High-precision piano division method based on pure pitch group test

Abstract

The invention discloses a high-precision piano rhythm dividing method based on pure pitch group inspection, which comprises the following steps: S1, based on different natural pitches, selecting a pure pitch group and an actual slow frequency pitch related to a pitch to be inspected, the pure pitch group being composed of known sounds and target sounds, and the actual slow frequency pitch being composed of the known sounds and the target sounds; calculating the frequency of the target tone in the pure tone group through a target tone frequency calculation formula f01 = f02 / n; s2, based on different natural ranges, substituting the frequency of the target tone obtained in the step S1 into a natural range beat frequency calculation formula f = (f03 * a)-(f04 * b) to calculate the beat frequency of a theoretical slow frequency range; when f03 represents the frequency of the target sound, f04 is the frequency of the sound to be tested; a represents a numerator in the natural pitch frequency ratio, and b represents a denominator in the natural pitch frequency ratio; and S3, comparing the beat frequency of the theoretical slow frequency interval calculated in the step S2 with the actual slow frequency interval in the step S1, and verifying the accuracy of the to-be-verified sound by taking the theoretical slow frequency interval and the sum sound interval of the to-be-verified sound as comparison data.

Description

Technical Field

[0001] The present invention belongs to the technical field of music acoustics and musical instrument tuning, and particularly relates to a high-precision piano tuning method based on the inspection of a pure interval group. Background Art

[0002] Since the birth of the piano tuning technology, it has undergone many improvements and developments, but there are still many deficiencies in the existing technology. Although the traditional "five-point tuning method of four up and five down" is widely used, it has obvious defects in the following aspects: First, the traditional method is limited to the interval inspection within the reference note group and fails to make full use of the notes outside the reference note group for auxiliary inspection, resulting in difficulty in ensuring the accuracy of certain key notes (such as F3). Second, the traditional method relies on fast beat frequencies for inspection, and fast beat frequencies are difficult to distinguish, especially in different temperaments (such as meantone temperament, irregular temperament, etc.), and many intervals between 3 and 6 beats per second are difficult to achieve ideal results through a single beat frequency inspection. Finally, the operation steps of the traditional method are complex and require a high technical level of the tuner, which limits its wide application. Summary of the Invention

[0003] In order to overcome the deficiencies of the existing technology, the purpose of the present invention is to provide a high-precision piano tuning method based on the inspection of a pure interval group, introducing low-frequency notes outside the reference note group for auxiliary inspection and breaking through the limitation of the traditional method that only relies on the interval inspection within the reference note group.

[0004] To solve the above problems, the technical solutions adopted by the present invention are as follows: S1: Based on different natural intervals, select a pure interval group and an actual slow frequency interval related to the interval to be inspected. The pure interval group consists of a known note - target note. Calculate the frequency of the target note in the pure interval group through the target interval frequency calculation formula f01 = f02 ÷ n, where f01 represents the frequency of the target note, f02 represents the frequency of the known note, and n represents the target interval frequency ratio;

[0005] S2: Based on different natural intervals, substitute the frequency of the target note obtained in step S1 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow frequency interval, where f represents the beat frequency of the theoretical slow frequency interval. When f03 represents the frequency of the note to be inspected, f04 is the frequency of the target note; when f03 represents the frequency of the target note, f04 is the frequency of the note to be inspected; a represents the numerator in the natural interval frequency ratio, and b represents the denominator in the natural interval frequency ratio;

[0006] S3: Compare the beat frequency of the theoretical slow frequency interval calculated in step S2 above with the actual slow frequency interval in step S1 above, and use the sum interval of the theoretical slow frequency interval and the note to be inspected as the control data to verify the accuracy of the note to be inspected.

[0007] Compared with the prior art, the beneficial effects of the present invention are as follows: By introducing the pure interval group inspection method and the low-frequency sound outside the reference tone group for auxiliary inspection, and taking advantage of the non-beating characteristic of the pure interval group to slow down the beat frequency of the relevant intervals, the problem of insufficient F3 accuracy in the traditional temperament method is effectively solved. For example, when generating F3, by adjusting A3-C3 into a pure interval group and verifying whether the beat frequency of C3-F3 conforms to the theoretical value, the accuracy of F3 is significantly improved. By introducing the auxiliary inspection beat division method, the intervals under different temperaments can be calibrated more precisely, and more possibilities are provided for the temperament of equal temperament and non-equal temperament (such as meantone temperament, Werckmeister temperament, etc.).

[0008] For the above-mentioned temperament method, the tone to be tested is D4, the known tone is A3, and the harmonic interval of the tone to be tested D4 is A3-D4. Set the pure interval group as A3-F3. At this time, press the actual slow-frequency interval F3-D4 to listen to the beat frequency. If the absolute error between the calculated beat frequency of the theoretical slow-frequency interval F3-D4 and the beat frequencies of the harmonic interval A3-D4 and the actual slow-frequency interval F3-D4 is within 2, then the D4 tone is accurate. The specific steps are as follows:

[0009] S21: Based on the verification of the descending major third natural interval, the beat frequency of the harmonic interval A3-D4 is 0.99 beats per second. Calculate the frequency of the target tone F3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n, and the target interval frequency ratio

[0010] S22: Based on the verification of the ascending major sixth natural interval, substitute the frequency of the target tone obtained in step S1 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow-frequency interval F3-D4, where f03 represents the frequency of the tone to be tested D4, f04 represents the frequency of the target tone F3, a is 3, and b is 5;

[0011] S23: Compare the beat frequency of the theoretical slow-frequency interval F3-D4 calculated in step S22 above with the actual slow-frequency interval F3-D4 and the harmonic interval A3-D4 in step S1 above to verify the accuracy of the tone to be tested.

