off from the
> tuning list, which is too bad. Can someone moderate him?

I wouldn't want this list to lose any music students by
me turning them off ... or for that matter, by me turning off
any self-centered ass who comes to the conclusion that i'm
using my valuable time posting stuff here just so that i can
*assume* that he/she lacks some knowledge that i have and
therefore allow myself to feel superior.

So ... here's the relevant section from Boethius, in *English*:

It's Chapter 10 from Book 1 of his treatise on music, in
Bower's translation, with ratios and standard musical interval
names added by me to clarify the Latin and Greek terminology.

-------

_In what manner Pythagoras investigated the ratios of consonances_

This, then was primarily the reason why Pythagoras, having
abandoned the judgment of hearing, had turned to the weights
of rules. He put no credence in human ears, which are subject
to change, in part thru nature, in part by external circumstance,
and undergo changes caused by age. Nor did he devote himself
to instruments, in conjunction with which much inconstancy and
uncertainty often arise. When you wish to examine strings, for
example, more humid air may deaden the pulsation, or drier air
may excite it, or the thickness of a string may render a sound
lower, or thinness may make it higher, or, by some other means,
one alters a state of previous stability. Moreover, the same
would be true of other instruments.

Assessing all these instruments as unreliable and granting
them a minimum of trust, yet remaining curious for some time,
Pythagoras was seeking a way to acquire thru reason,
unfalteringly and consistently, a full knowledge of the
criteria for consonances, In the meantime, by a kind of
divine will, while passing the workshop of blacksmiths, he
overheard the beating of hammers somehow emit a single
consonance from differing sounds. Thus in the presence of
what he had long sought, he approached the activity spellbound.
Reflecting for a time, he decided that the strength of the men
hammering caused the diversity of sounds, and in order to prove
this more clearly, he commanded them to exchange hammers among
themselves. But the property of sounds did not rest in the
muscles of the men; rather, it followed the exchanged hammers.
When he had observed this, he examined the weight of the hammers.
There happened to be five hammers, and those which sounded
together the consonance of the diapason [8ve] were found to
be double in weight. Pythagoras determined further that the
same one, the one that was the double of the second, was the
sesquitertian [4/3] of another, with which it sound a diatessaron
[4th]. Then he found that this same one, the duple [2/1] of the
above pair, formed the sesquialter [3/2] ratio of still another,
and that it joined with it in the consonance of the diapente
[5th]. These two, to which the first double proved to be
sesquitertian [4/3] and sesquialter [3/2], were discovered in
turn to hold the sesquioctave [9/8] ratio between themselves.
The fifth hammer, which was discordant with all, was discarded.

Altho some musical consonances were called "diapason" [8ve],
some "diapente" [5th], and some "diatessaron" [4th] (which
is the smallest consonance) before Pythagoras, Pythagoras
was the first to ascertain thru this means by what ratio the
concord of sounds was joined together. So that what has been
said might be clearer, for sake of illustration, let the
weights of the four hammers be contained in the numbers
written below.

12:9:8:6.

Thus the hammers which bring together 12 with 6 pounds sounded
the consonance of the diapason [8ve] in duple [2/1] ratio.
The hammer of 12 pounds with that of 9 (and the hammer of 8
with that of 6) joined in the consonance of the diatessaron
[4th] according to the epitrita [4/3] ratio. The one of
9 pounds with that of 6 (as well as those of 12 and 8)
commingled the consonance of the diapente [5th]. The one
of 9 with that of 8 sounded the tone [2nd] according to the
sesquioctave [9/8] ratio.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> So ... here's the relevant section from Boethius, in *English*:
>
> It's Chapter 10 from Book 1 of his treatise on music, in
> Bower's translation, with ratios and standard musical interval
> names added by me to clarify the Latin and Greek terminology.
>
> <snip>
>
> 12:9:8:6.

Note that that proportion defines the _hestotes_
(fixed framework notes) bounding the set of two
disjunct tetrachords within the central octave of
the ancient Greek "Greater Perfect System" --
analagous to the notes e:B:A:E. See:

http://tonalsoft.com/enc/g/gps.aspx

It's a good story, told well by Boethius ... but
remember that it's only correct when applied to
the measurement of string-lengths and (a little
less accurately) lengths of blown pipes. The actual
story about the ratios of weights of the hammers is
totally incorrect.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗oyarman@ozanyarman.com

Please please please do translate also the portion on Chapter XV I
mentioned... the one on modes.

