Accident history

Hi.

In this site http://www.uk-piano.org/history/compass.html

I've found this:

>The first sharp to be added to the keyboard was probably the F
>sharp, according to academic research.
>
>The interval of an augmented fourth, between the notes we would
>call F and B, was considered discordant, so the B was often
>lowered, bringing in an extra note, B flat, shorter and narrower,
>between the A and the B. After the B flat probably came the E flat,
>then C sharp and finally G sharp.

The author wrote me that those sections were taken from his notes at
history and tuning letures back in the 1970's.

Are these informations correct?

Lorenzo

Hi Lorenzo,

I think this is mostly correct. However, the Bb (which is called simply "B"
in German) was probably first for musical reasons. The B natural (which is
called "H" in German) was probably the development. In other words, the sound
of the interval is earlier than the spelling of its position in a theory.

best, Johnny

i was under the impression that Bb was introduced when the pythagorean
diatone was subsumed by the 5 limit ogdad ? however, i must admit to only
a superficial knowledge of the subject. best, buzzy^

--- Afmmjr@aol.com wrote:

> Hi Lorenzo,
>
> I think this is mostly correct. However, the Bb (which is called simply
> "B"
> in German) was probably first for musical reasons. The B natural (which is
>
> called "H" in German) was probably the development. In other words, the
> sound
> of the interval is earlier than the spelling of its position in a theory.
>
> best, Johnny
>

=====
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hi Lorenzo, Johnny, and Haresh,

--- In tuning@yahoogroups.com, "lorenzofrizzera" <lorenzo.frizzera@c..
.> wrote:

>
>
> Hi.
>
> In this site http://www.uk-piano.org/history/compass.html
>
> I've found this:
>
>> The first sharp to be added to the keyboard was probably the F
>> sharp, according to academic research.
>>
>> The interval of an augmented fourth, between the notes we
>> would call F and B, was considered discordant, so the B was
>> often lowered, bringing in an extra note, B flat, shorter
>> and narrower, between the A and the B. After the B flat
>> probably came the E flat, then C sharp and finally G sharp.
>
> The author wrote me that those sections were taken from his
> notes at history and tuning letures back in the 1970's.
>
> Are these informations correct?
>
> Lorenzo

it may be true that F# was the first accidental added to
the *keyboard*, i'm not sure ... but Bb came before any
other accidental in both theory and non-keyboard practice.

it arose as a result of the ancient Greek
"Perfect Immutable System" (PIS), which included
both the "Greater Perfect System" (GPS) and the
"Lesser Perfect System" (LPS).

all of these scales were based on "similar tetrachords",
i.e., tetrachords which all had the same interval structure.

the GPS had 2 pairs of tetrachords conjunct (connected
together by the same note serving simultaneously as the
bottom note of one tetrachord and the top note of the one
below it: the _hyperbolaion_-_diezeugmenon_ pair, and the
_meson_-_hypaton_ pair), but also a "tone of disjunction"
(9:8 ratio) between the main reference note _mese_ ("middle",
the top note of tetrachord _meson_) and the bottom note of
the tetrachord above it (tetrachord _diezeugmenon_).

the LPS used 3 tetrachords which were all conjunct:
_synemmenon_-_meson_-_hypaton_.

(and both the LPS and GPS had the "added tone"
_proslambanomenos_ at the bottom.)

when medieval theorists hit on the idea of naming the notes
with Roman letters, and then tried to give their scales cachet
by making analogies with ancient Greek theory, they named
_mese_ "a" and used the other letters b, c, d, e, f, g in
ascending order for the rest of the distinct notes in the PIS,
then repeated the letters for notes which were an "octave"
apart, which was an early recognition of "octave"-equivalence.

