A computer-implemented method of determining relationships between musical notes and a corresponding system

Abstract

A computer-implemented method of determining a relationship between musical notes. A first set of musical notes, such as a chord, is received 110. A shape associated with the first set of musical note

Description

Technical Field The present disclosure relates generally to methods and systems for determining relationships between musical notes, and more particularly relates to methods and systems for determining relationships between musical notes using shapes and an inversion table. Background Learning and composing music can be challenging as it typically relies on natural intuition. To assist with learning and composing music, there exists various guides and information sources which explain the fundamentals of learning and composing music. The information contained in these is generally based on memorized, documented, or manual music theory. However, even with such guides, the required information can be difficult to find and unintuitive, making learning and composing music difficult. Furthermore, not all information is contained in the existing guides and information sources as it is largely based on people manually writing such guides and information. For example, when learning and composing music, it is often useful to determine relationships associated with a given set of notes (e.g. chords and scales), such as inverted notes, equivalent notes, child notes and parent notes of the set of notes. This information is typically looked up using existing information. However, this existing information is not necessarily complete and intuitive to search. Accordingly, it is desirable to provide methods and systems for reliably determining relationships associated with a set of notes. Furthermore, other desirable features and characteristics of the present disclosure will become apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and the foregoing technical field and background. Summary In an aspect, there is provided a computer-implemented method of determining a relationship between musical notes, the computer-implemented method comprising: receiving a first set of musical notes; determining a shape associated with the first set of musical notes, wherein determining the shape includes calculating the intervals between the first set of musical notes; searching an inversion table based on the shape to determine a second set of musical notes and a relationship between the first set of musical notes and the second set of musical notes, wherein the inversion table comprises a list of a plurality of shapes where each shape of the plurality of shapes is associated with corresponding root information and inversion information. In embodiments, the root information comprises at least one root shape associated with the shape of the plurality of shapes, and, optionally, wherein the root information further comprises a root name associated with the at least one root shape. In embodiments, the root information further comprises two or more root names associated with the at least one root shape. In embodiments, the inversion information comprises an inversion index associated with the at least one root shape, and, optionally, wherein the inversion information further comprises an inversion name associated with the inversion index. In embodiments, the inversion information further comprises two or more inversion names associated with the inversion index. In embodiments, the method comprises determining the inversion table, optionally, wherein the determining of the inversion table occurs before receiving the first set of musical notes. In embodiments, determining the inversion table comprises receiving a list of a plurality of root shapes with associated root names. In embodiments, determining the inversion table further comprises inverting each of the plurality of root shapes to determine associated shapes. In embodiments, determining the inversion table further comprises iteratively inverting each of the plurality of root shapes to determine associated shapes. In embodiments, the inversion table is pre-determined. In embodiments, the inversion table is pre-determined and retrieved from storage, such as non-volatile memory storage and / or cloud storage. In embodiments, the relationship between the first set of musical notes and the second set of musical notes is an inversion relationship such that the first set of musical notes is an inversion of the second set of musical notes. In embodiments, the relationship between the first set of musical notes and the second set of musical notes is an equivalence relationship such that the first set of musical notes is an equivalent of the second set of musical notes. In embodiments, searching the inversion table based on the shape comprises: determining at least one inversion of the shape; and searching the inversion table for the at least one inversion of the shape to determine the second set of musical notes, and, optionally, wherein determining the at least one inversion of the shape comprises determining all inversions of the shape, and wherein searching the inversion table comprises searching the inversion table for all inversions of the shape to determine the second set of musical notes. In embodiments, the relationship between the first set of musical notes and the second set of musical notes is an upper structure relationship such that the second set of musical notes is an upper structure of the first set of musical notes. In embodiments, searching the inversion table based on the shape comprises: removing a lowest element of the shape to determine a reduced shape; adjusting the remaining elements of the reduced shape to obtain an adjusted shape; determining at least one inversion of the adjusted shape; and searching the inversion table for the at least one inversion of the adjusted shape to determine the second set of musical notes, and, optionally, wherein determining the at least one inversion of the adjusted shape comprises determining all inversions of the adjusted shape, and wherein searching the inversion table comprises searching the inversion table for all inversions of the adjusted shape to determine the