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

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

Piano: Unknown
Submitted by: 006

YOUR RECORDED NOTES:

CHROMATIC LADDERS

Should increase smoothly and evenly.
Should increase smoothly and evenly.
Should all sound “noisy” (around 1 bps)
Should all sound “rolling” (about 0.5 bps)
Should increase smoothly and evenly.
Should increase smoothly and evenly.

F3F4 and A3A4 Octaves

Criteria: Must be tuned to one of the following sizes.
(Note: Only one size is possible because of inharmonicity.)
Small Scale Octave: Pure 4:2 and Pure 6:3 (As best as you can tell) Common
Medium Scale Octave: Wide 4:2 and Narrow 6:3 (Barely audible differences in check intervals) Less Common
Large Scale Octave: Pure 4:2 and Very Narrow 6:3 (The 6:3 is obviously narrow 6:3 but the octave sounds nice) Rare
Reversed Octave: Narrow 4:2 and Wide 6:3. Very Rare.
(Click Here for the lesson on Octave Sizes.)

F3F4:

4:2 Octave:
6.7 bps
6.0 bps
Size of 4:2 F3F4: Narrow (10%)

6:3 Octave:

10 bps
8.6 bps
Size of 6:3 F3F4: Narrow (14%)

Comments on Your F3F4 Octave

The 4:2 and 6:3 are both narrow.

The 6:3 is much more narrow than the 4:2.

Possible correct sizes are:

Wide 4:2/Narrow 6:3 but so close that we cannot tell. (Small Scale)

Wide 4:2/Narrow 6:3 where the differences are discernable. (Medium Scale)

Pure 4:2/Very Narrow 6:3 that sounds better than the Wide 4:2/Narrow 6:3. (Large Scale)

The narrow 4:2 and the narrow 6:3 should be discernable and therefore correctable.

A3A4:

4:2 Octave:

6.3 bps
5.6 bps
Size of 4:2 A3A4: Narrow (10%)

6:3 Octave:

11 bps
9 bps
Size of 6:3 A3A4: Narrow (23%)

Comments on Your A3A4 Octave:
The 4:2 and 6:3 are both very narrow.

The 6:3 is much more narrow than the 4:2.

Possible correct sizes are:

Wide 4:2/Narrow 6:3 but so close that we cannot tell. (Small Scale)

Wide 4:2/Narrow 6:3 where the differences are discernable. (Medium Scale)

Pure 4:2/Very Narrow 6:3 that sounds better than the Wide 4:2/Narrow 6:3. (Large Scale)

The narrow 4:2 and the narrow 6:3 should be discernable and therefore correctable.

When confirming all the unfiltered beat speeds listed, it is always
better to have the piano with you and hopefully it hasn’t drifted too
much since you recorded it, so you can try to hear the beat speeds right from the piano in real time.
In some cases the computer speakers make it easier to hear beats; in others, listening
to the actual piano may make it easier to hear the beat speeds.

GRADING OF THE TEMPERAMENT

I have designed a grading scheme for measuring temperaments that is based on
beat speed ratios and not on actual frequencies of each note.

The method assigns a penalty for each beat speed that does not fall
within a certain limit.
M3’s must increase by 0 to 12%.
P4’s must beat between 0.5 and 1.5 beats per second.

A minimum mark of 80% in each test is required to pass.

YOUR TEMPERAMENT MARKS

M3 Mark: 64%

P4 Mark: 88%

M3 BEAT SPEED PROGRESSIONS

HOW TO USE THE M3 GRAPHS AND AUDIO

M3 intervals should increase speed chromatically as smoothly as possible.
1. Listen to the recordings below and look at the first graph.
2. Listen to the filtered recording and try to confirm aurally that speeds
are following what the graph says.
&nbsp&nbsp&nbsp&nbspThis 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.
&nbsp&nbsp&nbsp&nbspThis improves your Beat Speed Clarity – the
ability to hear beat speeds clearly.

YOUR M3 RESULTS:

M3, filtered:

M3, unfiltered:

---

P4 BEAT SPEED PROGRESSIONS

HOW TO USE THE P4 GRAPH AND AUDIO

P4 intervals should beat close to 1 bps.
1. Listen to the recordings below while looking at the graph.
2. Listen to the filtered recording and try to confirm aurally that speeds are following what the graph says.
&nbsp&nbsp&nbsp&nbspThis 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).
&nbsp&nbsp&nbsp&nbspIdentifying 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.

The logic used is to find a M3 that does not progress smoothly, and then find a P4 that
confirms which note needs correction.

SPECIFIC COMMENTS ON YOUR RESULTS

– Both the F3F4 and the A3A4 octaves were too narrow.

– There were a few M3 that slowed down when they should have sped up.

– Some of the P4’s were very close to pure.

SUGGESTIONS FOR REFINEMENT

By looking at the possible note errors that could produce the M3/P4 results above,
we can get a better idea of what corrections could improve both the M3 and P4 beat speed errors at the same time.

M3 ERRORS

We look for M3 that are too slow or too fast and postulate which note could be the problem.

F3-A3 too slow – F3 too high or A3 too low
G3-B3 too slow – G3 too high or B3 too low
A#3-D4 too slow – A#3 too high or D4 too low
C4-E4 too slow – C4 too high or E4 too low

P4 ERRORS

We look for pure or too fast P4 and postulate which note could be the problem.

F#3-B3 too slow – F#3 too high or B3 too low
G#3-C#4 too slow – G#3 too high or C#4 too low
A#3-D4 too slow – A#3 too high or D4 too low
C4-F4 too slow – C4 too high or F4 too low

CONFIRMATION

Look for identical postulations in each group

A#3 too high
B3 too low
D4 too low
C4 too high

Fixing these notes would improve both the M3 and P4 errors that they produced!

CONCLUSION

In refining a temperament, we identify two or more problems that suggest the same note may be too high or too low,
and then change that note and fix multiple 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 ability to rationalize the logic, and improve your ear to be
able to hear smaller and smaller beat speed differences.
Improving these skills will greatly improve your temperament.

Keep up the good work and don’t give up! You are getting better all the time!