Cents, Savarts, Merides and Jots!

Hi All,

I've posed the same question on the XA II Facebook group:

How many pitch difference measurement systems can you think of? I'm hoping to collate as many as possible in one article and also produce a calculator/converter to make sense of them all. Indian Shrutis, Mels and Turkish Cents have already been thrown in by the group.

Think historical, think esoteric…

Jim

On 8/2/2013 11:22 AM, jimrussell440 wrote:
> Hi All,
>
> I've posed the same question on the XA II Facebook group:
>
> How many pitch difference measurement systems can you think of? I'm
> hoping to collate as many as possible in one article and also produce
> a calculator/converter to make sense of them all. Indian Shrutis,
> Mels and Turkish Cents have already been thrown in by the group.
>
> Think historical, think esoteric�

Millioctaves.

Minas (the unit of Olympian Sagittal notation, 2460 steps to the octave).

http://xenharmonic.wikispaces.com/mina

How many have you found that are not already in Scala?

Andrew

--- In tuning@yahoogroups.com, "jimrussell440" <jimrussell440@...> wrote:
>
> Hi All,
>
> I've posed the same question on the XA II Facebook group:
>
> How many pitch difference measurement systems can you think of? I'm hoping to collate as many as possible in one article and also produce a calculator/converter to make sense of them all. Indian Shrutis, Mels and Turkish Cents have already been thrown in by the group.
>
> Think historical, think esoteric…
>
> Jim
>

--- In tuning@yahoogroups.com, "jimrussell440" <jimrussell440@...> wrote:
>
> Hi All,
>
> I've posed the same question on the XA II Facebook group:
>
> How many pitch difference measurement systems can you think of? I'm hoping to collate as many as possible in one article and also produce a calculator/converter to make sense of them all. Indian Shrutis, Mels and Turkish Cents have already been thrown in by the group.
>
> Think historical, think esoteric…
>
> Jim
>

How about MIDI Pitchbend Units (PBUs), 4096 per half-step.

Billy

Ah, good thought.

FYI, I created a spreadsheet that can calculate PBUs given just intonation ratios:

http://andrewmeronek.com/2013/03/05/ods-pitch-bend-spreadsheet-for-sibelius/

Might be useful.

Andrew

--- In tuning@yahoogroups.com, "Billy" <duckfeetbilly@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "jimrussell440" <jimrussell440@> wrote:
> >
> > Hi All,
> >
> > I've posed the same question on the XA II Facebook group:
> >
> > How many pitch difference measurement systems can you think of? I'm hoping to collate as many as possible in one article and also produce a calculator/converter to make sense of them all. Indian Shrutis, Mels and Turkish Cents have already been thrown in by the group.
> >
> > Think historical, think esoteric…
> >
> > Jim
> >
>
> How about MIDI Pitchbend Units (PBUs), 4096 per half-step.
>
> Billy
>

Yes, MIDI Pitchbend 'units' is a very good idea - thanks Billy :)

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> Ah, good thought.
>
> FYI, I created a spreadsheet that can calculate PBUs given just intonation ratios:
>
> http://andrewmeronek.com/2013/03/05/ods-pitch-bend-spreadsheet-for-sibelius/
>
> Might be useful.
>
> Andrew
>
>
> --- In tuning@yahoogroups.com, "Billy" <duckfeetbilly@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "jimrussell440" <jimrussell440@> wrote:
> > >
> > > Hi All,
> > >
> > > I've posed the same question on the XA II Facebook group:
> > >
> > > How many pitch difference measurement systems can you think of? I'm hoping to collate as many as possible in one article and also produce a calculator/converter to make sense of them all. Indian Shrutis, Mels and Turkish Cents have already been thrown in by the group.
> > >
> > > Think historical, think esoteric…
> > >
> > > Jim
> > >
> >
> > How about MIDI Pitchbend Units (PBUs), 4096 per half-step.
> >
> > Billy
> >
>

Large (L) and small (s) intervals as in meantone tunings.
tones and semitoes.