second set of musical notes. In embodiments, the relationship between the first set of musical notes and the second set of musical notes is a parent structure relationship such that the second set of musical notes is a parent structure of the first set of musical notes. In embodiments, searching the inversion table based on the shape comprises: determining at least one inversion of the shape; adding all possible additional lowest elements to the at least one inversion of the shape to create a plurality of increased shapes; adjusting the plurality of increased shapes to obtain a plurality of adjusted shapes; searching the inversion table for the plurality of adjusted shapes to determine the second set of musical notes, and, optionally, wherein determining the at least one inversion of the shape comprises determining all inversions of the shape. In another aspect, there is provided a system for determining a relationship between musical notes, the system comprising one or more servers, the one or more servers configured to be in communication with a user computer terminal, wherein: the one or more servers are configured to receive a first set of musical notes from the user computer terminal; the one or more servers are configured to determine a shape associated with the first set of musical notes, wherein determining the shape includes calculating the intervals between the first set of musical notes; the one or more servers are configured to search an inversion table based on the shape to determine a second set of musical notes and a relationship between the first set of musical notes and the second set of musical notes, wherein the inversion table comprises a list of a plurality of shapes where each shape of the plurality of shapes is associated with corresponding root information and inversion information; and the one or more servers are configured to transmit the second set of musical notes and the relationship between the first set of musical notes and the second set of musical notes to the user computer terminal. In another aspect, there is provided a computer system for determining a relationship between musical notes, the computer system is configured to receive a first set of musical notes from the user; the computer system is configured to determine a shape associated with the first set of musical notes, wherein determining the shape includes calculating the intervals between the first set of musical notes; the computer system is configured to search an inversion table based on the shape to determine a second set of musical notes and a relationship between the first set of musical notes and the second set of musical notes, wherein the inversion table comprises a list of a plurality of shapes where each shape of the plurality of shapes is associated with corresponding root information and inversion information; and the computer system is configured to output the second set of musical notes and the relationship between the first set of musical notes and the second set of musical notes. In embodiments, the computer system is a distributed computer system (e.g. cloud-based), a local computer system, a user computer terminal (e.g. a PC, laptop, mobile phone, tablet, etc.). In embodiments, the root information comprises at least one root shape associated with the shape of the plurality of shapes, and, optionally, wherein the root information further comprises a root name associated with the at least one root shape. In the methods / systems disclosed herein, the use of an inversion table is purely optional. Any other method of determining the relationship between the first set of musical notes and the second set of musical notes may be used, provided that it involves using the shape of the first set of notes. For example, instead of searching an inversion table, inversions / relationships between sets of musical notes may be calculated each time. In a further aspect, there is provided a computer-implemented method of determining a relationship between musical notes, the computer-implemented method comprising: receiving a first set of musical notes; determining a shape associated with the first set of musical notes, wherein determining the shape includes calculating the intervals between the first set of musical notes; using the shape to determine a second set of musical notes and a relationship between the first set of musical notes and the second set of musical notes, wherein using the shape to determine a second set of musical notes includes determining a plurality of shapes where each shape of the plurality of shapes is associated with corresponding root information and inversion information. In yet a further aspect, there is provided a system for determining a relationship between musical notes, the system comprising one or more servers, the one or more servers configured to be in communication with a user computer terminal, wherein: the one or more servers are configured to receive a first set of musical notes from the user computer terminal; the one or more servers are configured to determine a shape associated with the first set of musical notes, wherein determining the shape includes calculating the intervals between the first set of musical notes; the one or more servers are configured to use the shape to determine a second set of musical notes and a relationship between the first set of musical notes and the second set of musical notes, wherein using the shape to determine a second set of musical notes includes determining a plurality of shapes where each shape of the plurality of shapes is associated with corresponding root information and inversion information; and the one or more servers are configured to transmit the second set of musical notes and the relationship between the first set of musical notes and the second set of musical notes to the user computer terminal. In a further aspect, there is provided a computer system for determining a relationship between musical notes, the computer system is configured to receive a first set of musical notes from the user; the computer system is configured to determine a shape associated with the first set of musical notes, wherein determining the shape includes calculating the intervals between the first set