This is a free analysis generated by a F3F4 recording submitted to me by one of my subscribers.

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Piano: Unknown
Tuned by: 002

CHROMATIC LADDERS

GRADING OF THE TEMPERAMENT

I have designed two different grading schemes for measuring temperaments.

One is based on the error of the frequencies relative to a master tuning. This method is similar to the Registered Piano Technicians exam administered by the Piano Technicians Guild. The “master tuning” is determined by those frequencies that would produce beat speeds that increase by the same ratio as the average ratio of the actual beat speeds.

The second method assigns a penalty for each beat speed that does not fall within a certain limit. M3’s must increase by 0 to 10%. P4’s must beat between 0.5 and 1.5 beats per second.

Below are the marks calculated by each method. The PTG requires a minimum mark of 80% in many of it’s exams.

Temperament Mark for 002-02

Average Ratio Method: 88%
(Similar to RPT method)

Beat Speed Limit Method: 73%
(Represents more directly what the tuner can hear. Preferred method.)

M3 BEAT SPEED PROGRESSIONS

HOW TO USE THE M3 GRAPHS

M3 intervals should increase speed chromatically as smoothly as possible.

1.Listen to the recordings below and look at the graph above.

2.Listen to the filtered recording and try to confirm aurally that speeds are following what the graph says. This improves your Beat Speed Ratio Sensitivity.

3.Listen to the unfiltered recording and try to confirm aurally that speeds are following what the graph says. This improves your Beat Speed Clarity – the ability to hear beat speeds clearly.

M3, filtered:

M3, unfiltered:

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P4 BEAT SPEED PROGRESSIONS

HOW TO USE THE P4 GRAPH

P4 intervals should beat close to 1 bps.

1.Listen to the recordings below and look at the graph above.

2.Listen to the filtered recording and try to confirm aurally that speeds are following what the graph says. This improves your Beat Speed Ratio Sensitivity.

3.Listen to the unfiltered recording and try to hear the quality of a tuned P4 (1 bps), a pure P4 (0 bps), and an out of tune P4 (>1.5 bps). Identifying correct and incorrect P4’s are a very powerful refinement tool.

P4, filtered

P4, unfiltered

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INSIGHT

(You must understand interval sizes in Equal Temperament, and Wide, Narrow, and Pure Intervals, in order to follow the logic explained below.)

By looking at the speed of some M3 and P4 that could be improved, we can figure out how to move one note and fix two problems. That is how we refine a temperament.

The M3, G#3C4, is too slow, therefore G#3 is too high, and/or C4 is too low.
The P4, G3C4, is too slow, therefore G3 is too high, and/or C4 is too low.
Raising C4 will speed up the M3 and speed up the P4.

The M3, A#3D4, is too slow, therefore A#3 is too high, and/or D4 is too low.
The P4, A#3D#4, is too slow, therefore A#3 is too high, and/or D#4 is too low.
Lowering A#3 will speed up the M3 and speed up the P4.

The M3, C#4F4, is too slow, therefore C#4 is too high, and/or F4 is too low.
The P4, G#3C#4, is too fast, therefore G#3 is too low, and/or C#4 is too high.
Lowering C#4 will speed up the M3 and slow down the P4.

FURTHER CONFIRMATION

Errors
C4 too low
A#3 too high
C#4 too high

Try to hear the following inconsistencies in the following chromatic ladders:

Chromatic M6’s:
F3D4/F#3D#4/G3E4/G#3F4
No intervals available

Chromatic P5’s:
F3C4/F#3C#4/G3D4/G#3D#4/A3E4/A#3F4
1.F3C4 should sound too narrow,
2.F#3C#4 could sound too pure, if it is not wide.
3.A#3F4 should sound too narrow

Chromatic m3’s:
F3G#3/F#3A3/G3A#3/G#3B3/A3C4/A#3C#4/B3D4/C4D#4/C#4E4/D4F4
1.G3A#3 should sound too slow,
2.A3C4 should sound too fast,
3.A#3C#4 should sound too fast,
4.C4D#4 should sound too slow,
5.C#4E4 should sound too fast,

Chromatic m6’s:
F3C#4/F#3D4/G3D#4/G#3E4/A3F4
1.F3C#4 should sound too fast

Compare the above intervals with their neighbours.

Notice how we identify two problems that have the same note, and then look for a way to change that note and fix both problems. This reiterative method helps us improve the temperament bit by bit.

This is why it is imperative that, if you want to improve your aural tuning, you must improve your beat speed recognition. Exercises like these can help greatly.

You are encouraged to read the analysis and confirm aurally that you can hear the findings, and understand how the improvements suggested would improve the beat speed progressions.

In this way you will improve your ear and be able to hear smaller differences in beat speeds, which will ultimately improve your temperament.

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