(this had actually already been done with the Greek-letter
notation attested by Alypius, Aristides Quintilianus, and
Boethius ... but all three of these authors were well after
the absorption of Greece into the Roman Empire. my own
guess is that the Greeks themselves never recognized
"octave"-equivalence in their notation, because for them
everything was based on tetrachords.)

the whole PIS spanned 2 octaves, one each below and above
_mese_ "a", so capital letters were used for the notes in
the lower "octave" below _mese_ "a", and lower-case for the
notes in the upper "octave" above _mese_ "a".

however, the "b" in _diezeugmenon_ was a whole-tone (9:8,
i.e., the "tone of disjunction") above "a", whereas the "b"
in _synemmenon_ followed the tetrachord pattern of having
the semitone at the bottom of the tetrachord, and was thus
only a semitone above "b". so there were two different "b"s,
one a semitone higher than the other.

thus a means of distinguishing between them was necessary,
and so the regular round "b" ("soft-b") was used for the
lower "b", and a "b" whose round part was written with
straight lines so as to make a square ("hard-b") was used
for the higher "b".

the "soft-b" eventually evolved into our modern "flat" symbol
(quite obviously), and the "hard-b" evolved into both the
"natural" symbol and the "sharp" symbol, which for quite a
long time were used interchangeably -- this is because the
practice of "mutation" and _musica ficta_, based on solfege
syllables, preceded our modern practice of having specific
pitch-alteration meanings for the accidentals.

i've simplified the story a bit ... one big thing i left
out was that the boundaries of all the tetrachords were
shifted a tone lower in pitch, and the reference tetrachord
shifted down by one, to the one which contained D, E, F, G.
this was because the Frankish theorists wanted to use what
they could of the ancient Greek theory, but base their system
on the finals of the church modes which were then being used
in *their* music, the actual Greek music having become obsolete
long before then.

you should be able to piece together all of the details
from my relevant Encyclopaedia pages ... here are a few,
which should be consulted in this order:

http://tonalsoft.com/enc/index2.htm?../monzo/aristoxenus/tutorial.htm

http://tonalsoft.com/enc/index2.htm?pis.htm

http://tonalsoft.com/enc/index2.htm?gps.htm

http://tonalsoft.com/enc/index2.htm?lps.htm

http://tonalsoft.com/enc/index2.htm?mutation.htm

http://tonalsoft.com/enc/index2.htm?german-h.htm

-monz

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> <snip>
>
> however, the "b" in _diezeugmenon_ was a whole-tone (9:8,
> i.e., the "tone of disjunction") above "a", whereas the "b"
> in _synemmenon_ followed the tetrachord pattern of having
> the semitone at the bottom of the tetrachord, and was thus
> only a semitone above "b". so there were two different "b"s,
> one a semitone higher than the other.

oops ... my bad.

of course, i meant:

> ... the "b"
> in _synemmenon_ followed the tetrachord pattern of having
> the semitone at the bottom of the tetrachord, and was thus
> only a semitone above "a".

(BTW, i will be adding my whole explanation to the bottom
of the Encyclopaedia "accidental" webpage.)

-monz

Monz, that was a very fulfilling overview. But was Bb of Greek theory the same Bb in reference to A4=440hz? I think not. If we wanted to pinpoint it according to our recent understanding of tones, where would it be?

Cordially,
Ozan
----- Original Message -----
From: monz
To: tuning@yahoogroups.com
Sent: 04 Ocak 2005 Salı 8:13
Subject: [tuning] Re: Accident history

hi Lorenzo, Johnny, and Haresh,

--- In tuning@yahoogroups.com, "lorenzofrizzera" <lorenzo.frizzera@c..
.> wrote:

>
>
> Hi.
>
> In this site http://www.uk-piano.org/history/compass.html
>
> I've found this:
>
>> The first sharp to be added to the keyboard was probably the F
>> sharp, according to academic research.
>>
>> The interval of an augmented fourth, between the notes we
>> would call F and B, was considered discordant, so the B was
>> often lowered, bringing in an extra note, B flat, shorter
>> and narrower, between the A and the B. After the B flat
>> probably came the E flat, then C sharp and finally G sharp.
>
> The author wrote me that those sections were taken from his
> notes at history and tuning letures back in the 1970's.
>
> Are these informations correct?
>
> Lorenzo

it may be true that F# was the first accidental added to
the *keyboard*, i'm not sure ... but Bb came before any
other accidental in both theory and non-keyboard practice.