[0012] For the above-mentioned temperament method, the tone to be tested is F3, the known tone is A3, and the harmonic interval of the tone to be tested F3 is C4-F3. Set the pure interval group as A3-C3. At this time, press the actual slow-frequency interval C3-F3 to listen to the beat frequency. If the absolute error between the calculated beat frequency of the theoretical slow-frequency interval C3-F3 and the beat frequency of the actual slow-frequency interval C3-F3 is within 2, then the F3 tone is accurate. The specific steps are as follows:

[0013] S31: Based on the verification of the descending major sixth natural interval, the beat frequency of the harmonic interval C4 - F3 is 0.59 beats per second. Calculate the frequency of the target note C3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n, and the target interval frequency ratio

[0014] S32: Based on the verification of the ascending perfect fourth natural interval, substitute the frequency of the target note obtained in step S1 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow frequency interval C3 - F3, where f03 represents the frequency of the target note C3, f04 represents the frequency of the note to be verified F3, a is 4, and b is 3;

[0015] S33: Compare the beat frequency of the theoretical slow frequency interval C3 - F3 calculated in step S32 above with the actual slow frequency interval C3 - F3 in step S31 above, and verify the accuracy of the note to be verified with the harmonic interval C4 - F3.

[0016] For the above pitch division method, the note to be verified is b B3, the known note is F3, and the note to be verified is b The harmonic interval of B3 is F3 - b B3. Set the pure interval group as F3 - b D3. At this time, press the actual slow frequency interval b D3 - b B3 to listen and distinguish the beat frequency. If the calculated beat frequency of the theoretical slow frequency interval b D3 - b B3 and the actual slow frequency interval b D3 - b B3 has an absolute beat frequency error within 2, then b B3 is accurate. The specific steps are as follows:

[0017] S41: Based on the verification of the major third natural interval, the beat frequency of the harmonic interval F3 - b B3 is 0.79 beats per second. Calculate the frequency of the target note b D3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n, and the target interval frequency ratio

[0018] S42: Based on the verification of the ascending major sixth natural interval, substitute the frequency of the target interval obtained in step S41 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow frequency interval b D3 - b B3, where f03 represents the frequency of the note to be verified b B3, f04 represents the frequency of the target note b D3, a is 3, and b is 5;

[0019] S43: Take the theoretical slow frequency interval calculated in the above step S42 b D3 - b The beat frequency of B3 and the actual slow frequency interval in the above step S41 b D3 - b B3 and the harmonic interval F3 - b B3 are compared to verify b the accuracy of B3.

[0020] For the above temperament method, the note to be verified is G3 in Vallotti's irregular temperament, the known note is C4, the harmonic interval of the note to be verified G3 is C4 - G3, the pure interval group is set as C4 - E3. At this time, press the actual slow frequency interval E3 - G3 to listen to the beat frequency. If the absolute error between the calculated theoretical slow frequency interval E3 - G3 and the actual slow frequency interval E3 - G3 beat frequency is within 2, then G3 is accurate. The specific steps are as follows:

[0021] S51: Based on the verification of the descending minor sixth natural interval, the harmonic interval C4 - G3 is -1.61 beats per second. Calculate the frequency of the target note E3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n. The target interval frequency ratio

[0022] S52: Based on the verification of the ascending minor third natural interval, substitute the frequency of the target interval obtained in step S51 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow frequency interval E3 - G3, where f03 represents the frequency of the note to be verified G3, f04 represents the frequency of the target note E3, a is 5, and b is 6;

[0023] S53: Compare the beat frequency of the theoretical slow frequency interval E3 - G3 calculated in the above step S52 with the actual slow frequency interval E3 - G3 and the harmonic interval C4 - G3 in the above step S51 to verify the accuracy of G3.

[0024] For the above temperament method, the note to be verified is A3 in Zarlino's mean temperament. Use A3 below the C4 key. The C4 is the auxiliary note. The known note is A3. The harmonic interval of the note to be verified A3 is A3 - E4. Set the pure interval group as A3 - F3. At this time, press the actual slow frequency interval F3 - C4 to listen to the beat frequency. If the absolute error between the calculated theoretical slow frequency interval F3 - C4 and the actual slow frequency interval F3 - C4 beat frequency is within 2, then A3 is accurate. The specific steps are as follows:

[0025] S61: Based on the verification of the major third natural interval, the beat frequency of the harmonic interval A3 - E4 is 2.05 beats per second. Calculate the frequency of the target note F3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n. The target interval frequency ratio

[0026] S62: Based on the verification of the ascending perfect fifth natural interval, substitute the frequency of the target interval obtained in step S61 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the theoretical slow frequency interval F3-C4 beat frequency, where f03 represents the frequency of the auxiliary note C4, f04 represents the frequency of the target note F3, a is 5, and b is 6;

[0027] S63: Compare the theoretical slow frequency interval F3-C4 beat frequency calculated in the above step S62 with the actual slow frequency interval F3-C4 and the harmonic interval A3-E4 in the above step S61 to verify the accuracy of A3.