of musical notes; the computer system is configured to use the shape to determine a second set of musical notes and a relationship between the first set of musical notes and the second set of musical notes, wherein using the shape to determine a second set of musical notes includes determining a plurality of shapes where each shape of the plurality of shapes is associated with corresponding root information and inversion information; and the computer system is configured to output the second set of musical notes and the relationship between the first set of musical notes and the second set of musical notes. The present disclosure can be applied to any temperament system. For the examples given herein, the max number of notes is defined as 12, however, this can be freely changes. For example, the max number of notes can take any number, such as 31. Brief Description of the Drawings In order to better understand the subject matter that is disclosed herein and to exemplify how it may be carried out in practice, embodiments will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which: Fig. 1 is a flow chart showing a computer-implemented method of determining a relationship between musical notes; Fig. 2 is a flow chart showing exemplary specific steps in the method of Fig. 1; Fig. 3 is a flow chart showing further exemplary specific steps in the method of Fig. 1; Fig. 4 is a flow chart showing further exemplary specific steps in the method of Fig. 1; Fig. 5 is a flow chart showing further exemplary specific steps in the method of Fig. 1; and Fig. 6 shows a representation of a system for determining a relationship between musical notes. Detailed Description In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of embodiments of the disclosure. However, it will be understood by those of ordinary skill in the art that the disclosure may be practiced without these specific details. In other instances, well-known methods, procedures, components, modules, units and / or circuits have not been described in detail so as not to obscure the disclosure. The present disclosure may be computer implemented through any combination of static webpages, dynamic webpages and computer-executable programs of instructions, such as program modules, generally referred to as software applications or application programs executed by a server / computer. The website / software may include, for example, routines, programs, objects, components, and data structures that perform particular tasks or implement particular abstract data types. The website / software and its outputs / results may be transmitted over a variety of carrier media such as optical fiber, metallic wire, free space and / or through any of a variety of networks such as the Internet. Moreover, those skilled in the art will appreciate that the disclosure may be practiced with a variety of computer-system configurations, including any combination of hand-held devices, multiprocessor systems, microprocessor-based or programmable-consume electronics, minicomputers, mainframe computers, and the like. Any number of computersystems and computer networks are acceptable for use with the present disclosure. The disclosure may be practiced in distributed-computing environments where tasks are performed by remote-processing devices that are linked through a communications network. In a distributed-computing environment, program modules may be located in both local and remote computer-storage media including memory storage devices. The present disclosure may therefore, be implemented in connection with various hardware, software or a combination thereof, in a computer system or other processing system. This disclosure generally provides a dynamic search engine for musical notes. For example, a user may search, using the methods and systems disclosed herein, for a set of musical notes (e.g. a chord / scale) and may be presented with relevant information associated with the searched set of musical notes. The disclosure specifically relates to the methodology behind such a dynamic search engine. Fig. 1 is a flow chart showing a computer-implemented method 100 of determining a relationship between musical notes. The set of musical notes may be one or more notes, such as chords or scales. The set of musical notes may have a commonly accepted name by those in the art. At step 110, a first set of musical notes is received. The first set of musical notes may be received by any means. For example, the first set of musical notes may be received by: reading from an input file and / or input from a user (e.g. via a keyboard / touchscreen). The first set of musical notes may be a plurality of notes, such as a chord or scale. The first set of musical notes may have a commonly accepted name by those in the art. At step 120, a shape associated with the first set of musical notes is determined. The shape may comprise the intervals between each of the musical notes in the first set of musical notes. The intervals between each of the musical notes can be calculated by determining the number of half steps two notes are spaced apart by. For example, notes C and E are separated by an interval of 3; C and G are separated by an interval of 7; and C and A are separated by an interval of 9. Accordingly, in step 120, the shape of the first set of musical notes is calculated based on the intervals (in half steps) between the notes of the first set of musical notes. Various ways of calculating the intervals may be used. For example: the intervals between the notes may be defined relative to the previous note in the first set of musical notes; the intervals may be listed of all notes relative to all other notes; or the intervals between the notes may be defined relative to the first note in the first set of musical notes. For the present disclosure, the latter definition is used; however, all methods disclosed herein are suitable for use with the first definition. Table 1 provides a number of example sets of musical notes, their commonly used names, and their shapes. Set of Musical Notes Name Shape CEGA CMajor6 4,7,9 CEGB CMajor7 4,7,11 CE CMajor3rd 4 DF AC DMinor7 3,7,10 Table 1 In step 130, the shape of the first set of musical notes is searched in an inversion table to