it arose as a result of the ancient Greek
"Perfect Immutable System" (PIS), which included
both the "Greater Perfect System" (GPS) and the
"Lesser Perfect System" (LPS).

all of these scales were based on "similar tetrachords",
i.e., tetrachords which all had the same interval structure.

the GPS had 2 pairs of tetrachords conjunct (connected
together by the same note serving simultaneously as the
bottom note of one tetrachord and the top note of the one
below it: the _hyperbolaion_-_diezeugmenon_ pair, and the
_meson_-_hypaton_ pair), but also a "tone of disjunction"
(9:8 ratio) between the main reference note _mese_ ("middle",
the top note of tetrachord _meson_) and the bottom note of
the tetrachord above it (tetrachord _diezeugmenon_).

the LPS used 3 tetrachords which were all conjunct:
_synemmenon_-_meson_-_hypaton_.

(and both the LPS and GPS had the "added tone"
_proslambanomenos_ at the bottom.)

when medieval theorists hit on the idea of naming the notes
with Roman letters, and then tried to give their scales cachet
by making analogies with ancient Greek theory, they named
_mese_ "a" and used the other letters b, c, d, e, f, g in
ascending order for the rest of the distinct notes in the PIS,
then repeated the letters for notes which were an "octave"
apart, which was an early recognition of "octave"-equivalence.

(this had actually already been done with the Greek-letter
notation attested by Alypius, Aristides Quintilianus, and
Boethius ... but all three of these authors were well after
the absorption of Greece into the Roman Empire. my own
guess is that the Greeks themselves never recognized
"octave"-equivalence in their notation, because for them
everything was based on tetrachords.)

the whole PIS spanned 2 octaves, one each below and above
_mese_ "a", so capital letters were used for the notes in
the lower "octave" below _mese_ "a", and lower-case for the
notes in the upper "octave" above _mese_ "a".

however, the "b" in _diezeugmenon_ was a whole-tone (9:8,
i.e., the "tone of disjunction") above "a", whereas the "b"
in _synemmenon_ followed the tetrachord pattern of having
the semitone at the bottom of the tetrachord, and was thus
only a semitone above "b". so there were two different "b"s,
one a semitone higher than the other.

thus a means of distinguishing between them was necessary,
and so the regular round "b" ("soft-b") was used for the
lower "b", and a "b" whose round part was written with
straight lines so as to make a square ("hard-b") was used
for the higher "b".

the "soft-b" eventually evolved into our modern "flat" symbol
(quite obviously), and the "hard-b" evolved into both the
"natural" symbol and the "sharp" symbol, which for quite a
long time were used interchangeably -- this is because the
practice of "mutation" and _musica ficta_, based on solfege
syllables, preceded our modern practice of having specific
pitch-alteration meanings for the accidentals.

i've simplified the story a bit ... one big thing i left
out was that the boundaries of all the tetrachords were
shifted a tone lower in pitch, and the reference tetrachord
shifted down by one, to the one which contained D, E, F, G.
this was because the Frankish theorists wanted to use what
they could of the ancient Greek theory, but base their system
on the finals of the church modes which were then being used
in *their* music, the actual Greek music having become obsolete
long before then.

you should be able to piece together all of the details
from my relevant Encyclopaedia pages ... here are a few,
which should be consulted in this order:

http://tonalsoft.com/enc/index2.htm?../monzo/aristoxenus/tutorial.htm

http://tonalsoft.com/enc/index2.htm?pis.htm

http://tonalsoft.com/enc/index2.htm?gps.htm

http://tonalsoft.com/enc/index2.htm?lps.htm

http://tonalsoft.com/enc/index2.htm?mutation.htm

http://tonalsoft.com/enc/index2.htm?german-h.htm

-monz

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hi Ozan,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> Monz, that was a very fulfilling overview. But was
> Bb of Greek theory the same Bb in reference to A4=440hz?
> I think not. If we wanted to pinpoint it according to
> our recent understanding of tones, where would it be?
>
> Cordially,
> Ozan

i had meant to mention it but forgot ... no, when letters
were first applied to the ancient Greek theory, they had
only a *relative* meaning.