[0028] In the above temperament method, in the Zarlino quarter meantone temperament, the f03 can be the frequency of the set auxiliary note.

[0029] In the above temperament method, when selecting a pure interval group within the minor triad, the other slow beat interval is the relevant interval. For example, for the minor triad A3-C3-E3, when selecting A3-C3 as the pure interval group, the beat frequency of C3-E3 is 1.5 beats per second; when selecting C3-E3 as the pure interval group, the beat frequency of A3-C3 is also 1.5 beats per second.

[0030] In the above temperament method, the different intervals of the known notes in step S1 include but are not limited to major third, minor sixth, minor third, and major sixth.

[0031] In the above temperament method, the temperament includes equal temperament and non-equal temperament. Description of the Drawings

[0032] Figure 1 It is the equal temperament upper four and lower five temperament table data diagram of the embodiment of the present invention;

[0033] Figure 2 It is the Vallotti irregular temperament table data diagram of the embodiment of the present invention;

[0034] Figure 3 It is the Zarlino quarter meantone temperament table data diagram of the embodiment of the present invention. Detailed Embodiment

[0035] The following details the embodiments of the present invention, referring to Figures 1 to 3, an embodiment of the present invention provides a high-precision piano tuning method based on the inspection of pure interval groups, including the following steps: S1: Based on different natural intervals, select the pure interval group and the actual slow-frequency interval related to the interval to be inspected. The pure interval group consists of a known note - target note. Calculate the frequency of the target note in the pure interval group through the target interval frequency calculation formula f01 = f02 ÷ n, where f01 represents the frequency of the target note, f02 represents the frequency of the known note, and n represents the target interval frequency ratio; S2: Based on different natural intervals, substitute the frequency of the target note obtained in step S1 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow-frequency interval, where f represents the beat frequency of the theoretical slow-frequency interval. When f03 represents the frequency of the note to be inspected, f04 is the frequency of the target note; when f03 represents the frequency of the target note, f04 is the frequency of the note to be inspected; a represents the numerator in the natural interval frequency ratio, and b represents the denominator in the natural interval frequency ratio; S3: Compare the beat frequency of the theoretical slow-frequency interval calculated in step S2 above with the actual slow-frequency interval in step S1 above. Using the harmonic interval of the theoretical slow-frequency interval and the note to be inspected as the control data, verify the accuracy of the note to be inspected. Further, the tuning method proposed in this application introduces an auxiliary inspection mechanism when generating tuning tones. By comparing the beat frequencies of different intervals to verify the accuracy of the target note, the tuning accuracy is significantly improved. Furthermore, this method also takes into account the characteristics of different temperaments, enabling the generated note group to achieve the best harmony under a specific temperament and meet the requirements of multi-tonality music at the same time.

[0036] Further, the principle of the pure interval inspection method in this application is as follows: A pure interval refers to a completely consonant interval that naturally exists in the overtone series, such as intervals like 2:1, 3:2, 4:3, 5:4, 6:5, etc. in the overtone series. The auditory perception is without beats, so it is called a pure interval. The basic principle is to obtain a pure minor third (or pure minor sixth) or major third (or pure major sixth) by changing the root or fifth (or third) of the equal temperament major (or minor) triad. Such a chord with a changed frequency then has an interval with a slow beat frequency, thus increasing the possibility of selection for the accuracy inspection of the target note and facilitating the improvement and grasp of the accuracy of the target note. Preferably, select the average chord F3 - A3 - C4. When tuning C4 among them, form a pure interval group with A3. At this time, the beat frequencies of the intervals F3 - C4 and A3 - C4 are 4:0; if F3 is tuned at this time to form a pure interval with A3, the beat frequencies of the intervals F3 - C4 and A3 - C4 are 0:4. The calculation method is as follows: Given that A3 in the equal temperament chord A3 - C4 - E4 is 220Hz and E4 is 329.63Hz, and C4 forming a pure interval with E4 is 263.70Hz (i.e., the frequency of C4 is obtained by dividing C4 by the major third frequency ratio 5:4); at this time, the beat frequency of the interval A3 - C4 is:

[0037] (263.70 x 5) - (220 x 6)

[0038] = 1318.5 - 1320

[0039] = -1.5 beats per second

[0040] Furthermore, it is known that for the equally tempered chord A3 - C4 - E4, A3 is 220 Hz, E4 is 329.63 Hz, and C4, which forms a pure interval with A3, is 264 Hz (i.e., the frequency of C4 is obtained by multiplying the frequency of A3 by the minor third frequency ratio 6:5); at this time, the beat frequency of the interval C4 - E4 is:

[0041] (264 x 5) - (329.63 x 4)

[0042] = 1320 - 1318.52

[0043] = 1.48 beats per second (approximately 1.5 beats per second)