On 4 Aug 2013, at 00:43, jimrussell440 wrote:

> Yes, MIDI Pitchbend 'units' is a very good idea - thanks Billy :)
>
> --- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
> >
> > Ah, good thought.
> >
> > FYI, I created a spreadsheet that can calculate PBUs given just intonation ratios:
> >
> > http://andrewmeronek.com/2013/03/05/ods-pitch-bend-spreadsheet-for-sibelius/
> >
> > Might be useful.
> >
> > Andrew
> >
> >
> > --- In tuning@yahoogroups.com, "Billy" <duckfeetbilly@> wrote:
> > >
> > >
> > >
> > > --- In tuning@yahoogroups.com, "jimrussell440" <jimrussell440@> wrote:
> > > >
> > > > Hi All,
> > > >
> > > > I've posed the same question on the XA II Facebook group:
> > > >
> > > > How many pitch difference measurement systems can you think of? I'm hoping to collate as many as possible in one article and also produce a calculator/converter to make sense of them all. Indian Shrutis, Mels and Turkish Cents have already been thrown in by the group.
> > > >
> > > > Think historical, think esoteric…
> > > >
> > > > Jim
> > > >
> > >
> > > How about MIDI Pitchbend Units (PBUs), 4096 per half-step.
> > >
> > > Billy
> > >
> >
>
>

Charles Lucy
lucy@...

-- Promoting global harmony through LucyTuning --

For more information on LucyTuning go to:

http://www.lucytune.com

LucyTuned Lullabies (from around the world) can be found at:

http://www.lullabies.co.uk

I have some concepts in mind, but I don't know if they already have specific names:

* Octave fractions as angles:
Simply multiply 360° or 2pi to octave fractions. So 300 cents would be 90° or pi/2, 2400 cents are 720° or 4pi, and so on.

* Tritave fractions:
For a frequency ratio r, calculate log_3(r), s.th. the "tritave" 3:1 is notated as 1, the octave 2:1 as 0.6309, and so on. Of course fractions of other intervals are possible, too.

* Octave fractions in continued fraction representation.
For example, 13\31 is [0;2,2,1,1,2] = [0;2,2,1,1,1,1], and the golden meantone fourth (phi+3)\11 is [0;2,2,1,...], with repeating 1s at the end, and where phi is the golden ratio (1+sqrt5)/2. Also possible with frequency ratios.

Best
- Gedankenwelt

--- In tuning@yahoogroups.com, "jimrussell440" <jimrussell440@...> wrote:
>
> Hi All,
>
> I've posed the same question on the XA II Facebook group:
>
> How many pitch difference measurement systems can you think of? I'm hoping to collate as many as possible in one article and also produce a calculator/converter to make sense of them all. Indian Shrutis, Mels and Turkish Cents have already been thrown in by the group.
>
> Think historical, think esoteric…
>
> Jim

On Sun, 04 Aug 2013 01:58:22 -0000
"gedankenwelt94" <gedankenwelt94@yahoo.com> wrote:

> I have some concepts in mind, but I don't know if they already have
> specific names:
>
> * Octave fractions as angles:
> Simply multiply 360° or 2pi to octave fractions. So 300 cents would
> be 90° or pi/2, 2400 cents are 720° or 4pi, and so on.

A common, and theoretically backed, system for notation is 72 note
equal temperament. As an extension of 12 tone notation, this means
extra accidentals to divide the equal tempered semitone into 6 parts
(sextulas).

An alternative, and still not too bad, system is 60 note equal
temperament. This divides the equal tempered semitone into 5 parts
(quintulas). It works in some cases where 72 doesn't, like giving
unequal neutral thirds for middle-eastern scales and being a magic
temperament.

So, say you have a set of accidentals for the sextulas and another set
for the quintulas. If you use both together, with one denoting
divisions of the other as a kind of place notation, you have 12*5*6 =
360 divisions of the octave. Hence this is a notation for octave
degrees that degrades gracefully, in that if you ignore the secondary
accidentals you still have a notation for either 72- or 60-equal.

Graham