Yahoo Tuning Groups Ultimate Backup makemicromusic OUT of tune Tuning

Hey Folks, Im a new member on here. Recently I posted
the below to the Tuning Forum, and got some great
feedback from Charles Lucy of LucyTuning, he really
filled in some gaps. But Im still left trying to find
out something simple.... related to Just Tuning, and
Pythagorean Spiral of Fifth Tuning....
I've listed the question below, as well as the thread
between Charles and I. I now know how to get the
values for edo, thanks to Charles, but still do not
know hot to get these values for Pythagorean Spiral of
Fifths or Just. Lets assume we are using a Just
intonation interval of 3/2;
--------------------

Im new to music theory and am intrigued by two
questions that have
captured my imagination;

1.) A musician friend of mine told me, that if a band
were playing
together and everyones instrument was in tune except
for one person,
the one person with the out of tune instrument would
really stand out.

Normally, the one person would get his out of tune
instrument back in
tune. Alternatively however, a different approach
could be used to
normalize the sound within the band, relatively
speaking.

That is, all the other band members could re-tune
their in tune
instruments to be out of tune the in same way the
original un-tuned
instrument sounded. This way they would sound
relatively the same,
tuning wise.

So - this got me thinking....

In the below table, there are four instruments. They
could be guitars,
or something similiar.

Column (A) shows the frequency in hertz of four
different notes,
intervals played on the instruments when they are in
tune. Notes,
intervals, for example; b, diminished octave, C#, A#,
all sound
the same way on each instrument.

Column (B) on the other hand, represents a scenario,
where each of
the four instruments may be tuned quite differently
from each other.

Here comes the first question...

We want to match two instruments to each other in
accordance with
values listed in column (B)

The important instrument is 'INSTRUMENT # 1'.

Constraints;

We only get to play one note on 'INSTRUMENT # 1'. That
is 496.15104
as shown in the table.

============ ========= ========= ========= =========
========= ========= ===
Freq. in Hertz
COLUMN (A) COLUMN (B)
NOTE INTERVAL IN TUNE OUT OF TUNE
------------ --------- --------- --------- ---------
--------- -
INSTRUMENT # 1 B Mjr 7th 495.00 496.15104
INSTRUMENT # 2 Dim. Octave. 501.6 504.1152
INSTRUMENT # 3 C# Enharmonic 270.34 269.15072
INSTRUMENT # 4 A# Aug. 6th 448.8 452.05248
============ ========= ========= ========= =========
========= ========= ===
We can only play one note on instruments #2 through
#4, likewise
those notes being the ones listed in column (B) for
each instrument.

What simple rule, principle, formula, will allow us to
determine
which instrument from #2 to #4 is tuned most closely
to instrument # 1.

Further, by knowing ONLY INSTRUMENT #1's note listed
in Column (B),
how can we derive the rest of its entire 'out of tune'
scale?

____________ _________ _________ _________ _________
__

======
On 30 Sep 2006, at 02:23, Dan Amateur wrote:

Hi Charles,

I've heard a lot about you recently. Your work is
almost legend, thank you for taking the time to
respond to me. I very much appreciate it. I will
check out the website.

May I ask, how might this be done for a just scale,
Pythagorean, based on the circle of fifths? Rather
than edo?

From Charles Lucy;

Your question is paradoxical.

Neither Just nor Pythagorean tuning will have a CIRCLE
of fifths.

Pythagorean fifths result in a spiral, as do all
non-equal meantone-type tunings e.g. LucyTuning. Phi,
1/4 comma etc.

Just intonation won't result in a circle; in fact all
that it results (in my opinion) is postings on the
tuning list about how many angels can dance on the
head of a grasshopper;-) - but the answer is always in
the form of integer:integer. (whole number ratios).

Unless you particularly enjoy playing numerology, I
suggest that you avoid Just Intonation, as it doesn't
even produce interesting or harmonious music from my
experience and experimentations.

Circles of fifths and fourths only occur in some equal
temperaments e.g. 12 edo; 19 edo; 31 edo; 53 edo etc.

You could include other equal systems as being
circular, but that creates the problem of defining
what you consider to be a fifth;-)

As far as I can see, the problem that you are having
is in finding a consistent connection between
notenames and frequencies.