[0044] The above examples illustrate that pure intervals create favorable conditions for testing target tones, and the tuner can flexibly use the original or inverted forms of chords (the beat frequency is relatively slower when inverted downwards) to test the intervals therein. Specifically, referring to the above principle, the following embodiments mentioned in this application:

[0045] Embodiment 1, referring to Figure 1 , in the traditional piano tuning method, based on the equally tempered fourth and fifth degree tuning principle, there are two main tuning sequences. The first is the up-fourth and down-fifth degree tuning method, which starts with A3 and sequentially generates pure fourth intervals upwards and pure fifth intervals downwards to gradually expand to the entire reference note group. The specific tuning sequence is as follows: A3 → D4 → G3 → C4 → F3 → bB3 → bE4 → bA3 → bD4 → bG3 (#F3) → B3 → E4. In each step, the beat frequency of adjacent intervals is adjusted to make the generated tones conform to the frequency distribution requirements of the equal temperament; the second is the up-fifth and down-fourth degree tuning method, which also starts with A3 but uses the opposite tuning direction, that is, sequentially generates pure fifth intervals upwards and pure fourth intervals downwards to gradually expand to the entire reference note group. The specific tuning sequence is as follows: A3 → E4 → B3 → #F3 → #C4 → #G3 → #D4 → #A3( bB3) → F3 → C4 → G3 → D4. Similarly, the pitch beat frequency needs to be precisely adjusted at each step to meet the requirements of the equal temperament. For example, in the equal temperament's downward perfect fifth sub-temperament, using the sub-temperament method proposed in this application to verify the accuracy of the D4 temperament note, the specific idea is as follows: The note to be verified is D4, the known note is A3, and the harmonic interval of the note to be verified D4 is A3 - D4. Set the pure interval group as A3 - F3. At this time, press the actual slow frequency interval F3 - D4 to listen to the beat frequency. If the absolute error between the calculated theoretical slow frequency interval F3 - D4's beat frequency and the actual slow frequency interval F3 - D4's beat frequency is within 2, then the D4 temperament note is accurate. The specific steps are as follows: S21: Based on the verification of the downward major third natural interval, the beat frequency of the harmonic interval A3 - D4 is 0.99 beats per second. Refer to Figure 1 , the actual beat frequency designed in this chart is the harmonic interval mentioned in this application. Calculate the frequency of the target note F3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n. The target interval frequency ratio Furthermore, the frequency of the known note A3 is 220 Hz. Using the downward major third frequency calculation formula f01 = f02 ÷ 5 × 4, the frequency of F3 is obtained as: 220 Hz ÷ 5 × 4 = 176 Hz; S22: Based on the verification of the upward major sixth natural interval, substitute the frequency of the target note obtained in step S1 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow frequency interval F3 - D4. Here, f03 represents the frequency of the note to be verified D4, f04 represents the frequency of the target note F3, a is 3, and b is 5; Furthermore, substitute the frequencies of F3 and D4. According to Figure 1 it can be known that the frequency of D4 is 293.66 Hz. Then the beat frequency of the theoretical slow frequency interval F3 - D4 is: (293.66 Hz × 3) - (176 Hz × 5) = 880.98 Hz - 880 Hz = 0.98 beats per second; S23: Compare the beat frequency of the theoretical slow frequency interval F3 - D4 calculated in step S22 above with the actual slow frequency interval F3 - D4 and the harmonic interval A3 - D4 in step S1 above to verify the accuracy of the note to be verified; Therefore, there are two comparison data for verifying whether D4 is precise, that is, the calculated beat frequency of the theoretical slow frequency interval F3 - D4 is 0.98 beats per second and the beat frequency of its harmonic interval A3 - D4 is 0.99 beats per second, and their absolute error is 0.02.

[0046] Example 2: In the equal temperament of four lower and five upper fifths, the proposed temperament method of this application is used to verify the accuracy of the pitch F3. At the same time, the musical tones outside the reference tone group mainly refer to the musical tones below the reference tone group, and the principle of its participation in the test is based on the principle of using pure intervals to change the beat frequency in the above-mentioned triad. The difference is that since it is completed by means of the lower chord tones, it exceeds the limitations of traditional test intervals and can also use chord inversions. The specific idea is as follows: The pitch to be tested is F3, the known pitch is A3, the harmonic interval of the pitch to be tested F3 is C4 - F3, and the pure interval group is set as A3 - C3. At this time, press the actual slow frequency interval C3 - F3 to listen to the beat frequency. If the absolute error between the calculated beat frequency of the theoretical slow frequency interval C3 - F3 and the actual slow frequency interval C3 - F3 of the beat frequency is within 2, then the pitch F3 is accurate. The specific steps are as follows: S31: Based on the verification of the descending major sixth natural interval, the beat frequency of the harmonic interval C4 - F3 is 0.59 beats per second. Calculate the frequency of the target pitch C3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n, and the target interval frequency ratio Furthermore, the frequency of the known pitch A3 is 220 Hz. Using the descending major sixth frequency calculation formula f01 = f02 ÷ 5 × 4, the frequency of C3 is obtained as: = 220 Hz ÷ 5 × 3 = 132 Hz. S32: Based on the verification of the ascending perfect fourth natural interval, substitute the frequency of the target pitch obtained in step S1 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow frequency interval C3 - F3, where f03 represents the frequency of the target pitch C3, f04 represents the frequency of the pitch to be tested F3, a is 4, and b is 3; furthermore, substitute the frequencies of C3 and F3. According to Figure 1 it is known that the frequency of F3 is 174.61 Hz, then the beat frequency of the theoretical slow frequency interval C3 - F3 is: C3 × 4 - F3 × 3 = 132 Hz × 4 - 174.61 Hz × 3 = 528 Hz - 523.83 Hz = 4.17 beats per second; S33: Compare the beat frequency of the theoretical slow frequency interval C3 - F3 calculated in step S32 above with the actual slow frequency interval C3 - F3 in step S1 above and the harmonic interval C4 - F3 to verify the accuracy of the pitch to be tested. Therefore, there are two comparison data for verifying whether F3 is accurate, that is, the calculated beat frequency of the theoretical slow frequency interval C3 - F3 is 4.17 beats per second and the beat frequency of its harmonic interval C4 - F3 is 0.59 beats per second, and the absolute error between its theoretical slow frequency interval and the actual slow frequency interval C3 - F3 is 0.02.

