TEMPERAMENT REPORT for 003-01

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

It actually came from his electronic keyboard. It is the default tuning that comes with it.

Contact Me Now if you would like a free analysis of one of your temperaments.


Piano: Electronic Keyboard
Submitted by: 003

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 its exams.

Temperament Mark for 003-01

Average Ratio Method: 56%
(Similar to RPT method)

Beat Speed Limit Method: 67%
(Represents more directly what the tuner can hear. Preferred method.)


M3 BEAT SPEED PROGRESSIONS

Client 002-02 M3 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:


P4 BEAT SPEED PROGRESSIONS

Client 002-02 P4 Progression

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


INSIGHT

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

First off, it must be noticed how horribly the M3 follow a progressive beat speed. This confirms my theory that electronic pianos are not as well tuned as we think. But let's look closer.

B3D#4 is too slow. B3 is high and/or D#4 is low.
A#3D#4 is too slow. A#3 is high and/or D#4 is low.
D#4 is low.

C#4F4 is too slow. C#4 is high and/or F4 is low.
G#3C#4 is too fast. G#3 is low and/or C#4 is high.
C#4 is high

A3D4 is too fast. A3 is low and/or D4 is high.
A#3D4 is too fast. A#3 is low and/or D4 is high.
D4 is high


FURTHER CONFIRMATION

Try to hear the following inconsistencies in the following chromatic ladders. These are predicted by the findings above.

Chromatic M6's:
F3D4/F#3D#4/G3E4/G#3F4
1. D4 is too high. F3D4 should sound too fast.
2. D#4 is too low. F#3D#4 should sound too slow.

Chromatic P5's:
F3C4/F#3C#4/G3D4/G#3D#4/A3E4/A#3F4
1. C#4 is high. F#3C#4 may sound too pure, or be wide.
2. D4 is high. G3D4 may sound too pure, or be wide.
3. D#4 is low. G#3D#4 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. C#4 is high. A#3C#4 should sound too slow
2. D4 is high. B3D4 should sound too slow
3. D#4 is low. C4D#4 should sound too fast
4. C#4 is high. C#4E4 should sound too fast
5. D4 is high. D4F4 should sound too fast

Chromatic m6's:
F3C#4/F#3D4/G3D#4/G#3E4/A3F4
1. C#4 is high. F3C#4 should sound too slow
2. D4 is high. F#3D4 should sound too slow
3. D#4 is low. G3D#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.

This is not necessarily a definitive description of the actual beat rates of your temperament. Beat rates within a piano interval can vary over the sustain of the interval.

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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