The solution that I use is very simple:
multiple sharps and flats A to G derived from
A4=440Hz,
and the Large interval (i.e. between the fourth and
fifth) is:
the ratio of the two pi root of 2.
i.e. 2^(1/(2*pi))
or the radian angle in geometric terms = 360/2pi
degrees.

Sorry to be evasive, yet I believe that you need to re
think and restate your problem in order to be able to
find a solution
to getting your various instruments to play in tune
with eachother.

Charles Lucy <lucy@...> wrote:
Answer to your puzzle is easy for 12 edo, just
multiply the reference frequency in Hz. by 2^(1/12)
twelfth root of 2 to give all the other 11 frequency
values.

If you wish to really understand how tuning, harmony
etc. works in the practical world of multiple
microtuned instruments playing together, check out the
lucytune.com site.

Using A4 = 440 Hz, as your reference pitch; all the
other LucyTuned notes and instruments will play
exactly in tune with themselves and eachother for as
many notes per octave you choose to use.

From: "Charles Lucy" <lucy@...> Add to
Address Book
Subject: Re: OUT of tune Tuning - Question from new
member
Date: Sat, 30 Sep 2006 13:40:04 +0100
To: "Dan Amateur" <xamateur_dan@...>

On 30 Sep 2006, at 06:11, Dan Amateur wrote:

Hi Charles

I didnt think you were being evasive at all. In fact,
you intuited what I was really tring to ask and also
provided feedback, that was simply meaningful. Thank
you.

I understand your point about Just tuning, and I get
what you're saying. What Im really interested in is
the spiral aspect of Pythagorean tuning. Am I correct
in thinking that, in line with the sequence you
indicated of ;.."> e.g. 12 edo; 19 edo; 31 edo; 53 edo
etc." That 60 and 72 fit into this sequnce?

No 60 and 72 are exactly divisible by 12, and
therefore if you made steps of fifths, you would only
land on the notes in 12edo, and skip the other notes.

Also, if I wanted to convert these frequencies into
their related associated scale frequency values for
explicitly a 12 note based circle of fifths scale, how
would I do this.

To get 12 edo, you multiply each frequency but the
twelfth root of 2 to get the next note in the
sequence.
After 12 steps you will arrive at the octave, i.e.
double the frequency.

See this page to understand how these various tuning
systems are calculated:

http://www.lucytune.com/new_to_lt/pitch_01.html

Would I use the formula you provided
earlier using pi?

No pi is only required for LucyTuning, which is a
specific meantone tuning, which has many less obvious
benefits which you can read about on the lucytune.com
site.

A genuine thanks for helping me clarify what I was
really after. May I be so bold to ask, though I do
'get' your point, and it makes sense to me now, and I
agree it is unlikely to be satisfactory, how might
this be done in a Just scale also?

You first need to decide which Just Intonation
intervals you wish to use. 3/2, 4/3, 5/3, 5/4, 7/4.
...... etc.

Ask someone else about this, as they will know more
than I do about "this week's JI flavour" ;-)

Your site, by the way, Lucy Tuning is fantastic, nice
work!!!!

Thanks

best regards

Dan

Your question is paradoxical.

Neither Just nor Pythagorean tuning will have a
CIRCLE of fifths.

Pythagorean fifths result in a spiral, as do all
non-equal meantone-
type tunings e.g. LucyTuning. Phi, 1/4 comma etc.

Just intonation won't result in a circle; in fact
all that it results
(in my opinion) is postings on the tuning list about
how many angels
can dance on the head of a grasshopper;-) - but the
answer is always
in the form of integer:integer. (whole number
ratios).

Unless you particularly enjoy playing numerology, I
suggest that you
avoid Just Intonation, as it doesn't even produce
interesting or
harmonious music from my experience and
experimentations.

Circles of fifths and fourths only occur in some
equal temperaments
e.g. 12 edo; 19 edo; 31 edo; 53 edo etc.

You could include other equal systems as being
circular, but that
creates the problem of defining what you consider to
be a fifth;-)

As far as I can see, the problem that you are having
is in finding a
consistent connection between notenames and
frequencies.

Sorry to be evasive, yet I believe that you need to
re think and
restate your problem in order to be able to find a
solution
to getting your various instruments to play in tune
with eachother.

Charles Lucy <lucy@...> wrote:
Answer to your puzzle is easy for 12 edo, just
multiply the
reference frequency in Hz. by 2^(1/12) twelfth
root of 2 to give
all the other 11 frequency values.