[0047] Example 3: In the equal temperament of four lower and five upper fifths, the proposed temperament method of this application is used to verify the pitch b B3 for accuracy. The specific idea is as follows: The pitch to be tested is b B3, the known pitch is F3, and the pitch to be tested is b B3's harmonic interval is F3 - bB3, set the pure interval group to F3- b D3, then press the actual slow frequency interval b D3- b B3 to listen and distinguish the beat frequency. If the calculated theoretical slow frequency interval b D3- b B3 and the actual slow frequency interval b D3- b B3 beat frequency absolute error is within 2, then b B3 is accurate. The specific steps are as follows: S41: Based on the verification of the major third natural interval, the beat frequency of the harmonic interval F3- b B3 is 0.79 beats per second. Calculate the frequency of the target note b D3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n. The target interval frequency ratio Furthermore, given that the frequency of the known note F3 is 174.61 Hz, using the major third frequency calculation formula f01 = f02 ÷ 5 × 4, we get b The frequency of D3 is: b D3 = 174.61 Hz ÷ 5 × 4 = 139.69 Hz; S42: Based on the verification of the ascending major sixth natural interval, substitute the frequency of the target interval obtained in step S41 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the theoretical slow frequency interval b D3- b B3 beat frequency, where f03 represents the frequency of the note to be verified b B3, f04 represents the frequency of the target note b D3, a is 3, b is 5; Furthermore, substitute b D3 and b B3 frequencies, according to Figure 1 It can be known that b The frequency of B3 is 233.08 Hz, then the theoretical slow frequency interval b D3- b B3 beat frequency is: (233.08 Hz × 3) - (139.69 Hz × 5) = 699.24 Hz - 698.45 Hz = 0.79 beats per second (approx. 0.8 beats per second); S43: Compare the beat frequency of the theoretical slow frequency interval b D3- b B3 calculated in step S42 above with the actual slow frequency interval b D3- b B3 and the harmonic interval F3- b B3 above to verify b The accuracy of B3. Therefore, to verify b Whether B3 is accurate, there are two reference data, that is, the calculated theoretical slow frequency interval b D3-b The beat frequency of B3 is 0.79 beats per second and its harmonic interval is F3 - b The beat frequency of B3 is 0.79 beats per second, and its actual slow frequency interval b D3 - b The heard beat frequency of B3 is 0.8 beats per second, and the absolute error between its theoretical slow frequency interval and actual slow frequency interval C3 - F3 is 0.02.

[0048] Example 4: In Vallotti's irregular temperament, use the temperament division method proposed in this application to verify the accuracy of the pitch G3. The specific idea is as follows: The pitch to be verified is G3, the known pitch is C4, the harmonic interval of the pitch to be verified G3 is C4 - G3, and the pure interval group is set as C4 - E3. At this time, listen to the beat frequency of the actual slow frequency interval E3 - G3. If the absolute error between the calculated theoretical slow frequency interval E3 - G3 and the actual slow frequency interval E3 - G3 beat frequency is within 2, then G3 is accurate. The specific steps are as follows: S51: Verify based on the descending minor sixth natural interval. The harmonic interval C4 - G3 is -1.61 beats per second. Calculate the frequency of the target pitch E3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n. The target interval frequency ratio Further, the known pitch C4 has a frequency of 261.63 Hz. Using the descending minor sixth frequency calculation formula f01 = f02 ÷ 5 × 4, the frequency of E3 is obtained as: E3 = C4 ÷ 8 × 5 = 261.63 Hz ÷ 8 × 5 = 163.52 Hz; S52: Verify based on the ascending minor third natural interval. Substitute the frequency of the target interval obtained in step S51 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow frequency interval E3 - G3, where f03 represents the frequency of the pitch to be verified G3, f04 represents the frequency of the target pitch E3, a is 5, and b is 6; Further, substitute the frequencies of E3 and G3. According to Figure 2 It is known that the frequency of G3 is 195.78 Hz, then the beat frequency of the theoretical slow frequency interval E3 - G3 is: E3 - G3 = (G3 × 5) - (E3 × 6) = (195.78 Hz × 5) - (163.52 Hz × 6) = 978.9 Hz - 981.12 Hz = -2.22 beats per second (approximately equal to -2 beats per second); S53: Compare the beat frequency of the theoretical slow frequency interval E3 - G3 calculated in step S52 above with the actual slow frequency interval E3 - G3 and the harmonic interval C4 - G3 in step S51 above to verify the accuracy of G3. Therefore, there are two comparison data for verifying whether G3 is accurate, that is, the calculated beat frequency of the theoretical slow frequency interval E3 - G3 is -2.22 beats per second and its harmonic interval C4 - G3 is -1.61 beats per second, and its actual slow frequency interval E3 - G3 heard beat frequency is -2 beats per second, and the absolute error between its theoretical slow frequency interval and actual slow frequency interval C3 - F3 is 0.02.