Cordially,
Ozan

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 16 Kasï¿½m 2005 ï¿½arï¿½amba 6:29
Subject: [tuning] The harmonious blacksmith story, as told by Boethius

> --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
>
> > Here, with the quote at the end, he's just trying to show
> > that he knows Latin, and I don't. (Self-satisfied smugness
> > over knowledge that others don't have is a far thing from
> > wisdom.) People like him turn music students off from the
> > tuning list, which is too bad. Can someone moderate him?
>
>
> I wouldn't want this list to lose any music students by
> me turning them off ... or for that matter, by me turning off
> any self-centered ass who comes to the conclusion that i'm
> using my valuable time posting stuff here just so that i can
> *assume* that he/she lacks some knowledge that i have and
> therefore allow myself to feel superior.
>
> So ... here's the relevant section from Boethius, in *English*:
>
> It's Chapter 10 from Book 1 of his treatise on music, in
> Bower's translation, with ratios and standard musical interval
> names added by me to clarify the Latin and Greek terminology.
>
> -------
>
> _In what manner Pythagoras investigated the ratios of consonances_
>
> This, then was primarily the reason why Pythagoras, having
> abandoned the judgment of hearing, had turned to the weights
> of rules. He put no credence in human ears, which are subject
> to change, in part thru nature, in part by external circumstance,
> and undergo changes caused by age. Nor did he devote himself
> to instruments, in conjunction with which much inconstancy and
> uncertainty often arise. When you wish to examine strings, for
> example, more humid air may deaden the pulsation, or drier air
> may excite it, or the thickness of a string may render a sound
> lower, or thinness may make it higher, or, by some other means,
> one alters a state of previous stability. Moreover, the same
> would be true of other instruments.
>
> Assessing all these instruments as unreliable and granting
> them a minimum of trust, yet remaining curious for some time,
> Pythagoras was seeking a way to acquire thru reason,
> unfalteringly and consistently, a full knowledge of the
> criteria for consonances, In the meantime, by a kind of
> divine will, while passing the workshop of blacksmiths, he
> overheard the beating of hammers somehow emit a single
> consonance from differing sounds. Thus in the presence of
> what he had long sought, he approached the activity spellbound.
> Reflecting for a time, he decided that the strength of the men
> hammering caused the diversity of sounds, and in order to prove
> this more clearly, he commanded them to exchange hammers among
> themselves. But the property of sounds did not rest in the
> muscles of the men; rather, it followed the exchanged hammers.
> When he had observed this, he examined the weight of the hammers.
> There happened to be five hammers, and those which sounded
> together the consonance of the diapason [8ve] were found to
> be double in weight. Pythagoras determined further that the
> same one, the one that was the double of the second, was the
> sesquitertian [4/3] of another, with which it sound a diatessaron
> [4th]. Then he found that this same one, the duple [2/1] of the
> above pair, formed the sesquialter [3/2] ratio of still another,
> and that it joined with it in the consonance of the diapente
> [5th]. These two, to which the first double proved to be
> sesquitertian [4/3] and sesquialter [3/2], were discovered in
> turn to hold the sesquioctave [9/8] ratio between themselves.
> The fifth hammer, which was discordant with all, was discarded.
>
> Altho some musical consonances were called "diapason" [8ve],
> some "diapente" [5th], and some "diatessaron" [4th] (which
> is the smallest consonance) before Pythagoras, Pythagoras
> was the first to ascertain thru this means by what ratio the
> concord of sounds was joined together. So that what has been
> said might be clearer, for sake of illustration, let the
> weights of the four hammers be contained in the numbers
> written below.
>
> 12:9:8:6.
>
> Thus the hammers which bring together 12 with 6 pounds sounded
> the consonance of the diapason [8ve] in duple [2/1] ratio.
> The hammer of 12 pounds with that of 9 (and the hammer of 8
> with that of 6) joined in the consonance of the diatessaron
> [4th] according to the epitrita [4/3] ratio. The one of
> 9 pounds with that of 6 (as well as those of 12 and 8)
> commingled the consonance of the diapente [5th]. The one
> of 9 with that of 8 sounded the tone [2nd] according to the
> sesquioctave [9/8] ratio.
>
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>