there was no absolute pitch reference -- the singer just
used whatever range was most comfortable, and the interval
pattern determined which frequency was "A".

this remained the case thru-out the early medieval period
... i believe it was only the growing acceptance of keyboard
instruments which forced Europoean musicians into nailing
down the frequency of "A", beginning around 1300.

of course, there would be a bit more standardization of the
frequency-to-pitch relationship with regard to instruments,
but unfortunately none of them survive in playable condition.
the best data we can get there is from carefully-crafted
reproductions of archaeological finds.

in any case, i personally have no idea of the frequency-to-pitch
relationship for instruments prior to about 1500 or so.

Ellis, in one of his appendices to Helmholtz's book
("On the Sensations of Tone", p. 493-513), gives a fairly
exhaustive list of the pitch of "A" for several centuries
of European musical history. -- i wrote about this several
years ago on this list ... good luck finding it in the
archives.

here are some webpages which some good info on the subject
... but again, it only applies to the last few centuries of
Euro-centric music:

http://www.uk-piano.org/history/pitch.html

http://ourworld.compuserve.com/homepages/paulpoletti/pitch.PDF

http://www.wam.hr/Arhiva/US/Cavanagh_440Hz.pdf

http://web.archive.org/web/20031202212515/www.mozartpiano.com/pitch.
html

-monz

Dear Monz,

I read through all the material you have provided in the links. I knew beforehand the extent to which the frequency of A varied throughout the centuries but only now do I know for certain that A could have been anywhere from F4 to C#5 in quotidian terms since c.1500.

If the response you have prepared a few years ago on this subject in noteworthy, perhaps you would like to include it in your tonalpedia for quick reference?

Also, I would like to hear your opinion about the situation of Turkish Music where 440Hz is accepted as D4 (acknowledged as `Neva`, being the fifth degree from `Rast` - the actual fundamental tone historically). This would make A4 poised at c.660Hz and `Rast` poised at c. 294hz (The actual D4 today), an absurd practice with no logic behind it whatsoever. I propose that Rast is taken down to C4 at c. 262Hz where the sixth degree (perde Huseyni) coincides with A4=440Hz. What do you think?

Cordially,
Ozan

----- Original Message -----
From: monz
To: tuning@yahoogroups.com
Sent: 06 Ocak 2005 Perşembe 17:55
Subject: [tuning] Re: Accident history

hi Ozan,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> Monz, that was a very fulfilling overview. But was
> Bb of Greek theory the same Bb in reference to A4=440hz?
> I think not. If we wanted to pinpoint it according to
> our recent understanding of tones, where would it be?
>
> Cordially,
> Ozan

i had meant to mention it but forgot ... no, when letters
were first applied to the ancient Greek theory, they had
only a *relative* meaning.

there was no absolute pitch reference -- the singer just
used whatever range was most comfortable, and the interval
pattern determined which frequency was "A".

this remained the case thru-out the early medieval period
... i believe it was only the growing acceptance of keyboard
instruments which forced Europoean musicians into nailing
down the frequency of "A", beginning around 1300.

of course, there would be a bit more standardization of the
frequency-to-pitch relationship with regard to instruments,
but unfortunately none of them survive in playable condition.
the best data we can get there is from carefully-crafted
reproductions of archaeological finds.

in any case, i personally have no idea of the frequency-to-pitch
relationship for instruments prior to about 1500 or so.

Ellis, in one of his appendices to Helmholtz's book
("On the Sensations of Tone", p. 493-513), gives a fairly
exhaustive list of the pitch of "A" for several centuries
of European musical history. -- i wrote about this several
years ago on this list ... good luck finding it in the
archives.

here are some webpages which some good info on the subject
... but again, it only applies to the last few centuries of
Euro-centric music:

http://www.uk-piano.org/history/pitch.html

http://ourworld.compuserve.com/homepages/paulpoletti/pitch.PDF

http://www.wam.hr/Arhiva/US/Cavanagh_440Hz.pdf

http://web.archive.org/web/20031202212515/www.mozartpiano.com/pitch.
html

-monz

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