If you wish to really understand how tuning,
harmony etc. works in
the practical world of multiple microtuned
instruments playing
together, check out the lucytune.com site.

Using A4 = 440 Hz, as your reference pitch; all
the other LucyTuned
notes and instruments will play exactly in tune
with themselves and
eachother for as many notes per octave you choose
to use.

Charles Lucy - lucy@... ------------
Promoting global
harmony through LucyTuning ------- for
information on LucyTuning
go to:
http://www.lucytune.com
for LucyTuned Lullabies, contest and Flash cartoon
go to
http://www.lullabies.co.uk
Buy CD from:
http://www.cdbaby.com/cd/lucytuned2
Lullabies at iTunes (if you already have iTunes
installed):

http://phobos.apple.com/WebObjects/MZStore.woa/wa/viewArtist?

a=5165209&s=143441
To install iTunes go to:
http://www.apple.com/itunes/affiliates/download/

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Dan,

I'm not the best person to offer answers your questions by any
stretch, but I just wanted to say that I'm having trouble
understanding the problem. In particular, I'm not sure what you mean
by "matching" notes. What are your criteria? Approximating
consonance within a certain limit?

More generally, any 2 notes can "match" depending on the definition of
matching, which is up to you to decide. Being "in tune" or "out of
tune" is in practice a psychological categorization, not an objective
measurement.