[0049] Example 5: In Zarlino's law of the mean, the proposed sub-law method in this application is used to verify the accuracy of the pitch A3. The specific idea is as follows: The pitch to be verified is A3. Use A3 below the key of C4, with C4 as the auxiliary pitch. The known pitch is A3. The harmonic interval of the pitch A3 to be verified is A3-E4. Set the pure interval group as A3-F3. At this time, press the actual slow frequency interval F3-C4 to listen to the beat frequency. If the absolute error between the calculated theoretical slow frequency interval F3-C4 and the actual slow frequency interval F3-C4 beat frequency is within 2, then A3 is accurate. The specific steps are as follows: S61: Based on the verification of the major third natural interval, the beat frequency of the harmonic interval A3-E4 is 2.05 beats per second. Calculate the frequency of the target pitch F3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n. The target interval frequency ratio Further, the known pitch is A3 with a frequency of 218.71 Hz. Using the major third frequency calculation formula f01 = f02 ÷ 5 × 4, the frequency of F3 is obtained as follows: F3 = A3 ÷ 5 × 4 = 218.71 Hz ÷ 5 × 4 = 174.97 Hz; S62: Based on the verification of the ascending perfect fifth natural interval, substitute the frequency of the target interval obtained in step S61 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow frequency interval F3-C4. Where f03 represents the frequency of the auxiliary pitch C4, f04 represents the frequency of the target pitch F3, a is 2, and b is 3; Further, substitute the frequencies of F3 and C4. According to Figure 3 It is known that the frequency of C4 is 261.63 Hz. Then the beat frequency of the theoretical slow frequency interval F3-C4 is: F3-C4 = (C4 × 2) - (F3 × 3) = (261.63 Hz × 2) - (174.97 Hz × 3) = 523.26 Hz - 524.91 Hz = -1.65 beats per second; S63: Compare the beat frequency of the theoretical slow frequency interval F3-C4 calculated in step S62 above with the actual slow frequency interval F3-C4 and the harmonic interval A3-E4 in step S61 above to verify the accuracy of A3. Therefore, there are two control data for verifying whether A3 is accurate, that is, the calculated beat frequency of the theoretical slow frequency interval F3-C4 is -1.65 beats per second and the beat frequency of its harmonic interval A3-E4 is 2.05 beats per second, and referring to Figure 3 The beat frequency of its actual slow frequency interval F3-C4 listened to is -1.65 beats per second, and the absolute error between its theoretical slow frequency interval and the actual slow frequency interval F3-C4 is within 2.

[0050] Embodiment Six: In the Zarlino quarter mean-tone temperament, f03 can be the frequency for setting the auxiliary tone. The mean-tone temperament is also different from other temperaments, so the frequencies and beat frequencies of each tone are different. If the beat frequency obtained by using E3 (327.04 Hz) to tune the lower A3 (218.71 Hz) is 2.05 beats per second, in order to make this temperament relatively accurate, an auxiliary test can be added, that is, tuning A3 - F3 into a pure interval group. At this time, the beat frequency of F3 - C4 is about 1.65 beats per second. Comparing the beat frequencies of A3 - E3 and F3 - C4, the former is slightly faster than the latter. In this way, the A3 tone is relatively accurate. Further, in the temperament division method proposed in this application, when selecting a pure interval group within a minor triad, the other interval with a slow beat is the relevant interval. For example, for the minor triad A3 - C3 - E3, when selecting A3 - C3 as the pure interval group, the beat frequency of C3 - E3 is 1.5 beats per second; when selecting C3 - E3 as the pure interval group, the beat frequency of A3 - C3 is also 1.5 beats per second. Further, the different intervals of the known tones in step S1 include but are not limited to major thirds, minor sixths, minor thirds, and major sixths. Further still, the temperament includes equal temperament and non-equal temperament. Further still, in this application Figure 1 The actual beat frequencies involved are calculated by starting from the international standard pitch A440 Hz and cycling according to the ascending perfect fifth and descending perfect fourth (or ascending perfect fourth and descending perfect fifth). The calculation method for the ascending perfect fourth is (fundamental frequency × 4) - (crowning frequency × 3) = the beat frequency of this interval, and the calculation method for the descending perfect fifth is (fundamental frequency × 3) - (crowning frequency × 2) = the beat frequency of this interval. For example: To find the beat frequency of the perfect fourth A3 to D4, that is, (A3 × 4) - (D4 × 3) = (220 × 4) - (293.66 × 3) = 0.99 beats per second. Another example, to find the beat frequency of D4 to G3, that is, (196 × 3) - (293.66 × 2) = 0.66 beats per second. The actual beat frequencies in the entire figure can be analogously deduced in this way. Further, similarly, Figure 2 the number of beats is also calculated one by one according to the corresponding temperament using the above scheme. Similarly, Figure 3 the number of beats per second is also calculated using the same method.

