Patent Application
20060065107
The presently preferred embodiments of this invention relate generally to methods and apparatus for performing music transcription and, more specifically, relate to pitch estimation and extraction techniques for use during an automatic music transcription procedure.
Pitch perception plays an important role in human hearing and in the understanding of sounds. In an acoustic environment a human listener is capable of perceiving the pitches of several sounds simultaneously, and can use the pitch to separate sounds in a mixture of sounds. In general, a sound can be said to have a certain pitch if it can be reliably matched by adjusting the frequency of a sine wave of arbitrary amplitude.
Music transcription as employed herein may be considered to be an automatic process that analyzes a music signal so as to record the parameters of the sounds that occur in the music signal. Generally in music transcription, one attempts to find parameters that constitute music from an acoustic signal that contains the music. These parameters may include, for example, the pitches of notes, the rhythm and loudness.
Reference can be made, for example, to Anssi P. Klapuri, “Signal Processing Methods for the Automatic Transcription of Music”, Thesis for degree of Doctor of Technology, Tampere University of Technology, Tampere FI 2004 (ISBN 952-15-1147-8, ISSN 1459-2045), and to the six publications appended thereto.
Western music generally assumes equal temperament (i.e., equal tuning), in which the ratio of the frequencies of successive semi-tones (notes that are one half step apart) is a constant. For example, and referring to Klapuri, A. P., “Multiple Fundamental Frequency Estimation Based on Harmonicity and Spectral Smoothness”, IEEE Trans. On Speech and Audio Processing, Vol. 11, No. 6, 804-816, November 2003, it is known that notes can be arranged on a logarithmic scale where the fundamental frequency Fk of a note k is Fk=440×2(K/12) Hz. In this system, a′ (440 Hz) receives the value k=0. The notes below a′ (in pitch) receive negative values while the notes above a′ receive positive values. In this system k can be converted to a MIDI (Musical Instrument Digital Interface) note number by adding the value 69. General reference with regard to MIDI can be made to “MIDI 1.0 Detailed Specification”, The MIDI Manufacturers Association, Los Angeles, Calif.
A problem that can arise during pitch extraction is illustrated in the following examples that demonstrate an increase in the probability for an error to occur in pitch extraction when attempting to locate the best pitch estimates for sung, played, or whistled notes. The following examples assume that the relationship Fk=440×2(k/12) Hz is unmodified.
When a skilled vocalist sings a cappella (without an accompaniment), the vocalist is likely to use just intonation as a basis for the scale. Just intonation uses a scale where simple harmonic relations are favored (reference in regard to simple harmonic relations can be made to Klapuri, A. P., “Multipitch Estimation and Sound Separation by the Spectral Smoothness Principle”, Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, Salt Lake City, Utah 2001). In just intonation, ratios m/n (where m and n are integers greater than zero) between the frequencies in each note interval of the scale are adjusted so that m and n are small:
F=(m/n)Fr, where Fr is the frequency of the root note of the key (1)
In addition, an a cappella vocalist may loose the sense of a key and sing an interval so that m and n in the ratio of the frequencies of consecutive notes are small:
Fk+1=(m/n)Fk (2)
There may also be a constant error in tuning, where an a cappella vocalist may use his/her own temperament by singing constantly out of tune.
An additional problem can arise when music is composed to utilize a tuning other than equal temperament, e.g., as typically occurs in non-Western music.
Ryynänen, M., in “Probabilistic Modelling of Note Events in the Transcription of Monophonic Melodies”, Master of Science Thesis, Tampere University of Technology, 2004, has proposed an algorithm for the tuning of pitch estimates for pitch extraction in the automatic transcription of music. The algorithm initializes and updates a specific histogram mass center ct based on an initial pitch estimate x′t for an extracted frequency, where x′t is calculated as:
x′t=69+12 log2(Ft/440) (3)
A final pitch estimate is made as: xt=x′t+ct.
The foregoing algorithm is based on equal temperament. However, there are some applications that are not well served by an algorithm based on equal temperament, such as when it is desired to accurately extract pitch from audio signals that contain singing or whistling, or from audio signals that represent non-Western music or other music that does not exhibit equal temperament.
The foregoing and other problems are overcome, and other advantages are realized, in accordance with the presently preferred embodiments of this invention.