determine a second set of musical notes and a relationship between the first set of musical notes and the second set of musical notes. The inversion table may be pre-determined or calculated within step 120 (as described below). The inversion table may take any form so long as it allows sets of musical notes to be related to each other with other associated information. As noted in this disclosure, the use of an inversion table is purely optional. For example, in the present disclosure, a hash map is used as the inversion table. Below, an excerpt of an inversion table used with the present disclosure is provided: { "name": "Inversion Table", "payload": { "3,8": [ { "shape": { "elements": [3, 8], "key": "3,8" }, "rootshape": { "elements": [4, 7], "key": "4,7" }, "rootNames": ["Major", "Maj"], "inversionNames": [], "inversionindex": 1 } b "5,9": [ { "shape": { "elements": [5, 9], "key": "5,9" }, "rootshape": { "elements": [4, 7], "key": "4,7" }, "rootNames": ["Major", "Maj"], "inversionNames": [], "inversionindex": 2 } b "3,5,8": [ { "shape": { "elements": [3, 5, 8], "key": "3,5,8" }, "rootshape": { "elements": [4, 7, 9], "key": "4,7,9" }, "rootNames": ["Major6", "Maj6"], "inversionNames": [], "inversionindex": 1 b { "shape": { "elements": [3, 5, 8], "key": "3,5,8" }, "rootshape": { "elements": [3, 7, 10], "key": "3,7,10" } "rootNames": ["Minor7", "min7", "-7"], "inversionNames": [], "inversionindex": 2 } b "3j7j8": [ { "shape": { "elements": [3, 7, 8], "key": "3,7,8" }, "rootshape": { "elements": [4., 7, 11], "key": "4,7,11" }, "rootNames": ["Major7", "Maj7", "A", "A7"], "inversionNames": ["MinorAugmented", "minAug", "mAug", "-Aug"], "inversionindex": 1 } L } } As can be seen above, the inversion table has a plurality of shapes (3,8; 5,9; 3,5,8; 3,7,8 ...) which act as keys with associated values associated therewith. The keys are unique. This is merely an excerpt of the inversion table, and, as would be understood by those skilled in the art, the full inversion table may contain many more keys. When searching the inversion table, the keys are searched for matches with a search shape. For example, a match is found when there is an exact match between the search shape and a key. If a match is found, the information associated with the matched key is retrieved from the inversion table. Each key may be associated with values, including one or more corresponding roots, which may in turn include root information and inversion information. For example, in the above excerpt, key shape 3,5,8 has two related roots each of which include: a root shape, root name, inversion name and inversion index. For 3,5,8, a first root is provided with root shape 4,7,9; root name Major6 / Maj6; inversion name N / A; and inversion index 1. This shows that shape 3,5,8 may be considered as a first inversion of root shape 4,7,9 (i.e. Major6). A second root for 3,5,8 is provided with root shape 3,7,10; root name Minor7 / Min7 / -7; inversion name N / A; and inversion index 2. This shows that shape 3,5,8 may be considered as a second inversion of root shape 3,7,10 (i.e. Minor7). The inversion table may be calculated by any means. For example, as a starting point, a list of known shapes with known names may be used as an input for creating the inversion table. These known shapes with known names may be commonly used in the art and / or specifically defined by the user (using their own naming conventions). An example of an input of known shapes (or intervals) with known names is produced, in part, below: { / / Intervals "1": ["Minor2nd", "Min2nd"]J "2": ["Major2nd", "Maj2nd"], "3": ["Minor3rd", "Min3rd"], "4": ["Major3rd", "Maj3rd"], "5": ["Perfect4th", "Per4th"], "6": ["Tritone"., "DiminishedSth"} "DimSth", "b5"], "7": ["Perfect5th", "PerSth"], "8": ["MinorSth", "MinGth"], "9": ["MajorGth", "MajGth"], "10": ["Minor7th", "M^th"], "11": ["Major7th", "Maj7th"]J "12": ["Octave"]j / / Major Chords "4;7": ["Major"j "Maj"], "4;7;9": ["Major6", "Maj6"], "4,7,11": ["Major?", "Maj7", "A", "A7"], "4,11,17": ["Major7Addl3", "Maj7Addl3"], "4,11": ["MajorAdd7", "MajAdd7"], } These shapes / intervals with known names are inverted to find all inversions, and an inversion table that links shapes with their inverted forms (and associated information such as names) can be produced. The inversion table may take any form, however, as noted above, the present disclosure uses a hash map with keys for quick look up. In step 130, if an exact match between the searched shape and a key of the inversion table is found, a root (and corresponding root shape) associated with the key is obtained from the inversion table. From the obtained root (and corresponding root shape), a second set of musical notes is determined. In step 140, information relating to the second set of musical notes is outputted. For example, any combination of the following may be outputted: notes of the second set of musical notes; root information of the second set of musical notes (e.g. the root shape and / or root name); and inversion information of the second set of musical notes (e.g. the inversion name and / or inversion index). Fig. 2 shows one example method 1300 performed in step 130 of Fig. 1. The method relates to determining a second set of musical notes associated with the first set of musical notes by an inversion relationship. In other words, the method 1300 of Fig. 2 may be used to determine a root (without inversion form) of the first set of musical notes. At step 1312, a shape associated with the first set of musical notes is received from step 120 (as described above with relation to Fig. 1). For example, if the first set of musical notes is E G B C the shape associated therewith is 3,7,8. At step 1312, the shape is searched in the inversion table to obtain an associated root. The associated root may be associated with any combination of: the root shape, the root name, the inversion name and the inversion index. For example, with searched shape 3,7,8 an exact matched key is found in the inversion table. This match includes corresponding root information, in this case root shape 4,7,11; root name Major? inversion name Minor Augmented...; inversion index 1. Accordingly, method 1300 determines that 3,7,8 is the first inversion of 4,7,11. At step 