[0051] It should be noted that in the description of the present invention, if there are descriptions related to directions, such as the directions or position relationships indicated by up, down, front, back, left, right, etc., they are all based on the directions or position relationships shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed or operated in a specific direction, and should not be construed as a limitation to the present invention.

[0052] In the description of the present invention, "a number of" means one or more, "a plurality of" means two or more, "greater than", "less than", "exceeding", etc. are understood not to include the recited number, and "above", "below", "within", etc. are understood to include the recited number. If there is a description of "first" or "second", etc., it is only for the purpose of distinguishing technical features and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features or implicitly indicating the sequence relationship of the indicated technical features.

[0053] In the description of the present invention, unless otherwise clearly defined, terms such as "arrangement", "installation", "connection", etc. should be understood in a broad sense, and those skilled in the art can reasonably determine the specific meanings of the above terms in the present invention in combination with the specific content of the technical solution.

[0054] The above embodiments are only the preferred embodiments of the present invention, and the scope of protection of the present invention cannot be limited thereby. Any non-substantial changes and substitutions made by those skilled in the art based on the present invention fall within the scope of protection required by the present invention.

Claims

1. A high-precision piano tuning method based on the inspection of pure interval groups, characterized in that, It includes the following steps: S1: Based on different natural intervals, select a pure interval group and an actual slow-frequency interval related to the interval to be verified. The pure interval group consists of a known note - target note. Calculate the frequency of the target note in the pure interval group through the target interval frequency calculation formula f01 = f02 ÷ n, where f01 represents the frequency of the target note, f02 represents the known note frequency, and n represents the target interval frequency ratio; S2: Based on different natural intervals, substitute the frequency of the target note obtained in step S1 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow-frequency interval. Here, f represents the beat frequency of the theoretical slow-frequency interval. When f03 represents the frequency of the note to be verified, f04 is the frequency of the target note; when f03 represents the frequency of the target note, f04 is the frequency of the note to be verified; a represents the numerator in the natural interval frequency ratio, and b represents the denominator in the natural interval frequency ratio; S3: Compare the beat frequency of the theoretical slow-frequency interval calculated in step S2 above with the actual slow-frequency interval in step S1 above. Using the harmonic interval of the theoretical slow-frequency interval and the note to be verified as reference data, verify the accuracy of the note to be verified.

2. The distribution method according to claim 1, wherein The note to be verified is D4, the known note is A3, and the harmonic interval of the note to be verified D4 is A3 - D4. Set the pure interval group as A3 - F3. At this time, press the actual slow-frequency interval F3 - D4 to listen to the beat frequency. If the absolute error between the beat frequency of the calculated theoretical slow-frequency interval F3 - D4 and the beat frequency of the actual slow-frequency interval F3 - D4 is within 2, then the D4 pitch is accurate. The specific steps are as follows: S21: Based on the verification of the descending major third natural interval, the beat frequency of the harmonic interval A3 - D4 is 0.99 beats per second. Calculate the frequency of the target note F3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n, and the target interval frequency ratio S22: Based on the verification of the ascending major sixth natural interval, substitute the frequency of the target note obtained in step S1 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow-frequency interval F3 - D4. Here, f03 represents the frequency of the note to be verified D4, f04 represents the frequency of the target note F3, a is 3, and b is 5; S23: Use the beat frequency of the theoretical slow-frequency interval F3 - D4 calculated in step S22 above, the actual slow-frequency interval F3 - D4 in step S1 above, and the harmonic interval A3 - D4 to verify the accuracy of the note to be verified.

3. The distribution method according to claim 1, characterized in that The note to be verified is F3, the known note is A3, and the harmonic interval of the note to be verified F3 is C4 - F3. Set the pure interval group as A3 - C3. At this time, press the actual slow-frequency interval C3 - F3 to listen to the beat frequency. If the absolute error between the beat frequency of the calculated theoretical slow-frequency interval C3 - F3 and the beat frequency of the actual slow-frequency interval C3 - F3 is within 2, then the F3 pitch is accurate. The specific steps are as follows: S31: Based on the verification of the descending major sixth natural interval, the beat frequency of the harmonic interval C4 - F3 is 0.59 beats per second. Calculate the frequency of the target note C3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n, and the target interval frequency ratio S32: Based on the verification of the ascending perfect fourth natural interval, substitute the frequency of the target note obtained in step S1 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the beat frequency of the theoretical slow-frequency interval C3 - F3. Here, f03 represents the frequency of the target note C3, f04 represents the frequency of the note to be verified F3, a is 4, and b is 3; S33: Compare the beat frequency of the theoretical slow-frequency interval C3 - F3 calculated in step S32 above with the actual slow-frequency interval C3 - F3 in step S31 above, and verify the accuracy of the to-be-verified tone with the harmonic interval C4 - F3.