In one aspect thereof this invention provides a method to estimate pitch in an acoustic signal, and in another aspect thereof a computer-readable storage medium that stores a computer program for causing the computer to estimate pitch in an acoustic signal. The method, and the operations performed by the computer program, include initializing a function ƒt and a time t, where t=0, x′0 =ƒ0(F0), x′0 is a pitch estimate at time zero and F0 is a frequency of the acoustic signal at time zero; determining at least one pitch estimate using the function x′t=ƒt(Ft) by an iterative process of creating ƒt+1(Ft+1) based at least partly on pitch estimates x′t , x′t−1, x′t−2, x′t−3. . . , and functions ƒt(Ft), ƒt−1,(Ft−1), ƒt−2(Ft−2), ƒt−3(Ft−3) . . . and incrementing t; and calculating at least one final pitch estimate.
In another aspect thereof this invention provides a system that comprises means for receiving data representing an acoustic signal and processing means to process the received data to estimate a pitch of the acoustic signal. The processing means comprises means for initializing a function ƒt and a time t, where t=0, x′0=ƒ0(F0), x′0 is a pitch estimate at time zero and F0 is a frequency of the acoustic signal at time zero; means for determining at least one pitch estimate using the function x′t=ƒt(Ft) by an iterative process of creating ƒt+1,(Ft+1) based at least partly on pitch estimates x′t, x′t−1, x′t−2, x′t−3, . . . , and functions ƒt(Ft), ƒt−1(Ft−1), ƒt−2(Ft−2), ƒt−3(Ft−3) . . . and incrementing t; and means for calculating at least one final pitch estimate.
In one non-limiting example of embodiments of this invention the receiving means comprises a receiver means having an input coupled to a wired and/or a wireless data communications network. In another non-limiting example of embodiments of this invention the receiving means comprises an acoustic transducer means and an analog to digital conversion means for converting an acoustic signal to data that represents the acoustic signal. In another non-limiting example of embodiments of this invention the acoustic signal comprises a person's voice. Further in accordance with this further non-limiting example of embodiments of this invention the system comprises a telephone, and the processor means uses at least one final pitch estimate for generating a ringing tone.
The foregoing and other aspects of the presently preferred embodiments of this invention are made more evident in the following Detailed Description of the Preferred Embodiments, when read in conjunction with the attached Drawing Figures, wherein:
The preferred embodiments of this invention modify the pitch estimation function x′t=ƒ(Ft) so that relationships other than equal temperament are made possible between Ft and x′t. A method for performing pitch estimation in accordance with embodiments of this invention is shown in
The data processor 10 is further coupled to at least one memory 17, shown for convenience in
Also shown in
In general, the various embodiments of the system 1 can include, but are not limited to, cellular telephones, personal digital assistants (PDAs) having audio functionality and optionally wired or wireless communication capabilities, portable or desktop computers having audio functionality and optionally wired or wireless communication capabilities, image capture devices such as digital cameras having audio functionality and optionally wired or wireless communication capabilities, gaming devices having audio functionality and optionally wired or wireless communication capabilities, music storage and playback appliances optionally having wired or wireless communication capabilities, Internet appliances permitting wired or wireless Internet access and browsing and having audio functionality, as well as portable and generally non-portable units or terminals that incorporate combinations of such functions.
Returning now to
The operation of block B is preferably an iterative recursion, where at block B1 the method creates ƒt+1(Ft+1,) based at least partly on the pitch estimate(s) x′t, x′t−1, x′t−2, x′t−3, . . . , and function(s) ƒt(Ft), ƒt−1(Ft−1), ƒt−2(Ft−2), ƒt−3(Ft−3) . . . ; and at block B2 the method increments t.
The operation of block C, i.e., calculating the final pitch estimates, may involve calculating the final pitch estimate (xt) of a single note from multiple pitch estimates (xt,i) that have been produced for the same note. In a related sense, re-entering the recursion B1, B2 from block C is especially beneficial in the case of a loss of a sense of key, as described in further detail below. In this case, the final pitch estimate (which depends on all xt,i) should be determined for a note before the recursion may continue for the next note (with a slightly or clearly modified key).
It is noted that the operation of block C, i.e., calculating the final pitch estimates, may also include a shifting operation as in Ryynänen, discussed in further detail below, when adding ct to the result of the pitch estimation function.
It should be appreciated that the various blocks shown in
The embodiments of the invention can also be implemented using a combination of hardware blocks and software functions. Thus, the embodiments of this invention can be implemented using various different means and mechanisms.
Discussing the presently preferred embodiments of the method of
x′t=m+s*log2(Ft/Fb) (4)
where s defines the number of notes in an octave, and Fb is a reference frequency.