1314, a reverse inversion of the first set of musical notes by the inversion index determined at step 1312 is performed to determine a second set of musical notes. In the above example, the first set of musical notes E G B C is reverse inverted once (as the inversion index was determined to be 1) to obtain C E G B as the second set of musical notes. Accordingly, it is determined that the first set of musical notes (E G B C) is the first inversion of (root) second set of musical notes (C E G B). At step 1316, information relating to the second set of musical notes is determined. For example, any combination of the following may be determined: notes of the second set of musical notes; root information of the second set of musical notes (e.g. the root shape and / or root name); and inversion information of the second set of musical notes (e.g. the inversion name and / or inversion index). The information from step 1316 is provided at step 140 of Fig. 1 for outputting. Accordingly, in the method 1300 of Fig. 2, a second set of musical notes associated with the first set of musical notes by an inversion relationship may be outputted, along with information relating to the second set of musical notes. The steps 1312, 1314, 1316 may be used to determine inverted sets of notes in any of the other methods disclosed herein. These may act as sub-steps in other methods disclosed herein and the results thereof may therefore not be directly outputted. In other words, steps 1312, 1314, 1316 may be used in other methods to determine (but not necessarily output) one or more inversions of a set of musical notes / determine (but not necessarily output) a root shape associated with a set of musical notes. Fig. 3 shows another example method 1300 performed in step 130 of Fig. 1. The method relates to determining a second set of musical notes associated with the first set of musical notes by an equivalence relationship. In other words, the method 1300 of Fig. 3 may be used to determine an equivalent set of notes (the second set of notes) to the first set of musical notes. At step 1322, a shape associated with the first set of musical notes is received from step 120 (as described above with relation to Fig. 1). For example, if the first set of musical notes is C E G A (CMajor6) the shape associated therewith is 4,7,9. Some or all inverted shapes associated with the first shape are determined using the inversion table (e.g. by using the steps outlined in Fig. 2 above). For example, for the first set of musical notes C E G A (4,7,9), inverted shapes are 3,5,8 (first inversion, E G A C); 2,5,9 (second inversion, G A C E); and 3,7,10 (third inversion, A C E G). In this example, these shapes constitute the root shape and all inverted shapes thereof. At step 1324, at least one of the inverted shapes is searched for in the inversion table to determine a key shape which matches and includes two root shapes, wherein one root shape is the root shape of the first set of musical notes. The second root shape associated with the key shape is used to determine a second set of musical notes which is equivalent to the first set of musical notes. Specifically, information relating to the second root of the matching key such as any combination of the following is retrieved: root name; root shape; inversion name; and inversion index. Thereafter, in step 1324, a second set of musical notes is determined based on the associated root. For the above example when the first set of musical notes is C E G A (CMajor6), the first inversion 3,5,8 (E G A C) matches with a key of the inversion table with two corresponding roots: the first root has a root shape 4,7,9 which matches with the root shape of the first set of musical notes. The matching key has a second root with root shape 3,7,10; root name Minor7...; inversion name N / A; and inversion index 2. Accordingly, it may be determined that Major6 is equivalent to Minor7. At step 1324, to determine the specific notes of the second set of musical notes, we must determine the root of Minor 7 which is equivalent to CMajor6. To this end, the first root of the matched key of 3,5,8 shows that Major6 has an inversion index of 1, and the second root of the matched key of 3,5,8 shows that Minor7 has an inversion index of 2. A relative offset is determined by calculating inversion index of first root (associated with first set of musical notes) minus inversion index of second root = 1-2 = -1. Step 1324 determines the -1 element of the shape of the first set of musical notes, which is 9 (a negative index means that a count is performed from the right instead of the left of the shape). To calculate the root note of Minor7 which is equivalent to the CMajor6, step 1324 determines the musical note which is 9 half steps up from C, which is A. Therefore, step 1324 may determine that CMajor6 is equivalent to AMinor7. At step 1324, information relating to the second set of musical notes is determined. For example, any combination of the following may be determined: notes of the second set of musical notes; root information of the second set of musical notes (e.g. the root shape and / or root name); and inversion information of the second set of musical notes (e.g. the inversion name and / or inversion index). The information from step 1324 is provided at step 140 of Fig. 1 for outputting. Accordingly, in the method 1300 of Fig. 3, a second set of musical notes associated with the first set of musical notes by an equivalence relationship may be outputted, along with information relating to the second set of musical notes. Fig. 4 shows another example method 1300 performed in step 130 of Fig. 1. The method relates to determining a second set of musical notes associated with the first set of musical notes by an upper structure relationship. In other words, the method 1300 of Fig. 3 may be used to determine an upper structure to the first set of musical notes. At step 1332, a shape associated with the first set of musical notes is received from step 120 (as described above with relation to Fig. 1). For example, if the first set of musical notes is C E GB D (CMajor9) the shape associated therewith is 4,7,11,14. In step 1332, the lowest element of the shape is removed to determine a reduced