4. The partitioning method according to claim 1, characterized in that The sound to be tested is b B3, the known sound is F3, and the sound to be tested is b The harmonic interval of B3 is F3 - b B3, and the pure interval group is set as F3 - b D3. At this time, press the actual slow-frequency interval b D3 - b B3 to listen and distinguish the beat frequency. If the calculated theoretical slow-frequency interval b D3 - b B3 and the actual slow-frequency interval b D3 - b B3 have a beat frequency absolute error within 2, then b B3 is accurate. The specific steps are as follows: S41: Based on the verification of the major third natural interval, the beat frequency of the harmonic interval F3- b B3 is 0.79 beats per second. Calculate the frequency of the target note D3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n, and the target interval frequency ratio b ​ S42: Based on the verification of the ascending major sixth natural interval, substitute the frequency of the target interval obtained in step S41 into the natural interval beat frequency calculation formula f = (f03 × a) - (f04 × b) to calculate the theoretical slow frequency interval b D3- b B3 beat frequency, where f03 represents the sound to be verified b The frequency of B3, f04 represents the target sound b The frequency of D3, a is 3, b is 5; S43: Compare the beat frequency of the theoretical slow frequency interval b D3- b B3 calculated in step S42 above with the actual slow frequency interval b D3- b B3 and the harmonic interval F3- b B3 in step S41 above to verify b the accuracy of B3.

5. The distribution method according to claim 1, characterized in that, The to-be-verified tone is G3 in Vallotti's irregular temperament, the known tone is C4, the harmonic interval of the to-be-verified tone G3 is C4 - G3, set the pure interval group as C4 - E3, and at this time press the actual slow-frequency interval E3 - G3 to distinguish the beat frequency. If the absolute error between the calculated theoretical slow-frequency interval E3 - G3 and the actual slow-frequency interval E3 - G3 beat frequencies is within 2, then G3 is accurate. The specific steps are as follows: S51: Based on the verification of the descending minor sixth natural interval, the harmonic interval of C4 - G3 is -1.61 beats per second. Calculate the frequency of the target note E3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n, and the target interval frequency ratio S52: Based on the verification of the ascending minor third natural interval, substitute the frequency of the target interval obtained in step S51 into the natural interval beat frequency calculation formula f = (f03×a) - (f04×b) to calculate the beat frequency of the theoretical slow-frequency interval E3 - G3, where f03 represents the frequency of the to-be-verified tone G3, f04 represents the frequency of the target tone E3, a is 5, and b is 6; S53: Compare the beat frequency of the theoretical slow-frequency interval E3 - G3 calculated in step S52 above with the actual slow-frequency interval E3 - G3 and the harmonic interval C4 - G3 in step S51 above to verify the accuracy of G3.

6. The law division method according to claim 1, characterized in that The to-be-verified tone is A3 in Zarlino's mean temperament. Use A3 below the C4 key. The C4 is an auxiliary tone. The known tone is A3. The harmonic interval of the to-be-verified tone A3 is A3 - E4. Set the pure interval group as A3 - F3. At this time, press the actual slow-frequency interval F3 - C4 to distinguish the beat frequency. If the absolute error between the calculated theoretical slow-frequency interval F3 - C4 and the actual slow-frequency interval F3 - C4 beat frequencies is within 2, then A3 is accurate. The specific steps are as follows: S61: Based on the verification of the major third natural interval, the beat frequency of the harmonic interval A3 - E4 is 2.05 beats per second. Calculate the frequency of the target note F3 in the pure interval group through the target interval calculation formula f01 = f02 ÷ n, and the target interval frequency ratio S62: Based on the verification of the ascending perfect fifth natural interval, substitute the frequency of the target interval obtained in step S61 into the natural interval beat frequency calculation formula f = (f03×a) - (f04×b) to calculate the beat frequency of the theoretical slow-frequency interval F3 - C4, where f03 represents the frequency of the auxiliary tone C4, f04 represents the frequency of the target tone F3, a is 5, and b is 6; S63: Compare the beat frequency of the theoretical slow-frequency interval F3 - C4 calculated in step S62 above with the actual slow-frequency interval F3 - C4 and the harmonic interval A3 - E4 in step S61 above to verify the accuracy of A3.

7. The distribution method according to claim 6, characterized in that In Zarlino's quarter-mean temperament, f03 can be the frequency of the set auxiliary tone.

8. The distribution method according to claim 1, characterized in that When selecting the pure interval group within the minor triad, the other slow-beat interval is the relevant interval. For example, the minor triad is A3 - C3 - E3. When selecting A3 - C3 as the pure interval group, the beat frequency of C3 - E3 is 1.5 beats per second; when selecting C3 - E3 as the pure interval group, the beat frequency of A3 - C3 is also 1.5 beats per second.

9. The distribution method according to claim 1, characterized in that, The known tones and different intervals in step S1 include but are not limited to major third, minor sixth, minor third, and major sixth.

10. The law division method according to claim 1, characterized in that The temperaments include equal temperament and non-equal temperament.

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