For the case of just intonation, and if the key of the music is known, one may set s=12, m=the MIDI number of the root note in the key, and Fb=440×2((m−69)/12) Hz. One may then map the ratio Ft/Fb to an adjusted ratio Rt according to the following Table 1:
This mapping may be implemented with a continuous function or with multiple functions. The points between the values presented in the foregoing Table 1 may be estimated with a linear method or with a non-linear method. In practice, Table 1 may be permanently stored in the program memory 18, or it may be generated in the data memory 20 of
The embodiments of this invention also accommodate the case of the loss of a sense of key in just intonation (changing the reference key) by, after multiple final pitch estimates xt,i of the first note are calculated (including the special case when simply xt=x′t), one may set m=xt(where xt depends on all xt,i) and modify Fb to be the corresponding frequency. Then, the method in
The embodiments of this invention also accommodate the case of the constant error in tuning, as one may use x′t=m+s*log2(Rt), where s=12 and Rt=(Ft+(delta))/Fb. This approach is particularly useful if the vocalist or instrument has a constant error (delta), or shift in pitch, in the frequency domain.
One may use x′t=m+s*log2(Ft/Fb), where s=(alpha)*12, where the value of (alpha) defines by how much the scale is contracted or expanded. This can be useful, for example, if a vocalist sings low notes in tune but high notes out of tune. In this case, the references m and Fb are selected to be from the range of pitch where the vocalist sings in tune. Here the function x′t=ƒ(Ft) may contain multiple sub-functions, of which one is chosen based on a certain condition, for example, Ft>200 Hz.
The embodiments of this invention also accommodate the case of non-Western musical tuning and non-traditional tuning. In this case one may use x′t=s * log2(Rt), where Rt depends on Ft and Fb, and where s defines the number of steps in one octave. Rt may be simply Rt=Ft/Fb (equal tuning) or some other mapping (non-equal tuning), such as a mapping given by or similar to the examples shown above in Table 1.
In at least some of the conventional approaches known to the inventor the pitch estimation function remains constant. It should be appreciated that the embodiments of this invention enable improved precision when extracting pitch from audio signals that contain, as examples, singing or whistling.
As was noted previously, the use of pitch extraction can enable a user, as a non-limiting example, to compose his or her own ringing tones by singing a melody that is captured, digitized and processed by the system 1, such as a cellular telephone or some other device. The following Table 2 shows the differences “in cents” between an estimated just intonation scale (used by a human a cappella voice) and the equal temperament scale (used by most music synthesizers). It can be noted that because one semi-tone is 100 cents, the largest errors based on this difference are 17.6%
The use of the embodiments of this invention permits tuning compensation when there is a constant shift in pitch in the frequency domain, and when lower pitch sounds are in tune but higher pitch sounds are flat (out of tune). The use of the embodiments of this invention makes it possible to extract pitch from non-Western music, as well as from music with a non-traditional tuning. The use of the embodiments of this invention can be applied to pitch extraction with various different input acoustic signal characteristics, such as just intonation, pitch shift in the frequency domain, and non-12-step-equal-temperament tuning.
Referring again to the Ryynänen technique as explained in “Probabilistic Modelling of Note Events in the Transcription of Monophonic Melodies”, it can be noted that Ryynänen uses the following technique:
xt=x′t+ct, where x′t=69+12 log2(Ft/440) (see Equations 3.1 and 3. 10).
After calculating x′t, Ryynäen modifies the value by shifting it with ct, which is produced by a histogram that is updated based on values of x′t. Basically, then, Ryynänen corrects the mistakes of the pitch estimation function by shifting the result of the pitch estimation function by ct.
In the description of the preferred embodiments of this invention the function that produces x′t is a pitch estimation function. The preferred embodiments of this invention consider cases when this function itself is changed. In other words, the underlying model is changed so that it produces more accurate results, as opposed to simply correcting the results of the model by shifting the results.
The foregoing description has provided by way of exemplary and non-limiting examples a full and informative description of the best method and apparatus presently contemplated by the inventors for carrying out the invention. However, various modifications and adaptations may become apparent to those skilled in the relevant arts in view of the foregoing description, when read in conjunction with the accompanying drawings and the appended claims. As but some examples, the use of other similar or equivalent hardware and systems, and different types of acoustic inputs, may be attempted by those skilled in the art. However, all such and similar modifications of the teachings of this invention will still fall within the scope of the embodiments of this invention.
Furthermore, some of the features of the preferred embodiments of this invention may be used to advantage without the corresponding use of other features. As such, the foregoing description should be considered as merely illustrative of the principles, teachings and embodiments of this invention, and not in limitation thereof.