shape. In the example where the first set of musical notes is C E G B D (CMajor9), the reduced shape is 7,11,14. At step 1334, the reduced shape is adjusted by the amount of the removed element. Specifically, the value of the removed element is subtracted from all elements of the reduced shape. In the example where the first set of musical notes is C E G B D (CMajor9), the removed element is 4, and, therefore, the adjusted shape is equal to (7-4),(11-4),14-4) = 3,7,10. At step 1336, one or more inversions of the adjusted shape are determined. In certain examples, all inversions are determined (3,7,10, 4,7,9, 3,5,8, 2,5,9). The inversions of the adjusted shape may be determined using the inversion table or any other means. At step 1338, one or more of the inversions are searched in the inversion table to determine a second set of musical notes. In certain cases, any key in the inversion table which matches any of the inversions of the adjusted shape with a root which is a higher-order structure of the first set of musical notes is determined to be an upper structure of the first set of musical notes. A second of musical notes can be derived therefrom. In the example where the first set of musical notes is C E G B D (CMajor9), the only result is a match with 4,7,9 of the inversions of the adjusted shape, which has a root name of Major6. Accordingly, in step 1338, it is determined that Major6 + root = Major9. We can determine from the inversion table (or otherwise) that the searched shape 3,7,10 is the 3rd inversion of shape 4,7,9 (i.e. Major6). This can be retrieved from the inversion index of the inversion table or otherwise. We have determined that Major6 is an upper structure to CMajor9, and optionally the method may solve for the root note of Major6. To do this, the method determines an adjusted root by adding the first interval of the root shape of the first set of notes (in the example above, this is 4) to the root note of the first set of notes (in the example above, this is C). For example, in the example above, the adjusted root = C + 4 = E. To determine the root note of the second set of notes, the method determines (inversion index -1) x (-1). In our example, this is (3 - I) x (-1), which equals -2. The method then determines the interval which corresponds to this index of the adjusted shape. In our example, this interval is 3 (counting from the right-most element). The method determines root note of second set of notes = adjusted root + 3. In our example, this is E + 3 = G. Therefore, the method determines that GMajor6 is an upper structure of CMajor9. At step 1338, information relating to the second set of musical notes is determined. For example, any combination of the following may be determined: notes of the second set of musical notes; root information of the second set of musical notes (e.g. the root shape and / or root name); and inversion information of the second set of musical notes (e.g. the inversion name and / or inversion index). The information from step 1338 is provided at step 140 of Fig. 1 for outputting. Accordingly, in the method 1300 of Fig. 4, a second set of musical notes associated with the first set of musical notes by an upper structure relationship may be outputted, along with information relating to the second set of musical notes. Fig. 5 shows another example method 1300 performed in step 130 of Fig. 1. The method relates to determining a second set of musical notes associated with the first set of musical notes by a parent structure relationship. In other words, the method 1300 of Fig. 5 may be used to determine a parent structure to the first set of musical notes. This is generally determining the reverse of the method of Fig. 4. At step 1342, a shape associated with the first set of musical notes is received from step 120 (as described above with relation to Fig. 1). For example, if the first set of musical notes is C E G A (CMajor6) the shape associated therewith is 4,7,9. At step 1342, one or more inversions of the shape are determined. In certain cases, all inversions are determined. The inversions may be determined using the inversion table or any other means. In the example where the first set of musical notes is C E G A (CMajor6), all inversions are determined to be 4,7,9; 3,5,8; 2,5,9; and 3,7,10. At step 1344, a plurality of increased shapes is determined by adding additional elements to the beginning of each of the previously determined shapes (inversion shapes). Additional elements may be 1 to 11, meaning that each inversion shapes produces 11 new increased shapes. In the example where the first set of musical notes is C E G A (CMajor6), increased shapes for the root shape include 1,4,7,9; 2,4,7,9; 3,4,7,9 ... 11,4,7,9. Similar increased shapes are determined for all other inversion shapes. In step 1346, the increased shapes are adjusted to determine a plurality of adjusted shapes. Specifically, in step 1346, the additional element is added to all of the original elements of the shape. For example, if the increased shape is 1,4,7,9 (where 1 was the additional element added at the beginning to create the increased shape), then 1 is added to all of the remaining elements to form adjusted shape 1,5,8,10. At step 1348, the adjusted shapes are searched in the inversion table to determine a second set of musical notes. In certain cases, any key in the inversion table which matches any of the inversions of the adjusted shape with a root which is a lower-order structure of the first set of musical notes is determined to be an parent structure of the first set of musical notes. A second of musical notes can be derived therefrom. In the example where the first set of musical notes is C E G A (CMajor6), the only result is a match with 4,7,11,14 of the inversions of the adjusted shape, which has an inversion name of Major9. Accordingly, in step 1348, it is determined that Major6 + root = Major9. We have determined that Major9 is a parent structure to CMajor6, and optionally the method may solve for the root note of Major9. To do this, the method uses the match found in the previous step; in the above example, this is 4,7,11,14 which is CMajor6 (inversion^). The method determines the corresponding inverted root (i.e. of CMajor6 