-Chris

On 01/10/06, Dan Amateur <xamateur_dan@...> wrote:
>
>
>
>
>
>
> Hey Folks, Im a new member on here. Recently I posted
> the below to the Tuning Forum, and got some great
> feedback from Charles Lucy of LucyTuning, he really
> filled in some gaps. But Im still left trying to find
> out something simple.... related to Just Tuning, and
> Pythagorean Spiral of Fifth Tuning....
> I've listed the question below, as well as the thread
> between Charles and I. I now know how to get the
> values for edo, thanks to Charles, but still do not
> know hot to get these values for Pythagorean Spiral of
> Fifths or Just. Lets assume we are using a Just
> intonation interval of 3/2;
> --------------------
>
> Im new to music theory and am intrigued by two
> questions that have
> captured my imagination;
>
> 1.) A musician friend of mine told me, that if a band
> were playing
> together and everyones instrument was in tune except
> for one person,
> the one person with the out of tune instrument would
> really stand out.
>
> Normally, the one person would get his out of tune
> instrument back in
> tune. Alternatively however, a different approach
> could be used to
> normalize the sound within the band, relatively
> speaking.
>
> That is, all the other band members could re-tune
> their in tune
> instruments to be out of tune the in same way the
> original un-tuned
> instrument sounded. This way they would sound
> relatively the same,
> tuning wise.
>
> So - this got me thinking....
>
> In the below table, there are four instruments. They
> could be guitars,
> or something similiar.
>
> Column (A) shows the frequency in hertz of four
> different notes,
> intervals played on the instruments when they are in
> tune. Notes,
> intervals, for example; b, diminished octave, C#, A#,
> all sound
> the same way on each instrument.
>
> Column (B) on the other hand, represents a scenario,
> where each of
> the four instruments may be tuned quite differently
> from each other.
>
> Here comes the first question...
>
> We want to match two instruments to each other in
> accordance with
> values listed in column (B)
>
> The important instrument is 'INSTRUMENT # 1'.
>
> Constraints;
>
> We only get to play one note on 'INSTRUMENT # 1'. That
> is 496.15104
> as shown in the table.
>
> ============ ========= ========= ========= =========
> ========= ========= ===
> Freq. in Hertz
> COLUMN (A) COLUMN (B)
> NOTE INTERVAL IN TUNE OUT OF TUNE
> ------------ --------- --------- --------- ---------
> --------- -
> INSTRUMENT # 1 B Mjr 7th 495.00 496.15104
> INSTRUMENT # 2 Dim. Octave. 501.6 504.1152
> INSTRUMENT # 3 C# Enharmonic 270.34 269.15072
> INSTRUMENT # 4 A# Aug. 6th 448.8 452.05248
> ============ ========= ========= ========= =========
> ========= ========= ===
> We can only play one note on instruments #2 through
> #4, likewise
> those notes being the ones listed in column (B) for
> each instrument.
>
> What simple rule, principle, formula, will allow us to
> determine
> which instrument from #2 to #4 is tuned most closely
> to instrument # 1.
>
> Further, by knowing ONLY INSTRUMENT #1's note listed
> in Column (B),
> how can we derive the rest of its entire 'out of tune'
> scale?
>
> ____________ _________ _________ _________ _________
> __
>
> ======
> On 30 Sep 2006, at 02:23, Dan Amateur wrote:
>
> Hi Charles,
>
> I've heard a lot about you recently. Your work is
> almost legend, thank you for taking the time to
> respond to me. I very much appreciate it. I will
> check out the website.
>
> May I ask, how might this be done for a just scale,
> Pythagorean, based on the circle of fifths? Rather
> than edo?
>
> From Charles Lucy;
>
> Your question is paradoxical.
>
> Neither Just nor Pythagorean tuning will have a CIRCLE
> of fifths.
>
> Pythagorean fifths result in a spiral, as do all
> non-equal meantone-type tunings e.g. LucyTuning. Phi,
> 1/4 comma etc.
>
> Just intonation won't result in a circle; in fact all
> that it results (in my opinion) is postings on the
> tuning list about how many angels can dance on the
> head of a grasshopper;-) - but the answer is always in
> the form of integer:integer. (whole number ratios).
>
> Unless you particularly enjoy playing numerology, I
> suggest that you avoid Just Intonation, as it doesn't
> even produce interesting or harmonious music from my
> experience and experimentations.
>
> Circles of fifths and fourths only occur in some equal
> temperaments e.g. 12 edo; 19 edo; 31 edo; 53 edo etc.
>
> You could include other equal systems as being
> circular, but that creates the problem of defining
> what you consider to be a fifth;-)
>
> As far as I can see, the problem that you are having
> is in finding a consistent connection between
> notenames and frequencies.
>
> The solution that I use is very simple:
> multiple sharps and flats A to G derived from
> A4=440Hz,
> and the Large interval (i.e. between the fourth and
> fifth) is:
> the ratio of the two pi root of 2.
> i.e. 2^(1/(2*pi))
> or the radian angle in geometric terms = 360/2pi
> degrees.
>
> Sorry to be evasive, yet I believe that you need to re
> think and restate your problem in order to be able to
> find a solution
> to getting your various instruments to play in tune
> with eachother.
>
> Charles Lucy <lucy@...> wrote:
> Answer to your puzzle is easy for 12 edo, just
> multiply the reference frequency in Hz. by 2^(1/12)
> twelfth root of 2 to give all the other 11 frequency
> values.
>
> If you wish to really understand how tuning, harmony
> etc. works in the practical world of multiple
> microtuned instruments playing together, check out the
> lucytune.com site.
>
> Using A4 = 440 Hz, as your reference pitch; all the