🔗hstraub64 <hstraub64@telesonique.net>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> > Just please don't start a tuning-latin group.
>
>
> I know that was meant at least partly in jest, but
> you know what? There actually *is* so much medieval
> tuning theory written in Latin that starting a
> separate group for it might be a good idea!
>
> The index page of the Thesarus Musicarum Latinarum
> has the most complete collection i know of, and it's big:
>
> http://www.music.indiana.edu/tml/start.html
>
>
> A Yahoo tuning-latin group would be a good way to try
> to attract classical scholars who know Latin far better
> than most of us here, to help get this stuff translated
> into modern languages.
>

Heh, this reminds me I learned that thing once, long time ago. I am
just thinking I might try to get it out of the cellar - and a text on
tuning would be something to my liking. Any text that is especially
wanted to be translated?
--
Hans Straub

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

On Tue, 15 Nov 2005, "traktus5" wrote:
>
> Here, with the quote at the end, he's just trying to show that he
> knows Latin, and I don't. (Self-satisfied smugness over knowledge
> that others don't have is a far thing from wisdom.) People like him
> turn music students off from the tuning list, which is too bad. Can
> someone moderate him?

"traktus5",
(or whatever your _real_ name is),

I can't believe how rude you are! Here's monz going out
of his way to supply source material that you, or of not
you, other list members might find useful; then you turn
right around and insult the guy! Please grow up. If you
aren't adult enough to apologise to monz forthwith, I'll
ask the group to consider moderating your posts - at least
until you learn some manners.

Perhaps you were suffering a fit of frustration, and hit
"Send" by mistake? If so,

Best wishes for a speedy recovery,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.362 / Virus Database: 267.13.3/172 - Release Date: 15/11/05