inversion^). The method determines this by calculating (inversion index - 1) modulus root shape length. The method determines the interval of the (un-inverted root shape) which corresponds to this value, and adds this interval to the root note. For the above example, CMajor6 (inversion:3) | inversion index = 3 so C + root shape[3 - 1 % 3] = A. Finally, the method adjusts this note by the increased interval used to create the matched inverted increased shape. In our example, the matched inverted increased shape was 4,7,11,14 and this was increased by 4. Therefore, as an element was added to the left, the method adds a new root to the left of A. This means the method calculates A - 4 = F (i.e. 4 half steps down from A). Therefore, the method determines that FMajor9 is a parent structure of CMajor6. Fig. 6 shows a representation of a system 10 for determining a relationship between musical notes. The system 10 comprises a plurality of user systems 13, 14, 15 which are in selective communication with a server 11. In the embodiment shown in Fig. 1, the user systems 13, 14, 15 communicate with the server 11 via a computer network 12. Fig. 1 shows only three user systems 100a, 100b, 100c, however, this is purely for illustrative purposes and any number (e.g. one or more) of user systems 13, 14, 15 may be used with the present disclosure. Each user system 13, 14, 15 comprises a user 13a, 14a, 15a and a respective user computer terminal 13b, 14b, 15b. The users 13a, 14a, 15a have access to at least their respective user computer terminals 13b, 14b, 15b. Accordingly, they may operate their respective user computer terminals 13b, 14b, 15b to access features of the user computer terminals 13b, 14b, 15b such as applications (apps) and / or the internet (e.g. via a web browser). In certain embodiments, for the users 13a, 14a, 15a to access their respective user computer terminals 13b, 14b, 15b, they must identify and authenticate themselves, for example, by any combination of entry of a PIN code / password and facial recognition. In certain embodiments, access to the server 11 (and any software thereon) can only be obtained once the respective user 13a, 14a, 15a is authenticated. As would be understood by the skilled person in the art, the user computer terminals 13b, 14b, 15b may be any computing device, for example, a laptop computer, a desktop computer, a mobile phone, a tablet, etc. In certain cases, the computer terminals 13b, 14b, 15b include a screen and / or speakers. The server 11 may be any server known to those skilled in the art. The server 11 may be connected to the user systems 13, 14, 15 (and, in particular, the user computer terminals 13b, 14b, 15b) via the computer network 12, for example, the internet. The server 11 comprises a data store Ila. The data store Ila may take any form as known by those skilled in the art, for example, the data store 1 la may be non-volatile storage such as one or more hard disk drives. In certain embodiments, the server 11 may be a plurality of servers. In certain embodiments, the server 11 may not be owned by the users 13a, 14a, 15a, and instead may be a server also used by other users. In certain embodiments, the server 11 may not be located on a premises of any of the users 13a, 14a, 15a. As indicated by the arrows in Fig. 6, data may be transferred between the server 11 and each of the user computer terminals 13b, 14b, 15b in both directions. Specifically, the server 11 may transfer data to each of the user computer terminals 13b, 14b, 15b (i.e. the user computer terminals 13b, 14b, 15b may download data from the server 11) and each of the user computer terminals 13b, 14b, 15b may transfer data to the server 11 (i.e. the user computer terminals 13b, 14b, 15b may upload data to the server 11). In this way, the server 11 may be used to update information on the user computer terminals 13b, 14b, 15b (e.g. to display information on the user computer terminals 13b, 14b, 15b) and the user computer terminals 13b, 14b, 15b may be used to update information in the server (for example, data stored in the data 1 la). The server 11 is configured to host a web user interface portal, described in further detail below. The web user interface portal may be accessible by each of the users 13a, 14a, 15a, for example, by use of their respective user computer terminals 13b, 14b, 15b (or any other device able to access the web user interface portal). For example, each of the users 13a, 14a, 15a may use their respective user computer terminals 13b, 14b, 15b to open their web browser to the web user interface portal hosted by the server 11. The web user interface portal may result in the server 11 performing various functions such as calculations and data retrieval. For example, the web user interface portal may access data from the data store 1 la and display such data. For example, as detailed above, the web user interface portal may perform any of the methods (or parts thereof) disclosed herein. The users 13a, 14a, 15a may access the web user interface portal at the same or different times, as would be understood by those skilled in the art. For example, a first instance of the web user interface portal may be displayed on a first user computer terminal (e.g. user computer terminal 13b), and (at the same time or before / after) a second instance of the web user interface portal may be displayed on a second user computer terminal (e.g. user computer terminal 14b). Any of the methods disclosed herein may be implemented using the system 10 of Fig. 6. While at least one exemplary embodiment has been presented in the foregoing detailed description, it should be appreciated that a vast number of variations exist. It should also be appreciated that the exemplary embodiment or exemplary embodiments are only examples, and are not intended to limit the scope, applicability, or configuration of the disclosure in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient road map for implementing the exemplary embodiment or exemplary embodiments. It should be understood that various changes can be made in the function and arrangement of elements without departing from the scope of the disclosure as set forth in the appended claims and the legal equivalents thereof.

