More than 1600 diagrams , 175 tunings !

(Pinned post ) IMPORTANT :

For those of you who are familiar with cent values in several temperaments, please use the diagram called «Minor cent» in the beginning.

Here you will find cent values for fifths, major thirds and minor thirds within the same graph.

The red vectors is deviation from pure major third and blue vectors for minor third.

In the other diagrams I am using TU, but simply divide values by 30 to get a precise enough cent value.

Pythagorean comma = 23.46 cents = 720 TU

Syntonic comma = 21.51 cents = 660 TU.

(These numbers are easy to divide in 2,3,4,5,6...)

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The easiest way to get an overview of historical and newer tunings ! Read the Introduction (1) carefully and the diagrams will tell you much more than all the cent tables on the web.
Many of those who have found the key to the diagrams use this webside a lot.
If you have questions , let me hear, click HERE

The (un)musical comma !

DEMONSTRATIONS OF THE SYNTONIC COMMA AND THE PITFALLS 

The syntonic comma is a comma also for string players etc.(in practical playing) 
The pythagorean comma is only for keyboard players and has a very,very  distant relationship 531441/524288

The syntonic comma  is the main musical comma.(81/80) (The diesis comes afterwards 128/125)
 It gives huge challenges but also exiting possibilty for  musical redefinitions of tones.
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My bad spinet has been subjected to many tonal adjustments on these recordings + a little tinkering with my audio equipment.

This is my demonstration of the syntonic comma.
2 ways to lose our starting pitch completly
But I have also made 2 recordings where I am correcting this error (below) (if we had maaany tones available in an octave).

What you hear follow these premises:
a) All passing tones are absolutely identical from one chord to another (C as the passing tone between C major and F major )
b) I am always tuning a new chord completely pure from the base of the passing tone(s).

(Here I have to refer to my new blog containing my new tuning. In this guide I am demonstrating the problem of syntonic comma in a better way. 


Click  HERE       )



First audio files without graphs.
C-F Dm-G-C etc. (Maybe you have to download  to play )



How well did you keep the original tone inside you with your inner ear ??
Could this be one of the reasons why amateur choirs (in addition to that they are bad) often are sinking and losing their starting pitch ?
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The problem may also occur in the other direction.
Alike, but this time opposite . The pitch is ascending.

C- Gsus4-G Dsus4-Dm-Esus4-E-C-G-C, etc..


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You'll now see these problems visualized with graphs.
A brief introduction to the graphs. (If you do not understand this, you can of course just listen .):

This is a smaller part of the complete diagrams otherwise on the blog.
There is one black and one red graph. Identical,same shape but shifted.
A pure fifth is a horizontal line (sloping downward towards the right means a narrow fifth).
 The vertical distance between the red and black graph is
the deviation from a pure major third.
In our example, all played intervals are pure and located on straight horizontal lines
But I have a red and a dark green D on the black graph (in the second example, it also applies to the G).
These are still the same tones but makes the challenges of the syntonic commas  become visible.
So when a new chord suddenly jumps upwards to the left then it is not that big jump as it seems.
It is the tricky D as the passing tone.
Read more here :

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Here is the graphic representation of what you just heard. The blue dotted rings
means the passing tones. I also added a reference tone in this audio file.
The values ​​are in TU (1 cent = 30.69 TU)


What is strange here is that when we know the chord progression and what it leads us to , then we experience the A in F Major slightly impure even before the next chord is played and even if it is completely pure.
This A is the tone that pulls all the other tones downwards.

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What can we do if we have many tones available?
One round gives an error of 660 TU.
We have 4 distinct chord shifts in each example.
What I do is to compensate with 165 TU for each new chord.
In our first example, the pitch sank dramatically
 Now I raise each new chord with only 165 TU, this is not audible for my ears.
Even the keynote we raise a little bit. With this little adjustment we are keeping the starting pitch, while every chord is completely pure !
You can hear and watch the solution here :


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This also applies to our second example.
The example with audio and graphs, and with a reference tone:




In my last example the same chords but now with corrections:
Since the issue here is accending of the pitch, then I lower each new chord with 165 TU, still becoming inaudible (to me).
This solution looks and sounds like this:






Hope you could benefit from this !

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