🔗Tom Dent <stringph@gmail.com>

The piece is called Air & Variations from the Suite in E major. The
traditional name might or might not have come from Handel - another
one of these unverifiable music history legends. No way to
substantiate whether Handel was referring to anything.

~~~T~~~

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
>
> > I thought it might be a legend, but does anyone think
> > there is any chance that Handel was refering to the
> > legend when he named the piece "Harmonious Blacksmith"?
>
>
>
> Yes, Handel definitely was referring to the Pythagoras
> story in that piece. It was a famous tale which every
> schooled musician learned as part of his training,
> probably dying out only (i'm guessing) around Beethoven's
> time.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

🔗monz <monz@tonalsoft.com>

Hi Tom,

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@g...> wrote:

> The piece is called Air & Variations from the Suite
> in E major. The traditional name might or might not
> have come from Handel - another one of these unverifiable
> music history legends. No way to substantiate whether
> Handel was referring to anything.

Thanks for that!

I'm not a Handel scholar by any stretch of the imagination.
Other than his most popular pieces (Messiah, Water Music,
Royal Fireworks Music), i've never been a big fan.

I only know the piece because it's in a book of
"Easy Classics" that i use with my piano students, and
one of them played it in a recital last year. Glad to
know the accurate information.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗monz <monz@tonalsoft.com>

🔗Mark <mark@equiton.waitrose.com>

Somewhat belatedly,

I would support Monz' quoting of the Latin, after all it's not an
epigraph (as literary wits are often quoting in the manner of a
riddle), but a quote of actual text.

Just because students don't receive a classical education for free
doesn't mean that they should sit there and complain about it.

Of course a translation would be nice (or a link to one). Still it
didn't stop me from getting my Latin Dictionary out and having a go
myself.

The inquiring mind should not see the complex or obscure as a bastion
erected against ignorance, but rather a challenge to be scaled. Those
who merely jeer at it deserve to be on the outside.

Perhaps the respondent is in need of moderating?

Mark
(feeling particularly Sorabjian about this)

🔗hstraub64 <hstraub64@telesonique.net>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> > --- In tuning@yahoogroups.com, "hstraub64" <hstraub64@t...> wrote:
>
> > Any text that is especially wanted to be translated?
>
>
> How about any of the non-Boethius texts from here?
>
> http://www.music.indiana.edu/tml/6th-8th/6TH-8TH_INDEX.html
>
> The Fulgentius text goes to 12 chapters, the rest are all
> quite short ... and of enormous interest to me.
>
>
> (Be warned that you've opened a real can of worms now
> ...

Afraid so :-) *tremble*

To your information, I had latin for 6 1/2 years in grammar school,
but it was more than 20 years ago. Got to dig out my dictionaries first...

There are indeed a lot of quite short texts on the site above, so I
think there is a fair chance. But again, after reading one of your
previous post about all these subtle differences, tonus, modus, tropos
and all this... Dunno just now...
--
Hans Straub

🔗oyarman@ozanyarman.com

Hans, what are the resources you recommend for latin-beginners like myself?
Recommendations on software dictionaries and interactice CD-ROMs would be
most appreciated.

Cordially,
Ozan

----- Original Message -----
From: "hstraub64" <hstraub64@telesonique.net>
To: <tuning@yahoogroups.com>
Sent: 16 Kasï¿½m 2005 ï¿½arï¿½amba 19:01
Subject: [tuning] Re: tuning-latin group?

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> >
> > > --- In tuning@yahoogroups.com, "hstraub64" <hstraub64@t...> wrote:
> >
> > > Any text that is especially wanted to be translated?
> >
> >
> > How about any of the non-Boethius texts from here?
> >
> > http://www.music.indiana.edu/tml/6th-8th/6TH-8TH_INDEX.html
> >
> > The Fulgentius text goes to 12 chapters, the rest are all
> > quite short ... and of enormous interest to me.
> >
> >
> > (Be warned that you've opened a real can of worms now
> > ...
>
> Afraid so :-) *tremble*
>
> To your information, I had latin for 6 1/2 years in grammar school,
> but it was more than 20 years ago. Got to dig out my dictionaries first...
>
> There are indeed a lot of quite short texts on the site above, so I
> think there is a fair chance. But again, after reading one of your
> previous post about all these subtle differences, tonus, modus, tropos
> and all this... Dunno just now...
> --
> Hans Straub
>
>
>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>
>
>
>
>
>
>

🔗hstraub64 <hstraub64@telesonique.net>

🔗oyarman@ozanyarman.com

Thank you so much, I'm sure to benefit from these links.

----- Original Message -----
From: "hstraub64" <hstraub64@telesonique.net>
To: <tuning@yahoogroups.com>
Sent: 17 Kasï¿½m 2005 Perï¿½embe 10:28
Subject: [tuning] Re: tuning-latin group?

> --- In tuning@yahoogroups.com, <oyarman@o...> wrote:
> >
> > Hans, what are the resources you recommend for latin-beginners like
> > myself?
> > Recommendations on software dictionaries and interactice CD-ROMs would
> > be most appreciated.
> >
>
> You might start looking on http://www.yourdictionary.com, which is a
> good starting point for resources about almost any language. There are
> several entries for latin there, see at
>
> http://www.yourdictionary.com/languages/romance.html
> http://www.yourdictionary.com/grammars2.html#latin
>
> CD-ROMs I do not know - when I learnt latin, I didn't even know what a
> CD-ROM is...
> --
> Hans Straub
>
>
>
>

🔗Mark Rankin <markrankin95511@yahoo.com>

It may seem silly, you'se guys, but as for me, I raise
my eyebrow at all this supercilious accusing. Mr.
nearly Tetraktus, you distract us!

-- Mark Rankin

--- Mark <mark@equiton.waitrose.com> wrote:

> Somewhat belatedly,
>
> I would support Monz' quoting of the Latin, after
> all it's not an
> epigraph (as literary wits are often quoting in the
> manner of a
> riddle), but a quote of actual text.
>
> Just because students don't receive a classical
> education for free
> doesn't mean that they should sit there and complain
> about it.
>
> Of course a translation would be nice (or a link to
> one). Still it
> didn't stop me from getting my Latin Dictionary out
> and having a go
> myself.
>
> The inquiring mind should not see the complex or
> obscure as a bastion
> erected against ignorance, but rather a challenge to
> be scaled. Those
> who merely jeer at it deserve to be on the outside.
>
> Perhaps the respondent is in need of moderating?
>
> Mark
> (feeling particularly Sorabjian about this)
>
> --- In tuning@yahoogroups.com, "traktus5"
> <kj4321@h...> wrote:
> >
> > Here, with the quote at the end, he's just trying
> to show that he
> > knows Latin, and I don't. (Self-satisfied
> smugness over knowledge
> > that others don't have is a far thing from
> wisdom.) People like him
> > turn music students off from the tuning list,
> which is too bad. Can
> > someone moderate him?
>
>
>
>
>

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