Claims

1. A computer-implemented method of determining a relationship between musical notes, the computer-implemented method comprising:receiving a first set of musical notes;determining a shape associated with the first set of musical notes, wherein determining the shape includes calculating the intervals between the first set of musical notes;searching an inversion table based on the shape to determine a second set of musical notes and a relationship between the first set of musical notes and the second set of musical notes,wherein the inversion table comprises a list of a plurality of shapes where each shape of the plurality of shapes is associated with corresponding root information and inversion information.

2. The computer-implemented method of Claim 1, wherein the root information comprises at least one root shape associated with the shape of the plurality of shapes, and, optionally, wherein the root information further comprises a root name associated with the at least one root shape.

3. The computer-implemented method of Claim 2, wherein the inversion information comprises an inversion index associated with the at least one root shape, and, optionally, wherein the inversion information further comprises an inversion name associated with the inversion index.

4. The computer-implemented method of any preceding claim, comprising determining the inversion table, optionally, wherein the determining of the inversion table occurs before receiving the first set of musical notes.

5. The computer-implemented method of Claim 4, wherein determining the inversion table comprises receiving a list of a plurality of root shapes with associated root names.

6. The computer-implemented method of Claim 5, wherein determining the inversion table further comprises iteratively inverting each of the plurality of root shapes to determine associated shapes.

7. The computer-implemented method of any preceding claim, wherein the relationship between the first set of musical notes and the second set of musical notes is an inversion relationship such that the first set of musical notes is an inversion of the second set of musical notes.

8. The computer-implemented method of any preceding claim, wherein the relationship between the first set of musical notes and the second set of musical notes is an equivalence relationship such that the first set of musical notes is an equivalent of the second set of musical notes.

9. The computer-implemented method of Claim 8, wherein searching the inversion tablebased on the shape comprises:determining at least one inversion of the shape; andsearching the inversion table for the at least one inversion of the shape to determine the second set of musical notes,and, optionally, wherein determining the at least one inversion of the shape comprises determining all inversions of the shape, and wherein searching the inversion table comprises searching the inversion table for all inversions of the shape to determine the second set of musical notes.

10. The computer-implemented method of any preceding claim, wherein the relationship between the first set of musical notes and the second set of musical notes is an upper structure relationship such that the second set of musical notes is an upper structure of the first set of musical notes.

11. The computer-implemented method of Claim 10, wherein searching the inversion table based on the shape comprises:removing a lowest element of the shape to determine a reduced shape;adjusting the remaining elements of the reduced shape to obtain an adjusted shape;determining at least one inversion of the adjusted shape; andsearching the inversion table for the at least one inversion of the adjusted shape to determine the second set of musical notes,and, optionally, wherein determining the at least one inversion of the adjusted shape comprises determining all inversions of the adjusted shape, and wherein searching the inversion table comprises searching the inversion table for all inversions of the adjusted shape to determine the second set of musical notes.

12. The computer-implemented method of any preceding claim, wherein the relationship between the first set of musical notes and the second set of musical notes is a parent structure relationship such that the second set of musical notes is a parent structure of the first set of musical notes.

13. The computer-implemented method of Claim 12, wherein searching the inversion table based on the shape comprises:determining at least one inversion of the shape;adding all possible additional lowest elements to the at least one inversion of the shape to create a plurality of increased shapes;adjusting the plurality of increased shapes to obtain a plurality of adjusted shapes;searching the inversion table for the plurality of adjusted shapes to determine the second set of musical notes,and, optionally, wherein determining the at least one inversion of the shape comprises determining all inversions of the shape.

14. A system for determining a relationship between musical notes, the system comprising one or more servers, the one or more servers configured to be in communication with a user computer terminal, wherein:the one or more servers are configured to receive a first set of musical notes from the user computer terminal;the one or more servers are configured to determine a shape associated with the first set of musical notes, wherein determining the shape includes calculating the intervals between the first set of musical notes;the one or more servers are configured to search an inversion table based on the shape to determine a second set of musical notes and a relationship between the first set of musical notes and the second set of musical notes, wherein the inversion table comprises a list of a plurality of shapes where each shape of the plurality of shapes is associated with corresponding root information and inversion information; andthe one or more servers are configured to transmit the second set of musical notes and the relationship between the first set of musical notes and the second set of musical notes to the user computer terminal.

15. The system of Claim 14, wherein the root information comprises at least one root shape associated with the shape of the plurality of shapes, and, optionally, wherein the root information further comprises a root name associated with the at least one root shape.

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