> other LucyTuned notes and instruments will play
> exactly in tune with themselves and eachother for as
> many notes per octave you choose to use.
>
> From: "Charles Lucy" <lucy@...> Add to
> Address Book
> Subject: Re: OUT of tune Tuning - Question from new
> member
> Date: Sat, 30 Sep 2006 13:40:04 +0100
> To: "Dan Amateur" <xamateur_dan@...>
>
>
> On 30 Sep 2006, at 06:11, Dan Amateur wrote:
>
> Hi Charles
>
> I didnt think you were being evasive at all. In fact,
> you intuited what I was really tring to ask and also
> provided feedback, that was simply meaningful. Thank
> you.
>
> I understand your point about Just tuning, and I get
> what you're saying. What Im really interested in is
> the spiral aspect of Pythagorean tuning. Am I correct
> in thinking that, in line with the sequence you
> indicated of ;.."> e.g. 12 edo; 19 edo; 31 edo; 53 edo
> etc." That 60 and 72 fit into this sequnce?
>
> No 60 and 72 are exactly divisible by 12, and
> therefore if you made steps of fifths, you would only
> land on the notes in 12edo, and skip the other notes.
>
> Also, if I wanted to convert these frequencies into
> their related associated scale frequency values for
> explicitly a 12 note based circle of fifths scale, how
> would I do this.
>
> To get 12 edo, you multiply each frequency but the
> twelfth root of 2 to get the next note in the
> sequence.
> After 12 steps you will arrive at the octave, i.e.
> double the frequency.
>
> See this page to understand how these various tuning
> systems are calculated:
>
> http://www.lucytune.com/new_to_lt/pitch_01.html
>
> Would I use the formula you provided
> earlier using pi?
>
> No pi is only required for LucyTuning, which is a
> specific meantone tuning, which has many less obvious
> benefits which you can read about on the lucytune.com
> site.
>
> A genuine thanks for helping me clarify what I was
> really after. May I be so bold to ask, though I do
> 'get' your point, and it makes sense to me now, and I
> agree it is unlikely to be satisfactory, how might
> this be done in a Just scale also?
>
> You first need to decide which Just Intonation
> intervals you wish to use. 3/2, 4/3, 5/3, 5/4, 7/4.
> ...... etc.
>
> Ask someone else about this, as they will know more
> than I do about "this week's JI flavour" ;-)
>
> Your site, by the way, Lucy Tuning is fantastic, nice
> work!!!!
>
> Thanks
>
> best regards
>
> Dan
>
> Your question is paradoxical.
>
> Neither Just nor Pythagorean tuning will have a
> CIRCLE of fifths.
>
> Pythagorean fifths result in a spiral, as do all
> non-equal meantone-
> type tunings e.g. LucyTuning. Phi, 1/4 comma etc.
>
> Just intonation won't result in a circle; in fact
> all that it results
> (in my opinion) is postings on the tuning list about
> how many angels
> can dance on the head of a grasshopper;-) - but the
> answer is always
> in the form of integer:integer. (whole number
> ratios).
>
> Unless you particularly enjoy playing numerology, I
> suggest that you
> avoid Just Intonation, as it doesn't even produce
> interesting or
> harmonious music from my experience and
> experimentations.
>
> Circles of fifths and fourths only occur in some
> equal temperaments
> e.g. 12 edo; 19 edo; 31 edo; 53 edo etc.
>
> You could include other equal systems as being
> circular, but that
> creates the problem of defining what you consider to
> be a fifth;-)
>
> As far as I can see, the problem that you are having
> is in finding a
> consistent connection between notenames and
> frequencies.
>
> The solution that I use is very simple:
> multiple sharps and flats A to G derived from
> A4=440Hz,
> and the Large interval (i.e. between the fourth and
> fifth) is:
> the ratio of the two pi root of 2.
> i.e. 2^(1/(2*pi))
> or the radian angle in geometric terms = 360/2pi
> degrees.
>
> Sorry to be evasive, yet I believe that you need to
> re think and
> restate your problem in order to be able to find a
> solution
> to getting your various instruments to play in tune
> with eachother.
>
> Charles Lucy <lucy@...> wrote:
> Answer to your puzzle is easy for 12 edo, just
> multiply the
> reference frequency in Hz. by 2^(1/12) twelfth
> root of 2 to give
> all the other 11 frequency values.
>
> If you wish to really understand how tuning,
> harmony etc. works in
> the practical world of multiple microtuned
> instruments playing
> together, check out the lucytune.com site.
>
> Using A4 = 440 Hz, as your reference pitch; all
> the other LucyTuned
> notes and instruments will play exactly in tune
> with themselves and
> eachother for as many notes per octave you choose
> to use.
>
> Charles Lucy - lucy@... ------------
> Promoting global
> harmony through LucyTuning ------- for
> information on LucyTuning
> go to:
> http://www.lucytune.com
> for LucyTuned Lullabies, contest and Flash cartoon
> go to
> http://www.lullabies.co.uk
> Buy CD from:
> http://www.cdbaby.com/cd/lucytuned2
> Lullabies at iTunes (if you already have iTunes
> installed):
>
> http://phobos.apple.com/WebObjects/MZStore.woa/wa/viewArtist?
>
> a=5165209&s=143441
> To install iTunes go to:
> http://www.apple.com/itunes/affiliates/download/
>
> All new Yahoo! Mail
> Get news delivered. Enjoy RSS feeds right on your
> Mail page.
>
> __________________________________________________
> Do You Yahoo!?
> Tired of spam? Yahoo! Mail has the best spam protection around
> http://mail.yahoo.com
> -- 'We cannot love God unless we love each other, and to love we must
know each other.'

-Dorothy Day

OUT of tune Tuning - Question from new member

🔗Dan Amateur <xamateur_dan@...>

🔗c.m.bryan <chrismbryan@...>

🔗threesixesinarow <CACCOLA@...>

🔗Charles Lucy <makemicro@...>